%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO147+1 : TPTP v8.1.2. Released v2.4.0. % 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 : Wed Aug 30 23:21:41 EDT 2023 % Result : Theorem 16.17s 2.96s % Output : Proof 21.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.10 % Problem : GEO147+1 : TPTP v8.1.2. Released v2.4.0. % 0.03/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n003.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Tue Aug 29 21:58:41 EDT 2023 % 0.10/0.31 % CPUTime : % 0.16/0.59 ________ _____ % 0.16/0.60 ___ __ \_________(_)________________________________ % 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.60 % 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.60 (2023-06-19) % 0.16/0.60 % 0.16/0.60 (c) Philipp Rümmer, 2009-2023 % 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.60 Amanda Stjerna. % 0.16/0.60 Free software under BSD-3-Clause. % 0.16/0.60 % 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.60 % 0.16/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.56/0.61 Running up to 7 provers in parallel. % 0.56/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.56/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.56/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.56/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.56/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.56/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.56/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.38/1.24 Prover 4: Preprocessing ... % 3.38/1.24 Prover 1: Preprocessing ... % 3.38/1.29 Prover 0: Preprocessing ... % 3.38/1.29 Prover 6: Preprocessing ... % 3.38/1.29 Prover 2: Preprocessing ... % 3.38/1.29 Prover 5: Preprocessing ... % 3.38/1.30 Prover 3: Preprocessing ... % 9.64/2.10 Prover 5: Proving ... % 9.64/2.12 Prover 2: Proving ... % 10.67/2.19 Prover 3: Warning: ignoring some quantifiers % 10.67/2.21 Prover 6: Proving ... % 10.67/2.24 Prover 3: Constructing countermodel ... % 11.23/2.26 Prover 1: Warning: ignoring some quantifiers % 11.59/2.33 Prover 1: Constructing countermodel ... % 14.56/2.75 Prover 4: Warning: ignoring some quantifiers % 15.22/2.87 Prover 4: Constructing countermodel ... % 16.17/2.95 Prover 2: proved (2330ms) % 16.17/2.95 % 16.17/2.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.17/2.96 % 16.17/2.96 Prover 5: stopped % 16.17/2.96 Prover 6: stopped % 16.17/2.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.17/2.97 Prover 3: stopped % 16.17/2.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.17/2.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.17/2.98 Prover 0: Proving ... % 16.17/2.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.17/3.00 Prover 0: stopped % 16.88/3.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.41/3.09 Prover 10: Preprocessing ... % 17.41/3.09 Prover 8: Preprocessing ... % 17.41/3.14 Prover 13: Preprocessing ... % 17.41/3.17 Prover 11: Preprocessing ... % 17.41/3.18 Prover 7: Preprocessing ... % 17.41/3.23 Prover 10: Warning: ignoring some quantifiers % 17.41/3.27 Prover 10: Constructing countermodel ... % 19.08/3.34 Prover 13: Warning: ignoring some quantifiers % 19.08/3.37 Prover 8: Warning: ignoring some quantifiers % 19.08/3.37 Prover 13: Constructing countermodel ... % 19.08/3.39 Prover 7: Warning: ignoring some quantifiers % 19.70/3.41 Prover 8: Constructing countermodel ... % 19.70/3.44 Prover 7: Constructing countermodel ... % 20.34/3.50 Prover 4: Found proof (size 94) % 20.34/3.50 Prover 4: proved (2874ms) % 20.34/3.50 Prover 11: stopped % 20.34/3.50 Prover 7: stopped % 20.34/3.50 Prover 1: stopped % 20.34/3.50 Prover 10: stopped % 20.34/3.50 Prover 8: stopped % 20.34/3.51 Prover 13: stopped % 20.34/3.51 % 20.34/3.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.34/3.51 % 20.34/3.54 % SZS output start Proof for theBenchmark % 20.34/3.55 Assumptions after simplification: % 20.34/3.55 --------------------------------- % 20.34/3.55 % 20.34/3.55 (at_on_trajectory) % 20.84/3.