%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN550+1 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n003.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 : Fri Sep 1 03:28:14 EDT 2023 % Result : Theorem 6.53s 1.69s % Output : Proof 8.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYN550+1 : TPTP v8.1.2. Released v2.2.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n003.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 20:46:39 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.16/1.01 Prover 4: Preprocessing ... % 2.16/1.01 Prover 1: Preprocessing ... % 2.16/1.06 Prover 3: Preprocessing ... % 2.16/1.06 Prover 2: Preprocessing ... % 2.16/1.06 Prover 6: Preprocessing ... % 2.16/1.06 Prover 5: Preprocessing ... % 2.16/1.06 Prover 0: Preprocessing ... % 3.13/1.16 Prover 5: Proving ... % 3.13/1.16 Prover 2: Proving ... % 3.31/1.19 Prover 6: Proving ... % 3.31/1.19 Prover 3: Constructing countermodel ... % 3.31/1.19 Prover 1: Constructing countermodel ... % 3.59/1.23 Prover 0: Proving ... % 3.68/1.26 Prover 4: Constructing countermodel ... % 3.68/1.28 Prover 1: gave up % 3.68/1.28 Prover 3: gave up % 3.68/1.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.68/1.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.68/1.31 Prover 7: Preprocessing ... % 3.68/1.32 Prover 8: Preprocessing ... % 3.68/1.34 Prover 7: Warning: ignoring some quantifiers % 3.68/1.36 Prover 7: Constructing countermodel ... % 3.68/1.40 Prover 8: Warning: ignoring some quantifiers % 3.68/1.41 Prover 8: Constructing countermodel ... % 5.38/1.51 Prover 8: gave up % 5.38/1.51 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.38/1.52 Prover 9: Preprocessing ... % 6.05/1.58 Prover 9: Constructing countermodel ... % 6.53/1.69 Prover 0: proved (1052ms) % 6.53/1.69 % 6.53/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.53/1.69 % 6.53/1.69 Prover 9: stopped % 6.53/1.69 Prover 2: stopped % 6.53/1.69 Prover 6: stopped % 6.53/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.53/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.53/1.70 Prover 5: stopped % 6.53/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.53/1.71 Prover 10: Preprocessing ... % 6.53/1.71 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.53/1.71 Prover 11: Preprocessing ... % 6.53/1.71 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.20/1.72 Prover 13: Preprocessing ... % 7.20/1.73 Prover 10: Warning: ignoring some quantifiers % 7.20/1.73 Prover 10: Constructing countermodel ... % 7.20/1.73 Prover 19: Preprocessing ... % 7.20/1.74 Prover 16: Preprocessing ... % 7.20/1.74 Prover 13: Warning: ignoring some quantifiers % 7.20/1.75 Prover 13: Constructing countermodel ... % 7.20/1.75 Prover 16: Warning: ignoring some quantifiers % 7.20/1.76 Prover 16: Constructing countermodel ... % 7.64/1.78 Prover 11: Constructing countermodel ... % 7.64/1.81 Prover 19: Warning: ignoring some quantifiers % 7.64/1.81 Prover 19: Constructing countermodel ... % 7.64/1.86 Prover 19: gave up % 8.27/1.87 Prover 10: Found proof (size 34) % 8.27/1.87 Prover 10: proved (176ms) % 8.27/1.87 