TSTP Solution File: SEU130+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU130+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n028.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 17:42:39 EDT 2023

% Result   : Theorem 6.27s 1.67s
% Output   : Proof 8.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU130+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 23 20:44:34 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.60  ___  __ \_________(_)________________________________
% 0.20/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60  (2023-06-19)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2023
% 0.20/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60                Amanda Stjerna.
% 0.20/0.60  Free software under BSD-3-Clause.
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60  
% 0.20/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62  Running up to 7 provers in parallel.
% 0.20/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.08/1.02  Prover 4: Preprocessing ...
% 2.08/1.02  Prover 1: Preprocessing ...
% 2.08/1.06  Prover 0: Preprocessing ...
% 2.08/1.06  Prover 3: Preprocessing ...
% 2.08/1.06  Prover 6: Preprocessing ...
% 2.08/1.06  Prover 5: Preprocessing ...
% 2.08/1.06  Prover 2: Preprocessing ...
% 4.63/1.38  Prover 1: Warning: ignoring some quantifiers
% 4.63/1.39  Prover 3: Warning: ignoring some quantifiers
% 4.63/1.39  Prover 5: Proving ...
% 4.63/1.39  Prover 2: Proving ...
% 4.63/1.40  Prover 6: Proving ...
% 4.63/1.40  Prover 3: Constructing countermodel ...
% 4.63/1.40  Prover 1: Constructing countermodel ...
% 4.63/1.41  Prover 4: Warning: ignoring some quantifiers
% 4.63/1.42  Prover 4: Constructing countermodel ...
% 4.63/1.43  Prover 0: Proving ...
% 6.27/1.67  Prover 0: proved (1047ms)
% 6.27/1.67  
% 6.27/1.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.27/1.67  
% 6.27/1.67  Prover 3: gave up
% 6.27/1.68  Prover 2: stopped
% 6.27/1.68  Prover 5: stopped
% 6.74/1.69  Prover 6: stopped
% 6.74/1.69  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.74/1.69  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.74/1.69  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.74/1.69  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.74/1.69  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.74/1.71  Prover 7: Preprocessing ...
% 6.74/1.72  Prover 8: Preprocessing ...
% 6.74/1.72  Prover 11: Preprocessing ...
% 6.74/1.73  Prover 13: Preprocessing ...
% 6.74/1.73  Prover 10: Preprocessing ...
% 7.48/1.78  Prover 7: Warning: ignoring some quantifiers
% 7.48/1.79  Prover 13: Warning: ignoring some quantifiers
% 7.48/1.79  Prover 7: Constructing countermodel ...
% 7.48/1.80  Prover 10: Warning: ignoring some quantifiers
% 7.48/1.80  Prover 13: Constructing countermodel ...
% 7.48/1.81  Prover 10: Constructing countermodel ...
% 7.85/1.83  Prover 4: Found proof (size 53)
% 7.85/1.83  Prover 4: proved (1206ms)
% 7.85/1.83  Prover 1: stopped
% 7.85/1.84  Prover 7: stopped
% 7.85/1.84  Prover 13: stopped
% 7.85/1.84  Prover 10: stopped
% 7.85/1.86  Prover 8: Warning: ignoring some quantifiers
% 7.85/1.86  Prover 11: Warning: ignoring some quantifiers
% 7.85/1.87  Prover 8: Constructing countermodel ...
% 7.85/1.88  Prover 11: Constructing countermodel ...
% 7.85/1.88  Prover 8: stopped
% 7.85/1.89  Prover 11: stopped
% 7.85/1.89  
% 7.85/1.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.85/1.89  
% 7.85/1.90  % SZS output start Proof for theBenchmark
% 7.85/1.91  Assumptions after simplification:
% 7.85/1.91  ---------------------------------
% 7.85/1.91  
% 7.85/1.91    (commutativity_k3_xboole_0)
% 8.32/1.94     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 8.32/1.94      |  ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) &  !
% 8.32/1.94    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | 
% 8.32/1.94      ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 8.32/1.94  
% 8.32/1.94    (d10_xboole_0)
% 8.32/1.95     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ~ $i(v1) | 
% 8.32/1.95      ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) &  ! [v0: $i]
% 8.32/1.95    :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | 
% 8.32/1.95      ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) &  ! [v0: $i] :  ! [v1:
% 8.32/1.95      int] : (v1 = 0 |  ~ (subset(v0, v0) = v1) |  ~ $i(v0))
% 8.32/1.95  
% 8.32/1.95    (d3_tarski)
% 8.32/1.95     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 8.32/1.95      (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 8.32/1.95      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) &  ! [v0: $i] :  !
