TSTP Solution File: CSR015+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : CSR015+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n008.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 : Wed Aug 30 21:36:24 EDT 2023

% Result   : Theorem 11.18s 2.29s
% Output   : Proof 14.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : CSR015+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n008.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 07:13:02 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 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 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 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 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 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 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 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.57/1.18  Prover 1: Preprocessing ...
% 3.57/1.21  Prover 4: Preprocessing ...
% 3.57/1.23  Prover 3: Preprocessing ...
% 3.57/1.23  Prover 2: Preprocessing ...
% 3.57/1.23  Prover 6: Preprocessing ...
% 3.57/1.23  Prover 0: Preprocessing ...
% 3.57/1.23  Prover 5: Preprocessing ...
% 8.13/1.81  Prover 5: Proving ...
% 8.54/1.87  Prover 1: Constructing countermodel ...
% 8.54/1.92  Prover 3: Constructing countermodel ...
% 8.54/1.92  Prover 6: Proving ...
% 9.54/2.00  Prover 4: Constructing countermodel ...
% 9.90/2.08  Prover 3: gave up
% 9.90/2.09  Prover 1: gave up
% 9.90/2.09  Prover 0: Proving ...
% 9.90/2.09  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.90/2.10  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.90/2.12  Prover 6: gave up
% 9.90/2.13  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.90/2.15  Prover 8: Preprocessing ...
% 9.90/2.16  Prover 7: Preprocessing ...
% 9.90/2.20  Prover 9: Preprocessing ...
% 11.18/2.29  Prover 5: proved (1634ms)
% 11.18/2.29  
% 11.18/2.29  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.18/2.29  
% 11.18/2.30  Prover 0: stopped
% 11.18/2.30  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.80/2.32  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.80/2.33  Prover 2: Proving ...
% 11.80/2.33  Prover 2: stopped
% 11.80/2.35  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.80/2.35  Prover 11: Preprocessing ...
% 11.80/2.37  Prover 10: Preprocessing ...
% 11.80/2.39  Prover 8: Warning: ignoring some quantifiers
% 12.58/2.43  Prover 8: Constructing countermodel ...
% 12.58/2.44  Prover 13: Preprocessing ...
% 12.58/2.48  Prover 4: Found proof (size 43)
% 12.58/2.48  Prover 4: proved (1826ms)
% 12.58/2.48  Prover 13: stopped
% 12.58/2.48  Prover 8: stopped
% 12.58/2.49  Prover 9: Constructing countermodel ...
% 12.58/2.49  Prover 9: stopped
% 13.12/2.52  Prover 7: Warning: ignoring some quantifiers
% 13.12/2.55  Prover 7: Constructing countermodel ...
% 13.12/2.56  Prover 7: stopped
% 13.66/2.60  Prover 11: Constructing countermodel ...
% 13.66/2.62  Prover 11: stopped
% 13.66/2.63  Prover 10: Warning: ignoring some quantifiers
% 13.66/2.64  Prover 10: Constructing countermodel ...