Prover 13: stopped % 8.27/1.87 Prover 7: stopped % 8.27/1.87 Prover 16: stopped % 8.27/1.87 Prover 11: stopped % 8.27/1.87 Prover 4: stopped % 8.27/1.87 % 8.27/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.27/1.87 % 8.27/1.87 % SZS output start Proof for theBenchmark % 8.27/1.88 Assumptions after simplification: % 8.27/1.88 --------------------------------- % 8.27/1.88 % 8.27/1.88 (prove_this) % 8.36/1.88 $i(initial_world) & ? [v0: $i] : ($i(v0) & ((reachable(initial_world, v0) & % 8.36/1.88 ! [v1: $i] : ( ~ $i(v1) | ~ reachable(v0, v1) | p(v1)) & ! [v1: $i] : % 8.36/1.88 ( ~ $i(v1) | ~ reachable(initial_world, v1) | ? [v2: $i] : ($i(v2) & % 8.36/1.88 reachable(v1, v2) & ! [v3: $i] : ( ~ $i(v3) | ~ reachable(v2, v3) % 8.36/1.88 | ? [v4: $i] : ($i(v4) & reachable(v3, v4) & ~ p(v4)))))) | % 8.36/1.88 (reachable(initial_world, v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 8.36/1.88 reachable(v0, v1) | ? [v2: $i] : ($i(v2) & reachable(v1, v2) & ! % 8.36/1.88 [v3: $i] : ( ~ $i(v3) | ~ reachable(v2, v3) | p(v3)))) & ! [v1: % 8.36/1.88 $i] : ( ~ $i(v1) | ~ reachable(initial_world, v1) | ? [v2: $i] : % 8.36/1.88 ($i(v2) & reachable(v1, v2) & ~ p(v2)))))) % 8.36/1.88 % 8.36/1.88 (transitivity_of_reachable) % 8.36/1.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.36/1.89 ~ reachable(v1, v2) | ~ reachable(v0, v1) | reachable(v0, v2)) % 8.36/1.89 % 8.36/1.89 Further assumptions not needed in the proof: % 8.36/1.89 -------------------------------------------- % 8.36/1.89 reflexivity_of_reachable % 8.36/1.89 % 8.36/1.89 Those formulas are unsatisfiable: % 8.36/1.89 --------------------------------- % 8.36/1.89 % 8.36/1.89 Begin of proof % 8.36/1.89 | % 8.36/1.89 | ALPHA: (prove_this) implies: % 8.36/1.89 | (1) $i(initial_world) % 8.36/1.89 | (2) ? [v0: $i] : ($i(v0) & ((reachable(initial_world, v0) & ! [v1: $i] : % 8.36/1.89 | ( ~ $i(v1) | ~ reachable(v0, v1) | p(v1)) & ! [v1: $i] : ( ~ % 8.36/1.89 | $i(v1) | ~ reachable(initial_world, v1) | ? [v2: $i] : % 8.36/1.89 | ($i(v2) & reachable(v1, v2) & ! [v3: $i] : ( ~ $i(v3) | ~ % 8.36/1.89 | reachable(v2, v3) | ? [v4: $i] : ($i(v4) & reachable(v3, % 8.36/1.89 | v4) & ~ p(v4)))))) | (reachable(initial_world, v0) & % 8.36/1.89 | ! [v1: $i] : ( ~ $i(v1) | ~ reachable(v0, v1) | ? [v2: $i] : % 8.36/1.89 | ($i(v2) & reachable(v1, v2) & ! [v3: $i] : ( ~ $i(v3) | ~ % 8.36/1.89 | reachable(v2, v3) | p(v3)))) & ! [v1: $i] : ( ~ $i(v1) | % 8.36/1.89 | ~ reachable(initial_world, v1) | ? [v2: $i] : ($i(v2) & % 8.36/1.89 | reachable(v1, v2) & ~ p(v2)))))) % 8.36/1.89 | % 8.36/1.89 | DELTA: instantiating (2) with fresh symbol all_5_0 gives: % 8.36/1.90 | (3) $i(all_5_0) & ((reachable(initial_world, all_5_0) & ! [v0: $i] : ( ~ % 8.36/1.90 | $i(v0) | ~ reachable(all_5_0, v0) | p(v0)) & ! [v0: $i] : ( ~ % 8.36/1.90 | $i(v0) | ~ reachable(initial_world, v0) | ? [v1: $i] : ($i(v1) % 8.36/1.90 | & reachable(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | ~ % 8.36/1.90 | reachable(v1, v2) | ? [v3: $i] : ($i(v3) & reachable(v2, v3) % 8.36/1.90 | & ~ p(v3)))))) | (reachable(initial_world, all_5_0) & ! % 8.36/1.90 | [v0: $i] : ( ~ $i(v0) | ~ reachable(all_5_0, v0) | ? [v1: $i] : % 8.36/1.90 | ($i(v1) & reachable(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | ~ % 8.36/1.90 | reachable(v1, v2) | p(v2)))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 8.36/1.90 | reachable(initial_world, v0) | ? [v1: $i] : ($i(v1) & % 8.36/1.90 | reachable(v0, v1) & ~ p(v1))))) % 8.36/1.90 | % 8.36/1.90 | ALPHA: (3) implies: % 8.36/1.90 | (4) $i(all_5_0) % 8.36/1.90 | (5) (reachable(initial_world, all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 8.36/1.90 | reachable(all_5_0, v0) | p(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 8.36/1.90 | reachable(initial_world, v0) | ? [v1: $i] : ($i(v1) & % 8.36/1.90 | reachable(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | ~ reachable(v1, % 8.36/1.90 | v2) | ? [v3: $i] : ($i(v3) & reachable(v2, v3) & ~ % 8.36/1.90 | p(v3)))))) | (reachable(initial_world, all_5_0) & ! [v0: $i] % 8.36/1.90 | : ( ~ $i(v0) | ~ reachable(all_5_0, v0) | ? [v1: $i] : ($i(v1) & % 8.36/1.90 | reachable(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | ~ reachable(v1, % 8.36/1.90 | v2) | p(v2)))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 8.36/1.90 | reachable(initial_world, v0) | ? [v1: $i] : ($i(v1) & % 8.36/1.90 | reachable(v0, v1) & ~ p(v1)))) % 8.36/1.90 | % 8.36/1.90 | BETA: splitting (5) gives: % 8.36/1.90 | % 8.36/1.90 | Case 1: % 8.36/1.90 | | % 8.36/1.90 | | (6) reachable(initial_world, all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 8.36/1.90 | | reachable(all_5_0, v0) | p(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 8.36/1.90 | | reachable(initial_world, v0) | ? [v1: $i] : ($i(v1) & % 8.36/1.90 | | reachable(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | ~ reachable(v1, % 8.36/1.90 | | v2) | ? [v3: $i] : ($i(v3) & reachable(v2, v3) & ~ % 8.36/1.90 | | p(v3))))) % 8.36/1.90 | | % 8.36/1.90 | | ALPHA: (6) implies: % 8.36/1.90 | | (7) reachable(initial_world, all_5_0) % 8.36/1.90 | | (8) ! [v0: $i] : ( ~ $i(v0) | ~ reachable(initial_world, v0) | ? [v1: % 8.36/1.90 | | $i] : ($i(v1) & reachable(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | ~ % 8.36/1.90 | | reachable(v1, v2) | ? [v3: $i] : ($i(v3) & reachable(v2, v3) & % 8.36/1.90 | | ~ p(v3))))) % 8.36/1.91 | | (9) ! [v0: $i] : ( ~ $i(v0) | ~ reachable(all_5_0, v0) | p(v0)) % 8.36/1.91 | | % 8.36/1.91 | | GROUND_INST: instantiating (8) with all_5_0, simplifying with (4), (7) % 8.36/1.91 | | gives: % 8.36/1.91 | | (10) ? [v0: $i] : ($i(v0) & reachable(all_5_0, v0) & ! [v1: $i] : ( ~ % 8.36/1.91 | | $i(v1) | ~ reachable(v0, v1) | ? [v2: $i] : ($i(v2) & % 8.36/1.91 | | reachable(v1, v2) & ~ p(v2)))) % 8.36/1.91 | | % 8.36/1.91 | | DELTA: instantiating (10) with fresh symbol all_27_0 gives: % 8.36/1.91 | | (11) $i(all_27_0) & reachable(all_5_0, all_27_0) & ! [v0: $i] : ( ~ % 8.36/1.91 | | $i(v0) | ~ reachable(all_27_0, v0) | ? [v1: $i] : ($i(v1) & % 8.36/1.91 | | reachable(v0, v1) & ~ p(v1))) % 8.36/1.91 | | % 8.36/1.91 | | ALPHA: (11) implies: % 8.36/1.91 | | (12) reachable(all_5_0, all_27_0) % 8.36/1.91 | | (13) $i(all_27_0) % 