TSTP Solution File: PRO014+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : PRO014+2 : TPTP v8.1.2. Released v4.0.0.
% 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 13:08:50 EDT 2023

% Result   : Theorem 11.58s 2.41s
% Output   : Proof 14.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PRO014+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Aug 28 19:36:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 3.23/1.12  Prover 1: Preprocessing ...
% 3.23/1.12  Prover 4: Preprocessing ...
% 3.23/1.16  Prover 5: Preprocessing ...
% 3.23/1.16  Prover 2: Preprocessing ...
% 3.23/1.16  Prover 0: Preprocessing ...
% 3.23/1.16  Prover 6: Preprocessing ...
% 3.23/1.16  Prover 3: Preprocessing ...
% 6.52/1.61  Prover 2: Constructing countermodel ...
% 6.52/1.63  Prover 5: Proving ...
% 7.75/1.80  Prover 1: Constructing countermodel ...
% 7.75/1.84  Prover 3: Constructing countermodel ...
% 8.36/1.87  Prover 6: Proving ...
% 9.53/2.06  Prover 4: Constructing countermodel ...
% 9.53/2.13  Prover 0: Proving ...
% 11.58/2.40  Prover 3: proved (1753ms)
% 11.58/2.40  
% 11.58/2.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.58/2.41  
% 11.58/2.41  Prover 6: stopped
% 11.58/2.41  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.58/2.41  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.21/2.41  Prover 5: stopped
% 12.21/2.42  Prover 0: stopped
% 12.21/2.42  Prover 2: stopped
% 12.21/2.43  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.21/2.43  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.21/2.43  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.21/2.48  Prover 7: Preprocessing ...
% 12.79/2.51  Prover 8: Preprocessing ...
% 12.79/2.52  Prover 11: Preprocessing ...
% 12.79/2.52  Prover 13: Preprocessing ...
% 12.79/2.55  Prover 10: Preprocessing ...
% 13.73/2.61  Prover 7: Constructing countermodel ...
% 13.84/2.62  Prover 1: Found proof (size 54)
% 13.84/2.62  Prover 1: proved (1985ms)
% 13.84/2.62  Prover 11: stopped
% 13.84/2.62  Prover 4: stopped
% 13.84/2.63  Prover 13: Constructing countermodel ...
% 13.84/2.63  Prover 13: stopped
% 13.84/2.64  Prover 10: Constructing countermodel ...
% 13.84/2.64  Prover 7: stopped
% 13.84/2.65  Prover 10: stopped
% 13.84/2.67  Prover 8: Warning: ignoring some quantifiers
% 13.84/2.68  Prover 8: Constructing countermodel ...
% 13.84/2.69  Prover 8: stopped
% 13.84/2.69  
% 13.84/2.69  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.84/2.69  
% 13.84/2.70  % SZS output start Proof for theBenchmark
% 13.84/2.70  Assumptions after simplification:
% 13.84/2.70  ---------------------------------
% 13.84/2.70  
% 13.84/2.70    (goals)
% 14.32/2.73    $i(tptp1) & $i(tptp2) & $i(tptp3) & $i(tptp0) &  ? [v0: $i] :  ? [v1: $i] :  ?
% 14.32/2.73    [v2: int] : ( ~ (v2 = 0) & subactivity_occurrence(v0, v1) = 0 & arboreal(v0) =
% 14.32/2.73      0 & leaf_occ(v0, v1) = v2 & occurrence_of(v1, tptp0) = 0 & $i(v1) & $i(v0) &
% 14.32/2.73       ! [v3: $i] :  ! [v4: $i] : ( ~ (leaf(v4, tptp0) = 0) |  ~ (next_subocc(v0,
% 14.32/2.73            v3, tptp0) = 0) |  ~ $i(v4) |  ~ $i(v3) |  ? [v5: any] :  ? [v6: any]
% 14.32/2.73        :  ? [v7: any] :  ? [v8: any] : (occurrence_of(v4, tptp1) = v7 &
% 14.32/2.73          occurrence_of(v4, tptp2) = v6 & occurrence_of(v3, tptp3) = v5 &
% 14.32/2.73          min_precedes(v3, v4, tptp0) = v8 & ( ~ (v8 = 0) |  ~ (v5 = 0) | ( ~ (v7
% 14.32/2.73                = 0) &  ~ (v6 = 0))))))
% 14.32/2.73  
% 14.32/2.73    (sos)
% 14.32/2.73     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 14.32/2.73      |  ~ (min_precedes(v0, v2, v3) = v4) |  ~ (min_precedes(v0, v1, v3) = 0) | 
% 14.32/2.73      ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : ( ~ (v5 = 0) &
% 14.32/2.73        min_precedes(v1, v2, v3) = v5))
% 14.32/2.73  
% 14.32/2.73    (sos_04)
% 14.32/2.73     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 14.32/2.73      (next_subocc(v0, v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 14.32/2.74        int] : ( ~ (v4 = 0) & min_precedes(v0, v1, v2) = v4) |  ? [v4: $i] :
% 14.32/2.74      (min_precedes(v4, v1, v2) = 0 & min_precedes(v0, v4, v2) = 0 & $i(v4))) &  !