% 13.66/2.65  Prover 10: stopped
% 13.66/2.65  
% 13.66/2.65  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.66/2.65  
% 13.66/2.66  % SZS output start Proof for theBenchmark
% 13.66/2.66  Assumptions after simplification:
% 13.66/2.66  ---------------------------------
% 13.66/2.66  
% 13.66/2.66    (forwards_not_backwards)
% 13.66/2.67     ~ (backwards = forwards) & $i(backwards) & $i(forwards)
% 13.66/2.67  
% 13.66/2.67    (happens_all_defn)
% 14.22/2.71    $i(n2) & $i(pull) & $i(push) & $i(n1) & $i(n0) &  ! [v0: $i] :  ! [v1: $i] :
% 14.22/2.71    (v1 = n2 | v1 = n1 | v1 = n0 | v0 = pull |  ~ (happens(v0, v1) = 0) |  ~
% 14.22/2.71      $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = n2 | v1 = n1 | v1 =
% 14.22/2.71      n0 | v0 = push |  ~ (happens(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0:
% 14.22/2.71      $i] :  ! [v1: $i] : (v1 = n2 | v1 = n1 | v1 = n0 |  ~ (happens(v0, v1) = 0)
% 14.22/2.71      |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = n2 | v1 = n1 |
% 14.22/2.71      v0 = pull | v0 = push |  ~ (happens(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0)) & 
% 14.22/2.71    ! [v0: $i] :  ! [v1: $i] : (v1 = n2 | v1 = n1 | v0 = push |  ~ (happens(v0,
% 14.22/2.71          v1) = 0) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = n2
% 14.22/2.71      | v1 = n0 | v0 = pull | v0 = push |  ~ (happens(v0, v1) = 0) |  ~ $i(v1) | 
% 14.22/2.71      ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = n2 | v1 = n0 | v0 = pull |  ~
% 14.22/2.71      (happens(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] :
% 14.22/2.71    (v1 = n2 | v0 = pull | v0 = push |  ~ (happens(v0, v1) = 0) |  ~ $i(v1) |  ~
% 14.22/2.71      $i(v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = n1 | v1 = n0 | v0 = pull | v0 =
% 14.22/2.71      push |  ~ (happens(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  !
% 14.22/2.71    [v1: $i] : (v1 = n1 | v0 = pull | v0 = push |  ~ (happens(v0, v1) = 0) |  ~
% 14.22/2.71      $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = n0 | v0 = pull | v0
% 14.22/2.71      = push |  ~ (happens(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] : 
% 14.22/2.71    ! [v1: $i] : (v0 = pull | v0 = push |  ~ (happens(v0, v1) = 0) |  ~ $i(v1) | 
% 14.22/2.71      ~ $i(v0)) &  ! [v0: int] : (v0 = 0 |  ~ (happens(pull, n2) = v0)) &  ! [v0:
% 14.22/2.71      int] : (v0 = 0 |  ~ (happens(pull, n1) = v0)) &  ! [v0: int] : (v0 = 0 |  ~
% 14.22/2.71      (happens(push, n2) = v0)) &  ! [v0: int] : (v0 = 0 |  ~ (happens(push, n0) =
% 14.22/2.71        v0))
% 14.22/2.71  
% 14.22/2.71    (initiates_all_defn)
% 14.31/2.71    $i(spinning) & $i(backwards) & $i(pull) & $i(forwards) & $i(push) &  ! [v0:
% 14.31/2.71      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (initiates(v0,
% 14.31/2.71          v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ?
% 14.31/2.71      [v5: any] : (happens(pull, v2) = v4 & happens(push, v2) = v5 & ( ~ (v5 = 0)
% 14.31/2.71          |  ~ (v1 = spinning) |  ~ (v0 = pull)) & ( ~ (v1 = backwards) |  ~ (v0 =
% 14.31/2.71            pull) | v5 = 0) & ( ~ (v1 = forwards) |  ~ (v0 = push) | v4 = 0))) & 
% 14.31/2.71    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (initiates(v0, v1, v2) = 0) |  ~
% 14.31/2.71      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 14.31/2.71      (happens(pull, v2) = v3 & happens(push, v2) = v4 & ((v4 = 0 & v1 = spinning
% 14.31/2.71            & v0 = pull) | (v1 = backwards & v0 = pull &  ~ (v4 = 0)) | (v1 =
% 14.31/2.71            forwards & v0 = push &  ~ (v3 = 0)))))
% 14.31/2.71  
% 14.31/2.71    (keep_not_holding)
% 14.33/2.72    $i(n1) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 14.33/2.72      (releasedAt(v0, v2) = v3) |  ~ (plus(v1, n1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 14.33/2.72       ? [v4: any] :  ? [v5: any] :  ? [v6: $i] :  ? [v7: int] :  ? [v8: int] :
% 14.33/2.72      ($i(v6) & ((v8 = 0 & v7 = 0 & initiates(v6, v0, v1) = 0 & happens(v6, v1) =
% 14.33/2.72            0) | (holdsAt(v0, v2) = v5 & holdsAt(v0, v1) = v4 & ( ~ (v5 = 0) | v4
% 14.33/2.72              = 0))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 14.33/2.72      (holdsAt(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: any]
% 14.33/2.72      :  ? [v5: any] :  ? [v6: $i] :  ? [v7: int] :  ? [v8: int] : ($i(v6) & ((v8
% 14.33/2.72            = 0 & v7 = 0 & initiates(v6, v0, v1) = 0 & happens(v6, v1) = 0) |
% 14.33/2.72          (releasedAt(v0, v3) = v4 & plus(v1, n1) = v3 & holdsAt(v0, v3) = v5 &
% 14.33/2.72            $i(v3) & ( ~ (v5 = 0) | v4 = 0))))) &  ! [v0: $i] :  ! [v1: $i] :  !
