TSTP Solution File: PUZ047+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : PUZ047+1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n001.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 13:22:56 EDT 2023

% Result   : Theorem 15.69s 2.94s
% Output   : Proof 21.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PUZ047+1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n001.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 : Sat Aug 26 23:09:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.14/1.02  Prover 1: Preprocessing ...
% 2.14/1.03  Prover 4: Preprocessing ...
% 2.66/1.06  Prover 5: Preprocessing ...
% 2.66/1.06  Prover 6: Preprocessing ...
% 2.66/1.06  Prover 3: Preprocessing ...
% 2.66/1.06  Prover 2: Preprocessing ...
% 2.66/1.07  Prover 0: Preprocessing ...
% 4.80/1.36  Prover 5: Constructing countermodel ...
% 4.80/1.37  Prover 1: Constructing countermodel ...
% 4.80/1.38  Prover 6: Proving ...
% 4.80/1.38  Prover 3: Constructing countermodel ...
% 4.80/1.39  Prover 2: Proving ...
% 4.80/1.42  Prover 4: Constructing countermodel ...
% 5.30/1.48  Prover 3: gave up
% 5.30/1.49  Prover 1: gave up
% 5.30/1.49  Prover 0: Proving ...
% 5.30/1.49  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.30/1.50  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.30/1.52  Prover 8: Preprocessing ...
% 5.97/1.54  Prover 7: Preprocessing ...
% 6.24/1.59  Prover 7: Constructing countermodel ...
% 6.24/1.61  Prover 7: gave up
% 6.24/1.63  Prover 8: Warning: ignoring some quantifiers
% 6.81/1.63  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.81/1.65  Prover 8: Constructing countermodel ...
% 6.81/1.66  Prover 9: Preprocessing ...
% 7.08/1.72  Prover 8: gave up
% 7.08/1.73  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.72/1.76  Prover 10: Preprocessing ...
% 7.72/1.81  Prover 10: Constructing countermodel ...
% 7.72/1.82  Prover 10: gave up
% 8.10/1.82  Prover 9: Constructing countermodel ...
% 8.10/1.84  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.33/1.87  Prover 11: Preprocessing ...
% 9.15/2.03  Prover 11: Constructing countermodel ...
% 15.69/2.94  Prover 0: proved (2322ms)
% 15.69/2.94  
% 15.69/2.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.69/2.94  
% 16.25/2.94  Prover 2: stopped
% 16.25/2.95  Prover 9: stopped
% 16.25/2.95  Prover 6: stopped
% 16.25/2.95  Prover 5: stopped
% 16.25/2.95  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.25/2.95  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 16.25/2.95  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 16.25/2.96  Prover 13: Preprocessing ...
% 16.43/2.97  Prover 16: Preprocessing ...
% 16.43/2.97  Prover 19: Preprocessing ...
% 16.85/3.02  Prover 13: Constructing countermodel ...
% 16.85/3.04  Prover 16: Constructing countermodel ...
% 16.85/3.04  Prover 19: Warning: ignoring some quantifiers
% 16.85/3.04  Prover 19: Constructing countermodel ...
% 21.07/3.61  Prover 13: Found proof (size 24)
% 21.07/3.61  Prover 13: proved (669ms)
% 21.07/3.62  Prover 16: stopped
% 21.07/3.62  Prover 4: stopped
% 21.07/3.62  Prover 19: stopped
% 21.07/3.62  Prover 11: stopped
% 21.07/3.62  
% 21.07/3.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.07/3.62  
% 21.07/3.63  % SZS output start Proof for theBenchmark
% 21.07/3.63  Assumptions after simplification:
% 21.07/3.63  ---------------------------------
% 21.07/3.63  
% 21.07/3.63    (thm100)
% 21.41/3.67    $i(north) & $i(start) & $i(south) & p(south, south, south, south, start) &  !
% 21.41/3.67    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (take_goat(v2) = v3)
% 21.41/3.67      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ p(north, v0, north, v1, v2) |
% 21.41/3.67      p(south, v0, south, v1, v3)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 21.41/3.67    [v3: $i] : ( ~ (take_goat(v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 21.41/3.67      p(south, v0, south, v1, v2) | p(north, v0, north, v1, v3)) &  ! [v0: $i] : 
% 21.41/3.67    ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ p(north,
% 21.41/3.67        v0, north, v1, v2) |  ? [v3: $i] : (take_goat(v2) = v3 & $i(v3) & p(south,
% 21.41/3.67          v0, south, v1, v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 21.41/3.67      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ p(south, v0, south, v1, v2) |  ? [v3:
% 21.41/3.67        $i] : (take_goat(v2) = v3 & $i(v3) & p(north, v0, north, v1, v3))) &  !