% 14.32/2.74    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (next_subocc(v0, v1, v2) = 0) |  ~
% 14.32/2.74      $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (min_precedes(v0, v1, v2) = 0 &  ! [v3: $i]
% 14.32/2.74        : ( ~ (min_precedes(v0, v3, v2) = 0) |  ~ $i(v3) |  ? [v4: int] : ( ~ (v4
% 14.32/2.74              = 0) & min_precedes(v3, v1, v2) = v4))))
% 14.32/2.74  
% 14.32/2.74    (sos_32)
% 14.32/2.74    $i(tptp1) & $i(tptp2) & $i(tptp4) & $i(tptp3) & $i(tptp0) &  ! [v0: $i] :  !
% 14.32/2.74    [v1: $i] : ( ~ (arboreal(v0) = 0) |  ~ (occurrence_of(v1, tptp0) = 0) |  ~
% 14.32/2.74      $i(v1) |  ~ $i(v0) |  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: any]
% 14.32/2.74      :  ? [v6: any] : (leaf(v4, tptp0) = 0 & next_subocc(v3, v4, tptp0) = 0 &
% 14.32/2.74        next_subocc(v2, v3, tptp0) = 0 & next_subocc(v0, v2, tptp0) = 0 &
% 14.32/2.74        occurrence_of(v4, tptp1) = v6 & occurrence_of(v4, tptp2) = v5 &
% 14.32/2.74        occurrence_of(v3, tptp4) = 0 & occurrence_of(v2, tptp3) = 0 & $i(v4) &
% 14.32/2.74        $i(v3) & $i(v2) & (v6 = 0 | v5 = 0)) |  ? [v2: any] :  ? [v3: any] :
% 14.32/2.74      (subactivity_occurrence(v0, v1) = v2 & leaf_occ(v0, v1) = v3 & ( ~ (v2 = 0)
% 14.32/2.74          | v3 = 0)))
% 14.32/2.74  
% 14.32/2.74    (function-axioms)
% 14.32/2.75     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 14.32/2.75    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (next_subocc(v4, v3, v2) = v1) |  ~
% 14.32/2.75      (next_subocc(v4, v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 14.32/2.75      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~
% 14.32/2.75      (min_precedes(v4, v3, v2) = v1) |  ~ (min_precedes(v4, v3, v2) = v0)) &  !
% 14.32/2.75    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.32/2.75      $i] : (v1 = v0 |  ~ (atocc(v3, v2) = v1) |  ~ (atocc(v3, v2) = v0)) &  !
% 14.32/2.75    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.32/2.75      $i] : (v1 = v0 |  ~ (subactivity(v3, v2) = v1) |  ~ (subactivity(v3, v2) =
% 14.32/2.75        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 14.32/2.75      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (leaf(v3, v2) = v1) |  ~ (leaf(v3, v2) =
% 14.32/2.75        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 14.32/2.75      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (subactivity_occurrence(v3, v2) = v1) |  ~
% 14.32/2.75      (subactivity_occurrence(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 14.32/2.75    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (root(v3,
% 14.32/2.75          v2) = v1) |  ~ (root(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 14.32/2.75    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.32/2.75      (precedes(v3, v2) = v1) |  ~ (precedes(v3, v2) = v0)) &  ! [v0:
% 14.32/2.75      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 14.32/2.75    : (v1 = v0 |  ~ (leaf_occ(v3, v2) = v1) |  ~ (leaf_occ(v3, v2) = v0)) &  !