% 14.33/2.72    [v2: $i] : ( ~ (plus(v1, n1) = v2) |  ~ (holdsAt(v0, v2) = 0) |  ~ $i(v1) |  ~
% 14.33/2.72      $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] :  ? [v6: int] :  ? [v7:
% 14.33/2.72        int] : ($i(v5) & ((v7 = 0 & v6 = 0 & initiates(v5, v0, v1) = 0 &
% 14.33/2.72            happens(v5, v1) = 0) | (releasedAt(v0, v2) = v4 & holdsAt(v0, v1) = v3
% 14.33/2.72            & (v4 = 0 | v3 = 0)))))
% 14.33/2.72  
% 14.33/2.72    (not_backwards_0)
% 14.33/2.72    $i(backwards) & $i(n0) &  ? [v0: int] : ( ~ (v0 = 0) & holdsAt(backwards, n0)
% 14.33/2.72      = v0)
% 14.33/2.72  
% 14.33/2.72    (not_backwards_1)
% 14.33/2.72    holdsAt(backwards, n1) = 0 & $i(backwards) & $i(n1)
% 14.33/2.72  
% 14.33/2.72    (not_releasedAt)
% 14.33/2.72     ! [v0: $i] :  ! [v1: $i] : ( ~ (releasedAt(v0, v1) = 0) |  ~ $i(v1) |  ~
% 14.33/2.72      $i(v0))
% 14.33/2.72  
% 14.33/2.72    (not_splinning_0)
% 14.33/2.72    $i(spinning) & $i(n0) &  ? [v0: int] : ( ~ (v0 = 0) & holdsAt(spinning, n0) =
% 14.33/2.72      v0)
% 14.33/2.72  
% 14.33/2.72    (plus0_1)
% 14.33/2.72    plus(n0, n1) = n1 & $i(n1) & $i(n0)
% 14.33/2.72  
% 14.33/2.72    (spinning_not_backwards)
% 14.33/2.72     ~ (spinning = backwards) & $i(spinning) & $i(backwards)
% 14.33/2.72  
% 14.33/2.72    (function-axioms)
% 14.33/2.73     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 14.33/2.73    [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v1 = v0 |  ~ (antitrajectory(v5, v4,
% 14.33/2.73          v3, v2) = v1) |  ~ (antitrajectory(v5, v4, v3, v2) = v0)) &  ! [v0:
% 14.33/2.73      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 14.33/2.73    :  ! [v4: $i] :  ! [v5: $i] : (v1 = v0 |  ~ (trajectory(v5, v4, v3, v2) = v1)
% 14.33/2.73      |  ~ (trajectory(v5, v4, v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 14.33/2.73    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |
% 14.33/2.73       ~ (releases(v4, v3, v2) = v1) |  ~ (releases(v4, v3, v2) = v0)) &  ! [v0:
% 14.33/2.73      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 14.33/2.73    :  ! [v4: $i] : (v1 = v0 |  ~ (startedIn(v4, v3, v2) = v1) |  ~ (startedIn(v4,
% 14.33/2.73          v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 14.33/2.73    :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (initiates(v4, v3,
% 14.33/2.73          v2) = v1) |  ~ (initiates(v4, v3, v2) = v0)) &  ! [v0:
% 14.33/2.73      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 14.33/2.73    :  ! [v4: $i] : (v1 = v0 |  ~ (stoppedIn(v4, v3, v2) = v1) |  ~ (stoppedIn(v4,
% 14.33/2.73          v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 14.33/2.73    :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (terminates(v4, v3,
% 14.33/2.73          v2) = v1) |  ~ (terminates(v4, v3, v2) = v0)) &  ! [v0:
% 14.33/2.73      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 14.33/2.73    : (v1 = v0 |  ~ (less_or_equal(v3, v2) = v1) |  ~ (less_or_equal(v3, v2) =
% 14.33/2.73        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 14.33/2.73      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (releasedAt(v3, v2) = v1) |  ~
% 14.33/2.73      (releasedAt(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 14.33/2.73    [v3: $i] : (v1 = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  !