8.36/1.91 | | (14) ! [v0: $i] : ( ~ $i(v0) | ~ reachable(all_27_0, v0) | ? [v1: $i] % 8.36/1.91 | | : ($i(v1) & reachable(v0, v1) & ~ p(v1))) % 8.36/1.91 | | % 8.36/1.91 | | GROUND_INST: instantiating (transitivity_of_reachable) with initial_world, % 8.36/1.91 | | all_5_0, all_27_0, simplifying with (1), (4), (7), (12), (13) % 8.36/1.91 | | gives: % 8.36/1.91 | | (15) reachable(initial_world, all_27_0) % 8.36/1.91 | | % 8.36/1.91 | | GROUND_INST: instantiating (8) with all_27_0, simplifying with (13), (15) % 8.36/1.91 | | gives: % 8.36/1.91 | | (16) ? [v0: $i] : ($i(v0) & reachable(all_27_0, v0) & ! [v1: $i] : ( ~ % 8.36/1.91 | | $i(v1) | ~ reachable(v0, v1) | ? [v2: $i] : ($i(v2) & % 8.36/1.91 | | reachable(v1, v2) & ~ p(v2)))) % 8.36/1.91 | | % 8.36/1.91 | | DELTA: instantiating (16) with fresh symbol all_41_0 gives: % 8.52/1.91 | | (17) $i(all_41_0) & reachable(all_27_0, all_41_0) & ! [v0: $i] : ( ~ % 8.52/1.91 | | $i(v0) | ~ reachable(all_41_0, v0) | ? [v1: $i] : ($i(v1) & % 8.52/1.91 | | reachable(v0, v1) & ~ p(v1))) % 8.52/1.91 | | % 8.52/1.91 | | ALPHA: (17) implies: % 8.52/1.91 | | (18) reachable(all_27_0, all_41_0) % 8.52/1.91 | | (19) $i(all_41_0) % 8.52/1.91 | | % 8.52/1.91 | | GROUND_INST: instantiating (transitivity_of_reachable) with all_5_0, % 8.52/1.91 | | all_27_0, all_41_0, simplifying with (4), (12), (13), (18), % 8.52/1.91 | | (19) gives: % 8.52/1.91 | | (20) reachable(all_5_0, all_41_0) % 8.52/1.91 | | % 8.52/1.91 | | GROUND_INST: instantiating (14) with all_41_0, simplifying with (18), (19) % 8.52/1.91 | | gives: % 8.52/1.91 | | (21) ? [v0: $i] : ($i(v0) & reachable(all_41_0, v0) & ~ p(v0)) % 8.52/1.91 | | % 8.52/1.91 | | DELTA: instantiating (21) with fresh symbol all_50_0 gives: % 8.52/1.91 | | (22) $i(all_50_0) & reachable(all_41_0, all_50_0) & ~ p(all_50_0) % 8.52/1.91 | | % 8.52/1.91 | | ALPHA: (22) implies: % 8.52/1.91 | | (23) ~ p(all_50_0) % 8.52/1.92 | | (24) reachable(all_41_0, all_50_0) % 8.52/1.92 | | (25) $i(all_50_0) % 8.52/1.92 | | % 8.52/1.92 | | GROUND_INST: instantiating (transitivity_of_reachable) with all_5_0, % 8.52/1.92 | | all_41_0, all_50_0, simplifying with (4), (19), (20), (24), % 8.52/1.92 | | (25) gives: % 8.52/1.92 | | (26) reachable(all_5_0, all_50_0) % 8.52/1.92 | | % 8.52/1.92 | | GROUND_INST: instantiating (9) with all_50_0, simplifying with (23), (25), % 8.52/1.92 | | (26) gives: % 8.52/1.92 | | (27) $false % 8.52/1.92 | | % 8.52/1.92 | | CLOSE: (27) is inconsistent. % 8.52/1.92 | | % 8.52/1.92 | Case 2: % 8.52/1.92 | | % 8.52/1.92 | | (28) reachable(initial_world, all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 8.52/1.92 | | reachable(all_5_0, v0) | ? [v1: $i] : ($i(v1) & reachable(v0, v1) % 8.52/1.92 | | & ! [v2: $i] : ( ~ $i(v2) | ~ reachable(v1, v2) | p(v2)))) & % 8.52/1.92 | | ! [v0: $i] : ( ~ $i(v0) | ~ reachable(initial_world, v0) | ? [v1: % 8.52/1.92 | | $i] : ($i(v1) & reachable(v0, v1) & ~ p(v1))) % 8.52/1.92 | | % 8.52/1.92 | | ALPHA: (28) implies: % 8.52/1.92 | | (29) reachable(initial_world, all_5_0) % 8.52/1.92 | | (30) ! [v0: $i] : ( ~ $i(v0) | ~ reachable(initial_world, v0) | ? [v1: % 8.52/1.92 | | $i] : ($i(v1) & reachable(v0, v1) & ~ p(v1))) % 8.52/1.92 | | (31) ! [v0: $i] : ( ~ $i(v0) | ~ reachable(all_5_0, v0) | ? [v1: $i] : % 8.52/1.92 | | ($i(v1) & reachable(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | ~ % 8.52/1.92 | | reachable(v1, v2) | p(v2)))) % 8.52/1.92 | | % 8.52/1.92 | | GROUND_INST: instantiating (30) with all_5_0, simplifying with (4), (29) % 8.52/1.92 | | gives: % 8.52/1.92 | | (32) ? [v0: $i] : ($i(v0) & reachable(all_5_0, v0) & ~ p(v0)) % 8.52/1.92 | | % 8.52/1.92 | | DELTA: instantiating (32) with fresh symbol all_27_0 gives: % 8.52/1.92 | | (33) $i(all_27_0) & reachable(all_5_0, all_27_0) & ~ p(all_27_0) % 8.52/1.92 | | % 8.52/1.92 | | ALPHA: (33) implies: % 8.52/1.92 | | (34) reachable(all_5_0, all_27_0) % 8.52/1.92 | | (35) $i(all_27_0) % 8.52/1.92 | | % 8.52/1.92 | | GROUND_INST: instantiating (transitivity_of_reachable) with initial_world, % 8.52/1.92 | | all_5_0, all_27_0, simplifying with (1), (4), (29), (34), (35) % 8.52/1.92 | | gives: % 8.52/1.92 | | (36) reachable(initial_world, all_27_0) % 8.52/1.92 | | % 8.52/1.92 | | GROUND_INST: instantiating (31) with all_27_0, simplifying with (34), (35) % 8.52/1.92 | | gives: % 8.52/1.92 | | (37) ? [v0: $i] : ($i(v0) & reachable(all_27_0, v0) & ! [v1: $i] : ( ~ % 8.52/1.92 | | $i(v1) | ~ reachable(v0, v1) | p(v1))) % 8.52/1.92 | | % 8.52/1.92 | | DELTA: instantiating (37) with fresh symbol all_35_0 gives: % 8.52/1.92 | | (38) $i(all_35_0) & reachable(all_27_0, all_35_0) & ! [v0: $i] : ( ~ % 8.52/1.92 | | $i(v0) | ~ reachable(all_35_0, v0) | p(v0)) % 8.52/1.92 | | % 8.52/1.92 | | ALPHA: (38) implies: % 8.52/1.92 | | (39) reachable(all_27_0, all_35_0) % 8.52/1.92 | | (40) $i(all_35_0) % 8.52/1.93 | | (41) ! [v0: $i] : ( ~ $i(v0) | ~ reachable(all_35_0, v0) | p(v0)) % 8.52/1.93 | | % 8.52/1.93 | | GROUND_INST: instantiating (transitivity_of_reachable) with initial_world, % 8.52/1.93 | | all_27_0, all_35_0, simplifying with (1), (35), (36), (39), % 8.52/1.93 | | (40) gives: % 8.52/1.93 | | (42) reachable(initial_world, all_35_0) % 8.52/1.93 | | % 8.52/1.93 | | GROUND_INST: instantiating (30) with all_35_0, simplifying with (40), (42) % 8.52/1.93 | | gives: % 8.52/1.93 | | (43) ? [v0: $i] : ($i(v0) & reachable(all_35_0, v0) & ~ p(v0)) % 8.52/1.93 | | % 8.52/1.93 | | DELTA: instantiating (43) with fresh symbol all_52_0 gives: % 8.52/1.93 | | (44) $i(all_52_0) & reachable(all_35_0, all_52_0) & ~ p(all_52_0) % 8.52/1.93 | | % 8.52/1.93 | | ALPHA: (44) implies: % 8.52/1.93 | | (45) ~ p(all_52_0) % 8.52/1.93 | | (46) reachable(all_35_0, all_52_0) % 8.52/1.93 | | (47) $i(all_52_0) % 8.52/1.93 | | % 8.52/1.93 | | GROUND_INST: instantiating (41) with all_52_0, simplifying with (45), (46), % 8.52/1.93 | | (47) gives: % 8.52/1.93 | | (48) $false % 8.52/1.93 | | % 8.52/1.93 | | CLOSE: (48) is inconsistent. % 8.52/1.93 | | % 8.52/1.93 | End of split % 8.52/1.93 | % 8.52/1.93 End of proof % 8.52/1.93 % SZS output end Proof for theBenchmark % 8.52/1.93 % 8.52/1.93 1309ms %------------------------------------------------------------------------------