TSTP Solution File: SET155+4 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET155+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 : n027.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 15:24:04 EDT 2023

% Result   : Theorem 7.81s 1.86s
% Output   : Proof 10.31s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SET155+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36  % Computer : n027.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sat Aug 26 15:48:20 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.61  ________       _____
% 0.21/0.61  ___  __ \_________(_)________________________________
% 0.21/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61  
% 0.21/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61  (2023-06-19)
% 0.21/0.61  
% 0.21/0.61  (c) Philipp Rümmer, 2009-2023
% 0.21/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61                Amanda Stjerna.
% 0.21/0.61  Free software under BSD-3-Clause.
% 0.21/0.61  
% 0.21/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61  
% 0.21/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62  Running up to 7 provers in parallel.
% 0.21/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.10/1.09  Prover 4: Preprocessing ...
% 2.10/1.09  Prover 1: Preprocessing ...
% 2.76/1.11  Prover 6: Preprocessing ...
% 2.76/1.11  Prover 3: Preprocessing ...
% 2.76/1.11  Prover 5: Preprocessing ...
% 2.76/1.11  Prover 0: Preprocessing ...
% 2.76/1.11  Prover 2: Preprocessing ...
% 5.66/1.51  Prover 5: Proving ...
% 5.66/1.51  Prover 1: Constructing countermodel ...
% 5.66/1.52  Prover 2: Proving ...
% 5.66/1.52  Prover 6: Proving ...
% 5.66/1.53  Prover 0: Proving ...
% 5.66/1.54  Prover 3: Constructing countermodel ...
% 5.66/1.56  Prover 4: Constructing countermodel ...
% 7.81/1.86  Prover 3: proved (1227ms)
% 7.81/1.86  
% 7.81/1.86  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.81/1.86  
% 7.81/1.86  Prover 5: stopped
% 7.81/1.86  Prover 0: stopped
% 7.81/1.87  Prover 2: stopped
% 8.33/1.88  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.33/1.88  Prover 6: stopped
% 8.33/1.89  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.33/1.89  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.33/1.89  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.33/1.90  Prover 7: Preprocessing ...
% 8.33/1.90  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.33/1.90  Prover 8: Preprocessing ...
% 8.33/1.92  Prover 11: Preprocessing ...
% 8.33/1.92  Prover 10: Preprocessing ...
% 8.33/1.93  Prover 13: Preprocessing ...
% 8.33/1.96  Prover 7: Warning: ignoring some quantifiers
% 9.07/1.98  Prover 7: Constructing countermodel ...
% 9.40/2.03  Prover 10: Warning: ignoring some quantifiers
% 9.40/2.04  Prover 10: Constructing countermodel ...
% 9.40/2.05  Prover 8: Warning: ignoring some quantifiers
% 9.40/2.05  Prover 1: Found proof (size 109)
% 9.40/2.05  Prover 1: proved (1421ms)
% 9.40/2.05  Prover 4: stopped
% 9.40/2.05  Prover 10: stopped
% 9.40/2.06  Prover 7: stopped
% 9.40/2.06  Prover 8: Constructing countermodel ...
% 9.40/2.07  Prover 8: stopped
% 9.40/2.08  Prover 13: Warning: ignoring some quantifiers
% 9.40/2.09  Prover 13: Constructing countermodel ...
% 9.40/2.09  Prover 11: Constructing countermodel ...
% 9.40/2.09  Prover 13: stopped
% 9.40/2.10  Prover 11: stopped
% 9.40/2.10  
% 9.40/2.10  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.40/2.10  
% 9.94/2.11  % SZS output start Proof for theBenchmark
% 9.94/2.12  Assumptions after simplification:
% 9.94/2.12  ---------------------------------
% 9.94/2.12  
% 9.94/2.12    (difference)
% 9.94/2.14     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 9.94/2.14      |  ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = v4) |  ~ $i(v2) |  ~
% 9.94/2.14      $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (member(v0, v2) = v5 &
% 9.94/2.14        member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) &  ! [v0: $i] :  ! [v1: $i]
% 9.94/2.14    :  ! [v2: $i] :  ! [v3: $i] : ( ~ (difference(v2, v1) = v3) |  ~ (member(v0,
% 9.94/2.14          v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] : ( ~ (v4 =
% 9.94/2.14          0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 9.94/2.14  
% 9.94/2.14    (equal_set)
% 9.94/2.15     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0, v1) =
% 9.94/2.15        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (subset(v1,
% 9.94/2.15          v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0:
% 9.94/2.15      $i] :  ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 9.94/2.15      (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 9.94/2.15  
% 9.94/2.15    (intersection)
% 9.94/2.15     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 9.94/2.15      |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ~ $i(v2) |  ~
% 9.94/2.15      $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (member(v0, v2) = v6 &
% 9.94/2.15        member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0: $i] :  !
% 9.94/2.15    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) |  ~
% 9.94/2.15      (member(v0, v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (member(v0, v2) =
% 9.94/2.15        0 & member(v0, v1) = 0))
% 9.94/2.15  
% 9.94/2.15    (subset)
% 9.94/2.15     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 9.94/2.15      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) &
% 9.94/2.15        member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  !
