%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------