% 8.32/1.95    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ~ $i(v1) |  ~
% 8.32/1.95      $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 8.32/1.95        in(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 8.32/1.95      (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 8.32/1.95      $i(v0) | in(v2, v1) = 0)
% 8.32/1.95  
% 8.32/1.95    (d3_xboole_0)
% 8.32/1.96     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 8.32/1.96      |  ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) |  ~ $i(v3) | 
% 8.32/1.96      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3, v1)
% 8.32/1.96        = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0: $i] :  !
% 8.32/1.96    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: any] : ( ~
% 8.32/1.96      (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ~ $i(v3) |  ~
% 8.32/1.96      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) =
% 8.32/1.96        v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v0: $i] :
% 8.32/1.96     ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: any] : ( ~
% 8.32/1.96      (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ~ $i(v3) |  ~
% 8.32/1.96      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) =
% 8.32/1.96        v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v0: $i] :
% 8.32/1.96     ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 8.32/1.96      |  ~ (in(v3, v2) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 8.32/1.96      (in(v3, v1) = 0 & in(v3, v0) = 0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 8.32/1.96    :  ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = 0) | 
% 8.32/1.96      ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :
% 8.32/1.96      (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v0: $i]
% 8.32/1.96    :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 8.32/1.96        v2) |  ~ (in(v3, v0) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 8.32/1.96      |  ? [v4: any] :  ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 8.32/1.96            = 0) | v5 = 0))) &  ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 8.32/1.96      $i] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1)
% 8.32/1.96      |  ~ $i(v0) |  ? [v4: $i] :  ? [v5: any] :  ? [v6: any] :  ? [v7: any] :
% 8.32/1.96      (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 8.32/1.96          |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 8.32/1.96  
% 8.32/1.97    (t17_xboole_1)
% 8.32/1.97     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 8.32/1.97      |  ~ $i(v1) |  ~ $i(v0) | subset(v2, v0) = 0)
% 8.32/1.97  
% 8.32/1.97    (t28_xboole_1)
% 8.32/1.97     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = v0) & subset(v0, v1) = 0 &
% 8.32/1.97      set_intersection2(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 8.32/1.97  
% 8.32/1.97    (function-axioms)
% 8.32/1.97     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 8.32/1.97    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 8.32/1.97    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.32/1.97      (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  !
% 8.32/1.97    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 8.32/1.97      $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 8.32/1.97      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 8.32/1.97      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 8.32/1.97  
% 8.32/1.97  Further assumptions not needed in the proof:
% 8.32/1.97  --------------------------------------------
% 8.32/1.97  antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0,
% 8.32/1.97  idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 8.32/1.97  t2_boole, t6_boole, t7_boole, t8_boole
% 8.32/1.97  
% 8.32/1.97  Those formulas are unsatisfiable:
% 8.32/1.97  ---------------------------------
% 8.32/1.97  
% 8.32/1.97  Begin of proof
% 8.32/1.97  | 
% 8.32/1.97  | ALPHA: (commutativity_k3_xboole_0) implies:
% 8.32/1.97  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v1,
% 8.32/1.97  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v0, v1) =
% 8.32/1.97  |            v2 & $i(v2)))
% 8.32/1.97  | 
% 8.32/1.97  | ALPHA: (d10_xboole_0) implies:
% 8.32/1.97  |   (2)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ~
% 8.32/1.97  |          $i(v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) =
% 8.32/1.97  |            v2))
% 8.32/1.97  | 
% 8.32/1.97  | ALPHA: (d3_tarski) implies:
% 8.32/1.97  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (subset(v0, v1) = 0) |  ~