% 21.41/3.67    [v0: $i] :  ! [v1: $i] : ( ~ (take_cabbage(v0) = v1) |  ~ $i(v0) |  ~ p(north,
% 21.41/3.67        north, south, north, v0) | p(south, north, south, south, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (take_cabbage(v0) = v1) |  ~ $i(v0) |  ~ p(north,
% 21.41/3.67        south, north, north, v0) | p(south, south, north, south, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (take_cabbage(v0) = v1) |  ~ $i(v0) |  ~ p(south,
% 21.41/3.67        north, south, south, v0) | p(north, north, south, north, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (take_cabbage(v0) = v1) |  ~ $i(v0) |  ~ p(south,
% 21.41/3.67        south, north, south, v0) | p(north, south, north, north, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (take_wolf(v0) = v1) |  ~ $i(v0) |  ~ p(north,
% 21.41/3.67        north, north, south, v0) | p(south, south, north, south, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (take_wolf(v0) = v1) |  ~ $i(v0) |  ~ p(north,
% 21.41/3.67        north, south, north, v0) | p(south, south, south, north, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (take_wolf(v0) = v1) |  ~ $i(v0) |  ~ p(south,
% 21.41/3.67        south, north, south, v0) | p(north, north, north, south, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (take_wolf(v0) = v1) |  ~ $i(v0) |  ~ p(south,
% 21.41/3.67        south, south, north, v0) | p(north, north, south, north, v1)) &  ! [v0:
% 21.41/3.67      $i] :  ! [v1: $i] : ( ~ (go_alone(v0) = v1) |  ~ $i(v0) |  ~ p(north, north,
% 21.41/3.67        south, north, v0) | p(south, north, south, north, v1)) &  ! [v0: $i] :  !
% 21.41/3.67    [v1: $i] : ( ~ (go_alone(v0) = v1) |  ~ $i(v0) |  ~ p(north, south, north,
% 21.41/3.67        south, v0) | p(south, south, north, south, v1)) &  ! [v0: $i] :  ! [v1:
% 21.41/3.67      $i] : ( ~ (go_alone(v0) = v1) |  ~ $i(v0) |  ~ p(south, north, south, north,
% 21.41/3.67        v0) | p(north, north, south, north, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 21.41/3.67      (go_alone(v0) = v1) |  ~ $i(v0) |  ~ p(south, south, north, south, v0) |
% 21.41/3.67      p(north, south, north, south, v1)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ p(north,
% 21.41/3.67        north, north, north, v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ p(north, north,
% 21.41/3.67        north, south, v0) |  ? [v1: $i] : (take_wolf(v0) = v1 & $i(v1) & p(south,
% 21.41/3.67          south, north, south, v1))) &  ! [v0: $i] : ( ~ $i(v0) |  ~ p(north,
% 21.41/3.67        north, south, north, v0) |  ? [v1: $i] : (take_cabbage(v0) = v1 & $i(v1) &
% 21.41/3.67        p(south, north, south, south, v1))) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 21.41/3.67      p(north, north, south, north, v0) |  ? [v1: $i] : (take_wolf(v0) = v1 &
% 21.41/3.67        $i(v1) & p(south, south, south, north, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(north, north, south, north, v0) |  ? [v1: $i] : (go_alone(v0) = v1 &
% 21.41/3.67        $i(v1) & p(south, north, south, north, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(north, south, north, north, v0) |  ? [v1: $i] : (take_cabbage(v0) = v1 &
% 21.41/3.67        $i(v1) & p(south, south, north, south, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(north, south, north, south, v0) |  ? [v1: $i] : (go_alone(v0) = v1 &
% 21.41/3.67        $i(v1) & p(south, south, north, south, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(south, north, south, north, v0) |  ? [v1: $i] : (go_alone(v0) = v1 &
% 21.41/3.67        $i(v1) & p(north, north, south, north, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(south, north, south, south, v0) |  ? [v1: $i] : (take_cabbage(v0) = v1 &
% 21.41/3.67        $i(v1) & p(north, north, south, north, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(south, south, north, south, v0) |  ? [v1: $i] : (take_cabbage(v0) = v1 &
% 21.41/3.67        $i(v1) & p(north, south, north, north, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(south, south, north, south, v0) |  ? [v1: $i] : (take_wolf(v0) = v1 &
% 21.41/3.67        $i(v1) & p(north, north, north, south, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(south, south, north, south, v0) |  ? [v1: $i] : (go_alone(v0) = v1 &
% 21.41/3.67        $i(v1) & p(north, south, north, south, v1))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 21.41/3.67      ~ p(south, south, south, north, v0) |  ? [v1: $i] : (take_wolf(v0) = v1 &
% 21.41/3.67        $i(v1) & p(north, north, south, north, v1)))
% 21.41/3.67  
% 21.41/3.67  Those formulas are unsatisfiable:
% 21.41/3.67  ---------------------------------
% 21.41/3.67  
% 21.41/3.67  Begin of proof
% 21.41/3.67  | 
% 21.41/3.67  | ALPHA: (thm100) implies:
% 21.41/3.67  |   (1)  p(south, south, south, south, start)
% 21.41/3.67  |   (2)  $i(south)
% 21.41/3.67  |   (3)  $i(start)
% 21.41/3.67  |   (4)  $i(north)
% 21.41/3.68  |   (5)   ! [v0: $i] : ( ~ $i(v0) |  ~ p(south, south, south, north, v0) |  ?