% 9.94/2.15    [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : (
% 9.94/2.15        ~ (member(v2, v0) = 0) |  ~ $i(v2) | member(v2, v1) = 0))
% 9.94/2.15  
% 9.94/2.15    (thI26)
% 9.94/2.15     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 9.94/2.15      $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: int] : ( ~ (v8 = 0) &
% 9.94/2.15      difference(v2, v3) = v4 & difference(v2, v1) = v6 & difference(v2, v0) = v5
% 9.94/2.15      & union(v0, v1) = v3 & intersection(v5, v6) = v7 & equal_set(v4, v7) = v8 &
% 9.94/2.15      subset(v1, v2) = 0 & subset(v0, v2) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4)
% 9.94/2.15      & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.94/2.15  
% 9.94/2.15    (union)
% 9.94/2.16     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 9.94/2.16      |  ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ~ $i(v2) |  ~ $i(v1)
% 9.94/2.16      |  ~ $i(v0) |  ? [v5: int] :  ? [v6: int] : ( ~ (v6 = 0) &  ~ (v5 = 0) &
% 9.94/2.16        member(v0, v2) = v6 & member(v0, v1) = v5)) &  ! [v0: $i] :  ! [v1: $i] : 
% 9.94/2.16    ! [v2: $i] :  ! [v3: $i] : ( ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = 0)
% 9.94/2.16      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :
% 9.94/2.16      (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 9.94/2.16  
% 9.94/2.16    (function-axioms)
% 9.94/2.16     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.94/2.16      (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0:
% 9.94/2.16      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.94/2.16      (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0: $i] :  !
% 9.94/2.16    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~
% 9.94/2.16      (union(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 9.94/2.16      $i] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) =
% 9.94/2.16        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.94/2.16      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~
% 9.94/2.16      (equal_set(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.94/2.16      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (subset(v3,
% 9.94/2.16          v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 9.94/2.16    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.94/2.16      (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1:
% 9.94/2.16      $i] :  ! [v2: $i] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) =
% 9.94/2.16        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (sum(v2) =
% 9.94/2.16        v1) |  ~ (sum(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 9.94/2.16      v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0: $i] :  !
% 9.94/2.16    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~
% 9.94/2.16      (power_set(v2) = v0))
% 9.94/2.16  
% 9.94/2.16  Further assumptions not needed in the proof:
% 9.94/2.16  --------------------------------------------
% 9.94/2.16  empty_set, power_set, product, singleton, sum, unordered_pair
% 9.94/2.16  
% 9.94/2.16  Those formulas are unsatisfiable:
% 9.94/2.16  ---------------------------------
% 9.94/2.16  
% 9.94/2.16  Begin of proof
% 9.94/2.16  | 
% 9.94/2.16  | ALPHA: (subset) implies:
% 9.94/2.16  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 9.94/2.16  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 9.94/2.16  |            (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 9.94/2.16  | 
% 9.94/2.16  | ALPHA: (equal_set) implies:
% 9.94/2.16  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0,
% 9.94/2.16  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 9.94/2.16  |          (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 9.94/2.16  |                0))))
% 9.94/2.16  | 
% 9.94/2.16  | ALPHA: (intersection) implies:
% 9.94/2.17  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 9.94/2.17  |          (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = 0) |  ~ $i(v2) | 
% 9.94/2.17  |          ~ $i(v1) |  ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 9.94/2.17  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 9.94/2.17  |        (v4 = 0 |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) | 
% 9.94/2.17  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :
% 9.94/2.17  |          (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 =
% 9.94/2.17  |                0))))
% 9.94/2.17  | 
% 9.94/2.17  | ALPHA: (union) implies:
% 9.94/2.17  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (union(v1,
% 9.94/2.17  |              v2) = v3) |  ~ (member(v0, v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 9.94/2.17  |          $i(v0) |  ? [v4: any] :  ? [v5: any] : (member(v0, v2) = v5 &
% 9.94/2.17  |            member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 9.94/2.17  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 9.94/2.17  |        (v4 = 0 |  ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ~
% 9.94/2.17  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6: int] : ( ~
% 9.94/2.17  |            (v6 = 0) &  ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 9.94/2.17  |            v5))