% 8.32/1.97  |          (in(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | in(v2, v1) =
% 8.32/1.97  |          0)
% 8.32/1.97  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 8.32/1.97  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 8.32/1.97  |            (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 8.32/1.97  | 
% 8.32/1.97  | ALPHA: (d3_xboole_0) implies:
% 8.32/1.98  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.32/1.98  |          (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ~ $i(v3) | 
% 8.32/1.98  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :
% 8.32/1.98  |          (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 8.32/1.98  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: any] :
% 8.32/1.98  |        ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ~ $i(v3)
% 8.32/1.98  |          |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :
% 8.32/1.98  |          (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 8.32/1.98  |                0))))
% 8.32/1.98  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 8.32/1.98  |        (v4 = 0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) | 
% 8.32/1.98  |          ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6:
% 8.32/1.98  |            any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 =
% 8.32/1.98  |                0))))
% 8.32/1.98  | 
% 8.32/1.98  | ALPHA: (function-axioms) implies:
% 8.32/1.98  |   (8)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 8.32/1.98  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 8.32/1.98  | 
% 8.64/1.98  | DELTA: instantiating (t28_xboole_1) with fresh symbols all_20_0, all_20_1,
% 8.64/1.98  |        all_20_2 gives:
% 8.64/1.98  |   (9)   ~ (all_20_0 = all_20_2) & subset(all_20_2, all_20_1) = 0 &
% 8.64/1.98  |        set_intersection2(all_20_2, all_20_1) = all_20_0 & $i(all_20_0) &
% 8.64/1.98  |        $i(all_20_1) & $i(all_20_2)
% 8.64/1.98  | 
% 8.64/1.98  | ALPHA: (9) implies:
% 8.64/1.98  |   (10)   ~ (all_20_0 = all_20_2)
% 8.64/1.98  |   (11)  $i(all_20_2)
% 8.64/1.98  |   (12)  $i(all_20_1)
% 8.64/1.98  |   (13)  set_intersection2(all_20_2, all_20_1) = all_20_0
% 8.64/1.98  |   (14)  subset(all_20_2, all_20_1) = 0
% 8.64/1.98  | 
% 8.64/1.98  | GROUND_INST: instantiating (1) with all_20_1, all_20_2, all_20_0, simplifying
% 8.64/1.98  |              with (11), (12), (13) gives:
% 8.64/1.98  |   (15)  set_intersection2(all_20_1, all_20_2) = all_20_0 & $i(all_20_0)
% 8.64/1.98  | 
% 8.64/1.98  | ALPHA: (15) implies:
% 8.64/1.98  |   (16)  $i(all_20_0)
% 8.64/1.98  |   (17)  set_intersection2(all_20_1, all_20_2) = all_20_0
% 8.64/1.98  | 
% 8.64/1.99  | GROUND_INST: instantiating (t17_xboole_1) with all_20_2, all_20_1, all_20_0,
% 8.64/1.99  |              simplifying with (11), (12), (13) gives:
% 8.64/1.99  |   (18)  subset(all_20_0, all_20_2) = 0
% 8.64/1.99  | 
% 8.64/1.99  | GROUND_INST: instantiating (2) with all_20_2, all_20_0, simplifying with (11),
% 8.64/1.99  |              (16), (18) gives:
% 8.64/1.99  |   (19)  all_20_0 = all_20_2 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_20_2,
% 8.64/1.99  |             all_20_0) = v0)
% 8.64/1.99  | 
% 8.64/1.99  | BETA: splitting (19) gives:
% 8.64/1.99  | 
% 8.64/1.99  | Case 1:
% 8.64/1.99  | | 
% 8.64/1.99  | |   (20)  all_20_0 = all_20_2
% 8.64/1.99  | | 
% 8.64/1.99  | | REDUCE: (10), (20) imply:
% 8.64/1.99  | |   (21)  $false
% 8.64/1.99  | | 
% 8.64/1.99  | | CLOSE: (21) is inconsistent.
% 8.64/1.99  | | 
% 8.64/1.99  | Case 2:
% 8.64/1.99  | | 
% 8.64/1.99  | |   (22)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_20_2, all_20_0) = v0)
% 8.64/1.99  | | 
% 8.64/1.99  | | DELTA: instantiating (22) with fresh symbol all_40_0 gives:
% 8.64/1.99  | |   (23)   ~ (all_40_0 = 0) & subset(all_20_2, all_20_0) = all_40_0
% 8.64/1.99  | | 
% 8.64/1.99  | | ALPHA: (23) implies:
% 8.64/1.99  | |   (24)   ~ (all_40_0 = 0)
% 8.64/1.99  | |   (25)  subset(all_20_2, all_20_0) = all_40_0
% 8.64/1.99  | | 
% 8.64/1.99  | | GROUND_INST: instantiating (4) with all_20_2, all_20_0, all_40_0,
% 8.64/1.99  | |              simplifying with (11), (16), (25) gives:
% 8.64/1.99  | |   (26)  all_40_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.64/1.99  | |             all_20_0) = v1 & in(v0, all_20_2) = 0 & $i(v0))
% 8.64/1.99  | | 
% 8.64/1.99  | | BETA: splitting (26) gives:
% 8.64/1.99  | | 
% 8.64/1.99  | | Case 1:
% 8.64/1.99  | | | 
% 8.64/1.99  | | |   (27)  all_40_0 = 0
% 8.64/1.99  | | | 
% 8.64/1.99  | | | REDUCE: (24), (27) imply:
% 8.64/1.99  | | |   (28)  $false
% 8.64/1.99  | | | 
% 8.64/1.99  | | | CLOSE: (28) is inconsistent.