% 14.33/2.73    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.33/2.73      $i] : (v1 = v0 |  ~ (holdsAt(v3, v2) = v1) |  ~ (holdsAt(v3, v2) = v0)) &  !
% 14.33/2.73    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.33/2.73      $i] : (v1 = v0 |  ~ (happens(v3, v2) = v1) |  ~ (happens(v3, v2) = v0)) &  !
% 14.33/2.73    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.33/2.73      $i] : (v1 = v0 |  ~ (less(v3, v2) = v1) |  ~ (less(v3, v2) = v0))
% 14.33/2.73  
% 14.33/2.73  Further assumptions not needed in the proof:
% 14.33/2.73  --------------------------------------------
% 14.33/2.73  antitrajectory, change_holding, forwards_not_spinning, happens_holds,
% 14.33/2.73  happens_not_released, happens_releases, happens_terminates_not_holds,
% 14.33/2.73  keep_holding, keep_not_released, keep_released, less0, less1, less2, less3,
% 14.33/2.73  less4, less5, less6, less7, less8, less9, less_or_equal, less_property,
% 14.33/2.73  not_forwards_0, plus0_0, plus0_2, plus0_3, plus1_1, plus1_2, plus1_3, plus2_2,
% 14.33/2.73  plus2_3, plus3_3, push_not_pull, releases_all_defn, startedin_defn,
% 14.33/2.73  stoppedin_defn, symmetry_of_plus, terminates_all_defn
% 14.33/2.73  
% 14.33/2.73  Those formulas are unsatisfiable:
% 14.33/2.73  ---------------------------------
% 14.33/2.73  
% 14.33/2.73  Begin of proof
% 14.33/2.73  | 
% 14.33/2.73  | ALPHA: (keep_not_holding) implies:
% 14.33/2.73  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (plus(v1, n1) = v2) |  ~
% 14.33/2.73  |          (holdsAt(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ?
% 14.33/2.73  |          [v4: any] :  ? [v5: $i] :  ? [v6: int] :  ? [v7: int] : ($i(v5) &
% 14.33/2.73  |            ((v7 = 0 & v6 = 0 & initiates(v5, v0, v1) = 0 & happens(v5, v1) =
% 14.33/2.73  |                0) | (releasedAt(v0, v2) = v4 & holdsAt(v0, v1) = v3 & (v4 = 0
% 14.33/2.73  |                  | v3 = 0)))))
% 14.33/2.73  | 
% 14.33/2.73  | ALPHA: (initiates_all_defn) implies:
% 14.33/2.73  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (initiates(v0, v1, v2) =
% 14.33/2.73  |            0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4:
% 14.33/2.73  |            any] : (happens(pull, v2) = v3 & happens(push, v2) = v4 & ((v4 = 0
% 14.33/2.73  |                & v1 = spinning & v0 = pull) | (v1 = backwards & v0 = pull &  ~
% 14.33/2.73  |                (v4 = 0)) | (v1 = forwards & v0 = push &  ~ (v3 = 0)))))
% 14.33/2.73  | 
% 14.33/2.73  | ALPHA: (happens_all_defn) implies:
% 14.33/2.73  |   (3)   ! [v0: int] : (v0 = 0 |  ~ (happens(push, n0) = v0))
% 14.33/2.73  | 
% 14.33/2.73  | ALPHA: (forwards_not_backwards) implies:
% 14.33/2.73  |   (4)   ~ (backwards = forwards)
% 14.33/2.73  | 
% 14.33/2.73  | ALPHA: (spinning_not_backwards) implies:
% 14.33/2.73  |   (5)   ~ (spinning = backwards)
% 14.33/2.73  | 