% 9.94/2.17  | 
% 9.94/2.17  | ALPHA: (difference) implies:
% 9.94/2.17  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 9.94/2.17  |          (difference(v2, v1) = v3) |  ~ (member(v0, v3) = 0) |  ~ $i(v2) |  ~
% 9.94/2.17  |          $i(v1) |  ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0
% 9.94/2.17  |            & member(v0, v1) = v4))
% 9.94/2.17  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 9.94/2.17  |        (v4 = 0 |  ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = v4) |  ~
% 9.94/2.17  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :
% 9.94/2.17  |          (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 9.94/2.17  | 
% 9.94/2.17  | ALPHA: (function-axioms) implies:
% 9.94/2.17  |   (9)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.94/2.17  |         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2)
% 9.94/2.17  |            = v0))
% 9.94/2.17  | 
% 9.94/2.17  | DELTA: instantiating (thI26) with fresh symbols all_15_0, all_15_1, all_15_2,
% 9.94/2.17  |        all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8 gives:
% 9.94/2.17  |   (10)   ~ (all_15_0 = 0) & difference(all_15_6, all_15_5) = all_15_4 &
% 9.94/2.17  |         difference(all_15_6, all_15_7) = all_15_2 & difference(all_15_6,
% 9.94/2.17  |           all_15_8) = all_15_3 & union(all_15_8, all_15_7) = all_15_5 &
% 9.94/2.17  |         intersection(all_15_3, all_15_2) = all_15_1 & equal_set(all_15_4,
% 9.94/2.17  |           all_15_1) = all_15_0 & subset(all_15_7, all_15_6) = 0 &
% 9.94/2.17  |         subset(all_15_8, all_15_6) = 0 & $i(all_15_1) & $i(all_15_2) &
% 9.94/2.17  |         $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) &
% 9.94/2.17  |         $i(all_15_7) & $i(all_15_8)
% 9.94/2.17  | 
% 9.94/2.17  | ALPHA: (10) implies:
% 9.94/2.17  |   (11)   ~ (all_15_0 = 0)
% 9.94/2.17  |   (12)  $i(all_15_8)
% 9.94/2.17  |   (13)  $i(all_15_7)
% 9.94/2.17  |   (14)  $i(all_15_6)
% 9.94/2.17  |   (15)  $i(all_15_5)
% 9.94/2.17  |   (16)  $i(all_15_4)
% 9.94/2.17  |   (17)  $i(all_15_3)
% 9.94/2.17  |   (18)  $i(all_15_2)
% 9.94/2.17  |   (19)  $i(all_15_1)
% 9.94/2.17  |   (20)  equal_set(all_15_4, all_15_1) = all_15_0
% 9.94/2.18  |   (21)  intersection(all_15_3, all_15_2) = all_15_1
% 9.94/2.18  |   (22)  union(all_15_8, all_15_7) = all_15_5
% 9.94/2.18  |   (23)  difference(all_15_6, all_15_8) = all_15_3
% 9.94/2.18  |   (24)  difference(all_15_6, all_15_7) = all_15_2
% 9.94/2.18  |   (25)  difference(all_15_6, all_15_5) = all_15_4
% 9.94/2.18  | 
% 9.94/2.18  | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_0, simplifying
% 9.94/2.18  |              with (16), (19), (20) gives:
% 10.31/2.18  |   (26)  all_15_0 = 0 |  ? [v0: any] :  ? [v1: any] : (subset(all_15_1,
% 10.31/2.18  |             all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | 
% 10.31/2.18  |             ~ (v0 = 0)))
% 10.31/2.18  | 
% 10.31/2.18  | BETA: splitting (26) gives:
% 10.31/2.18  | 
% 10.31/2.18  | Case 1:
% 10.31/2.18  | | 
% 10.31/2.18  | |   (27)  all_15_0 = 0
% 10.31/2.18  | | 
% 10.31/2.18  | | REDUCE: (11), (27) imply:
% 10.31/2.18  | |   (28)  $false
% 10.31/2.18  | | 
% 10.31/2.18  | | CLOSE: (28) is inconsistent.
% 10.31/2.18  | | 
% 10.31/2.18  | Case 2:
% 10.31/2.18  | | 
% 10.31/2.18  | |   (29)   ? [v0: any] :  ? [v1: any] : (subset(all_15_1, all_15_4) = v1 &
% 10.31/2.18  | |           subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 10.31/2.18  | | 
% 10.31/2.18  | | DELTA: instantiating (29) with fresh symbols all_27_0, all_27_1 gives:
% 10.31/2.18  | |   (30)  subset(all_15_1, all_15_4) = all_27_0 & subset(all_15_4, all_15_1) =
% 10.31/2.18  | |         all_27_1 & ( ~ (all_27_0 = 0) |  ~ (all_27_1 = 0))
% 10.31/2.18  | | 
% 10.31/2.18  | | ALPHA: (30) implies:
% 10.31/2.18  | |   (31)  subset(all_15_4, all_15_1) = all_27_1
% 10.31/2.18  | |   (32)  subset(all_15_1, all_15_4) = all_27_0
% 10.31/2.18  | |   (33)   ~ (all_27_0 = 0) |  ~ (all_27_1 = 0)
% 10.31/2.18  | | 
% 10.31/2.18  | | GROUND_INST: instantiating (1) with all_15_4, all_15_1, all_27_1,
% 10.31/2.18  | |              simplifying with (16), (19), (31) gives:
% 10.31/2.18  | |   (34)  all_27_1 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 10.31/2.18  | |           member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 10.31/2.18  | | 
% 10.31/2.18  | | GROUND_INST: instantiating (1) with all_15_1, all_15_4, all_27_0,
% 10.31/2.18  | |              simplifying with (16), (19), (32) gives:
% 10.31/2.18  | |   (35)  all_27_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 10.31/2.18  | |           member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 10.31/2.18  | | 
% 10.31/2.18  | | BETA: splitting (33) gives:
% 10.31/2.18  | | 
% 10.31/2.18  | | Case 1:
% 10.31/2.18  | | | 
% 10.31/2.18  | | |   (36)   ~ (all_27_0 = 0)
% 10.31/2.18  | | | 
% 10.31/2.18  | | | BETA: splitting (35) gives:
% 10.31/2.18  | | | 
% 10.31/2.18  | | | Case 1:
% 10.31/2.18  | | | | 
% 10.31/2.18  | | | |   (37)  all_27_0 = 0
% 10.31/2.18  | | | | 
% 10.31/2.18  | | | | REDUCE: (36), (37) imply:
% 10.31/2.18  | | | |   (38)  $false
% 10.31/2.18  | | | | 
% 10.31/2.18  | | | | CLOSE: (38) is inconsistent.