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.91/3.60 (trajectory_of(v0) = v2) | ~ (incident_o(v1, v2) = v3) | ~ $i(v1) | ~ % 20.91/3.60 $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & at(v0, v1) = v4 & % 20.91/3.60 once(v4) = v5 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 20.91/3.60 (trajectory_of(v0) = v2) | ~ (incident_o(v1, v2) = 0) | ~ $i(v1) | ~ % 20.91/3.60 $i(v0) | ? [v3: $i] : (at(v0, v1) = v3 & once(v3) = 0 & $i(v3))) & ! [v0: % 20.91/3.60 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at(v0, v1) = v2) | ~ $i(v1) | ~ % 20.91/3.60 $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : (trajectory_of(v0) = v4 % 20.91/3.60 & once(v2) = v3 & incident_o(v1, v4) = v5 & $i(v4) & ( ~ (v3 = 0) | v5 = % 20.91/3.60 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at(v0, v1) = v2) | % 20.91/3.60 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 20.91/3.60 (trajectory_of(v0) = v3 & once(v2) = v5 & incident_o(v1, v3) = v4 & $i(v3) & % 20.91/3.60 ( ~ (v4 = 0) | v5 = 0))) % 20.91/3.60 % 20.91/3.60 (conjunction_at_the_same_time) % 20.91/3.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v0, v1) = v2) % 20.91/3.60 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 20.91/3.60 (once(v2) = v3 & once(v1) = v5 & once(v0) = v4 & ( ~ (v3 = 0) | (v5 = 0 & v4 % 20.91/3.60 = 0)))) % 20.91/3.60 % 20.91/3.60 (connect_defn) % 20.91/3.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.91/3.61 $i] : ( ~ (at(v1, v2) = v4) | ~ (at(v0, v2) = v3) | ~ % 20.91/3.61 (at_the_same_time(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.91/3.61 [v6: any] : ? [v7: any] : (connect(v0, v1, v2) = v7 & once(v5) = v6 & ( ~ % 20.91/3.61 (v6 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 20.91/3.61 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (at(v1, v2) = v4) | ~ (at(v0, v2) = % 20.91/3.61 v3) | ~ (at_the_same_time(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 20.91/3.61 $i(v0) | ? [v6: any] : ? [v7: any] : (connect(v0, v1, v2) = v6 & once(v5) % 20.91/3.61 = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 20.91/3.61 : ! [v3: int] : (v3 = 0 | ~ (connect(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 20.91/3.61 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] % 20.91/3.61 : ( ~ (v7 = 0) & at(v1, v2) = v5 & at(v0, v2) = v4 & at_the_same_time(v4, % 20.91/3.61 v5) = v6 & once(v6) = v7 & $i(v6) & $i(v5) & $i(v4))) & ! [v0: $i] : ! % 20.91/3.61 [v1: $i] : ! [v2: $i] : ( ~ (connect(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 20.91/3.61 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (at(v1, v2) = v4 & % 20.91/3.61 at(v0, v2) = v3 & at_the_same_time(v3, v4) = v5 & once(v5) = 0 & $i(v5) & % 20.91/3.61 $i(v4) & $i(v3))) % 20.91/3.61 % 20.91/3.61 (homogeneous_behaviour) % 21.00/3.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.00/3.62 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 21.00/3.62 ! [v11: $i] : ( ~ (at(v5, v3) = v10) | ~ (at(v5, v1) = v7) | ~ (at(v4, v2) % 21.00/3.62 = v9) | ~ (at(v4, v0) = v6) | ~ (at_the_same_time(v9, v10) = v11) | ~ % 21.00/3.62 (at_the_same_time(v6, v7) = v8) | ~ (once(v11) = 0) | ~ (once(v8) = 0) | % 21.00/3.62 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.00/3.62 [v12: $i] : ? [v13: any] : ? [v14: $i] : ? [v15: any] : % 21.00/3.62 (trajectory_of(v5) = v14 & trajectory_of(v4) = v12 & ordered_by(v14, v3, v1) % 21.00/3.62 = v15 & ordered_by(v12, v0, v2) = v13 & $i(v14) & $i(v12) & ( ~ (v15 = 0) % 21.00/3.62 | ~ (v13 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 21.00/3.62 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 21.00/3.62 (trajectory_of(v5) = v7) | ~ (trajectory_of(v4) = v6) | ~ (ordered_by(v7, % 21.00/3.62 v3, v1) = 0) | ~ (ordered_by(v6, v0, v2) = 0) | ~ $i(v5) | ~ $i(v4) | % 21.00/3.62 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : % 21.00/3.62 ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 21.00/3.62 ? [v15: any] : (at(v5, v3) = v13 & at(v5, v1) = v9 & at(v4, v2) = v12 & % 21.00/3.62 at(v4, v0) = v8 & at_the_same_time(v12, v13) = v14 & at_the_same_time(v8, % 21.00/3.62 v9) = v10 & once(v14) = v15 & once(v10) = v11 & $i(v14) & $i(v13) & % 21.00/3.62 $i(v12) & $i(v10) & $i(v9) & $i(v8) & ( ~ (v15 = 0) | ~ (v11 = 0)))) % 21.00/3.62 % 21.00/3.62 (symmetry_of_at_the_same_time) % 21.00/3.