% 14.33/2.73  | ALPHA: (plus0_1) implies:
% 14.33/2.73  |   (6)  plus(n0, n1) = n1
% 14.33/2.73  | 
% 14.33/2.73  | ALPHA: (not_backwards_0) implies:
% 14.33/2.73  |   (7)   ? [v0: int] : ( ~ (v0 = 0) & holdsAt(backwards, n0) = v0)
% 14.33/2.74  | 
% 14.33/2.74  | ALPHA: (not_splinning_0) implies:
% 14.33/2.74  |   (8)  $i(n0)
% 14.33/2.74  | 
% 14.33/2.74  | ALPHA: (not_backwards_1) implies:
% 14.33/2.74  |   (9)  $i(n1)
% 14.33/2.74  |   (10)  $i(backwards)
% 14.33/2.74  |   (11)  holdsAt(backwards, n1) = 0
% 14.33/2.74  | 
% 14.33/2.74  | ALPHA: (function-axioms) implies:
% 14.33/2.74  |   (12)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 14.33/2.74  |         :  ! [v3: $i] : (v1 = v0 |  ~ (holdsAt(v3, v2) = v1) |  ~ (holdsAt(v3,
% 14.33/2.74  |               v2) = v0))
% 14.33/2.74  | 
% 14.33/2.74  | DELTA: instantiating (7) with fresh symbol all_38_0 gives:
% 14.33/2.74  |   (13)   ~ (all_38_0 = 0) & holdsAt(backwards, n0) = all_38_0
% 14.33/2.74  | 
% 14.33/2.74  | ALPHA: (13) implies:
% 14.33/2.74  |   (14)   ~ (all_38_0 = 0)
% 14.33/2.74  |   (15)  holdsAt(backwards, n0) = all_38_0
% 14.33/2.74  | 
% 14.33/2.74  | GROUND_INST: instantiating (1) with backwards, n0, n1, simplifying with (6),
% 14.33/2.74  |              (8), (10), (11) gives:
% 14.33/2.74  |   (16)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :  ? [v3: int] :  ? [v4:
% 14.33/2.74  |           int] : ($i(v2) & ((v4 = 0 & v3 = 0 & initiates(v2, backwards, n0) =
% 14.33/2.74  |               0 & happens(v2, n0) = 0) | (releasedAt(backwards, n1) = v1 &
% 14.33/2.74  |               holdsAt(backwards, n0) = v0 & (v1 = 0 | v0 = 0))))
% 14.33/2.74  | 
% 14.33/2.74  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2,
% 14.33/2.74  |        all_46_3, all_46_4 gives:
% 14.33/2.74  |   (17)  $i(all_46_2) & ((all_46_0 = 0 & all_46_1 = 0 & initiates(all_46_2,
% 14.33/2.74  |               backwards, n0) = 0 & happens(all_46_2, n0) = 0) |
% 14.33/2.74  |           (releasedAt(backwards, n1) = all_46_3 & holdsAt(backwards, n0) =
% 14.33/2.74  |             all_46_4 & (all_46_3 = 0 | all_46_4 = 0)))
% 14.33/2.74  | 
% 14.33/2.74  | ALPHA: (17) implies:
% 14.33/2.74  |   (18)  $i(all_46_2)
% 14.33/2.74  |   (19)  (all_46_0 = 0 & all_46_1 = 0 & initiates(all_46_2, backwards, n0) = 0
% 14.33/2.74  |           & happens(all_46_2, n0) = 0) | (releasedAt(backwards, n1) = all_46_3
% 14.33/2.74  |           & holdsAt(backwards, n0) = all_46_4 & (all_46_3 = 0 | all_46_4 = 0))
% 14.33/2.74  | 
% 14.33/2.74  | BETA: splitting (19) gives:
% 14.33/2.74  | 
% 14.33/2.74  | Case 1:
% 14.33/2.74  | | 
% 14.33/2.74  | |   (20)  all_46_0 = 0 & all_46_1 = 0 & initiates(all_46_2, backwards, n0) = 0
% 14.33/2.74  | |         & happens(all_46_2, n0) = 0
% 14.33/2.74  | | 
% 14.33/2.74  | | ALPHA: (20) implies:
% 14.33/2.74  | |   (21)  initiates(all_46_2, backwards, n0) = 0
% 14.33/2.74  | | 
% 14.33/2.74  | | GROUND_INST: instantiating (2) with all_46_2, backwards, n0, simplifying
% 14.33/2.74  | |              with (8), (10), (18), (21) gives:
% 14.33/2.74  | |   (22)   ? [v0: any] :  ? [v1: any] : (happens(pull, n0) = v0 &
% 14.33/2.74  | |           happens(push, n0) = v1 & ((v1 = 0 & all_46_2 = pull & spinning =
% 14.33/2.74  | |               backwards) | (all_46_2 = pull &  ~ (v1 = 0)) | (all_46_2 =
% 14.33/2.74  | |               push & backwards = forwards &  ~ (v0 = 0))))
% 14.33/2.74  | | 
% 14.33/2.75  | | DELTA: instantiating (22) with fresh symbols all_80_0, all_80_1 gives:
% 14.33/2.75  | |   (23)  happens(pull, n0) = all_80_1 & happens(push, n0) = all_80_0 &
% 14.33/2.75  | |         ((all_80_0 = 0 & all_46_2 = pull & spinning = backwards) | (all_46_2
% 14.33/2.75  | |             = pull &  ~ (all_80_0 = 0)) | (all_46_2 = push & backwards =
% 14.33/2.75  | |             forwards &  ~ (all_80_1 = 0)))
% 14.33/2.75  | | 
% 14.33/2.75  | | ALPHA: (23) implies:
% 14.33/2.75  | |   (24)  happens(push, n0) = all_80_0
% 14.33/2.75  | |   (25)  (all_80_0 = 0 & all_46_2 = pull & spinning = backwards) | (all_46_2
% 14.33/2.75  | |           = pull &  ~ (all_80_0 = 0)) | (all_46_2 = push & backwards =
% 14.33/2.75  | |           forwards &  ~ (all_80_1 = 0))
% 14.33/2.75  | | 
% 14.33/2.75  | | BETA: splitting (25) gives:
% 14.33/2.75  | | 
% 14.33/2.75  | | Case 1:
% 14.33/2.75  | | | 
% 14.33/2.75  | | |   (26)  all_80_0 = 0 & all_46_2 = pull & spinning = backwards
% 14.33/2.75  | | | 
% 14.33/2.75  | | | ALPHA: (26) implies:
% 14.33/2.75  | | |   (27)  spinning = backwards
% 14.33/2.75  | | | 
% 14.33/2.75  | | | REDUCE: (5), (27) imply:
% 14.33/2.75  | | |   (28)  $false
% 14.33/2.75  | | | 
% 14.33/2.75  | | | CLOSE: (28) is inconsistent.
% 14.33/2.75  | | | 
% 14.33/2.75  | | Case 2:
% 14.33/2.75  | | | 
% 14.33/2.75  | | |   (29)  (all_46_2 = pull &  ~ (all_80_0 = 0)) | (all_46_2 = push &
% 14.33/2.75  | | |           backwards = forwards &  ~ (all_80_1 = 0))
% 14.33/2.75  | | | 
% 14.33/2.75  | | | BETA: splitting (29) gives:
% 14.33/2.75  | | | 
% 14.33/2.75  | | | Case 1:
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | |   (30)  all_46_2 = pull &  ~ (all_80_0 = 0)
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | | ALPHA: (30) implies:
% 14.33/2.75  | | | |   (31)   ~ (all_80_0 = 0)
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | | GROUND_INST: instantiating (3) with all_80_0, simplifying with (24)
% 14.33/2.75  | | | |              gives:
% 14.33/2.75  | | | |   (32)  all_80_0 = 0
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | | REDUCE: (31), (32) imply:
% 14.33/2.75  | | | |   (33)  $false
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | | CLOSE: (33) is inconsistent.
