%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO148+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 : n012.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 23:21:42 EDT 2023 % Result : Theorem 14.14s 2.60s % Output : Proof 16.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO148+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.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 : Tue Aug 29 23:14:53 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 ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.44/1.15 Prover 4: Preprocessing ... % 3.44/1.15 Prover 1: Preprocessing ... % 3.44/1.19 Prover 3: Preprocessing ... % 3.44/1.19 Prover 5: Preprocessing ... % 3.44/1.19 Prover 0: Preprocessing ... % 3.44/1.19 Prover 6: Preprocessing ... % 3.44/1.19 Prover 2: Preprocessing ... % 8.27/1.83 Prover 5: Proving ... % 8.27/1.84 Prover 2: Proving ... % 8.81/1.88 Prover 1: Warning: ignoring some quantifiers % 9.13/1.91 Prover 6: Proving ... % 9.13/1.91 Prover 3: Warning: ignoring some quantifiers % 9.13/1.93 Prover 3: Constructing countermodel ... % 9.13/1.95 Prover 1: Constructing countermodel ... % 11.15/2.23 Prover 4: Warning: ignoring some quantifiers % 12.19/2.32 Prover 4: Constructing countermodel ... % 12.99/2.47 Prover 0: Proving ... % 14.14/2.60 Prover 0: proved (1974ms) % 14.14/2.60 % 14.14/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.14/2.60 % 14.14/2.60 Prover 3: stopped % 14.14/2.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.14/2.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.14/2.61 Prover 6: stopped % 14.14/2.61 Prover 2: stopped % 14.14/2.61 Prover 5: stopped % 14.14/2.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.14/2.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.14/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.14/2.71 Prover 10: Preprocessing ... % 14.14/2.71 Prover 7: Preprocessing ... % 14.53/2.72 Prover 13: Preprocessing ... % 14.53/2.73 Prover 8: Preprocessing ... % 14.53/2.73 Prover 11: Preprocessing ... % 15.31/2.76 Prover 4: Found proof (size 89) % 15.31/2.76 Prover 4: proved (2131ms) % 15.31/2.76 Prover 10: stopped % 15.31/2.76 Prover 1: stopped % 15.31/2.77 Prover 7: stopped % 15.31/2.79 Prover 13: stopped % 15.87/2.83 Prover 11: stopped % 15.87/2.88 Prover 8: Warning: ignoring some quantifiers % 16.17/2.89 Prover 8: Constructing countermodel ... % 16.17/2.90 Prover 8: stopped % 16.17/2.90 % 16.17/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.17/2.90 % 16.17/2.93 % SZS output start Proof for theBenchmark % 16.17/2.93 Assumptions after simplification: % 16.17/2.93 --------------------------------- % 16.17/2.93 % 16.17/2.93 (conjunction_at_the_same_time) % 16.17/2.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v0, v1) = v2) % 16.17/2.96 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 16.17/2.96 (once(v2) = v3 & once(v1) = v5 & once(v0) = v4 & ( ~ (v3 = 0) | (v5 = 0 & v4 % 16.17/2.96 = 0)))) % 16.17/2.96 % 16.17/2.96 (connect_defn) % 16.54/2.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.54/2.96 $i] : ( ~ (at(v1, v2) = v4) | ~ (at(v0, v2) = v3) | ~ % 16.54/2.96 (at_the_same_time(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.54/2.96 [v6: any] : ? [v7: any] : (connect(v0, v1, v2) = v7 & once(v5) = v6 & ( ~ % 16.54/2.96 (v6 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.54/2.96 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (at(v1, v2) = v4) | ~ (at(v0, v2) = % 16.54/2.96 v3) | ~ (at_the_same_time(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 16.54/2.96 $i(v0) | ? [v6: any] : ? [v7: any] : (connect(v0, v1, v2) = v6 & once(v5) % 16.54/2.96 = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 16.54/2.96 : ! [v3: int] : (v3 = 0 | ~ (connect(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 16.54/2.96 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] % 16.54/2.96 : ( ~ (v7 = 0) & at(v1, v2) = v5 & at(v0, v2) = v4 & at_the_same_time(v4, % 16.54/2.96 v5) = v6 & once(v6) = v7 & $i(v6) & $i(v5) & $i(v4))) & ! [v0: $i] : ! % 16.54/2.96 [v1: $i] : ! [v2: $i] : ( ~ (connect(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 16.54/2.96 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (at(v1, v2) = v4 & % 16.54/2.96 at(v0, v2) = v3 & at_the_same_time(v3, v4) = v5 & once(v5) = 0 & $i(v5) & % 16.54/2.96 $i(v4) & $i(v3))) % 16.54/2.96 % 16.54/2.96 (homogeneous_behaviour) % 16.54/2.