% 8.64/1.99  | | | 
% 8.64/1.99  | | Case 2:
% 8.64/1.99  | | | 
% 8.64/1.99  | | |   (29)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_20_0) = v1
% 8.64/1.99  | | |           & in(v0, all_20_2) = 0 & $i(v0))
% 8.64/1.99  | | | 
% 8.64/1.99  | | | DELTA: instantiating (29) with fresh symbols all_53_0, all_53_1 gives:
% 8.64/1.99  | | |   (30)   ~ (all_53_0 = 0) & in(all_53_1, all_20_0) = all_53_0 &
% 8.64/1.99  | | |         in(all_53_1, all_20_2) = 0 & $i(all_53_1)
% 8.64/1.99  | | | 
% 8.64/1.99  | | | ALPHA: (30) implies:
% 8.64/1.99  | | |   (31)   ~ (all_53_0 = 0)
% 8.64/1.99  | | |   (32)  $i(all_53_1)
% 8.64/1.99  | | |   (33)  in(all_53_1, all_20_2) = 0
% 8.64/1.99  | | |   (34)  in(all_53_1, all_20_0) = all_53_0
% 8.64/1.99  | | | 
% 8.64/1.99  | | | GROUND_INST: instantiating (6) with all_20_2, all_20_1, all_20_0,
% 8.64/1.99  | | |              all_53_1, 0, simplifying with (11), (12), (13), (16), (32),
% 8.64/1.99  | | |              (33) gives:
% 8.64/1.99  | | |   (35)   ? [v0: any] :  ? [v1: any] : (in(all_53_1, all_20_0) = v0 &
% 8.64/1.99  | | |           in(all_53_1, all_20_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 8.64/1.99  | | | 
% 8.64/2.00  | | | GROUND_INST: instantiating (5) with all_20_2, all_20_1, all_20_0,
% 8.64/2.00  | | |              all_53_1, simplifying with (11), (12), (13), (16), (32), (33)
% 8.64/2.00  | | |              gives:
% 8.64/2.00  | | |   (36)   ? [v0: any] :  ? [v1: any] : (in(all_53_1, all_20_0) = v1 &
% 8.64/2.00  | | |           in(all_53_1, all_20_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 8.64/2.00  | | | 
% 8.64/2.00  | | | GROUND_INST: instantiating (3) with all_20_2, all_20_1, all_53_1,
% 8.64/2.00  | | |              simplifying with (11), (12), (14), (32), (33) gives:
% 8.64/2.00  | | |   (37)  in(all_53_1, all_20_1) = 0
% 8.64/2.00  | | | 
% 8.64/2.00  | | | GROUND_INST: instantiating (7) with all_20_1, all_20_2, all_20_0,
% 8.64/2.00  | | |              all_53_1, all_53_0, simplifying with (11), (12), (16), (17),
% 8.64/2.00  | | |              (32), (34) gives:
% 8.64/2.00  | | |   (38)  all_53_0 = 0 |  ? [v0: any] :  ? [v1: any] : (in(all_53_1,
% 8.64/2.00  | | |             all_20_1) = v0 & in(all_53_1, all_20_2) = v1 & ( ~ (v1 = 0) | 
% 8.64/2.00  | | |             ~ (v0 = 0)))
% 8.64/2.00  | | | 
% 8.64/2.00  | | | DELTA: instantiating (36) with fresh symbols all_65_0, all_65_1 gives:
% 8.64/2.00  | | |   (39)  in(all_53_1, all_20_0) = all_65_0 & in(all_53_1, all_20_1) =
% 8.64/2.00  | | |         all_65_1 & ( ~ (all_65_1 = 0) | all_65_0 = 0)
% 8.64/2.00  | | | 
% 8.64/2.00  | | | ALPHA: (39) implies:
% 8.64/2.00  | | |   (40)  in(all_53_1, all_20_1) = all_65_1
% 8.64/2.00  | | |   (41)  in(all_53_1, all_20_0) = all_65_0
% 8.64/2.00  | | |   (42)   ~ (all_65_1 = 0) | all_65_0 = 0
% 8.64/2.00  | | | 
% 8.64/2.00  | | | DELTA: instantiating (35) with fresh symbols all_67_0, all_67_1 gives:
% 8.64/2.00  | | |   (43)  in(all_53_1, all_20_0) = all_67_1 & in(all_53_1, all_20_1) =
% 8.64/2.00  | | |         all_67_0 & ( ~ (all_67_1 = 0) | all_67_0 = 0)
% 8.64/2.00  | | | 
% 8.64/2.00  | | | ALPHA: (43) implies:
% 8.64/2.00  | | |   (44)  in(all_53_1, all_20_1) = all_67_0
% 8.64/2.00  | | |   (45)  in(all_53_1, all_20_0) = all_67_1
% 8.64/2.00  | | | 
% 8.64/2.00  | | | BETA: splitting (38) gives:
% 8.64/2.00  | | | 
% 8.64/2.00  | | | Case 1:
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | |   (46)  all_53_0 = 0
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | | REDUCE: (31), (46) imply:
% 8.64/2.00  | | | |   (47)  $false
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | | CLOSE: (47) is inconsistent.