% 14.32/2.75    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.32/2.75      $i] : (v1 = v0 |  ~ (occurrence_of(v3, v2) = v1) |  ~ (occurrence_of(v3, v2)
% 14.32/2.75        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 14.32/2.75      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (root_occ(v3, v2) = v1) |  ~ (root_occ(v3,
% 14.32/2.75          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 14.32/2.75    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (earlier(v3, v2) = v1) |  ~
% 14.32/2.75      (earlier(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 14.32/2.75      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (activity_occurrence(v2) =
% 14.32/2.75        v1) |  ~ (activity_occurrence(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 14.32/2.75    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (activity(v2) = v1) |  ~
% 14.32/2.75      (activity(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 14.32/2.75      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (legal(v2) = v1) |  ~
% 14.32/2.75      (legal(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 14.32/2.75    :  ! [v2: $i] : (v1 = v0 |  ~ (arboreal(v2) = v1) |  ~ (arboreal(v2) = v0)) & 
% 14.32/2.75    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 =
% 14.32/2.75      v0 |  ~ (atomic(v2) = v1) |  ~ (atomic(v2) = v0))
% 14.32/2.75  
% 14.32/2.75  Further assumptions not needed in the proof:
% 14.32/2.75  --------------------------------------------
% 14.32/2.75  sos_01, sos_02, sos_03, sos_05, sos_06, sos_07, sos_08, sos_09, sos_10, sos_11,
% 14.32/2.75  sos_12, sos_13, sos_14, sos_15, sos_16, sos_17, sos_18, sos_19, sos_20, sos_21,
% 14.32/2.75  sos_22, sos_23, sos_24, sos_25, sos_26, sos_27, sos_28, sos_29, sos_30, sos_31,
% 14.32/2.75  sos_33, sos_34, sos_35, sos_36, sos_37, sos_38, sos_39, sos_40, sos_41, sos_42,
% 14.32/2.75  sos_43, sos_44
% 14.32/2.75  
% 14.32/2.75  Those formulas are unsatisfiable:
% 14.32/2.75  ---------------------------------
% 14.32/2.75  
% 14.32/2.75  Begin of proof
% 14.32/2.75  | 
% 14.32/2.75  | ALPHA: (sos_04) implies:
% 14.32/2.75  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (next_subocc(v0, v1, v2)
% 14.32/2.75  |            = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (min_precedes(v0, v1,
% 14.32/2.75  |              v2) = 0 &  ! [v3: $i] : ( ~ (min_precedes(v0, v3, v2) = 0) |  ~
% 14.32/2.75  |              $i(v3) |  ? [v4: int] : ( ~ (v4 = 0) & min_precedes(v3, v1, v2) =
% 14.32/2.75  |                v4))))
% 14.32/2.75  | 
% 14.32/2.75  | ALPHA: (sos_32) implies:
% 14.32/2.75  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (arboreal(v0) = 0) |  ~
% 14.32/2.75  |          (occurrence_of(v1, tptp0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i]
% 14.32/2.75  |          :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: any] :  ? [v6: any] : (leaf(v4,
% 14.32/2.75  |              tptp0) = 0 & next_subocc(v3, v4, tptp0) = 0 & next_subocc(v2, v3,
% 14.32/2.75  |              tptp0) = 0 & next_subocc(v0, v2, tptp0) = 0 & occurrence_of(v4,
% 14.32/2.75  |              tptp1) = v6 & occurrence_of(v4, tptp2) = v5 & occurrence_of(v3,
% 14.32/2.75  |              tptp4) = 0 & occurrence_of(v2, tptp3) = 0 & $i(v4) & $i(v3) &
% 14.32/2.75  |            $i(v2) & (v6 = 0 | v5 = 0)) |  ? [v2: any] :  ? [v3: any] :
% 14.32/2.75  |          (subactivity_occurrence(v0, v1) = v2 & leaf_occ(v0, v1) = v3 & ( ~
% 14.32/2.75  |              (v2 = 0) | v3 = 0)))
% 14.32/2.75  | 
% 14.32/2.75  | ALPHA: (goals) implies:
% 14.32/2.75  |   (3)  $i(tptp0)
% 14.32/2.75  |   (4)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) &
% 14.32/2.75  |          subactivity_occurrence(v0, v1) = 0 & arboreal(v0) = 0 & leaf_occ(v0,
% 14.32/2.75  |            v1) = v2 & occurrence_of(v1, tptp0) = 0 & $i(v1) & $i(v0) &  ! [v3:
% 14.32/2.76  |            $i] :  ! [v4: $i] : ( ~ (leaf(v4, tptp0) = 0) |  ~ (next_subocc(v0,
% 14.32/2.76  |                v3, tptp0) = 0) |  ~ $i(v4) |  ~ $i(v3) |  ? [v5: any] :  ?