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.54/2.97 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 16.54/2.97 ! [v11: $i] : ( ~ (at(v5, v3) = v10) | ~ (at(v5, v1) = v7) | ~ (at(v4, v2) % 16.54/2.97 = v9) | ~ (at(v4, v0) = v6) | ~ (at_the_same_time(v9, v10) = v11) | ~ % 16.54/2.97 (at_the_same_time(v6, v7) = v8) | ~ (once(v11) = 0) | ~ (once(v8) = 0) | % 16.54/2.97 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.54/2.97 [v12: $i] : ? [v13: any] : ? [v14: $i] : ? [v15: any] : % 16.54/2.97 (trajectory_of(v5) = v14 & trajectory_of(v4) = v12 & ordered_by(v14, v3, v1) % 16.54/2.97 = v15 & ordered_by(v12, v0, v2) = v13 & $i(v14) & $i(v12) & ( ~ (v15 = 0) % 16.54/2.97 | ~ (v13 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.54/2.97 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 16.54/2.97 (trajectory_of(v5) = v7) | ~ (trajectory_of(v4) = v6) | ~ (ordered_by(v7, % 16.54/2.97 v3, v1) = 0) | ~ (ordered_by(v6, v0, v2) = 0) | ~ $i(v5) | ~ $i(v4) | % 16.54/2.97 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : % 16.54/2.97 ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 16.54/2.97 ? [v15: any] : (at(v5, v3) = v13 & at(v5, v1) = v9 & at(v4, v2) = v12 & % 16.54/2.97 at(v4, v0) = v8 & at_the_same_time(v12, v13) = v14 & at_the_same_time(v8, % 16.54/2.97 v9) = v10 & once(v14) = v15 & once(v10) = v11 & $i(v14) & $i(v13) & % 16.54/2.97 $i(v12) & $i(v10) & $i(v9) & $i(v8) & ( ~ (v15 = 0) | ~ (v11 = 0)))) % 16.54/2.97 % 16.54/2.97 (symmetry_of_at_the_same_time) % 16.54/2.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) = v2) % 16.54/2.97 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 16.54/2.97 (at_the_same_time(v0, v1) = v4 & once(v4) = v5 & once(v2) = v3 & $i(v4) & ( % 16.54/2.97 ~ (v3 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.54/2.97 (at_the_same_time(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 16.54/2.97 [v4: any] : ? [v5: any] : (at_the_same_time(v0, v1) = v3 & once(v3) = v4 & % 16.54/2.97 once(v2) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: % 16.54/2.97 $i] : ! [v2: $i] : ( ~ (at_the_same_time(v0, v1) = v2) | ~ $i(v1) | ~ % 16.54/2.97 $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : (at_the_same_time(v1, % 16.54/2.97 v0) = v4 & once(v4) = v5 & once(v2) = v3 & $i(v4) & ( ~ (v3 = 0) | v5 = % 16.54/2.97 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.54/2.97 (at_the_same_time(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 16.54/2.97 [v4: any] : ? [v5: any] : (at_the_same_time(v1, v0) = v3 & once(v3) = v4 & % 16.54/2.97 once(v2) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) % 16.54/2.97 % 16.54/2.97 (t14) % 16.54/2.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.54/2.98 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 16.54/2.98 (trajectory_of(v2) = v3 & trajectory_of(v1) = v4 & at(v2, v6) = v8 & at(v1, % 16.54/2.98 v5) = v7 & at_the_same_time(v7, v8) = v9 & connect(v1, v2, v0) = 0 & % 16.54/2.98 once(v9) = 0 & ordered_by(v4, v0, v5) = 0 & ordered_by(v3, v6, v0) = 0 & % 16.63/2.98 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 16.63/2.98 $i(v1) & $i(v0)) % 16.63/2.98 % 16.63/2.98 (function-axioms) % 16.63/2.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.63/2.98 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_o(v5, v4, v3, % 16.63/2.98 v2) = v1) | ~ (between_o(v5, v4, v3, v2) = v0)) & ! [v0: % 16.63/2.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/2.98 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_c(v5, v4, v3, v2) = v1) | % 16.63/2.98 ~ (between_c(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.63/2.98 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 16.63/2.98 (connect(v4, v3, v2) = v1) | ~ (connect(v4, v3, v2) = v0)) & ! [v0: % 16.63/2.