% 10.31/2.18  | | | | 
% 10.31/2.18  | | | Case 2:
% 10.31/2.18  | | | | 
% 10.31/2.18  | | | |   (39)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 10.31/2.18  | | | |           = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 10.31/2.18  | | | | 
% 10.31/2.18  | | | | DELTA: instantiating (39) with fresh symbols all_40_0, all_40_1 gives:
% 10.31/2.18  | | | |   (40)   ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 &
% 10.31/2.18  | | | |         member(all_40_1, all_15_4) = all_40_0 & $i(all_40_1)
% 10.31/2.18  | | | | 
% 10.31/2.18  | | | | ALPHA: (40) implies:
% 10.31/2.19  | | | |   (41)   ~ (all_40_0 = 0)
% 10.31/2.19  | | | |   (42)  $i(all_40_1)
% 10.31/2.19  | | | |   (43)  member(all_40_1, all_15_4) = all_40_0
% 10.31/2.19  | | | |   (44)  member(all_40_1, all_15_1) = 0
% 10.31/2.19  | | | | 
% 10.31/2.19  | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_5, all_15_6,
% 10.31/2.19  | | | |              all_15_4, all_40_0, simplifying with (14), (15), (25),
% 10.31/2.19  | | | |              (42), (43) gives:
% 10.31/2.19  | | | |   (45)  all_40_0 = 0 |  ? [v0: any] :  ? [v1: any] : (member(all_40_1,
% 10.31/2.19  | | | |             all_15_5) = v1 & member(all_40_1, all_15_6) = v0 & ( ~ (v0 =
% 10.31/2.19  | | | |               0) | v1 = 0))
% 10.31/2.19  | | | | 
% 10.31/2.19  | | | | GROUND_INST: instantiating (3) with all_40_1, all_15_3, all_15_2,
% 10.31/2.19  | | | |              all_15_1, simplifying with (17), (18), (21), (42), (44)
% 10.31/2.19  | | | |              gives:
% 10.31/2.19  | | | |   (46)  member(all_40_1, all_15_2) = 0 & member(all_40_1, all_15_3) = 0
% 10.31/2.19  | | | | 
% 10.31/2.19  | | | | ALPHA: (46) implies:
% 10.31/2.19  | | | |   (47)  member(all_40_1, all_15_3) = 0
% 10.31/2.19  | | | |   (48)  member(all_40_1, all_15_2) = 0
% 10.31/2.19  | | | | 
% 10.31/2.19  | | | | BETA: splitting (45) gives:
% 10.31/2.19  | | | | 
% 10.31/2.19  | | | | Case 1:
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | |   (49)  all_40_0 = 0
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | REDUCE: (41), (49) imply:
% 10.31/2.19  | | | | |   (50)  $false
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | CLOSE: (50) is inconsistent.
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | Case 2:
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | |   (51)   ? [v0: any] :  ? [v1: any] : (member(all_40_1, all_15_5) = v1
% 10.31/2.19  | | | | |           & member(all_40_1, all_15_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | DELTA: instantiating (51) with fresh symbols all_52_0, all_52_1 gives:
% 10.31/2.19  | | | | |   (52)  member(all_40_1, all_15_5) = all_52_0 & member(all_40_1,
% 10.31/2.19  | | | | |           all_15_6) = all_52_1 & ( ~ (all_52_1 = 0) | all_52_0 = 0)
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | ALPHA: (52) implies:
% 10.31/2.19  | | | | |   (53)  member(all_40_1, all_15_6) = all_52_1
% 10.31/2.19  | | | | |   (54)  member(all_40_1, all_15_5) = all_52_0
% 10.31/2.19  | | | | |   (55)   ~ (all_52_1 = 0) | all_52_0 = 0
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_8, all_15_6,
% 10.31/2.19  | | | | |              all_15_3, simplifying with (12), (14), (23), (42), (47)
% 10.31/2.19  | | | | |              gives:
% 10.31/2.19  | | | | |   (56)   ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_6) = 0 &
% 10.31/2.19  | | | | |           member(all_40_1, all_15_8) = v0)
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_7, all_15_6,
% 10.31/2.19  | | | | |              all_15_2, simplifying with (13), (14), (24), (42), (48)
% 10.31/2.19  | | | | |              gives:
% 10.31/2.19  | | | | |   (57)   ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_6) = 0 &
% 10.31/2.19  | | | | |           member(all_40_1, all_15_7) = v0)
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | DELTA: instantiating (57) with fresh symbol all_59_0 gives:
% 10.31/2.19  | | | | |   (58)   ~ (all_59_0 = 0) & member(all_40_1, all_15_6) = 0 &
% 10.31/2.19  | | | | |         member(all_40_1, all_15_7) = all_59_0
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | ALPHA: (58) implies:
% 10.31/2.19  | | | | |   (59)   ~ (all_59_0 = 0)
% 10.31/2.19  | | | | |   (60)  member(all_40_1, all_15_7) = all_59_0
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | DELTA: instantiating (56) with fresh symbol all_61_0 gives:
% 10.31/2.19  | | | | |   (61)   ~ (all_61_0 = 0) & member(all_40_1, all_15_6) = 0 &
% 10.31/2.19  | | | | |         member(all_40_1, all_15_8) = all_61_0
% 10.31/2.19  | | | | | 
% 10.31/2.19  | | | | | ALPHA: (61) implies:
% 10.31/2.19  | | | | |   (62)   ~ (all_61_0 = 0)
% 10.31/2.20  | | | | |   (63)  member(all_40_1, all_15_8) = all_61_0
% 10.31/2.20  | | | | |   (64)  member(all_40_1, all_15_6) = 0
% 10.31/2.20  | | | | | 
% 10.31/2.20  | | | | | GROUND_INST: instantiating (9) with all_52_1, 0, all_15_6, all_40_1,
% 10.31/2.20  | | | | |              simplifying with (53), (64) gives:
% 10.31/2.20  | | | | |   (65)  all_52_1 = 0
% 10.31/2.20  | | | | | 
% 10.31/2.20  | | | | | BETA: splitting (55) gives:
% 10.31/2.20  | | | | | 
% 10.31/2.20  | | | | | Case 1:
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | |   (66)   ~ (all_52_1 = 0)
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | | REDUCE: (65), (66) imply:
% 10.31/2.20  | | | | | |   (67)  $false
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | | CLOSE: (67) is inconsistent.