% 14.32/2.76  |            [v6: any] :  ? [v7: any] :  ? [v8: any] : (occurrence_of(v4, tptp1)
% 14.32/2.76  |              = v7 & occurrence_of(v4, tptp2) = v6 & occurrence_of(v3, tptp3) =
% 14.32/2.76  |              v5 & min_precedes(v3, v4, tptp0) = v8 & ( ~ (v8 = 0) |  ~ (v5 =
% 14.32/2.76  |                  0) | ( ~ (v7 = 0) &  ~ (v6 = 0))))))
% 14.32/2.76  | 
% 14.32/2.76  | ALPHA: (function-axioms) implies:
% 14.32/2.76  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.32/2.76  |         ! [v3: $i] : (v1 = v0 |  ~ (occurrence_of(v3, v2) = v1) |  ~
% 14.32/2.76  |          (occurrence_of(v3, v2) = v0))
% 14.32/2.76  |   (6)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.32/2.76  |         ! [v3: $i] : (v1 = v0 |  ~ (leaf_occ(v3, v2) = v1) |  ~ (leaf_occ(v3,
% 14.32/2.76  |              v2) = v0))
% 14.32/2.76  |   (7)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.32/2.76  |         ! [v3: $i] : (v1 = v0 |  ~ (subactivity_occurrence(v3, v2) = v1) |  ~
% 14.32/2.76  |          (subactivity_occurrence(v3, v2) = v0))
% 14.32/2.76  |   (8)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.32/2.76  |         ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (min_precedes(v4, v3, v2) =
% 14.32/2.76  |            v1) |  ~ (min_precedes(v4, v3, v2) = v0))
% 14.32/2.76  | 
% 14.32/2.76  | DELTA: instantiating (4) with fresh symbols all_39_0, all_39_1, all_39_2
% 14.32/2.76  |        gives:
% 14.32/2.76  |   (9)   ~ (all_39_0 = 0) & subactivity_occurrence(all_39_2, all_39_1) = 0 &
% 14.32/2.76  |        arboreal(all_39_2) = 0 & leaf_occ(all_39_2, all_39_1) = all_39_0 &
% 14.32/2.76  |        occurrence_of(all_39_1, tptp0) = 0 & $i(all_39_1) & $i(all_39_2) &  !
% 14.32/2.76  |        [v0: $i] :  ! [v1: $i] : ( ~ (leaf(v1, tptp0) = 0) |  ~
% 14.32/2.76  |          (next_subocc(all_39_2, v0, tptp0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 14.32/2.76  |          [v2: any] :  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 14.32/2.76  |          (occurrence_of(v1, tptp1) = v4 & occurrence_of(v1, tptp2) = v3 &
% 14.32/2.76  |            occurrence_of(v0, tptp3) = v2 & min_precedes(v0, v1, tptp0) = v5 &
% 14.32/2.76  |            ( ~ (v5 = 0) |  ~ (v2 = 0) | ( ~ (v4 = 0) &  ~ (v3 = 0)))))
% 14.32/2.76  | 
% 14.32/2.76  | ALPHA: (9) implies:
% 14.32/2.76  |   (10)   ~ (all_39_0 = 0)
% 14.32/2.76  |   (11)  $i(all_39_2)
% 14.32/2.76  |   (12)  $i(all_39_1)
% 14.32/2.76  |   (13)  occurrence_of(all_39_1, tptp0) = 0
% 14.32/2.76  |   (14)  leaf_occ(all_39_2, all_39_1) = all_39_0
% 14.32/2.76  |   (15)  arboreal(all_39_2) = 0
% 14.32/2.76  |   (16)  subactivity_occurrence(all_39_2, all_39_1) = 0
% 14.32/2.76  |   (17)   ! [v0: $i] :  ! [v1: $i] : ( ~ (leaf(v1, tptp0) = 0) |  ~
% 14.32/2.76  |           (next_subocc(all_39_2, v0, tptp0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 14.32/2.76  |           [v2: any] :  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 14.32/2.76  |           (occurrence_of(v1, tptp1) = v4 & occurrence_of(v1, tptp2) = v3 &
% 14.32/2.76  |             occurrence_of(v0, tptp3) = v2 & min_precedes(v0, v1, tptp0) = v5 &
% 14.32/2.76  |             ( ~ (v5 = 0) |  ~ (v2 = 0) | ( ~ (v4 = 0) &  ~ (v3 = 0)))))
% 14.32/2.76  | 
% 14.32/2.76  | GROUND_INST: instantiating (2) with all_39_2, all_39_1, simplifying with (11),
% 14.32/2.76  |              (12), (13), (15) gives:
% 14.32/2.77  |   (18)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: any] :  ? [v4: any]