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) = v2) % 21.00/3.62 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 21.00/3.62 (at_the_same_time(v0, v1) = v4 & once(v4) = v5 & once(v2) = v3 & $i(v4) & ( % 21.00/3.62 ~ (v3 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.00/3.62 (at_the_same_time(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 21.00/3.62 [v4: any] : ? [v5: any] : (at_the_same_time(v0, v1) = v3 & once(v3) = v4 & % 21.00/3.62 once(v2) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: % 21.00/3.62 $i] : ! [v2: $i] : ( ~ (at_the_same_time(v0, v1) = v2) | ~ $i(v1) | ~ % 21.00/3.62 $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : (at_the_same_time(v1, % 21.00/3.62 v0) = v4 & once(v4) = v5 & once(v2) = v3 & $i(v4) & ( ~ (v3 = 0) | v5 = % 21.00/3.62 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.00/3.62 (at_the_same_time(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 21.00/3.62 [v4: any] : ? [v5: any] : (at_the_same_time(v1, v0) = v3 & once(v3) = v4 & % 21.00/3.62 once(v2) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) % 21.00/3.62 % 21.00/3.62 (t13) % 21.00/3.63 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 21.00/3.63 $i] : ? [v6: any] : (trajectory_of(v2) = v5 & trajectory_of(v1) = v3 & % 21.00/3.63 connect(v1, v2, v0) = 0 & incident_o(v0, v5) = v6 & incident_o(v0, v3) = v4 % 21.00/3.63 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v6 = 0) | ~ (v4 = 0))) % 21.00/3.63 % 21.00/3.63 (function-axioms) % 21.00/3.64 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.00/3.64 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_o(v5, v4, v3, % 21.00/3.64 v2) = v1) | ~ (between_o(v5, v4, v3, v2) = v0)) & ! [v0: % 21.00/3.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.00/3.64 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_c(v5, v4, v3, v2) = v1) | % 21.00/3.64 ~ (between_c(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.00/3.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 21.00/3.64 (connect(v4, v3, v2) = v1) | ~ (connect(v4, v3, v2) = v0)) & ! [v0: % 21.00/3.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.00/3.64 : ! [v4: $i] : (v1 = v0 | ~ (ordered_by(v4, v3, v2) = v1) | ~ % 21.00/3.64 (ordered_by(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.00/3.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 21.00/3.64 (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 21.00/3.64 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (at(v3, v2) = v1) | ~ % 21.00/3.64 (at(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 21.00/3.64 (v1 = v0 | ~ (at_the_same_time(v3, v2) = v1) | ~ (at_the_same_time(v3, v2) = % 21.00/3.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.00/3.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (finish_point(v3, v2) = v1) | ~ % 21.00/3.64 (finish_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.00/3.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.00/3.64 (start_point(v3, v2) = v1) | ~ (start_point(v3, v2) = v0)) & ! [v0: % 21.00/3.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.00/3.64 : (v1 = v0 | ~ (incident_o(v3, v2) = v1) | ~ (incident_o(v3, v2) = v0)) & ! % 21.00/3.64 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.00/3.64 $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = % 21.00/3.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.00/3.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ % 21.00/3.64 (end_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.00/3.64 [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0: % 21.00/3.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.00/3.64 : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: % 21.00/3.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.00/3.64 : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! % 21.00/3.64 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trajectory_of(v2) = v1) % 21.00/3.64 | ~ (trajectory_of(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.00/3.64 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (once(v2) = v1) | ~ % 21.00/3.64 (once(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.00/3.64 (underlying_curve(v2) = v1) | ~ (underlying_curve(v2) = v0)) & ! [v0: % 21.00/3.