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | Case 2:
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | |   (68)  all_52_0 = 0
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | | REDUCE: (54), (68) imply:
% 10.31/2.20  | | | | | |   (69)  member(all_40_1, all_15_5) = 0
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_8, all_15_7,
% 10.31/2.20  | | | | | |              all_15_5, simplifying with (12), (13), (22), (42), (69)
% 10.31/2.20  | | | | | |              gives:
% 10.31/2.20  | | | | | |   (70)   ? [v0: any] :  ? [v1: any] : (member(all_40_1, all_15_7) =
% 10.31/2.20  | | | | | |           v1 & member(all_40_1, all_15_8) = v0 & (v1 = 0 | v0 = 0))
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | | DELTA: instantiating (70) with fresh symbols all_76_0, all_76_1
% 10.31/2.20  | | | | | |        gives:
% 10.31/2.20  | | | | | |   (71)  member(all_40_1, all_15_7) = all_76_0 & member(all_40_1,
% 10.31/2.20  | | | | | |           all_15_8) = all_76_1 & (all_76_0 = 0 | all_76_1 = 0)
% 10.31/2.20  | | | | | | 
% 10.31/2.20  | | | | | | ALPHA: (71) implies:
% 10.31/2.20  | | | | | |   (72)  member(all_40_1, all_15_8) = all_76_1
% 10.31/2.21  | | | | | |   (73)  member(all_40_1, all_15_7) = all_76_0
% 10.31/2.21  | | | | | |   (74)  all_76_0 = 0 | all_76_1 = 0
% 10.31/2.21  | | | | | | 
% 10.31/2.21  | | | | | | GROUND_INST: instantiating (9) with all_61_0, all_76_1, all_15_8,
% 10.31/2.21  | | | | | |              all_40_1, simplifying with (63), (72) gives:
% 10.31/2.21  | | | | | |   (75)  all_76_1 = all_61_0
% 10.31/2.21  | | | | | | 
% 10.31/2.21  | | | | | | GROUND_INST: instantiating (9) with all_59_0, all_76_0, all_15_7,
% 10.31/2.21  | | | | | |              all_40_1, simplifying with (60), (73) gives:
% 10.31/2.21  | | | | | |   (76)  all_76_0 = all_59_0
% 10.31/2.21  | | | | | | 
% 10.31/2.21  | | | | | | BETA: splitting (74) gives:
% 10.31/2.21  | | | | | | 
% 10.31/2.21  | | | | | | Case 1:
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | |   (77)  all_76_0 = 0
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | | COMBINE_EQS: (76), (77) imply:
% 10.31/2.21  | | | | | | |   (78)  all_59_0 = 0
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | | REDUCE: (59), (78) imply:
% 10.31/2.21  | | | | | | |   (79)  $false
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | | CLOSE: (79) is inconsistent.
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | Case 2:
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | |   (80)  all_76_1 = 0
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | | COMBINE_EQS: (75), (80) imply:
% 10.31/2.21  | | | | | | |   (81)  all_61_0 = 0
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | | SIMP: (81) implies:
% 10.31/2.21  | | | | | | |   (82)  all_61_0 = 0
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | | REDUCE: (62), (82) imply:
% 10.31/2.21  | | | | | | |   (83)  $false
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | | CLOSE: (83) is inconsistent.
% 10.31/2.21  | | | | | | | 
% 10.31/2.21  | | | | | | End of split
% 10.31/2.21  | | | | | | 
% 10.31/2.21  | | | | | End of split
% 10.31/2.21  | | | | | 
% 10.31/2.21  | | | | End of split
% 10.31/2.21  | | | | 
% 10.31/2.21  | | | End of split
% 10.31/2.21  | | | 
% 10.31/2.21  | | Case 2:
% 10.31/2.21  | | | 
% 10.31/2.21  | | |   (84)   ~ (all_27_1 = 0)
% 10.31/2.21  | | | 
% 10.31/2.21  | | | BETA: splitting (34) gives:
% 10.31/2.21  | | | 
% 10.31/2.21  | | | Case 1:
% 10.31/2.21  | | | | 
% 10.31/2.21  | | | |   (85)  all_27_1 = 0
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | REDUCE: (84), (85) imply:
% 10.31/2.22  | | | |   (86)  $false
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | CLOSE: (86) is inconsistent.