% 21.41/3.68  |          [v1: $i] : (take_wolf(v0) = v1 & $i(v1) & p(north, north, south,
% 21.41/3.68  |              north, v1)))
% 21.41/3.68  |   (6)   ! [v0: $i] : ( ~ $i(v0) |  ~ p(south, south, north, south, v0) |  ?
% 21.41/3.68  |          [v1: $i] : (take_cabbage(v0) = v1 & $i(v1) & p(north, south, north,
% 21.41/3.68  |              north, v1)))
% 21.41/3.68  |   (7)   ! [v0: $i] : ( ~ $i(v0) |  ~ p(north, south, north, south, v0) |  ?
% 21.41/3.68  |          [v1: $i] : (go_alone(v0) = v1 & $i(v1) & p(south, south, north,
% 21.41/3.68  |              south, v1)))
% 21.41/3.68  |   (8)   ! [v0: $i] : ( ~ $i(v0) |  ~ p(north, north, south, north, v0) |  ?
% 21.41/3.68  |          [v1: $i] : (go_alone(v0) = v1 & $i(v1) & p(south, north, south,
% 21.41/3.68  |              north, v1)))
% 21.41/3.68  |   (9)   ! [v0: $i] : ( ~ $i(v0) |  ~ p(north, north, north, north, v0))
% 21.41/3.68  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~
% 21.41/3.68  |           $i(v0) |  ~ p(south, v0, south, v1, v2) |  ? [v3: $i] :
% 21.41/3.68  |           (take_goat(v2) = v3 & $i(v3) & p(north, v0, north, v1, v3)))
% 21.41/3.68  |   (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~
% 21.41/3.68  |           $i(v0) |  ~ p(north, v0, north, v1, v2) |  ? [v3: $i] :
% 21.41/3.68  |           (take_goat(v2) = v3 & $i(v3) & p(south, v0, south, v1, v3)))
% 21.41/3.68  | 
% 21.41/3.68  | GROUND_INST: instantiating (10) with south, south, start, simplifying with
% 21.41/3.68  |              (1), (2), (3) gives:
% 21.41/3.68  |   (12)   ? [v0: $i] : (take_goat(start) = v0 & $i(v0) & p(north, south, north,
% 21.41/3.68  |             south, v0))
% 21.41/3.68  | 
% 21.41/3.68  | DELTA: instantiating (12) with fresh symbol all_10_0 gives:
% 21.41/3.68  |   (13)  take_goat(start) = all_10_0 & $i(all_10_0) & p(north, south, north,
% 21.41/3.68  |           south, all_10_0)
% 21.41/3.68  | 
% 21.41/3.68  | ALPHA: (13) implies:
% 21.41/3.68  |   (14)  p(north, south, north, south, all_10_0)
% 21.41/3.68  |   (15)  $i(all_10_0)
% 21.41/3.68  | 
% 21.41/3.68  | GROUND_INST: instantiating (7) with all_10_0, simplifying with (14), (15)
% 21.41/3.68  |              gives:
% 21.41/3.68  |   (16)   ? [v0: $i] : (go_alone(all_10_0) = v0 & $i(v0) & p(south, south,
% 21.41/3.68  |             north, south, v0))
% 21.41/3.68  | 
% 21.41/3.68  | DELTA: instantiating (16) with fresh symbol all_19_0 gives:
% 21.41/3.68  |   (17)  go_alone(all_10_0) = all_19_0 & $i(all_19_0) & p(south, south, north,
% 21.41/3.68  |           south, all_19_0)
% 21.41/3.68  | 
% 21.41/3.68  | ALPHA: (17) implies:
% 21.41/3.68  |   (18)  p(south, south, north, south, all_19_0)
% 21.41/3.68  |   (19)  $i(all_19_0)
% 21.41/3.68  | 
% 21.41/3.68  | GROUND_INST: instantiating (6) with all_19_0, simplifying with (18), (19)
% 21.41/3.68  |              gives:
% 21.41/3.68  |   (20)   ? [v0: $i] : (take_cabbage(all_19_0) = v0 & $i(v0) & p(north, south,
% 21.41/3.68  |             north, north, v0))
% 21.41/3.68  | 
% 21.41/3.68  | DELTA: instantiating (20) with fresh symbol all_28_0 gives:
% 21.41/3.68  |   (21)  take_cabbage(all_19_0) = all_28_0 & $i(all_28_0) & p(north, south,
% 21.41/3.68  |           north, north, all_28_0)
% 21.41/3.68  | 
% 21.41/3.68  | ALPHA: (21) implies:
% 21.41/3.68  |   (22)  p(north, south, north, north, all_28_0)
% 21.41/3.68  |   (23)  $i(all_28_0)
% 21.41/3.68  | 
% 21.41/3.68  | GROUND_INST: instantiating (11) with south, north, all_28_0, simplifying with
% 21.41/3.68  |              (2), (4), (22), (23) gives:
% 21.41/3.68  |   (24)   ? [v0: $i] : (take_goat(all_28_0) = v0 & $i(v0) & p(south, south,
% 21.41/3.68  |             south, north, v0))
% 21.41/3.68  | 
% 21.41/3.68  | DELTA: instantiating (24) with fresh symbol all_43_0 gives:
% 21.41/3.68  |   (25)  take_goat(all_28_0) = all_43_0 & $i(all_43_0) & p(south, south, south,
% 21.41/3.69  |           north, all_43_0)
% 21.41/3.69  | 
% 21.41/3.69  | ALPHA: (25) implies:
% 21.41/3.69  |   (26)  p(south, south, south, north, all_43_0)
% 21.41/3.69  |   (27)  $i(all_43_0)
% 21.41/3.69  | 
% 21.41/3.69  | GROUND_INST: instantiating (5) with all_43_0, simplifying with (26), (27)
% 21.41/3.69  |              gives:
% 21.41/3.69  |   (28)   ? [v0: $i] : (take_wolf(all_43_0) = v0 & $i(v0) & p(north, north,
% 21.41/3.69  |             south, north, v0))
% 21.41/3.69  | 
% 21.41/3.69  | DELTA: instantiating (28) with fresh symbol all_90_0 gives:
% 21.41/3.69  |   (29)  take_wolf(all_43_0) = all_90_0 & $i(all_90_0) & p(north, north, south,
% 21.41/3.69  |           north, all_90_0)
% 21.41/3.69  | 
% 21.41/3.69  | ALPHA: (29) implies:
% 21.41/3.69  |   (30)  p(north, north, south, north, all_90_0)
% 21.41/3.69  |   (31)  $i(all_90_0)
% 21.41/3.69  | 
% 21.41/3.69  | GROUND_INST: instantiating (8) with all_90_0, simplifying with (30), (31)
% 21.41/3.69  |              gives:
% 21.41/3.69  |   (32)   ? [v0: $i] : (go_alone(all_90_0) = v0 & $i(v0) & p(south, north,
% 21.41/3.69  |             south, north, v0))
% 21.41/3.69  | 
% 21.41/3.69  | DELTA: instantiating (32) with fresh symbol all_117_0 gives:
% 21.41/3.69  |   (33)  go_alone(all_90_0) = all_117_0 & $i(all_117_0) & p(south, north,
% 21.41/3.69  |           south, north, all_117_0)
% 21.41/3.69  | 
% 21.41/3.69  | ALPHA: (33) implies:
% 21.41/3.69  |   (34)  p(south, north, south, north, all_117_0)
% 21.41/3.69  |   (35)  $i(all_117_0)
% 21.41/3.69  | 
% 21.41/3.69  | GROUND_INST: instantiating (10) with north, north, all_117_0, simplifying with
% 21.41/3.69  |              (4), (34), (35) gives:
% 21.41/3.69  |   (36)   ? [v0: $i] : (take_goat(all_117_0) = v0 & $i(v0) & p(north, north,
% 21.41/3.69  |             north, north, v0))
% 21.41/3.69  | 
% 21.41/3.69  | DELTA: instantiating (36) with fresh symbol all_280_0 gives:
% 21.41/3.69  |   (37)  take_goat(all_117_0) = all_280_0 & $i(all_280_0) & p(north, north,
% 21.41/3.69  |           north, north, all_280_0)
% 21.41/3.69  | 
% 21.41/3.69  | ALPHA: (37) implies:
% 21.41/3.69  |   (38)  p(north, north, north, north, all_280_0)
% 21.41/3.69  |   (39)  $i(all_280_0)
% 21.41/3.69  | 
% 21.41/3.69  | GROUND_INST: instantiating (9) with all_280_0, simplifying with (38), (39)
% 21.41/3.69  |              gives:
% 21.41/3.69  |   (40)  $false
% 21.41/3.69  | 
% 21.41/3.69  | CLOSE: (40) is inconsistent.
% 21.41/3.69  | 
% 21.41/3.69  End of proof
% 21.41/3.69  % SZS output end Proof for theBenchmark
% 21.41/3.69  
% 21.41/3.69  3089ms
%------------------------------------------------------------------------------