% 14.32/2.77  |         : (leaf(v2, tptp0) = 0 & next_subocc(v1, v2, tptp0) = 0 &
% 14.32/2.77  |           next_subocc(v0, v1, tptp0) = 0 & next_subocc(all_39_2, v0, tptp0) =
% 14.32/2.77  |           0 & occurrence_of(v2, tptp1) = v4 & occurrence_of(v2, tptp2) = v3 &
% 14.32/2.77  |           occurrence_of(v1, tptp4) = 0 & occurrence_of(v0, tptp3) = 0 & $i(v2)
% 14.32/2.77  |           & $i(v1) & $i(v0) & (v4 = 0 | v3 = 0)) |  ? [v0: any] :  ? [v1: any]
% 14.32/2.77  |         : (subactivity_occurrence(all_39_2, all_39_1) = v0 &
% 14.32/2.77  |           leaf_occ(all_39_2, all_39_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 14.32/2.77  | 
% 14.32/2.77  | BETA: splitting (18) gives:
% 14.32/2.77  | 
% 14.32/2.77  | Case 1:
% 14.32/2.77  | | 
% 14.32/2.77  | |   (19)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: any] :  ? [v4:
% 14.32/2.77  | |           any] : (leaf(v2, tptp0) = 0 & next_subocc(v1, v2, tptp0) = 0 &
% 14.32/2.77  | |           next_subocc(v0, v1, tptp0) = 0 & next_subocc(all_39_2, v0, tptp0)
% 14.32/2.77  | |           = 0 & occurrence_of(v2, tptp1) = v4 & occurrence_of(v2, tptp2) =
% 14.32/2.77  | |           v3 & occurrence_of(v1, tptp4) = 0 & occurrence_of(v0, tptp3) = 0 &
% 14.32/2.77  | |           $i(v2) & $i(v1) & $i(v0) & (v4 = 0 | v3 = 0))
% 14.32/2.77  | | 
% 14.32/2.77  | | DELTA: instantiating (19) with fresh symbols all_67_0, all_67_1, all_67_2,
% 14.32/2.77  | |        all_67_3, all_67_4 gives:
% 14.32/2.77  | |   (20)  leaf(all_67_2, tptp0) = 0 & next_subocc(all_67_3, all_67_2, tptp0) =
% 14.32/2.77  | |         0 & next_subocc(all_67_4, all_67_3, tptp0) = 0 &
% 14.32/2.77  | |         next_subocc(all_39_2, all_67_4, tptp0) = 0 & occurrence_of(all_67_2,
% 14.32/2.77  | |           tptp1) = all_67_0 & occurrence_of(all_67_2, tptp2) = all_67_1 &
% 14.32/2.77  | |         occurrence_of(all_67_3, tptp4) = 0 & occurrence_of(all_67_4, tptp3)
% 14.32/2.77  | |         = 0 & $i(all_67_2) & $i(all_67_3) & $i(all_67_4) & (all_67_0 = 0 |
% 14.32/2.77  | |           all_67_1 = 0)
% 14.32/2.77  | | 
% 14.32/2.77  | | ALPHA: (20) implies:
% 14.32/2.77  | |   (21)  $i(all_67_4)
% 14.32/2.77  | |   (22)  $i(all_67_3)
% 14.32/2.77  | |   (23)  $i(all_67_2)
% 14.32/2.77  | |   (24)  occurrence_of(all_67_4, tptp3) = 0
% 14.32/2.77  | |   (25)  occurrence_of(all_67_2, tptp2) = all_67_1
% 14.32/2.77  | |   (26)  occurrence_of(all_67_2, tptp1) = all_67_0
% 14.32/2.77  | |   (27)  next_subocc(all_39_2, all_67_4, tptp0) = 0
% 14.32/2.77  | |   (28)  next_subocc(all_67_4, all_67_3, tptp0) = 0
% 14.32/2.77  | |   (29)  next_subocc(all_67_3, all_67_2, tptp0) = 0
% 14.32/2.77  | |   (30)  leaf(all_67_2, tptp0) = 0
% 14.32/2.77  | |   (31)  all_67_0 = 0 | all_67_1 = 0
% 14.32/2.77  | | 
% 14.32/2.77  | | GROUND_INST: instantiating (1) with all_67_4, all_67_3, tptp0, simplifying
% 14.32/2.77  | |              with (3), (21), (22), (28) gives:
% 14.32/2.77  | |   (32)  min_precedes(all_67_4, all_67_3, tptp0) = 0 &  ! [v0: $i] : ( ~
% 14.32/2.77  | |           (min_precedes(all_67_4, v0, tptp0) = 0) |  ~ $i(v0) |  ? [v1: int]
% 14.32/2.77  | |           : ( ~ (v1 = 0) & min_precedes(v0, all_67_3, tptp0) = v1))
% 14.32/2.77  | | 
% 14.32/2.77  | | ALPHA: (32) implies:
% 14.32/2.77  | |   (33)  min_precedes(all_67_4, all_67_3, tptp0) = 0
% 14.32/2.77  | | 
% 14.32/2.77  | | GROUND_INST: instantiating (1) with all_67_3, all_67_2, tptp0, simplifying