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | Case 2:
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | |   (87)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 10.31/2.22  | | | |           = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | DELTA: instantiating (87) with fresh symbols all_40_0, all_40_1 gives:
% 10.31/2.22  | | | |   (88)   ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = all_40_0 &
% 10.31/2.22  | | | |         member(all_40_1, all_15_4) = 0 & $i(all_40_1)
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | ALPHA: (88) implies:
% 10.31/2.22  | | | |   (89)   ~ (all_40_0 = 0)
% 10.31/2.22  | | | |   (90)  $i(all_40_1)
% 10.31/2.22  | | | |   (91)  member(all_40_1, all_15_4) = 0
% 10.31/2.22  | | | |   (92)  member(all_40_1, all_15_1) = all_40_0
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_5, all_15_6,
% 10.31/2.22  | | | |              all_15_4, simplifying with (14), (15), (25), (90), (91)
% 10.31/2.22  | | | |              gives:
% 10.31/2.22  | | | |   (93)   ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_5) = v0 &
% 10.31/2.22  | | | |           member(all_40_1, all_15_6) = 0)
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_3, all_15_2,
% 10.31/2.22  | | | |              all_15_1, all_40_0, simplifying with (17), (18), (21),
% 10.31/2.22  | | | |              (90), (92) gives:
% 10.31/2.22  | | | |   (94)  all_40_0 = 0 |  ? [v0: any] :  ? [v1: any] : (member(all_40_1,
% 10.31/2.22  | | | |             all_15_2) = v1 & member(all_40_1, all_15_3) = v0 & ( ~ (v1 =
% 10.31/2.22  | | | |               0) |  ~ (v0 = 0)))
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | DELTA: instantiating (93) with fresh symbol all_48_0 gives:
% 10.31/2.22  | | | |   (95)   ~ (all_48_0 = 0) & member(all_40_1, all_15_5) = all_48_0 &
% 10.31/2.22  | | | |         member(all_40_1, all_15_6) = 0
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | ALPHA: (95) implies:
% 10.31/2.22  | | | |   (96)   ~ (all_48_0 = 0)
% 10.31/2.22  | | | |   (97)  member(all_40_1, all_15_6) = 0
% 10.31/2.22  | | | |   (98)  member(all_40_1, all_15_5) = all_48_0
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | BETA: splitting (94) gives:
% 10.31/2.22  | | | | 
% 10.31/2.22  | | | | Case 1:
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | |   (99)  all_40_0 = 0
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | | REDUCE: (89), (99) imply:
% 10.31/2.22  | | | | |   (100)  $false
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | | CLOSE: (100) is inconsistent.
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | Case 2:
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | |   (101)   ? [v0: any] :  ? [v1: any] : (member(all_40_1, all_15_2) =
% 10.31/2.22  | | | | |            v1 & member(all_40_1, all_15_3) = v0 & ( ~ (v1 = 0) |  ~
% 10.31/2.22  | | | | |              (v0 = 0)))
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | | DELTA: instantiating (101) with fresh symbols all_54_0, all_54_1
% 10.31/2.22  | | | | |        gives:
% 10.31/2.22  | | | | |   (102)  member(all_40_1, all_15_2) = all_54_0 & member(all_40_1,
% 10.31/2.22  | | | | |            all_15_3) = all_54_1 & ( ~ (all_54_0 = 0) |  ~ (all_54_1 =
% 10.31/2.22  | | | | |              0))
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | | ALPHA: (102) implies:
% 10.31/2.22  | | | | |   (103)  member(all_40_1, all_15_3) = all_54_1
% 10.31/2.22  | | | | |   (104)  member(all_40_1, all_15_2) = all_54_0
% 10.31/2.22  | | | | |   (105)   ~ (all_54_0 = 0) |  ~ (all_54_1 = 0)
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | | GROUND_INST: instantiating (6) with all_40_1, all_15_8, all_15_7,
% 10.31/2.22  | | | | |              all_15_5, all_48_0, simplifying with (12), (13), (22),
% 10.31/2.22  | | | | |              (90), (98) gives:
% 10.31/2.22  | | | | |   (106)  all_48_0 = 0 |  ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) & 
% 10.31/2.22  | | | | |            ~ (v0 = 0) & member(all_40_1, all_15_7) = v1 &
% 10.31/2.22  | | | | |            member(all_40_1, all_15_8) = v0)
% 10.31/2.22  | | | | | 
% 10.31/2.22  | | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_8, all_15_6,
% 10.31/2.22  | | | | |              all_15_3, all_54_1, simplifying with (12), (14), (23),
% 10.31/2.22  | | | | |              (90), (103) gives:
% 10.31/2.23  | | | | |   (107)  all_54_1 = 0 |  ? [v0: any] :  ? [v1: any] :
% 10.31/2.23  | | | | |          (member(all_40_1, all_15_6) = v0 & member(all_40_1, all_15_8)
% 10.31/2.23  | | | | |            = v1 & ( ~ (v0 = 0) | v1 = 0))
% 10.31/2.23  | | | | | 
% 10.31/2.23  | | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_7, all_15_6,
% 10.31/2.23  | | | | |              all_15_2, all_54_0, simplifying with (13), (14), (24),
% 10.31/2.23  | | | | |              (90), (104) gives:
% 10.31/2.23  | | | | |   (108)  all_54_0 = 0 |  ? [v0: any] :  ? [v1: any] :
% 10.31/2.23  | | | | |          (member(all_40_1, all_15_6) = v0 & member(all_40_1, all_15_7)
% 10.31/2.23  | | | | |            = v1 & ( ~ (v0 = 0) | v1 = 0))
% 10.31/2.23  | | | | | 
% 10.31/2.23  | | | | | BETA: splitting (105) gives:
% 10.31/2.23  | | | | | 
% 10.31/2.23  | | | | | Case 1:
% 10.31/2.23  | | | | | | 
% 10.31/2.23  | | | | | |   (109)   ~ (all_54_0 = 0)
% 10.31/2.23  | | | | | | 
% 10.31/2.23  | | | | | | BETA: splitting (108) gives:
% 10.31/2.23  | | | | | | 
% 10.31/2.23  | | | | | | Case 1:
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | |   (110)  all_54_0 = 0
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | REDUCE: (109), (110) imply:
% 10.31/2.23  | | | | | | |   (111)  $false
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | CLOSE: (111) is inconsistent.
