%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO146+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 : n026.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 13.54s 2.65s % Output : Proof 27.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : GEO146+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.37 % Computer : n026.cluster.edu % 0.14/0.37 % Model : x86_64 x86_64 % 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.37 % Memory : 8042.1875MB % 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.37 % CPULimit : 300 % 0.14/0.37 % WCLimit : 300 % 0.14/0.37 % DateTime : Tue Aug 29 22:00:35 EDT 2023 % 0.14/0.37 % 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 ... % 0.21/0.64 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 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 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 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 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 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 % 3.97/1.34 Prover 1: Preprocessing ... % 3.97/1.35 Prover 4: Preprocessing ... % 3.97/1.37 Prover 3: Preprocessing ... % 3.97/1.37 Prover 5: Preprocessing ... % 3.97/1.37 Prover 0: Preprocessing ... % 3.97/1.37 Prover 6: Preprocessing ... % 3.97/1.37 Prover 2: Preprocessing ... % 9.33/2.06 Prover 2: Proving ... % 9.33/2.08 Prover 5: Proving ... % 9.33/2.10 Prover 1: Warning: ignoring some quantifiers % 9.33/2.12 Prover 3: Warning: ignoring some quantifiers % 9.33/2.13 Prover 6: Proving ... % 9.33/2.15 Prover 3: Constructing countermodel ... % 9.33/2.17 Prover 1: Constructing countermodel ... % 13.36/2.59 Prover 4: Warning: ignoring some quantifiers % 13.54/2.65 Prover 2: proved (2001ms) % 13.54/2.65 % 13.54/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.54/2.65 % 13.54/2.67 Prover 5: stopped % 13.54/2.68 Prover 6: stopped % 13.54/2.68 Prover 3: stopped % 13.54/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.54/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.54/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.54/2.69 Prover 4: Constructing countermodel ... % 13.54/2.69 Prover 0: Proving ... % 13.54/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.19/2.72 Prover 0: stopped % 14.19/2.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.19/2.77 Prover 10: Preprocessing ... % 14.19/2.78 Prover 7: Preprocessing ... % 14.19/2.78 Prover 8: Preprocessing ... % 14.19/2.81 Prover 11: Preprocessing ... % 14.19/2.84 Prover 13: Preprocessing ... % 14.90/2.91 Prover 10: Warning: ignoring some quantifiers % 14.90/2.93 Prover 7: Warning: ignoring some quantifiers % 14.90/2.95 Prover 10: Constructing countermodel ... % 14.90/2.97 Prover 7: Constructing countermodel ... % 16.37/3.03 Prover 13: Warning: ignoring some quantifiers % 16.37/3.04 Prover 8: Warning: ignoring some quantifiers % 16.37/3.06 Prover 13: Constructing countermodel ... % 16.37/3.07 Prover 8: Constructing countermodel ... % 19.27/3.51 Prover 11: Warning: ignoring some quantifiers % 19.27/3.60 Prover 11: Constructing countermodel ... % 26.74/4.41 Prover 11: Found proof (size 67) % 26.74/4.41 Prover 11: proved (1715ms) % 26.74/4.41 Prover 8: stopped % 26.74/4.41 Prover 4: stopped % 26.74/4.41 Prover 1: stopped % 26.86/4.41 Prover 13: stopped % 26.86/4.42 Prover 7: stopped % 26.86/4.42 Prover 10: stopped % 26.86/4.42 % 26.86/4.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.86/4.42 % 26.86/4.43 % SZS output start Proof for theBenchmark % 26.86/4.43 Assumptions after simplification: % 26.86/4.43 --------------------------------- % 26.86/4.43 % 26.86/4.43 (connect_defn) % 26.86/4.