% 14.32/2.77  | |              with (3), (22), (23), (29) gives:
% 14.32/2.77  | |   (34)  min_precedes(all_67_3, all_67_2, tptp0) = 0 &  ! [v0: $i] : ( ~
% 14.32/2.77  | |           (min_precedes(all_67_3, v0, tptp0) = 0) |  ~ $i(v0) |  ? [v1: int]
% 14.32/2.77  | |           : ( ~ (v1 = 0) & min_precedes(v0, all_67_2, tptp0) = v1))
% 14.32/2.77  | | 
% 14.32/2.77  | | ALPHA: (34) implies:
% 14.32/2.77  | |   (35)  min_precedes(all_67_3, all_67_2, tptp0) = 0
% 14.32/2.77  | | 
% 14.32/2.77  | | GROUND_INST: instantiating (17) with all_67_4, all_67_2, simplifying with
% 14.32/2.77  | |              (21), (23), (27), (30) gives:
% 14.32/2.77  | |   (36)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 14.32/2.77  | |         (occurrence_of(all_67_2, tptp1) = v2 & occurrence_of(all_67_2,
% 14.32/2.77  | |             tptp2) = v1 & occurrence_of(all_67_4, tptp3) = v0 &
% 14.32/2.77  | |           min_precedes(all_67_4, all_67_2, tptp0) = v3 & ( ~ (v3 = 0) |  ~
% 14.32/2.77  | |             (v0 = 0) | ( ~ (v2 = 0) &  ~ (v1 = 0))))
% 14.32/2.77  | | 
% 14.32/2.77  | | DELTA: instantiating (36) with fresh symbols all_87_0, all_87_1, all_87_2,
% 14.32/2.77  | |        all_87_3 gives:
% 14.32/2.77  | |   (37)  occurrence_of(all_67_2, tptp1) = all_87_1 & occurrence_of(all_67_2,
% 14.32/2.77  | |           tptp2) = all_87_2 & occurrence_of(all_67_4, tptp3) = all_87_3 &
% 14.32/2.77  | |         min_precedes(all_67_4, all_67_2, tptp0) = all_87_0 & ( ~ (all_87_0 =
% 14.32/2.77  | |             0) |  ~ (all_87_3 = 0) | ( ~ (all_87_1 = 0) &  ~ (all_87_2 =
% 14.32/2.77  | |               0)))
% 14.32/2.77  | | 
% 14.32/2.77  | | ALPHA: (37) implies:
% 14.32/2.78  | |   (38)  min_precedes(all_67_4, all_67_2, tptp0) = all_87_0
% 14.32/2.78  | |   (39)  occurrence_of(all_67_4, tptp3) = all_87_3
% 14.32/2.78  | |   (40)  occurrence_of(all_67_2, tptp2) = all_87_2
% 14.32/2.78  | |   (41)  occurrence_of(all_67_2, tptp1) = all_87_1
% 14.32/2.78  | |   (42)   ~ (all_87_0 = 0) |  ~ (all_87_3 = 0) | ( ~ (all_87_1 = 0) &  ~
% 14.32/2.78  | |           (all_87_2 = 0))
% 14.32/2.78  | | 
% 14.32/2.78  | | GROUND_INST: instantiating (5) with 0, all_87_3, tptp3, all_67_4,
% 14.32/2.78  | |              simplifying with (24), (39) gives:
% 14.32/2.78  | |   (43)  all_87_3 = 0
% 14.32/2.78  | | 
% 14.32/2.78  | | GROUND_INST: instantiating (5) with all_67_1, all_87_2, tptp2, all_67_2,
% 14.32/2.78  | |              simplifying with (25), (40) gives:
% 14.32/2.78  | |   (44)  all_87_2 = all_67_1
% 14.32/2.78  | | 
% 14.32/2.78  | | GROUND_INST: instantiating (5) with all_67_0, all_87_1, tptp1, all_67_2,
% 14.32/2.78  | |              simplifying with (26), (41) gives:
% 14.32/2.78  | |   (45)  all_87_1 = all_67_0
% 14.32/2.78  | | 
% 14.32/2.78  | | GROUND_INST: instantiating (sos) with all_67_4, all_67_3, all_67_2, tptp0,
% 14.32/2.78  | |              all_87_0, simplifying with (3), (21), (22), (23), (33), (38)
% 14.32/2.78  | |              gives:
% 14.32/2.78  | |   (46)  all_87_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & min_precedes(all_67_3,
% 14.32/2.78  | |             all_67_2, tptp0) = v0)
% 14.32/2.78  | | 
% 14.32/2.78  | | BETA: splitting (46) gives:
% 14.32/2.78  | | 
% 14.32/2.78  | | Case 1:
% 14.32/2.78  | | | 
% 14.32/2.78  | | |   (47)  all_87_0 = 0
% 14.32/2.78  | | | 
% 14.32/2.78  | | | BETA: splitting (42) gives:
% 14.32/2.78  | | | 
% 14.32/2.78  | | | Case 1:
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | |   (48)   ~ (all_87_0 = 0)