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | Case 2:
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | |   (112)   ? [v0: any] :  ? [v1: any] : (member(all_40_1, all_15_6)
% 10.31/2.23  | | | | | | |            = v0 & member(all_40_1, all_15_7) = v1 & ( ~ (v0 = 0) |
% 10.31/2.23  | | | | | | |              v1 = 0))
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | DELTA: instantiating (112) with fresh symbols all_67_0, all_67_1
% 10.31/2.23  | | | | | | |        gives:
% 10.31/2.23  | | | | | | |   (113)  member(all_40_1, all_15_6) = all_67_1 & member(all_40_1,
% 10.31/2.23  | | | | | | |            all_15_7) = all_67_0 & ( ~ (all_67_1 = 0) | all_67_0 =
% 10.31/2.23  | | | | | | |            0)
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | ALPHA: (113) implies:
% 10.31/2.23  | | | | | | |   (114)  member(all_40_1, all_15_7) = all_67_0
% 10.31/2.23  | | | | | | |   (115)  member(all_40_1, all_15_6) = all_67_1
% 10.31/2.23  | | | | | | |   (116)   ~ (all_67_1 = 0) | all_67_0 = 0
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | BETA: splitting (106) gives:
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | Case 1:
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | |   (117)  all_48_0 = 0
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | REDUCE: (96), (117) imply:
% 10.31/2.23  | | | | | | | |   (118)  $false
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | CLOSE: (118) is inconsistent.
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | Case 2:
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | |   (119)   ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 =
% 10.31/2.23  | | | | | | | |              0) & member(all_40_1, all_15_7) = v1 &
% 10.31/2.23  | | | | | | | |            member(all_40_1, all_15_8) = v0)
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | DELTA: instantiating (119) with fresh symbols all_73_0, all_73_1
% 10.31/2.23  | | | | | | | |        gives:
% 10.31/2.23  | | | | | | | |   (120)   ~ (all_73_0 = 0) &  ~ (all_73_1 = 0) &
% 10.31/2.23  | | | | | | | |          member(all_40_1, all_15_7) = all_73_0 &
% 10.31/2.23  | | | | | | | |          member(all_40_1, all_15_8) = all_73_1
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | ALPHA: (120) implies:
% 10.31/2.23  | | | | | | | |   (121)   ~ (all_73_0 = 0)
% 10.31/2.23  | | | | | | | |   (122)  member(all_40_1, all_15_7) = all_73_0
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | GROUND_INST: instantiating (9) with all_67_0, all_73_0,
% 10.31/2.23  | | | | | | | |              all_15_7, all_40_1, simplifying with (114), (122)
% 10.31/2.23  | | | | | | | |              gives:
% 10.31/2.23  | | | | | | | |   (123)  all_73_0 = all_67_0
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | GROUND_INST: instantiating (9) with 0, all_67_1, all_15_6,
% 10.31/2.23  | | | | | | | |              all_40_1, simplifying with (97), (115) gives:
% 10.31/2.23  | | | | | | | |   (124)  all_67_1 = 0
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | REDUCE: (121), (123) imply:
% 10.31/2.23  | | | | | | | |   (125)   ~ (all_67_0 = 0)
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | BETA: splitting (116) gives:
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | Case 1:
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | |   (126)   ~ (all_67_1 = 0)
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | | REDUCE: (124), (126) imply:
% 10.31/2.23  | | | | | | | | |   (127)  $false
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | | CLOSE: (127) is inconsistent.
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | Case 2:
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | |   (128)  all_67_0 = 0
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | | REDUCE: (125), (128) imply:
% 10.31/2.23  | | | | | | | | |   (129)  $false
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | | CLOSE: (129) is inconsistent.