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.00/3.64 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 21.00/3.64 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~ % 21.00/3.64 (closed(v2) = v0)) % 21.00/3.64 % 21.00/3.64 Further assumptions not needed in the proof: % 21.00/3.64 -------------------------------------------- % 21.00/3.64 assciativity_of_at_the_same_time, between_c_defn, between_o_defn, c1, c2, c3, % 21.00/3.64 c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn, finish_point_defn, % 21.00/3.64 idempotence_of_at_the_same_time, inner_point_defn, localization, meet_defn, o1, % 21.00/3.64 o2, o3, o4, o5, o6, open_defn, part_of_defn, start_point_defn, sum_defn, % 21.00/3.64 trajectories_are_oriented_curves, underlying_curve_defn % 21.00/3.64 % 21.00/3.64 Those formulas are unsatisfiable: % 21.00/3.64 --------------------------------- % 21.00/3.64 % 21.00/3.64 Begin of proof % 21.00/3.64 | % 21.00/3.64 | ALPHA: (connect_defn) implies: % 21.00/3.64 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (connect(v0, v1, v2) = 0) % 21.00/3.64 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 21.00/3.64 | [v5: $i] : (at(v1, v2) = v4 & at(v0, v2) = v3 & at_the_same_time(v3, % 21.00/3.64 | v4) = v5 & once(v5) = 0 & $i(v5) & $i(v4) & $i(v3))) % 21.00/3.65 | % 21.00/3.65 | ALPHA: (symmetry_of_at_the_same_time) implies: % 21.00/3.65 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) % 21.00/3.65 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? % 21.00/3.65 | [v5: any] : (at_the_same_time(v0, v1) = v3 & once(v3) = v4 & once(v2) % 21.00/3.65 | = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) % 21.00/3.65 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) % 21.00/3.65 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? % 21.00/3.65 | [v5: any] : (at_the_same_time(v0, v1) = v4 & once(v4) = v5 & once(v2) % 21.00/3.65 | = v3 & $i(v4) & ( ~ (v3 = 0) | v5 = 0))) % 21.00/3.65 | % 21.00/3.65 | ALPHA: (at_on_trajectory) implies: % 21.00/3.65 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at(v0, v1) = v2) | ~ % 21.00/3.65 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 21.00/3.65 | (trajectory_of(v0) = v3 & once(v2) = v5 & incident_o(v1, v3) = v4 & % 21.00/3.65 | $i(v3) & ( ~ (v4 = 0) | v5 = 0))) % 21.00/3.65 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at(v0, v1) = v2) | ~ % 21.00/3.65 | $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 21.00/3.65 | (trajectory_of(v0) = v4 & once(v2) = v3 & incident_o(v1, v4) = v5 & % 21.00/3.65 | $i(v4) & ( ~ (v3 = 0) | v5 = 0))) % 21.00/3.65 | % 21.00/3.65 | ALPHA: (homogeneous_behaviour) implies: % 21.00/3.66 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.00/3.66 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 21.00/3.66 | [v10: $i] : ! [v11: $i] : ( ~ (at(v5, v3) = v10) | ~ (at(v5, v1) = % 21.00/3.66 | v7) | ~ (at(v4, v2) = v9) | ~ (at(v4, v0) = v6) | ~ % 21.00/3.66 | (at_the_same_time(v9, v10) = v11) | ~ (at_the_same_time(v6, v7) = % 21.00/3.66 | v8) | ~ (once(v11) = 0) | ~ (once(v8) = 0) | ~ $i(v5) | ~ % 21.00/3.66 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: $i] % 21.00/3.66 | : ? [v13: any] : ? [v14: $i] : ? [v15: any] : (trajectory_of(v5) = % 21.00/3.66 | v14 & trajectory_of(v4) = v12 & ordered_by(v14, v3, v1) = v15 & % 21.00/3.66 | ordered_by(v12, v0, v2) = v13 & $i(v14) & $i(v12) & ( ~ (v15 = 0) | % 21.00/3.66 | ~ (v13 = 0)))) % 21.00/3.66 | % 21.00/3.66 | ALPHA: (function-axioms) implies: % 21.00/3.66 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.00/3.66 | (v1 = v0 | ~ (once(v2) = v1) | ~ (once(v2) = v0)) % 21.00/3.66 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.00/3.66 | (trajectory_of(v2) = v1) | ~ (trajectory_of(v2) = v0)) % 21.00/3.66 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.00/3.66 | ! [v3: $i] : (v1 = v0 | ~ (incident_o(v3, v2) = v1) | ~ % 21.00/3.66 | (incident_o(v3, v2) = v0)) % 21.00/3.66 | % 21.00/3.66 | DELTA: instantiating (t13) with fresh symbols all_41_0, all_41_1, all_41_2, % 21.00/3.66 | all_41_3, all_41_4, all_41_5, all_41_6 gives: % 21.00/3.66 | (10) trajectory_of(all_41_4) = all_41_1 & trajectory_of(all_41_5) = % 21.00/3.66 | all_41_3 & connect(all_41_5, all_41_4, all_41_6) = 0 & % 21.00/3.66 | incident_o(all_41_6, all_41_1) = all_41_0 & incident_o(all_41_6, % 21.00/3.66 | all_41_3) = all_41_2 & $i(all_41_1) & $i(all_41_3) & $i(all_41_4) & % 21.00/3.66 | $i(all_41_5) & $i(all_41_6) & ( ~ (all_41_0 = 0) | ~ (all_41_2 = 0)) % 21.00/3.66 | % 21.00/3.66 | ALPHA: (10) implies: % 21.00/3.66 | (11) $i(all_41_6) % 21.00/3.66 | (12) $i(all_41_5) % 21.00/3.66 | (13) $i(all_41_4) % 21.00/3.67 | (14) incident_o(all_41_6, all_41_3) = all_41_2 % 21.00/3.67 | (15) incident_o(all_41_6, all_41_1) = all_41_0 % 21.00/3.67 | (16) connect(all_41_5, all_41_4, all_41_6) = 0 % 21.00/3.67 | (17) trajectory_of(all_41_5) = all_41_3 % 21.00/3.67 | (18) trajectory_of(all_41_4) = all_41_1 % 21.00/3.67 | (19) ~ (all_41_0 = 0) | ~ (all_41_2 = 0) % 21.00/3.67 | % 21.00/3.67 | GROUND_INST: instantiating (1) with all_41_5, all_41_4, all_41_6, simplifying % 21.00/3.67 | with (11), (12), (13), (16) gives: % 21.00/3.67 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (at(all_41_4, all_41_6) = v1 % 21.00/3.67 | & at(all_41_5, all_41_6) = v0 & at_the_same_time(v0, v1) = v2 & % 21.00/3.67 | once(v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 21.00/3.67 | % 21.00/3.67 | DELTA: instantiating (20) with fresh symbols all_51_0, all_51_1, all_51_2 % 21.00/3.67 | gives: % 21.00/3.67 | (21) at(all_41_4, all_41_6) = all_51_1 & at(all_41_5, all_41_6) = all_51_2 % 21.00/3.67 | & at_the_same_time(all_51_2, all_51_1) = all_51_0 & once(all_51_0) = 0 % 21.00/3.67 | & $i(all_51_0) & $i(all_51_1) & $i(all_51_2) % 21.00/3.67 | % 21.00/3.67 | ALPHA: (21) implies: % 21.00/3.67 | (22) $i(all_51_2) % 21.00/3.67 | (23) $i(all_51_1) % 21.00/3.67 | (24) once(all_51_0) = 0 % 21.00/3.67 | (25) at_the_same_time(all_51_2, all_51_1) = all_51_0 % 21.00/3.67 | (26) at(all_41_5, all_41_6) = all_51_2 % 21.00/3.67 | (27) at(all_41_4, all_41_6) = all_51_1 % 21.00/3.67 | % 21.00/3.67 | GROUND_INST: instantiating (3) with all_51_1, all_51_2, all_51_0, simplifying % 21.00/3.67 | with (22), (23), (25) gives: % 21.00/3.68 | (28) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 21.00/3.68 | (at_the_same_time(all_51_1, all_51_2) = v1 & once(v1) = v2 & % 21.00/3.68 | once(all_51_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v2 = 0)) % 21.00/3.68 | % 21.00/3.68 | GROUND_INST: instantiating (2) with all_51_1, all_51_2, all_51_0, simplifying % 21.00/3.68 | with (22), (23), (25) gives: % 21.00/3.68 | (29) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 21.00/3.68 | (at_the_same_time(all_51_1, all_51_2) = v0 & once(v0) = v1 & % 21.00/3.68 | once(all_51_0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 21.00/3.68 | % 21.00/3.68 | GROUND_INST: instantiating (conjunction_at_the_same_time) with all_51_2, % 21.00/3.68 | all_51_1, all_51_0, simplifying with (22), (23), (25) gives: % 21.00/3.68 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : (once(all_51_0) = v0 & % 21.00/3.68 | once(all_51_1) = v2 & once(all_51_2) = v1 & ( ~ (v0 = 0) | (v2 = 0 & % 21.00/3.68 | v1 = 0))) % 21.00/3.68 | % 21.00/3.68 | GROUND_INST: instantiating (5) with all_41_5, all_41_6, all_51_2, simplifying % 21.00/3.68 | with (11), (12), (26) gives: % 21.00/3.68 | (31) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (trajectory_of(all_41_5) = % 21.00/3.68 | v1 & once(all_51_2) = v0 & incident_o(all_41_6, v1) = v2 & $i(v1) & % 21.00/3.68 | ( ~ (v0 = 0) | v2 = 0)) % 21.00/3.68 | % 21.00/3.68 | GROUND_INST: instantiating (4) with all_41_5, all_41_6, all_51_2, simplifying % 21.00/3.68 | with (11), (12), (26) gives: % 21.00/3.68 | (32) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (trajectory_of(all_41_5) = % 21.00/3.68 | v0 & once(all_51_2) = v2 & incident_o(all_41_6, v0) = v1 & $i(v0) & % 21.00/3.68 | ( ~ (v1 = 0) | v2 = 0)) % 21.00/3.68 | % 21.00/3.68 | GROUND_INST: instantiating (6) with all_41_6, all_41_6, all_41_6, all_41_6, % 21.00/3.68 | all_41_5, all_41_4, all_51_2, all_51_1, all_51_0, all_51_2, % 21.00/3.69 | all_51_1, all_51_0, simplifying with (11), (12), (13), (24), % 21.00/3.69 | (25), (26), (27) gives: % 21.00/3.69 | (33) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 21.00/3.69 | (trajectory_of(all_41_4) = v2 & trajectory_of(all_41_5) = v0 & % 21.00/3.69 | ordered_by(v2, all_41_6, all_41_6) = v3 & ordered_by(v0, all_41_6, % 21.00/3.69 | all_41_6) = v1 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0))) % 21.00/3.69 | % 21.00/3.69 | GROUND_INST: instantiating (5) with all_41_4, all_41_6, all_51_1, simplifying % 21.00/3.69 | with (11), (13), (27) gives: % 21.00/3.69 | (34) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (trajectory_of(all_41_4) = % 21.00/3.69 | v1 & once(all_51_1) = v0 & incident_o(all_41_6, v1) = v2 & $i(v1) & % 21.00/3.69 | ( ~ (v0 = 0) | v2 = 0)) % 21.00/3.69 | % 21.00/3.69 | GROUND_INST: instantiating (4) with all_41_4, all_41_6, all_51_1, simplifying % 21.00/3.69 | with (11), (13), (27) gives: % 21.00/3.69 | (35) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (trajectory_of(all_41_4) = % 21.00/3.69 | v0 & once(all_51_1) = v2 & incident_o(all_41_6, v0) = v1 & $i(v0) & % 21.00/3.69 | ( ~ (v1 = 0) | v2 = 0)) % 21.00/3.69 | % 21.00/3.69 | DELTA: instantiating (32) with fresh symbols all_60_0, all_60_1, all_60_2 % 21.00/3.69 | gives: % 21.00/3.69 | (36) trajectory_of(all_41_5) = all_60_2 & once(all_51_2) = all_60_0 & % 21.00/3.69 | incident_o(all_41_6, all_60_2) = all_60_1 & $i(all_60_2) & ( ~ % 21.00/3.69 | (all_60_1 = 0) | all_60_0 = 0) % 21.00/3.69 | % 21.00/3.69 | ALPHA: (36) implies: % 21.00/3.69 | (37) incident_o(all_41_6, all_60_2) = all_60_1 % 21.00/3.69 | (38) once(all_51_2) = all_60_0 % 21.00/3.69 | (39) trajectory_of(all_41_5) = all_60_2 % 21.00/3.69 | % 21.00/3.69 | DELTA: instantiating (31) with fresh symbols all_62_0, all_62_1, all_62_2 % 21.00/3.69 | gives: % 21.00/3.69 | (40) trajectory_of(all_41_5) = all_62_1 & once(all_51_2) = all_62_2 & % 21.00/3.69 | incident_o(all_41_6, all_62_1) = all_62_0 & $i(all_62_1) & ( ~ % 21.00/3.69 | (all_62_2 = 0) | all_62_0 = 0) % 21.00/3.69 | % 21.00/3.69 | ALPHA: (40) implies: % 21.00/3.69 | (41) incident_o(all_41_6, all_62_1) = all_62_0 % 21.00/3.69 | (42) once(all_51_2) = all_62_2 % 21.00/3.69 | (43) trajectory_of(all_41_5) = all_62_1 % 21.00/3.69 | (44) ~ (all_62_2 = 0) | all_62_0 = 0 % 21.00/3.69 | % 21.00/3.69 | DELTA: instantiating (30) with fresh symbols all_64_0, all_64_1, all_64_2 % 21.00/3.69 | gives: % 21.00/3.70 | (45) once(all_51_0) = all_64_2 & once(all_51_1) = all_64_0 & once(all_51_2) % 21.00/3.70 | = all_64_1 & ( ~ (all_64_2 = 0) | (all_64_0 = 0 & all_64_1 = 0)) % 21.00/3.70 | % 21.00/3.70 | ALPHA: (45) implies: % 21.00/3.70 | (46) once(all_51_2) = all_64_1 % 21.00/3.70 | (47) once(all_51_1) = all_64_0 % 21.00/3.70 | (48) once(all_51_0) = all_64_2 % 21.00/3.70 | (49) ~ (all_64_2 = 0) | (all_64_0 = 0 & all_64_1 = 0) % 21.00/3.70 | % 21.00/3.70 | DELTA: instantiating (35) with fresh symbols all_66_0, all_66_1, all_66_2 % 21.00/3.70 | gives: % 21.38/3.70 | (50) trajectory_of(all_41_4) = all_66_2 & once(all_51_1) = all_66_0 & % 21.38/3.70 | incident_o(all_41_6, all_66_2) = all_66_1 & $i(all_66_2) & ( ~ % 21.38/3.70 | (all_66_1 = 0) | all_66_0 = 0) % 21.38/3.70 | % 21.38/3.70 | ALPHA: (50) implies: % 21.38/3.70 | (51) incident_o(all_41_6, all_66_2) = all_66_1 % 21.38/3.70 | (52) trajectory_of(all_41_4) = all_66_2 % 21.38/3.70 | % 21.38/3.70 | DELTA: instantiating (34) with fresh symbols all_68_0, all_68_1, all_68_2 % 21.38/3.70 | gives: % 21.38/3.70 | (53) trajectory_of(all_41_4) = all_68_1 & once(all_51_1) = all_68_2 & % 21.38/3.70 | incident_o(all_41_6, all_68_1) = all_68_0 & $i(all_68_1) & ( ~ % 21.38/3.70 | (all_68_2 = 0) | all_68_0 = 0) % 21.38/3.70 | % 21.38/3.70 | ALPHA: (53) implies: % 21.38/3.70 | (54) incident_o(all_41_6, all_68_1) = all_68_0 % 21.38/3.70 | (55) once(all_51_1) = all_68_2 % 21.38/3.70 | (56) trajectory_of(all_41_4) = all_68_1 % 21.38/3.70 | (57) ~ (all_68_2 = 0) | all_68_0 = 0 % 21.38/3.70 | % 21.38/3.70 | DELTA: instantiating (29) with fresh symbols all_70_0, all_70_1, all_70_2 % 21.38/3.70 | gives: % 21.38/3.70 | (58) at_the_same_time(all_51_1, all_51_2) = all_70_2 & once(all_70_2) = % 21.38/3.70 | all_70_1 & once(all_51_0) = all_70_0 & $i(all_70_2) & ( ~ (all_70_1 = % 21.38/3.70 | 0) | all_70_0 = 0) % 21.38/3.70 | % 21.38/3.70 | ALPHA: (58) implies: % 21.38/3.70 | (59) once(all_51_0) = all_70_0 % 21.38/3.70 | % 21.38/3.70 | DELTA: instantiating (28) with fresh symbols all_72_0, all_72_1, all_72_2 % 21.38/3.70 | gives: % 21.38/3.70 | (60) at_the_same_time(all_51_1, all_51_2) = all_72_1 & once(all_72_1) = % 21.38/3.70 | all_72_0 & once(all_51_0) = all_72_2 & $i(all_72_1) & ( ~ (all_72_2 = % 21.38/3.70 | 0) | all_72_0 = 0) % 21.38/3.70 | % 21.38/3.70 | ALPHA: (60) implies: % 21.38/3.70 | (61) once(all_51_0) = all_72_2 % 21.38/3.70 | % 21.38/3.70 | DELTA: instantiating (33) with fresh symbols all_74_0, all_74_1, all_74_2, % 21.38/3.70 | all_74_3 gives: % 21.38/3.71 | (62) trajectory_of(all_41_4) = all_74_1 & trajectory_of(all_41_5) = % 21.38/3.71 | all_74_3 & ordered_by(all_74_1, all_41_6, all_41_6) = all_74_0 & % 21.38/3.71 | ordered_by(all_74_3, all_41_6, all_41_6) = all_74_2 & $i(all_74_1) & % 21.38/3.71 | $i(all_74_3) & ( ~ (all_74_0 = 0) | ~ (all_74_2 = 0)) % 21.38/3.71 | % 21.38/3.71 | ALPHA: (62) implies: % 21.38/3.71 | (63) trajectory_of(all_41_5) = all_74_3 % 21.38/3.71 | (64) trajectory_of(all_41_4) = all_74_1 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (7) with all_62_2, all_64_1, all_51_2, simplifying % 21.38/3.71 | with (42), (46) gives: % 21.38/3.71 | (65) all_64_1 = all_62_2 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (7) with all_60_0, all_64_1, all_51_2, simplifying % 21.38/3.71 | with (38), (46) gives: % 21.38/3.71 | (66) all_64_1 = all_60_0 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (7) with all_64_0, all_68_2, all_51_1, simplifying % 21.38/3.71 | with (47), (55) gives: % 21.38/3.71 | (67) all_68_2 = all_64_0 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (7) with 0, all_70_0, all_51_0, simplifying with % 21.38/3.71 | (24), (59) gives: % 21.38/3.71 | (68) all_70_0 = 0 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (7) with all_70_0, all_72_2, all_51_0, simplifying % 21.38/3.71 | with (59), (61) gives: % 21.38/3.71 | (69) all_72_2 = all_70_0 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (7) with all_64_2, all_72_2, all_51_0, simplifying % 21.38/3.71 | with (48), (61) gives: % 21.38/3.71 | (70) all_72_2 = all_64_2 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (8) with all_60_2, all_62_1, all_41_5, simplifying % 21.38/3.71 | with (39), (43) gives: % 21.38/3.71 | (71) all_62_1 = all_60_2 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (8) with all_41_3, all_74_3, all_41_5, simplifying % 21.38/3.71 | with (17), (63) gives: % 21.38/3.71 | (72) all_74_3 = all_41_3 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (8) with all_62_1, all_74_3, all_41_5, simplifying % 21.38/3.71 | with (43), (63) gives: % 21.38/3.71 | (73) all_74_3 = all_62_1 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (8) with all_41_1, all_68_1, all_41_4, simplifying % 21.38/3.71 | with (18), (56) gives: % 21.38/3.71 | (74) all_68_1 = all_41_1 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (8) with all_68_1, all_74_1, all_41_4, simplifying % 21.38/3.71 | with (56), (64) gives: % 21.38/3.71 | (75) all_74_1 = all_68_1 % 21.38/3.71 | % 21.38/3.71 | GROUND_INST: instantiating (8) with all_66_2, all_74_1, all_41_4, simplifying % 21.38/3.71 | with (52), (64) gives: % 21.38/3.71 | (76) all_74_1 = all_66_2 % 21.38/3.71 | % 21.38/3.71 | COMBINE_EQS: (75), (76) imply: % 21.38/3.71 | (77) all_68_1 = all_66_2 % 21.38/3.71 | % 21.38/3.71 | SIMP: (77) implies: % 21.38/3.71 | (78) all_68_1 = all_66_2 % 21.38/3.71 | % 21.38/3.71 | COMBINE_EQS: (72), (73) imply: % 21.38/3.71 | (79) all_62_1 = all_41_3 % 21.38/3.71 | % 21.38/3.71 | SIMP: (79) implies: % 21.38/3.71 | (80) all_62_1 = all_41_3 % 21.38/3.71 | % 21.38/3.71 | COMBINE_EQS: (69), (70) imply: % 21.38/3.72 | (81) all_70_0 = all_64_2 % 21.38/3.72 | % 21.38/3.72 | SIMP: (81) implies: % 21.38/3.72 | (82) all_70_0 = all_64_2 % 21.38/3.72 | % 21.38/3.72 | COMBINE_EQS: (68), (82) imply: % 21.38/3.72 | (83) all_64_2 = 0 % 21.38/3.72 | % 21.38/3.72 | SIMP: (83) implies: % 21.38/3.72 | (84) all_64_2 = 0 % 21.38/3.72 | % 21.38/3.72 | COMBINE_EQS: (74), (78) imply: % 21.38/3.72 | (85) all_66_2 = all_41_1 % 21.38/3.72 | % 21.38/3.72 | COMBINE_EQS: (65), (66) imply: % 21.38/3.72 | (86) all_62_2 = all_60_0 % 21.38/3.72 | % 21.38/3.72 | COMBINE_EQS: (71), (80) imply: % 21.38/3.72 | (87) all_60_2 = all_41_3 % 21.38/3.72 | % 21.38/3.72 | SIMP: (87) implies: % 21.38/3.72 | (88) all_60_2 = all_41_3 % 21.38/3.72 | % 21.38/3.72 | REDUCE: (54), (74) imply: % 21.38/3.72 | (89) incident_o(all_41_6, all_41_1) = all_68_0 % 21.38/3.72 | % 21.38/3.72 | REDUCE: (51), (85) imply: % 21.38/3.72 | (90) incident_o(all_41_6, all_41_1) = all_66_1 % 21.38/3.72 | % 21.38/3.72 | REDUCE: (41), (80) imply: % 21.38/3.72 | (91) incident_o(all_41_6, all_41_3) = all_62_0 % 21.38/3.72 | % 21.38/3.72 | REDUCE: (37), (88) imply: % 21.38/3.72 | (92) incident_o(all_41_6, all_41_3) = all_60_1 % 21.38/3.72 | % 21.38/3.72 | BETA: splitting (49) gives: % 21.38/3.72 | % 21.38/3.72 | Case 1: % 21.38/3.72 | | % 21.38/3.72 | | (93) ~ (all_64_2 = 0) % 21.38/3.72 | | % 21.38/3.72 | | REDUCE: (84), (93) imply: % 21.38/3.72 | | (94) $false % 21.38/3.72 | | % 21.38/3.72 | | CLOSE: (94) is inconsistent. % 21.38/3.72 | | % 21.38/3.72 | Case 2: % 21.38/3.72 | | % 21.38/3.72 | | (95) all_64_0 = 0 & all_64_1 = 0 % 21.38/3.72 | | % 21.38/3.72 | | ALPHA: (95) implies: % 21.38/3.72 | | (96) all_64_1 = 0 % 21.38/3.72 | | (97) all_64_0 = 0 % 21.38/3.72 | | % 21.38/3.72 | | COMBINE_EQS: (66), (96) imply: % 21.38/3.72 | | (98) all_60_0 = 0 % 21.38/3.72 | | % 21.38/3.72 | | COMBINE_EQS: (86), (98) imply: % 21.38/3.72 | | (99) all_62_2 = 0 % 21.38/3.73 | | % 21.38/3.73 | | COMBINE_EQS: (67), (97) imply: % 21.38/3.73 | | (100) all_68_2 = 0 % 21.38/3.73 | | % 21.38/3.73 | | BETA: splitting (57) gives: % 21.38/3.73 | | % 21.38/3.73 | | Case 1: % 21.38/3.73 | | | % 21.38/3.73 | | | (101) ~ (all_68_2 = 0) % 21.38/3.73 | | | % 21.38/3.73 | | | REDUCE: (100), (101) imply: % 21.38/3.73 | | | (102) $false % 21.38/3.73 | | | % 21.38/3.73 | | | CLOSE: (102) is inconsistent. % 21.38/3.73 | | | % 21.38/3.73 | | Case 2: % 21.38/3.73 | | | % 21.38/3.73 | | | (103) all_68_0 = 0 % 21.38/3.73 | | | % 21.38/3.73 | | | REDUCE: (89), (103) imply: % 21.38/3.73 | | | (104) incident_o(all_41_6, all_41_1) = 0 % 21.38/3.73 | | | % 21.38/3.73 | | | BETA: splitting (44) gives: % 21.38/3.73 | | | % 21.38/3.73 | | | Case 1: % 21.38/3.73 | | | | % 21.38/3.73 | | | | (105) ~ (all_62_2 = 0) % 21.38/3.73 | | | | % 21.38/3.73 | | | | REDUCE: (99), (105) imply: % 21.38/3.73 | | | | (106) $false % 21.38/3.73 | | | | % 21.38/3.73 | | | | CLOSE: (106) is inconsistent. % 21.38/3.73 | | | | % 21.38/3.73 | | | Case 2: % 21.38/3.73 | | | | % 21.38/3.73 | | | | (107) all_62_0 = 0 % 21.38/3.73 | | | | % 21.38/3.73 | | | | REDUCE: (91), (107) imply: % 21.38/3.73 | | | | (108) incident_o(all_41_6, all_41_3) = 0 % 21.38/3.73 | | | | % 21.38/3.73 | | | | BETA: splitting (19) gives: % 21.38/3.73 | | | | % 21.38/3.73 | | | | Case 1: % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | (109) ~ (all_41_0 = 0) % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | GROUND_INST: instantiating (9) with all_41_0, all_66_1, all_41_1, % 21.38/3.73 | | | | | all_41_6, simplifying with (15), (90) gives: % 21.38/3.73 | | | | | (110) all_66_1 = all_41_0 % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | GROUND_INST: instantiating (9) with 0, all_66_1, all_41_1, all_41_6, % 21.38/3.73 | | | | | simplifying with (90), (104) gives: % 21.38/3.73 | | | | | (111) all_66_1 = 0 % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | COMBINE_EQS: (110), (111) imply: % 21.38/3.73 | | | | | (112) all_41_0 = 0 % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | REDUCE: (109), (112) imply: % 21.38/3.73 | | | | | (113) $false % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | CLOSE: (113) is inconsistent. % 21.38/3.73 | | | | | % 21.38/3.73 | | | | Case 2: % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | (114) ~ (all_41_2 = 0) % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | GROUND_INST: instantiating (9) with all_41_2, all_60_1, all_41_3, % 21.38/3.73 | | | | | all_41_6, simplifying with (14), (92) gives: % 21.38/3.73 | | | | | (115) all_60_1 = all_41_2 % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | GROUND_INST: instantiating (9) with 0, all_60_1, all_41_3, all_41_6, % 21.38/3.73 | | | | | simplifying with (92), (108) gives: % 21.38/3.73 | | | | | (116) all_60_1 = 0 % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | COMBINE_EQS: (115), (116) imply: % 21.38/3.73 | | | | | (117) all_41_2 = 0 % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | SIMP: (117) implies: % 21.38/3.73 | | | | | (118) all_41_2 = 0 % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | REDUCE: (114), (118) imply: % 21.38/3.73 | | | | | (119) $false % 21.38/3.73 | | | | | % 21.38/3.73 | | | | | CLOSE: (119) is inconsistent. % 21.38/3.73 | | | | | % 21.38/3.73 | | | | End of split % 21.38/3.73 | | | | % 21.38/3.73 | | | End of split % 21.38/3.73 | | | % 21.38/3.73 | | End of split % 21.38/3.73 | | % 21.38/3.73 | End of split % 21.38/3.73 | % 21.38/3.73 End of proof % 21.38/3.73 % SZS output end Proof for theBenchmark % 21.38/3.73 % 21.38/3.73 3137ms %------------------------------------------------------------------------------