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | | REDUCE: (47), (48) imply:
% 14.32/2.78  | | | |   (49)  $false
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | | CLOSE: (49) is inconsistent.
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | Case 2:
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | |   (50)   ~ (all_87_3 = 0) | ( ~ (all_87_1 = 0) &  ~ (all_87_2 = 0))
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | | BETA: splitting (50) gives:
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | | Case 1:
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | |   (51)   ~ (all_87_3 = 0)
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | | REDUCE: (43), (51) imply:
% 14.32/2.78  | | | | |   (52)  $false
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | | CLOSE: (52) is inconsistent.
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | Case 2:
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | |   (53)   ~ (all_87_1 = 0) &  ~ (all_87_2 = 0)
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | | ALPHA: (53) implies:
% 14.32/2.78  | | | | |   (54)   ~ (all_87_2 = 0)
% 14.32/2.78  | | | | |   (55)   ~ (all_87_1 = 0)
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | | REDUCE: (45), (55) imply:
% 14.32/2.78  | | | | |   (56)   ~ (all_67_0 = 0)
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | | REDUCE: (44), (54) imply:
% 14.32/2.78  | | | | |   (57)   ~ (all_67_1 = 0)
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | | BETA: splitting (31) gives:
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | | Case 1:
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | |   (58)  all_67_0 = 0
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | | REDUCE: (56), (58) imply:
% 14.32/2.78  | | | | | |   (59)  $false
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | | CLOSE: (59) is inconsistent.
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | Case 2:
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | |   (60)  all_67_1 = 0
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | | REDUCE: (57), (60) imply:
% 14.32/2.78  | | | | | |   (61)  $false
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | | CLOSE: (61) is inconsistent.
% 14.32/2.78  | | | | | | 
% 14.32/2.78  | | | | | End of split
% 14.32/2.78  | | | | | 
% 14.32/2.78  | | | | End of split
% 14.32/2.78  | | | | 
% 14.32/2.78  | | | End of split
% 14.32/2.78  | | | 
% 14.32/2.78  | | Case 2:
% 14.32/2.78  | | | 
% 14.32/2.78  | | |   (62)   ? [v0: int] : ( ~ (v0 = 0) & min_precedes(all_67_3, all_67_2,
% 14.32/2.78  | | |             tptp0) = v0)
% 14.32/2.78  | | | 
% 14.32/2.78  | | | DELTA: instantiating (62) with fresh symbol all_138_0 gives:
% 14.32/2.78  | | |   (63)   ~ (all_138_0 = 0) & min_precedes(all_67_3, all_67_2, tptp0) =
% 14.32/2.78  | | |         all_138_0
% 14.32/2.78  | | | 
% 14.32/2.78  | | | ALPHA: (63) implies:
% 14.32/2.78  | | |   (64)   ~ (all_138_0 = 0)
% 14.32/2.78  | | |   (65)  min_precedes(all_67_3, all_67_2, tptp0) = all_138_0
% 14.32/2.78  | | | 
% 14.32/2.78  | | | GROUND_INST: instantiating (8) with 0, all_138_0, tptp0, all_67_2,
% 14.32/2.78  | | |              all_67_3, simplifying with (35), (65) gives:
% 14.32/2.78  | | |   (66)  all_138_0 = 0
% 14.32/2.78  | | | 
% 14.32/2.78  | | | REDUCE: (64), (66) imply:
% 14.32/2.78  | | |   (67)  $false
% 14.32/2.78  | | | 
% 14.32/2.78  | | | CLOSE: (67) is inconsistent.