% 10.31/2.23  | | | | | | | | | 
% 10.31/2.23  | | | | | | | | End of split
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | End of split
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | End of split
% 10.31/2.23  | | | | | | 
% 10.31/2.23  | | | | | Case 2:
% 10.31/2.23  | | | | | | 
% 10.31/2.23  | | | | | |   (130)   ~ (all_54_1 = 0)
% 10.31/2.23  | | | | | | 
% 10.31/2.23  | | | | | | BETA: splitting (107) gives:
% 10.31/2.23  | | | | | | 
% 10.31/2.23  | | | | | | Case 1:
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | |   (131)  all_54_1 = 0
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | REDUCE: (130), (131) imply:
% 10.31/2.23  | | | | | | |   (132)  $false
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | CLOSE: (132) is inconsistent.
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | Case 2:
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | |   (133)   ? [v0: any] :  ? [v1: any] : (member(all_40_1, all_15_6)
% 10.31/2.23  | | | | | | |            = v0 & member(all_40_1, all_15_8) = v1 & ( ~ (v0 = 0) |
% 10.31/2.23  | | | | | | |              v1 = 0))
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | DELTA: instantiating (133) with fresh symbols all_67_0, all_67_1
% 10.31/2.23  | | | | | | |        gives:
% 10.31/2.23  | | | | | | |   (134)  member(all_40_1, all_15_6) = all_67_1 & member(all_40_1,
% 10.31/2.23  | | | | | | |            all_15_8) = all_67_0 & ( ~ (all_67_1 = 0) | all_67_0 =
% 10.31/2.23  | | | | | | |            0)
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | ALPHA: (134) implies:
% 10.31/2.23  | | | | | | |   (135)  member(all_40_1, all_15_8) = all_67_0
% 10.31/2.23  | | | | | | |   (136)  member(all_40_1, all_15_6) = all_67_1
% 10.31/2.23  | | | | | | |   (137)   ~ (all_67_1 = 0) | all_67_0 = 0
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | BETA: splitting (106) gives:
% 10.31/2.23  | | | | | | | 
% 10.31/2.23  | | | | | | | Case 1:
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | |   (138)  all_48_0 = 0
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | REDUCE: (96), (138) imply:
% 10.31/2.23  | | | | | | | |   (139)  $false
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | | CLOSE: (139) is inconsistent.
% 10.31/2.23  | | | | | | | | 
% 10.31/2.23  | | | | | | | Case 2:
% 10.31/2.23  | | | | | | | | 
% 10.31/2.24  | | | | | | | |   (140)   ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 =
% 10.31/2.24  | | | | | | | |              0) & member(all_40_1, all_15_7) = v1 &
% 10.31/2.24  | | | | | | | |            member(all_40_1, all_15_8) = v0)
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | | DELTA: instantiating (140) with fresh symbols all_72_0, all_72_1
% 10.31/2.24  | | | | | | | |        gives:
% 10.31/2.24  | | | | | | | |   (141)   ~ (all_72_0 = 0) &  ~ (all_72_1 = 0) &
% 10.31/2.24  | | | | | | | |          member(all_40_1, all_15_7) = all_72_0 &
% 10.31/2.24  | | | | | | | |          member(all_40_1, all_15_8) = all_72_1
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | | ALPHA: (141) implies:
% 10.31/2.24  | | | | | | | |   (142)   ~ (all_72_1 = 0)
% 10.31/2.24  | | | | | | | |   (143)  member(all_40_1, all_15_8) = all_72_1
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | | GROUND_INST: instantiating (9) with all_67_0, all_72_1,
% 10.31/2.24  | | | | | | | |              all_15_8, all_40_1, simplifying with (135), (143)
% 10.31/2.24  | | | | | | | |              gives:
% 10.31/2.24  | | | | | | | |   (144)  all_72_1 = all_67_0
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | | GROUND_INST: instantiating (9) with 0, all_67_1, all_15_6,
% 10.31/2.24  | | | | | | | |              all_40_1, simplifying with (97), (136) gives:
% 10.31/2.24  | | | | | | | |   (145)  all_67_1 = 0
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | | REDUCE: (142), (144) imply:
% 10.31/2.24  | | | | | | | |   (146)   ~ (all_67_0 = 0)
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | | BETA: splitting (137) gives:
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | | Case 1:
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | |   (147)   ~ (all_67_1 = 0)
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | | REDUCE: (145), (147) imply:
% 10.31/2.24  | | | | | | | | |   (148)  $false
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | | CLOSE: (148) is inconsistent.
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | Case 2:
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | |   (149)  all_67_0 = 0
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | | REDUCE: (146), (149) imply:
% 10.31/2.24  | | | | | | | | |   (150)  $false
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | | CLOSE: (150) is inconsistent.
% 10.31/2.24  | | | | | | | | | 
% 10.31/2.24  | | | | | | | | End of split
% 10.31/2.24  | | | | | | | | 
% 10.31/2.24  | | | | | | | End of split
% 10.31/2.24  | | | | | | | 
% 10.31/2.24  | | | | | | End of split
% 10.31/2.24  | | | | | | 
% 10.31/2.24  | | | | | End of split
% 10.31/2.24  | | | | | 
% 10.31/2.24  | | | | End of split
% 10.31/2.24  | | | | 
% 10.31/2.24  | | | End of split
% 10.31/2.24  | | | 
% 10.31/2.24  | | End of split
% 10.31/2.24  | | 
% 10.31/2.24  | End of split
% 10.31/2.24  | 
% 10.31/2.24  End of proof
% 10.31/2.24  % SZS output end Proof for theBenchmark
% 10.31/2.24  
% 10.31/2.24  1626ms
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