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | Case 2:
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | |   (48)   ? [v0: any] :  ? [v1: any] : (in(all_53_1, all_20_1) = v0 &
% 8.64/2.00  | | | |           in(all_53_1, all_20_2) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | | DELTA: instantiating (48) with fresh symbols all_73_0, all_73_1 gives:
% 8.64/2.00  | | | |   (49)  in(all_53_1, all_20_1) = all_73_1 & in(all_53_1, all_20_2) =
% 8.64/2.00  | | | |         all_73_0 & ( ~ (all_73_0 = 0) |  ~ (all_73_1 = 0))
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | | ALPHA: (49) implies:
% 8.64/2.00  | | | |   (50)  in(all_53_1, all_20_1) = all_73_1
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | | GROUND_INST: instantiating (8) with 0, all_67_0, all_20_1, all_53_1,
% 8.64/2.00  | | | |              simplifying with (37), (44) gives:
% 8.64/2.00  | | | |   (51)  all_67_0 = 0
% 8.64/2.00  | | | | 
% 8.64/2.00  | | | | GROUND_INST: instantiating (8) with all_67_0, all_73_1, all_20_1,
% 8.64/2.00  | | | |              all_53_1, simplifying with (44), (50) gives:
% 8.64/2.01  | | | |   (52)  all_73_1 = all_67_0
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | GROUND_INST: instantiating (8) with all_65_1, all_73_1, all_20_1,
% 8.64/2.01  | | | |              all_53_1, simplifying with (40), (50) gives:
% 8.64/2.01  | | | |   (53)  all_73_1 = all_65_1
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | GROUND_INST: instantiating (8) with all_53_0, all_67_1, all_20_0,
% 8.64/2.01  | | | |              all_53_1, simplifying with (34), (45) gives:
% 8.64/2.01  | | | |   (54)  all_67_1 = all_53_0
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | GROUND_INST: instantiating (8) with all_65_0, all_67_1, all_20_0,
% 8.64/2.01  | | | |              all_53_1, simplifying with (41), (45) gives:
% 8.64/2.01  | | | |   (55)  all_67_1 = all_65_0
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | COMBINE_EQS: (52), (53) imply:
% 8.64/2.01  | | | |   (56)  all_67_0 = all_65_1
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | SIMP: (56) implies:
% 8.64/2.01  | | | |   (57)  all_67_0 = all_65_1
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | COMBINE_EQS: (51), (57) imply:
% 8.64/2.01  | | | |   (58)  all_65_1 = 0
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | COMBINE_EQS: (54), (55) imply:
% 8.64/2.01  | | | |   (59)  all_65_0 = all_53_0
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | SIMP: (59) implies:
% 8.64/2.01  | | | |   (60)  all_65_0 = all_53_0
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | BETA: splitting (42) gives:
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | | Case 1:
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | |   (61)   ~ (all_65_1 = 0)
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | | REDUCE: (58), (61) imply:
% 8.64/2.01  | | | | |   (62)  $false
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | | CLOSE: (62) is inconsistent.
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | Case 2:
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | |   (63)  all_65_0 = 0
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | | COMBINE_EQS: (60), (63) imply:
% 8.64/2.01  | | | | |   (64)  all_53_0 = 0
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | | REDUCE: (31), (64) imply:
% 8.64/2.01  | | | | |   (65)  $false
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | | CLOSE: (65) is inconsistent.
% 8.64/2.01  | | | | | 
% 8.64/2.01  | | | | End of split
% 8.64/2.01  | | | | 
% 8.64/2.01  | | | End of split
% 8.64/2.01  | | | 
% 8.64/2.01  | | End of split
% 8.64/2.01  | | 
% 8.64/2.01  | End of split
% 8.64/2.01  | 
% 8.64/2.01  End of proof
% 8.64/2.01  % SZS output end Proof for theBenchmark
% 8.64/2.01  
% 8.64/2.01  1406ms
%------------------------------------------------------------------------------