% 14.32/2.78  | | | 
% 14.32/2.78  | | End of split
% 14.32/2.78  | | 
% 14.32/2.78  | Case 2:
% 14.32/2.78  | | 
% 14.69/2.79  | |   (68)   ? [v0: any] :  ? [v1: any] : (subactivity_occurrence(all_39_2,
% 14.69/2.79  | |             all_39_1) = v0 & leaf_occ(all_39_2, all_39_1) = v1 & ( ~ (v0 =
% 14.69/2.79  | |               0) | v1 = 0))
% 14.69/2.79  | | 
% 14.69/2.79  | | DELTA: instantiating (68) with fresh symbols all_67_0, all_67_1 gives:
% 14.69/2.79  | |   (69)  subactivity_occurrence(all_39_2, all_39_1) = all_67_1 &
% 14.69/2.79  | |         leaf_occ(all_39_2, all_39_1) = all_67_0 & ( ~ (all_67_1 = 0) |
% 14.69/2.79  | |           all_67_0 = 0)
% 14.69/2.79  | | 
% 14.69/2.79  | | ALPHA: (69) implies:
% 14.69/2.79  | |   (70)  leaf_occ(all_39_2, all_39_1) = all_67_0
% 14.69/2.79  | |   (71)  subactivity_occurrence(all_39_2, all_39_1) = all_67_1
% 14.69/2.79  | |   (72)   ~ (all_67_1 = 0) | all_67_0 = 0
% 14.69/2.79  | | 
% 14.69/2.79  | | GROUND_INST: instantiating (6) with all_39_0, all_67_0, all_39_1, all_39_2,
% 14.69/2.79  | |              simplifying with (14), (70) gives:
% 14.69/2.79  | |   (73)  all_67_0 = all_39_0
% 14.69/2.79  | | 
% 14.69/2.79  | | GROUND_INST: instantiating (7) with 0, all_67_1, all_39_1, all_39_2,
% 14.69/2.79  | |              simplifying with (16), (71) gives:
% 14.69/2.79  | |   (74)  all_67_1 = 0
% 14.69/2.79  | | 
% 14.69/2.79  | | BETA: splitting (72) gives:
% 14.69/2.79  | | 
% 14.69/2.79  | | Case 1:
% 14.69/2.79  | | | 
% 14.69/2.79  | | |   (75)   ~ (all_67_1 = 0)
% 14.69/2.79  | | | 
% 14.69/2.79  | | | REDUCE: (74), (75) imply:
% 14.69/2.79  | | |   (76)  $false
% 14.69/2.79  | | | 
% 14.69/2.79  | | | CLOSE: (76) is inconsistent.
% 14.69/2.79  | | | 
% 14.69/2.79  | | Case 2:
% 14.69/2.79  | | | 
% 14.69/2.79  | | |   (77)  all_67_0 = 0
% 14.69/2.79  | | | 
% 14.69/2.79  | | | COMBINE_EQS: (73), (77) imply:
% 14.69/2.79  | | |   (78)  all_39_0 = 0
% 14.69/2.79  | | | 
% 14.69/2.79  | | | REDUCE: (10), (78) imply:
% 14.69/2.79  | | |   (79)  $false
% 14.69/2.79  | | | 
% 14.69/2.79  | | | CLOSE: (79) is inconsistent.
% 14.69/2.79  | | | 
% 14.69/2.79  | | End of split
% 14.69/2.79  | | 
% 14.69/2.79  | End of split
% 14.69/2.79  | 
% 14.69/2.79  End of proof
% 14.69/2.79  % SZS output end Proof for theBenchmark
% 14.69/2.79  
% 14.69/2.79  2168ms
%------------------------------------------------------------------------------