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