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | Case 2:
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | |   (34)  all_46_2 = push & backwards = forwards &  ~ (all_80_1 = 0)
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | | ALPHA: (34) implies:
% 14.33/2.75  | | | |   (35)  backwards = forwards
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | | REDUCE: (4), (35) imply:
% 14.33/2.75  | | | |   (36)  $false
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | | CLOSE: (36) is inconsistent.
% 14.33/2.75  | | | | 
% 14.33/2.75  | | | End of split
% 14.33/2.75  | | | 
% 14.33/2.75  | | End of split
% 14.33/2.75  | | 
% 14.33/2.75  | Case 2:
% 14.33/2.75  | | 
% 14.33/2.75  | |   (37)  releasedAt(backwards, n1) = all_46_3 & holdsAt(backwards, n0) =
% 14.33/2.75  | |         all_46_4 & (all_46_3 = 0 | all_46_4 = 0)
% 14.33/2.75  | | 
% 14.33/2.75  | | ALPHA: (37) implies:
% 14.33/2.75  | |   (38)  holdsAt(backwards, n0) = all_46_4
% 14.33/2.75  | |   (39)  releasedAt(backwards, n1) = all_46_3
% 14.33/2.75  | |   (40)  all_46_3 = 0 | all_46_4 = 0
% 14.33/2.75  | | 
% 14.33/2.75  | | GROUND_INST: instantiating (12) with all_38_0, all_46_4, n0, backwards,
% 14.33/2.75  | |              simplifying with (15), (38) gives:
% 14.33/2.75  | |   (41)  all_46_4 = all_38_0
% 14.33/2.75  | | 
% 14.33/2.75  | | BETA: splitting (40) gives:
% 14.33/2.75  | | 
% 14.33/2.75  | | Case 1:
% 14.33/2.75  | | | 
% 14.33/2.75  | | |   (42)  all_46_3 = 0
% 14.33/2.75  | | | 
% 14.33/2.75  | | | REDUCE: (39), (42) imply:
% 14.33/2.75  | | |   (43)  releasedAt(backwards, n1) = 0
% 14.33/2.75  | | | 
% 14.33/2.75  | | | GROUND_INST: instantiating (not_releasedAt) with backwards, n1,
% 14.33/2.75  | | |              simplifying with (9), (10), (43) gives:
% 14.33/2.75  | | |   (44)  $false
% 14.33/2.75  | | | 
% 14.33/2.75  | | | CLOSE: (44) is inconsistent.
% 14.33/2.75  | | | 
% 14.33/2.75  | | Case 2:
% 14.33/2.75  | | | 
% 14.33/2.75  | | |   (45)  all_46_4 = 0
% 14.33/2.75  | | | 
% 14.33/2.75  | | | COMBINE_EQS: (41), (45) imply:
% 14.33/2.75  | | |   (46)  all_38_0 = 0
% 14.33/2.75  | | | 
% 14.33/2.75  | | | REDUCE: (14), (46) imply:
% 14.33/2.75  | | |   (47)  $false
% 14.33/2.75  | | | 
% 14.33/2.75  | | | CLOSE: (47) is inconsistent.
% 14.33/2.75  | | | 
% 14.33/2.75  | | End of split
% 14.33/2.75  | | 
% 14.33/2.75  | End of split
% 14.33/2.75  | 
% 14.33/2.75  End of proof
% 14.33/2.75  % SZS output end Proof for theBenchmark
% 14.33/2.75  
% 14.33/2.75  2138ms
%------------------------------------------------------------------------------