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.86/4.46 $i] : ( ~ (at(v1, v2) = v4) | ~ (at(v0, v2) = v3) | ~ % 26.86/4.46 (at_the_same_time(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.86/4.46 [v6: int] : ? [v7: int] : ((v7 = 0 & connect(v0, v1, v2) = 0) | ( ~ (v6 = % 26.86/4.46 0) & once(v5) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.86/4.46 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (at(v1, v2) = v4) | ~ (at(v0, v2) % 26.86/4.46 = v3) | ~ (at_the_same_time(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 26.86/4.46 $i(v0) | ? [v6: int] : ? [v7: int] : ((v7 = 0 & once(v5) = 0) | ( ~ (v6 = % 26.86/4.46 0) & connect(v0, v1, v2) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.86/4.46 $i] : ! [v3: int] : (v3 = 0 | ~ (connect(v0, v1, v2) = v3) | ~ $i(v2) | % 26.86/4.46 ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 26.86/4.46 int] : ( ~ (v7 = 0) & at(v1, v2) = v5 & at(v0, v2) = v4 & % 26.86/4.46 at_the_same_time(v4, v5) = v6 & once(v6) = v7 & $i(v6) & $i(v5) & $i(v4))) % 26.86/4.46 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (connect(v0, v1, v2) = 0) | ~ % 26.86/4.46 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 26.86/4.46 (at(v1, v2) = v4 & at(v0, v2) = v3 & at_the_same_time(v3, v4) = v5 & % 26.86/4.46 once(v5) = 0 & $i(v5) & $i(v4) & $i(v3))) % 26.86/4.46 % 26.86/4.46 (symmetry_of_at_the_same_time) % 26.86/4.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) = v2) % 26.86/4.47 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = % 26.86/4.47 0 & at_the_same_time(v0, v1) = v4 & once(v4) = 0 & $i(v4)) | ( ~ (v3 = % 26.86/4.47 0) & once(v2) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 26.86/4.47 (at_the_same_time(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 26.86/4.47 [v4: int] : ? [v5: int] : ((v5 = 0 & once(v2) = 0) | ( ~ (v4 = 0) & % 26.86/4.47 at_the_same_time(v0, v1) = v3 & once(v3) = v4 & $i(v3)))) & ! [v0: $i] % 26.86/4.47 : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v0, v1) = v2) | ~ $i(v1) % 26.86/4.47 | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 & % 26.86/4.47 at_the_same_time(v1, v0) = v4 & once(v4) = 0 & $i(v4)) | ( ~ (v3 = 0) & % 26.86/4.47 once(v2) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 26.86/4.47 (at_the_same_time(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 26.86/4.47 [v4: int] : ? [v5: int] : ((v5 = 0 & once(v2) = 0) | ( ~ (v4 = 0) & % 26.86/4.47 at_the_same_time(v1, v0) = v3 & once(v3) = v4 & $i(v3)))) % 26.86/4.47 % 26.86/4.47 (t12) % 26.86/4.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 26.86/4.47 (connect(v1, v0, v2) = v4 & connect(v0, v1, v2) = v3 & $i(v2) & $i(v1) & % 26.86/4.47 $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 26.86/4.47 % 26.86/4.47 (function-axioms) % 26.86/4.48 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.86/4.48 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_o(v5, v4, v3, % 26.86/4.48 v2) = v1) | ~ (between_o(v5, v4, v3, v2) = v0)) & ! [v0: % 26.86/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.86/4.48 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_c(v5, v4, v3, v2) = v1) | % 26.86/4.48 ~ (between_c(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.86/4.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 26.86/4.48 (connect(v4, v3, v2) = v1) | ~ (connect(v4, v3, v2) = v0)) & ! [v0: % 26.86/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.86/4.48 : ! [v4: $i] : (v1 = v0 | ~ (ordered_by(v4, v3, v2) = v1) | ~ % 26.86/4.48 (ordered_by(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.86/4.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 26.86/4.48 (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 26.86/4.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (at(v3, v2) = v1) | ~ % 26.86/4.48 (at(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 26.86/4.48 (v1 = v0 | ~ (at_the_same_time(v3, v2) = v1) | ~ (at_the_same_time(v3, v2) = % 26.86/4.48 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.86/4.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (finish_point(v3, v2) = v1) | ~ % 26.86/4.48 (finish_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.86/4.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.86/4.48 (start_point(v3, v2) = v1) | ~ (start_point(v3, v2) = v0)) & ! [v0: % 26.86/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.86/4.48 : (v1 = v0 | ~ (incident_o(v3, v2) = v1) | ~ (incident_o(v3, v2) = v0)) & ! % 26.86/4.48 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.86/4.48 $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = % 26.86/4.48 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.86/4.