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/2.98 : ! [v4: $i] : (v1 = v0 | ~ (ordered_by(v4, v3, v2) = v1) | ~ % 16.63/2.98 (ordered_by(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.63/2.98 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 16.63/2.98 (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 16.63/2.98 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (at(v3, v2) = v1) | ~ % 16.63/2.98 (at(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.63/2.98 (v1 = v0 | ~ (at_the_same_time(v3, v2) = v1) | ~ (at_the_same_time(v3, v2) = % 16.63/2.98 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.63/2.98 $i] : ! [v3: $i] : (v1 = v0 | ~ (finish_point(v3, v2) = v1) | ~ % 16.63/2.98 (finish_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.63/2.98 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.63/2.98 (start_point(v3, v2) = v1) | ~ (start_point(v3, v2) = v0)) & ! [v0: % 16.63/2.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/2.98 : (v1 = v0 | ~ (incident_o(v3, v2) = v1) | ~ (incident_o(v3, v2) = v0)) & ! % 16.63/2.98 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.63/2.98 $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = % 16.63/2.98 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.63/2.98 $i] : ! [v3: $i] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ % 16.63/2.98 (end_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.63/2.98 [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0: % 16.63/2.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/2.98 : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: % 16.63/2.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/2.98 : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! % 16.63/2.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trajectory_of(v2) = v1) % 16.63/2.98 | ~ (trajectory_of(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.63/2.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (once(v2) = v1) | ~ % 16.63/2.98 (once(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.63/2.98 (underlying_curve(v2) = v1) | ~ (underlying_curve(v2) = v0)) & ! [v0: % 16.63/2.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 16.63/2.98 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.63/2.98 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~ % 16.63/2.98 (closed(v2) = v0)) % 16.63/2.98 % 16.63/2.98 Further assumptions not needed in the proof: % 16.63/2.98 -------------------------------------------- % 16.63/2.98 assciativity_of_at_the_same_time, at_on_trajectory, between_c_defn, % 16.63/2.98 between_o_defn, c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn, % 16.63/2.98 finish_point_defn, idempotence_of_at_the_same_time, inner_point_defn, % 16.63/2.98 localization, meet_defn, o1, o2, o3, o4, o5, o6, open_defn, part_of_defn, % 16.63/2.98 start_point_defn, sum_defn, trajectories_are_oriented_curves, % 16.63/2.98 underlying_curve_defn % 16.63/2.98 % 16.63/2.98 Those formulas are unsatisfiable: % 16.63/2.98 --------------------------------- % 16.63/2.98 % 16.63/2.98 Begin of proof % 16.63/2.98 | % 16.63/2.98 | ALPHA: (connect_defn) implies: % 16.63/2.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (connect(v0, v1, v2) = 0) % 16.63/2.99 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 16.63/2.99 | [v5: $i] : (at(v1, v2) = v4 & at(v0, v2) = v3 & at_the_same_time(v3, % 16.63/2.99 | v4) = v5 & once(v5) = 0 & $i(v5) & $i(v4) & $i(v3))) % 16.63/2.99 | % 16.63/2.99 | ALPHA: (symmetry_of_at_the_same_time) implies: % 16.63/2.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) % 16.63/2.99 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? % 16.63/2.99 | [v5: any] : (at_the_same_time(v0, v1) = v3 & once(v3) = v4 & once(v2) % 16.63/2.99 | = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) % 16.63/2.99 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) % 16.63/2.99 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? % 16.63/2.99 | [v5: any] : (at_the_same_time(v0, v1) = v4 & once(v4) = v5 & once(v2) % 16.63/2.99 | = v3 & $i(v4) & ( ~ (v3 = 0) | v5 = 0))) % 16.63/2.99 | % 16.63/2.99 | ALPHA: (homogeneous_behaviour) implies: % 16.63/2.99 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.63/2.99 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (trajectory_of(v5) = v7) | % 16.63/2.99 | ~ (trajectory_of(v4) = v6) | ~ (ordered_by(v7, v3, v1) = 0) | ~ % 16.63/2.99 | (ordered_by(v6, v0, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 16.63/2.99 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: % 16.63/2.99 | $i] : ? [v11: any] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 16.63/2.99 | ? [v15: any] : (at(v5, v3) = v13 & at(v5, v1) = v9 & at(v4, v2) = v12 % 16.63/2.99 | & at(v4, v0) = v8 & at_the_same_time(v12, v13) = v14 & % 16.63/2.99 | at_the_same_time(v8, v9) = v10 & once(v14) = v15 & once(v10) = v11 % 16.63/2.99 | & $i(v14) & $i(v13) & $i(v12) & $i(v10) & $i(v9) & $i(v8) & ( ~ % 16.63/2.99 | (v15 = 0) | ~ (v11 = 0)))) % 16.63/2.99 | % 16.63/2.99 | ALPHA: (function-axioms) implies: % 16.63/2.99 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.63/2.99 | (v1 = v0 | ~ (once(v2) = v1) | ~ (once(v2) = v0)) % 16.63/2.99 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.63/2.99 | (at_the_same_time(v3, v2) = v1) | ~ (at_the_same_time(v3, v2) = v0)) % 16.63/2.99 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.63/2.99 | (at(v3, v2) = v1) | ~ (at(v3, v2) = v0)) % 16.63/2.99 | % 16.63/2.99 | DELTA: instantiating (t14) with fresh symbols all_43_0, all_43_1, all_43_2, % 16.63/2.99 | all_43_3, all_43_4, all_43_5, all_43_6, all_43_7, all_43_8, all_43_9 % 16.63/2.99 | gives: % 16.63/3.00 | (8) trajectory_of(all_43_7) = all_43_6 & trajectory_of(all_43_8) = all_43_5 % 16.63/3.00 | & at(all_43_7, all_43_3) = all_43_1 & at(all_43_8, all_43_4) = all_43_2 % 16.63/3.00 | & at_the_same_time(all_43_2, all_43_1) = all_43_0 & connect(all_43_8, % 16.63/3.00 | all_43_7, all_43_9) = 0 & once(all_43_0) = 0 & ordered_by(all_43_5, % 16.63/3.00 | all_43_9, all_43_4) = 0 & ordered_by(all_43_6, all_43_3, all_43_9) = % 16.63/3.00 | 0 & $i(all_43_0) & $i(all_43_1) & $i(all_43_2) & $i(all_43_3) & % 16.63/3.00 | $i(all_43_4) & $i(all_43_5) & $i(all_43_6) & $i(all_43_7) & % 16.63/3.00 | $i(all_43_8) & $i(all_43_9) % 16.63/3.00 | % 16.63/3.00 | ALPHA: (8) implies: % 16.63/3.00 | (9) $i(all_43_9) % 16.63/3.00 | (10) $i(all_43_8) % 16.63/3.00 | (11) $i(all_43_7) % 16.63/3.00 | (12) $i(all_43_4) % 16.63/3.00 | (13) $i(all_43_3) % 16.63/3.00 | (14) $i(all_43_2) % 16.63/3.00 | (15) $i(all_43_1) % 16.63/3.00 | (16) ordered_by(all_43_6, all_43_3, all_43_9) = 0 % 16.63/3.00 | (17) ordered_by(all_43_5, all_43_9, all_43_4) = 0 % 16.63/3.00 | (18) once(all_43_0) = 0 % 16.63/3.00 | (19) connect(all_43_8, all_43_7, all_43_9) = 0 % 16.63/3.00 | (20) at_the_same_time(all_43_2, all_43_1) = all_43_0 % 16.63/3.00 | (21) at(all_43_8, all_43_4) = all_43_2 % 16.63/3.00 | (22) at(all_43_7, all_43_3) = all_43_1 % 16.63/3.00 | (23) trajectory_of(all_43_8) = all_43_5 % 16.63/3.00 | (24) trajectory_of(all_43_7) = all_43_6 % 16.63/3.00 | % 16.63/3.00 | GROUND_INST: instantiating (1) with all_43_8, all_43_7, all_43_9, simplifying % 16.63/3.00 | with (9), (10), (11), (19) gives: % 16.63/3.00 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (at(all_43_7, all_43_9) = v1 % 16.63/3.00 | & at(all_43_8, all_43_9) = v0 & at_the_same_time(v0, v1) = v2 & % 16.63/3.00 | once(v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 16.63/3.00 | % 16.63/3.00 | GROUND_INST: instantiating (3) with all_43_1, all_43_2, all_43_0, simplifying % 16.63/3.00 | with (14), (15), (20) gives: % 16.63/3.00 | (26) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 16.63/3.00 | (at_the_same_time(all_43_1, all_43_2) = v1 & once(v1) = v2 & % 16.63/3.00 | once(all_43_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v2 = 0)) % 16.63/3.00 | % 16.63/3.00 | GROUND_INST: instantiating (2) with all_43_1, all_43_2, all_43_0, simplifying % 16.63/3.00 | with (14), (15), (20) gives: % 16.63/3.00 | (27) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 16.63/3.00 | (at_the_same_time(all_43_1, all_43_2) = v0 & once(v0) = v1 & % 16.63/3.00 | once(all_43_0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 16.63/3.00 | % 16.63/3.00 | GROUND_INST: instantiating (conjunction_at_the_same_time) with all_43_2, % 16.63/3.00 | all_43_1, all_43_0, simplifying with (14), (15), (20) gives: % 16.63/3.00 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (once(all_43_0) = v0 & % 16.63/3.00 | once(all_43_1) = v2 & once(all_43_2) = v1 & ( ~ (v0 = 0) | (v2 = 0 & % 16.63/3.00 | v1 = 0))) % 16.63/3.00 | % 16.63/3.00 | GROUND_INST: instantiating (4) with all_43_9, all_43_4, all_43_4, all_43_9, % 16.63/3.00 | all_43_8, all_43_8, all_43_5, all_43_5, simplifying with (9), % 16.63/3.00 | (10), (12), (17), (23) gives: % 16.63/3.01 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 16.63/3.01 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (at(all_43_8, all_43_4) = % 16.63/3.01 | v4 & at(all_43_8, all_43_4) = v1 & at(all_43_8, all_43_9) = v5 & % 16.63/3.01 | at(all_43_8, all_43_9) = v0 & at_the_same_time(v4, v5) = v6 & % 16.63/3.01 | at_the_same_time(v0, v1) = v2 & once(v6) = v7 & once(v2) = v3 & % 16.63/3.01 | $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | % 16.63/3.01 | ~ (v3 = 0))) % 16.63/3.01 | % 16.63/3.01 | GROUND_INST: instantiating (4) with all_43_3, all_43_9, all_43_9, all_43_3, % 16.63/3.01 | all_43_7, all_43_7, all_43_6, all_43_6, simplifying with (9), % 16.63/3.01 | (11), (13), (16), (24) gives: % 16.63/3.01 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 16.63/3.01 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (at(all_43_7, all_43_3) = % 16.63/3.01 | v5 & at(all_43_7, all_43_3) = v0 & at(all_43_7, all_43_9) = v4 & % 16.63/3.01 | at(all_43_7, all_43_9) = v1 & at_the_same_time(v4, v5) = v6 & % 16.63/3.01 | at_the_same_time(v0, v1) = v2 & once(v6) = v7 & once(v2) = v3 & % 16.63/3.01 | $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | % 16.63/3.01 | ~ (v3 = 0))) % 16.63/3.01 | % 16.63/3.01 | GROUND_INST: instantiating (4) with all_43_3, all_43_4, all_43_9, all_43_9, % 16.63/3.01 | all_43_7, all_43_8, all_43_6, all_43_5, simplifying with (9), % 16.63/3.01 | (10), (11), (12), (13), (16), (17), (23), (24) gives: % 16.63/3.01 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 16.63/3.01 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (at(all_43_7, all_43_3) = % 16.63/3.01 | v0 & at(all_43_7, all_43_9) = v4 & at(all_43_8, all_43_4) = v1 & % 16.63/3.01 | at(all_43_8, all_43_9) = v5 & at_the_same_time(v4, v5) = v6 & % 16.63/3.01 | at_the_same_time(v0, v1) = v2 & once(v6) = v7 & once(v2) = v3 & % 16.63/3.01 | $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | % 16.63/3.01 | ~ (v3 = 0))) % 16.63/3.01 | % 16.63/3.01 | GROUND_INST: instantiating (4) with all_43_9, all_43_9, all_43_4, all_43_3, % 16.63/3.01 | all_43_8, all_43_7, all_43_5, all_43_6, simplifying with (9), % 16.63/3.01 | (10), (11), (12), (13), (16), (17), (23), (24) gives: % 16.63/3.01 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 16.63/3.01 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (at(all_43_7, all_43_3) = % 16.63/3.01 | v5 & at(all_43_7, all_43_9) = v1 & at(all_43_8, all_43_4) = v4 & % 16.63/3.01 | at(all_43_8, all_43_9) = v0 & at_the_same_time(v4, v5) = v6 & % 16.63/3.01 | at_the_same_time(v0, v1) = v2 & once(v6) = v7 & once(v2) = v3 & % 16.63/3.01 | $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | % 16.63/3.01 | ~ (v3 = 0))) % 16.63/3.01 | % 16.63/3.01 | DELTA: instantiating (28) with fresh symbols all_60_0, all_60_1, all_60_2 % 16.63/3.01 | gives: % 16.63/3.01 | (33) once(all_43_0) = all_60_2 & once(all_43_1) = all_60_0 & once(all_43_2) % 16.82/3.01 | = all_60_1 & ( ~ (all_60_2 = 0) | (all_60_0 = 0 & all_60_1 = 0)) % 16.82/3.01 | % 16.82/3.01 | ALPHA: (33) implies: % 16.82/3.01 | (34) once(all_43_0) = all_60_2 % 16.82/3.01 | % 16.82/3.01 | DELTA: instantiating (27) with fresh symbols all_62_0, all_62_1, all_62_2 % 16.82/3.01 | gives: % 16.82/3.01 | (35) at_the_same_time(all_43_1, all_43_2) = all_62_2 & once(all_62_2) = % 16.82/3.02 | all_62_1 & once(all_43_0) = all_62_0 & $i(all_62_2) & ( ~ (all_62_1 = % 16.82/3.02 | 0) | all_62_0 = 0) % 16.82/3.02 | % 16.82/3.02 | ALPHA: (35) implies: % 16.82/3.02 | (36) once(all_43_0) = all_62_0 % 16.82/3.02 | % 16.82/3.02 | DELTA: instantiating (26) with fresh symbols all_64_0, all_64_1, all_64_2 % 16.82/3.02 | gives: % 16.82/3.02 | (37) at_the_same_time(all_43_1, all_43_2) = all_64_1 & once(all_64_1) = % 16.82/3.02 | all_64_0 & once(all_43_0) = all_64_2 & $i(all_64_1) & ( ~ (all_64_2 = % 16.82/3.02 | 0) | all_64_0 = 0) % 16.82/3.02 | % 16.82/3.02 | ALPHA: (37) implies: % 16.82/3.02 | (38) once(all_43_0) = all_64_2 % 16.82/3.02 | % 16.82/3.02 | DELTA: instantiating (25) with fresh symbols all_68_0, all_68_1, all_68_2 % 16.82/3.02 | gives: % 16.82/3.02 | (39) at(all_43_7, all_43_9) = all_68_1 & at(all_43_8, all_43_9) = all_68_2 % 16.82/3.02 | & at_the_same_time(all_68_2, all_68_1) = all_68_0 & once(all_68_0) = 0 % 16.82/3.02 | & $i(all_68_0) & $i(all_68_1) & $i(all_68_2) % 16.82/3.02 | % 16.82/3.02 | ALPHA: (39) implies: % 16.82/3.02 | (40) once(all_68_0) = 0 % 16.82/3.02 | (41) at_the_same_time(all_68_2, all_68_1) = all_68_0 % 16.82/3.02 | (42) at(all_43_8, all_43_9) = all_68_2 % 16.82/3.02 | (43) at(all_43_7, all_43_9) = all_68_1 % 16.82/3.02 | % 16.82/3.02 | DELTA: instantiating (32) with fresh symbols all_72_0, all_72_1, all_72_2, % 16.82/3.02 | all_72_3, all_72_4, all_72_5, all_72_6, all_72_7 gives: % 16.82/3.02 | (44) at(all_43_7, all_43_3) = all_72_2 & at(all_43_7, all_43_9) = all_72_6 % 16.82/3.02 | & at(all_43_8, all_43_4) = all_72_3 & at(all_43_8, all_43_9) = % 16.82/3.02 | all_72_7 & at_the_same_time(all_72_3, all_72_2) = all_72_1 & % 16.82/3.02 | at_the_same_time(all_72_7, all_72_6) = all_72_5 & once(all_72_1) = % 16.82/3.02 | all_72_0 & once(all_72_5) = all_72_4 & $i(all_72_1) & $i(all_72_2) & % 16.82/3.02 | $i(all_72_3) & $i(all_72_5) & $i(all_72_6) & $i(all_72_7) & ( ~ % 16.82/3.02 | (all_72_0 = 0) | ~ (all_72_4 = 0)) % 16.82/3.02 | % 16.82/3.02 | ALPHA: (44) implies: % 16.82/3.02 | (45) once(all_72_5) = all_72_4 % 16.82/3.02 | (46) once(all_72_1) = all_72_0 % 16.82/3.02 | (47) at_the_same_time(all_72_7, all_72_6) = all_72_5 % 16.82/3.02 | (48) at_the_same_time(all_72_3, all_72_2) = all_72_1 % 16.82/3.02 | (49) at(all_43_8, all_43_9) = all_72_7 % 16.82/3.02 | (50) at(all_43_8, all_43_4) = all_72_3 % 16.82/3.02 | (51) at(all_43_7, all_43_9) = all_72_6 % 16.82/3.02 | (52) at(all_43_7, all_43_3) = all_72_2 % 16.82/3.02 | (53) ~ (all_72_0 = 0) | ~ (all_72_4 = 0) % 16.82/3.02 | % 16.82/3.02 | DELTA: instantiating (29) with fresh symbols all_74_0, all_74_1, all_74_2, % 16.82/3.02 | all_74_3, all_74_4, all_74_5, all_74_6, all_74_7 gives: % 16.82/3.02 | (54) at(all_43_8, all_43_4) = all_74_3 & at(all_43_8, all_43_4) = all_74_6 % 16.82/3.02 | & at(all_43_8, all_43_9) = all_74_2 & at(all_43_8, all_43_9) = % 16.82/3.02 | all_74_7 & at_the_same_time(all_74_3, all_74_2) = all_74_1 & % 16.82/3.02 | at_the_same_time(all_74_7, all_74_6) = all_74_5 & once(all_74_1) = % 16.82/3.02 | all_74_0 & once(all_74_5) = all_74_4 & $i(all_74_1) & $i(all_74_2) & % 16.82/3.02 | $i(all_74_3) & $i(all_74_5) & $i(all_74_6) & $i(all_74_7) & ( ~ % 16.82/3.02 | (all_74_0 = 0) | ~ (all_74_4 = 0)) % 16.82/3.02 | % 16.82/3.02 | ALPHA: (54) implies: % 16.82/3.02 | (55) at(all_43_8, all_43_9) = all_74_7 % 16.82/3.02 | (56) at(all_43_8, all_43_9) = all_74_2 % 16.82/3.02 | (57) at(all_43_8, all_43_4) = all_74_6 % 16.82/3.02 | (58) at(all_43_8, all_43_4) = all_74_3 % 16.82/3.02 | % 16.82/3.02 | DELTA: instantiating (31) with fresh symbols all_76_0, all_76_1, all_76_2, % 16.82/3.02 | all_76_3, all_76_4, all_76_5, all_76_6, all_76_7 gives: % 16.82/3.02 | (59) at(all_43_7, all_43_3) = all_76_7 & at(all_43_7, all_43_9) = all_76_3 % 16.82/3.02 | & at(all_43_8, all_43_4) = all_76_6 & at(all_43_8, all_43_9) = % 16.82/3.02 | all_76_2 & at_the_same_time(all_76_3, all_76_2) = all_76_1 & % 16.82/3.02 | at_the_same_time(all_76_7, all_76_6) = all_76_5 & once(all_76_1) = % 16.82/3.02 | all_76_0 & once(all_76_5) = all_76_4 & $i(all_76_1) & $i(all_76_2) & % 16.82/3.02 | $i(all_76_3) & $i(all_76_5) & $i(all_76_6) & $i(all_76_7) & ( ~ % 16.82/3.02 | (all_76_0 = 0) | ~ (all_76_4 = 0)) % 16.82/3.02 | % 16.82/3.02 | ALPHA: (59) implies: % 16.82/3.02 | (60) at(all_43_8, all_43_9) = all_76_2 % 16.82/3.03 | (61) at(all_43_8, all_43_4) = all_76_6 % 16.82/3.03 | (62) at(all_43_7, all_43_9) = all_76_3 % 16.82/3.03 | (63) at(all_43_7, all_43_3) = all_76_7 % 16.82/3.03 | % 16.82/3.03 | DELTA: instantiating (30) with fresh symbols all_78_0, all_78_1, all_78_2, % 16.82/3.03 | all_78_3, all_78_4, all_78_5, all_78_6, all_78_7 gives: % 16.82/3.03 | (64) at(all_43_7, all_43_3) = all_78_2 & at(all_43_7, all_43_3) = all_78_7 % 16.82/3.03 | & at(all_43_7, all_43_9) = all_78_3 & at(all_43_7, all_43_9) = % 16.82/3.03 | all_78_6 & at_the_same_time(all_78_3, all_78_2) = all_78_1 & % 16.82/3.03 | at_the_same_time(all_78_7, all_78_6) = all_78_5 & once(all_78_1) = % 16.82/3.03 | all_78_0 & once(all_78_5) = all_78_4 & $i(all_78_1) & $i(all_78_2) & % 16.82/3.03 | $i(all_78_3) & $i(all_78_5) & $i(all_78_6) & $i(all_78_7) & ( ~ % 16.82/3.03 | (all_78_0 = 0) | ~ (all_78_4 = 0)) % 16.82/3.03 | % 16.82/3.03 | ALPHA: (64) implies: % 16.82/3.03 | (65) at(all_43_7, all_43_9) = all_78_6 % 16.82/3.03 | (66) at(all_43_7, all_43_9) = all_78_3 % 16.82/3.03 | (67) at(all_43_7, all_43_3) = all_78_7 % 16.82/3.03 | (68) at(all_43_7, all_43_3) = all_78_2 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (5) with all_60_2, all_62_0, all_43_0, simplifying % 16.82/3.03 | with (34), (36) gives: % 16.82/3.03 | (69) all_62_0 = all_60_2 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (5) with 0, all_64_2, all_43_0, simplifying with % 16.82/3.03 | (18), (38) gives: % 16.82/3.03 | (70) all_64_2 = 0 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (5) with all_62_0, all_64_2, all_43_0, simplifying % 16.82/3.03 | with (36), (38) gives: % 16.82/3.03 | (71) all_64_2 = all_62_0 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_74_7, all_74_2, all_43_9, all_43_8, % 16.82/3.03 | simplifying with (55), (56) gives: % 16.82/3.03 | (72) all_74_2 = all_74_7 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_68_2, all_74_2, all_43_9, all_43_8, % 16.82/3.03 | simplifying with (42), (56) gives: % 16.82/3.03 | (73) all_74_2 = all_68_2 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_74_2, all_76_2, all_43_9, all_43_8, % 16.82/3.03 | simplifying with (56), (60) gives: % 16.82/3.03 | (74) all_76_2 = all_74_2 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_72_7, all_76_2, all_43_9, all_43_8, % 16.82/3.03 | simplifying with (49), (60) gives: % 16.82/3.03 | (75) all_76_2 = all_72_7 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_43_2, all_74_6, all_43_4, all_43_8, % 16.82/3.03 | simplifying with (21), (57) gives: % 16.82/3.03 | (76) all_74_6 = all_43_2 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_74_3, all_76_6, all_43_4, all_43_8, % 16.82/3.03 | simplifying with (58), (61) gives: % 16.82/3.03 | (77) all_76_6 = all_74_3 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_74_6, all_76_6, all_43_4, all_43_8, % 16.82/3.03 | simplifying with (57), (61) gives: % 16.82/3.03 | (78) all_76_6 = all_74_6 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_72_3, all_76_6, all_43_4, all_43_8, % 16.82/3.03 | simplifying with (50), (61) gives: % 16.82/3.03 | (79) all_76_6 = all_72_3 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_68_1, all_76_3, all_43_9, all_43_7, % 16.82/3.03 | simplifying with (43), (62) gives: % 16.82/3.03 | (80) all_76_3 = all_68_1 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_76_3, all_78_6, all_43_9, all_43_7, % 16.82/3.03 | simplifying with (62), (65) gives: % 16.82/3.03 | (81) all_78_6 = all_76_3 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_78_6, all_78_3, all_43_9, all_43_7, % 16.82/3.03 | simplifying with (65), (66) gives: % 16.82/3.03 | (82) all_78_3 = all_78_6 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_72_6, all_78_3, all_43_9, all_43_7, % 16.82/3.03 | simplifying with (51), (66) gives: % 16.82/3.03 | (83) all_78_3 = all_72_6 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_72_2, all_78_7, all_43_3, all_43_7, % 16.82/3.03 | simplifying with (52), (67) gives: % 16.82/3.03 | (84) all_78_7 = all_72_2 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_43_1, all_78_2, all_43_3, all_43_7, % 16.82/3.03 | simplifying with (22), (68) gives: % 16.82/3.03 | (85) all_78_2 = all_43_1 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_78_7, all_78_2, all_43_3, all_43_7, % 16.82/3.03 | simplifying with (67), (68) gives: % 16.82/3.03 | (86) all_78_2 = all_78_7 % 16.82/3.03 | % 16.82/3.03 | GROUND_INST: instantiating (7) with all_76_7, all_78_2, all_43_3, all_43_7, % 16.82/3.03 | simplifying with (63), (68) gives: % 16.92/3.03 | (87) all_78_2 = all_76_7 % 16.92/3.03 | % 16.92/3.04 | COMBINE_EQS: (86), (87) imply: % 16.92/3.04 | (88) all_78_7 = all_76_7 % 16.92/3.04 | % 16.92/3.04 | SIMP: (88) implies: % 16.92/3.04 | (89) all_78_7 = all_76_7 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (85), (87) imply: % 16.92/3.04 | (90) all_76_7 = all_43_1 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (82), (83) imply: % 16.92/3.04 | (91) all_78_6 = all_72_6 % 16.92/3.04 | % 16.92/3.04 | SIMP: (91) implies: % 16.92/3.04 | (92) all_78_6 = all_72_6 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (81), (92) imply: % 16.92/3.04 | (93) all_76_3 = all_72_6 % 16.92/3.04 | % 16.92/3.04 | SIMP: (93) implies: % 16.92/3.04 | (94) all_76_3 = all_72_6 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (84), (89) imply: % 16.92/3.04 | (95) all_76_7 = all_72_2 % 16.92/3.04 | % 16.92/3.04 | SIMP: (95) implies: % 16.92/3.04 | (96) all_76_7 = all_72_2 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (74), (75) imply: % 16.92/3.04 | (97) all_74_2 = all_72_7 % 16.92/3.04 | % 16.92/3.04 | SIMP: (97) implies: % 16.92/3.04 | (98) all_74_2 = all_72_7 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (80), (94) imply: % 16.92/3.04 | (99) all_72_6 = all_68_1 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (77), (79) imply: % 16.92/3.04 | (100) all_74_3 = all_72_3 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (77), (78) imply: % 16.92/3.04 | (101) all_74_3 = all_74_6 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (90), (96) imply: % 16.92/3.04 | (102) all_72_2 = all_43_1 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (72), (73) imply: % 16.92/3.04 | (103) all_74_7 = all_68_2 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (72), (98) imply: % 16.92/3.04 | (104) all_74_7 = all_72_7 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (100), (101) imply: % 16.92/3.04 | (105) all_74_6 = all_72_3 % 16.92/3.04 | % 16.92/3.04 | SIMP: (105) implies: % 16.92/3.04 | (106) all_74_6 = all_72_3 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (76), (106) imply: % 16.92/3.04 | (107) all_72_3 = all_43_2 % 16.92/3.04 | % 16.92/3.04 | SIMP: (107) implies: % 16.92/3.04 | (108) all_72_3 = all_43_2 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (103), (104) imply: % 16.92/3.04 | (109) all_72_7 = all_68_2 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (70), (71) imply: % 16.92/3.04 | (110) all_62_0 = 0 % 16.92/3.04 | % 16.92/3.04 | SIMP: (110) implies: % 16.92/3.04 | (111) all_62_0 = 0 % 16.92/3.04 | % 16.92/3.04 | COMBINE_EQS: (69), (111) imply: % 16.92/3.04 | (112) all_60_2 = 0 % 16.92/3.04 | % 16.92/3.04 | REDUCE: (48), (102), (108) imply: % 16.92/3.04 | (113) at_the_same_time(all_43_2, all_43_1) = all_72_1 % 16.92/3.04 | % 16.92/3.04 | REDUCE: (47), (99), (109) imply: % 16.92/3.04 | (114) at_the_same_time(all_68_2, all_68_1) = all_72_5 % 16.92/3.04 | % 16.92/3.04 | GROUND_INST: instantiating (6) with all_43_0, all_72_1, all_43_1, all_43_2, % 16.92/3.04 | simplifying with (20), (113) gives: % 16.92/3.04 | (115) all_72_1 = all_43_0 % 16.92/3.04 | % 16.92/3.04 | GROUND_INST: instantiating (6) with all_68_0, all_72_5, all_68_1, all_68_2, % 16.92/3.04 | simplifying with (41), (114) gives: % 16.92/3.04 | (116) all_72_5 = all_68_0 % 16.92/3.04 | % 16.92/3.04 | REDUCE: (46), (115) imply: % 16.92/3.04 | (117) once(all_43_0) = all_72_0 % 16.92/3.04 | % 16.92/3.04 | REDUCE: (45), (116) imply: % 16.92/3.04 | (118) once(all_68_0) = all_72_4 % 16.92/3.04 | % 16.92/3.04 | GROUND_INST: instantiating (5) with 0, all_72_0, all_43_0, simplifying with % 16.92/3.04 | (18), (117) gives: % 16.92/3.04 | (119) all_72_0 = 0 % 16.92/3.04 | % 16.92/3.04 | GROUND_INST: instantiating (5) with 0, all_72_4, all_68_0, simplifying with % 16.92/3.04 | (40), (118) gives: % 16.92/3.04 | (120) all_72_4 = 0 % 16.92/3.04 | % 16.92/3.04 | BETA: splitting (53) gives: % 16.92/3.04 | % 16.92/3.04 | Case 1: % 16.92/3.04 | | % 16.92/3.04 | | (121) ~ (all_72_0 = 0) % 16.92/3.04 | | % 16.92/3.04 | | REDUCE: (119), (121) imply: % 16.92/3.04 | | (122) $false % 16.92/3.04 | | % 16.92/3.04 | | CLOSE: (122) is inconsistent. % 16.92/3.04 | | % 16.92/3.04 | Case 2: % 16.92/3.04 | | % 16.92/3.04 | | (123) ~ (all_72_4 = 0) % 16.92/3.04 | | % 16.92/3.04 | | REDUCE: (120), (123) imply: % 16.92/3.04 | | (124) $false % 16.92/3.04 | | % 16.92/3.04 | | CLOSE: (124) is inconsistent. % 16.92/3.04 | | % 16.92/3.04 | End of split % 16.92/3.04 | % 16.92/3.04 End of proof % 16.92/3.04 % SZS output end Proof for theBenchmark % 16.92/3.05 % 16.92/3.05 2441ms %------------------------------------------------------------------------------