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ % 26.86/4.48 (end_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.86/4.48 [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0: % 26.86/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.86/4.48 : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: % 26.86/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.86/4.48 : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! % 26.86/4.48 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trajectory_of(v2) = v1) % 26.86/4.48 | ~ (trajectory_of(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.86/4.48 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (once(v2) = v1) | ~ % 26.86/4.48 (once(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 26.86/4.48 (underlying_curve(v2) = v1) | ~ (underlying_curve(v2) = v0)) & ! [v0: % 26.86/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.86/4.48 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.86/4.48 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~ % 26.86/4.48 (closed(v2) = v0)) % 26.86/4.48 % 26.86/4.48 Further assumptions not needed in the proof: % 26.86/4.48 -------------------------------------------- % 26.86/4.48 assciativity_of_at_the_same_time, at_on_trajectory, between_c_defn, % 26.86/4.48 between_o_defn, c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, % 26.86/4.48 conjunction_at_the_same_time, end_point_defn, finish_point_defn, % 26.86/4.48 homogeneous_behaviour, idempotence_of_at_the_same_time, inner_point_defn, % 26.86/4.48 localization, meet_defn, o1, o2, o3, o4, o5, o6, open_defn, part_of_defn, % 26.86/4.48 start_point_defn, sum_defn, trajectories_are_oriented_curves, % 26.86/4.48 underlying_curve_defn % 26.86/4.48 % 26.86/4.48 Those formulas are unsatisfiable: % 26.86/4.48 --------------------------------- % 26.86/4.48 % 26.86/4.48 Begin of proof % 26.86/4.48 | % 26.86/4.48 | ALPHA: (connect_defn) implies: % 26.86/4.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (connect(v0, v1, v2) = 0) % 26.86/4.48 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 26.86/4.48 | [v5: $i] : (at(v1, v2) = v4 & at(v0, v2) = v3 & at_the_same_time(v3, % 26.86/4.48 | v4) = v5 & once(v5) = 0 & $i(v5) & $i(v4) & $i(v3))) % 26.86/4.48 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.86/4.48 | (connect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.86/4.48 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & % 26.86/4.48 | at(v1, v2) = v5 & at(v0, v2) = v4 & at_the_same_time(v4, v5) = v6 & % 26.86/4.48 | once(v6) = v7 & $i(v6) & $i(v5) & $i(v4))) % 26.86/4.48 | % 26.86/4.48 | ALPHA: (symmetry_of_at_the_same_time) implies: % 26.86/4.49 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (at_the_same_time(v1, v0) % 26.86/4.49 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? % 26.86/4.49 | [v5: int] : ((v5 = 0 & once(v2) = 0) | ( ~ (v4 = 0) & % 26.86/4.49 | at_the_same_time(v0, v1) = v3 & once(v3) = v4 & $i(v3)))) % 26.86/4.49 | % 26.86/4.49 | ALPHA: (function-axioms) implies: % 26.86/4.49 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.86/4.49 | (v1 = v0 | ~ (once(v2) = v1) | ~ (once(v2) = v0)) % 26.86/4.49 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.86/4.49 | (at_the_same_time(v3, v2) = v1) | ~ (at_the_same_time(v3, v2) = v0)) % 26.86/4.49 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.86/4.49 | (at(v3, v2) = v1) | ~ (at(v3, v2) = v0)) % 26.86/4.49 | % 26.86/4.49 | DELTA: instantiating (t12) with fresh symbols all_37_0, all_37_1, all_37_2, % 26.86/4.49 | all_37_3, all_37_4 gives: % 26.86/4.49 | (7) connect(all_37_3, all_37_4, all_37_2) = all_37_0 & connect(all_37_4, % 26.86/4.49 | all_37_3, all_37_2) = all_37_1 & $i(all_37_2) & $i(all_37_3) & % 26.86/4.49 | $i(all_37_4) & ((all_37_0 = 0 & ~ (all_37_1 = 0)) | (all_37_1 = 0 & ~ % 26.86/4.49 | (all_37_0 = 0))) % 26.86/4.49 | % 26.86/4.49 | ALPHA: (7) implies: % 26.86/4.49 | (8) $i(all_37_4) % 26.86/4.49 | (9) $i(all_37_3) % 26.86/4.49 | (10) $i(all_37_2) % 26.86/4.49 | (11) connect(all_37_4, all_37_3, all_37_2) = all_37_1 % 26.86/4.49 | (12) connect(all_37_3, all_37_4, all_37_2) = all_37_0 % 26.86/4.49 | (13) (all_37_0 = 0 & ~ (all_37_1 = 0)) | (all_37_1 = 0 & ~ (all_37_0 = % 26.86/4.49 | 0)) % 26.86/4.49 | % 26.86/4.49 | GROUND_INST: instantiating (2) with all_37_4, all_37_3, all_37_2, all_37_1, % 26.86/4.49 | simplifying with (8), (9), (10), (11) gives: % 26.86/4.49 | (14) all_37_1 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 26.86/4.49 | : ( ~ (v3 = 0) & at(all_37_3, all_37_2) = v1 & at(all_37_4, all_37_2) % 26.86/4.49 | = v0 & at_the_same_time(v0, v1) = v2 & once(v2) = v3 & $i(v2) & % 26.86/4.49 | $i(v1) & $i(v0)) % 26.86/4.49 | % 26.86/4.49 | GROUND_INST: instantiating (2) with all_37_3, all_37_4, all_37_2, all_37_0, % 26.86/4.49 | simplifying with (8), (9), (10), (12) gives: % 26.86/4.49 | (15) all_37_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 26.86/4.49 | : ( ~ (v3 = 0) & at(all_37_3, all_37_2) = v0 & at(all_37_4, all_37_2) % 26.86/4.49 | = v1 & at_the_same_time(v0, v1) = v2 & once(v2) = v3 & $i(v2) & % 26.86/4.49 | $i(v1) & $i(v0)) % 26.86/4.49 | % 26.86/4.49 | BETA: splitting (13) gives: % 26.86/4.49 | % 26.86/4.49 | Case 1: % 26.86/4.49 | | % 26.86/4.49 | | (16) all_37_0 = 0 & ~ (all_37_1 = 0) % 26.86/4.49 | | % 26.86/4.49 | | ALPHA: (16) implies: % 26.86/4.49 | | (17) all_37_0 = 0 % 26.86/4.49 | | (18) ~ (all_37_1 = 0) % 26.86/4.49 | | % 26.86/4.49 | | REDUCE: (12), (17) imply: % 26.86/4.50 | | (19) connect(all_37_3, all_37_4, all_37_2) = 0 % 26.86/4.50 | | % 26.86/4.50 | | BETA: splitting (14) gives: % 26.86/4.50 | | % 26.86/4.50 | | Case 1: % 26.86/4.50 | | | % 26.86/4.50 | | | (20) all_37_1 = 0 % 26.86/4.50 | | | % 26.86/4.50 | | | REDUCE: (18), (20) imply: % 26.86/4.50 | | | (21) $false % 26.86/4.50 | | | % 26.86/4.50 | | | CLOSE: (21) is inconsistent. % 26.86/4.50 | | | % 26.86/4.50 | | Case 2: % 26.86/4.50 | | | % 26.86/4.50 | | | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 26.86/4.50 | | | 0) & at(all_37_3, all_37_2) = v1 & at(all_37_4, all_37_2) = v0 % 26.86/4.50 | | | & at_the_same_time(v0, v1) = v2 & once(v2) = v3 & $i(v2) & % 26.86/4.50 | | | $i(v1) & $i(v0)) % 26.86/4.50 | | | % 26.86/4.50 | | | DELTA: instantiating (22) with fresh symbols all_252_0, all_252_1, % 26.86/4.50 | | | all_252_2, all_252_3 gives: % 26.86/4.50 | | | (23) ~ (all_252_0 = 0) & at(all_37_3, all_37_2) = all_252_2 & % 26.86/4.50 | | | at(all_37_4, all_37_2) = all_252_3 & at_the_same_time(all_252_3, % 26.86/4.50 | | | all_252_2) = all_252_1 & once(all_252_1) = all_252_0 & % 26.86/4.50 | | | $i(all_252_1) & $i(all_252_2) & $i(all_252_3) % 26.86/4.50 | | | % 26.86/4.50 | | | ALPHA: (23) implies: % 26.86/4.50 | | | (24) ~ (all_252_0 = 0) % 26.86/4.50 | | | (25) $i(all_252_3) % 26.86/4.50 | | | (26) $i(all_252_2) % 26.86/4.50 | | | (27) once(all_252_1) = all_252_0 % 26.86/4.50 | | | (28) at_the_same_time(all_252_3, all_252_2) = all_252_1 % 26.86/4.50 | | | (29) at(all_37_4, all_37_2) = all_252_3 % 26.86/4.50 | | | (30) at(all_37_3, all_37_2) = all_252_2 % 26.86/4.50 | | | % 26.86/4.50 | | | GROUND_INST: instantiating (1) with all_37_3, all_37_4, all_37_2, % 26.86/4.50 | | | simplifying with (8), (9), (10), (19) gives: % 26.86/4.50 | | | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (at(all_37_3, all_37_2) % 26.86/4.50 | | | = v0 & at(all_37_4, all_37_2) = v1 & at_the_same_time(v0, v1) = % 26.86/4.50 | | | v2 & once(v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 26.86/4.50 | | | % 26.86/4.50 | | | GROUND_INST: instantiating (3) with all_252_2, all_252_3, all_252_1, % 26.86/4.50 | | | simplifying with (25), (26), (28) gives: % 26.86/4.50 | | | (32) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 26.86/4.50 | | | once(all_252_1) = 0) | ( ~ (v1 = 0) & % 26.86/4.50 | | | at_the_same_time(all_252_2, all_252_3) = v0 & once(v0) = v1 & % 26.86/4.50 | | | $i(v0))) % 26.86/4.50 | | | % 26.86/4.50 | | | DELTA: instantiating (32) with fresh symbols all_275_0, all_275_1, % 26.86/4.50 | | | all_275_2 gives: % 26.86/4.50 | | | (33) (all_275_0 = 0 & once(all_252_1) = 0) | ( ~ (all_275_1 = 0) & % 26.86/4.50 | | | at_the_same_time(all_252_2, all_252_3) = all_275_2 & % 26.86/4.50 | | | once(all_275_2) = all_275_1 & $i(all_275_2)) % 26.86/4.50 | | | % 26.86/4.50 | | | DELTA: instantiating (31) with fresh symbols all_277_0, all_277_1, % 26.86/4.50 | | | all_277_2 gives: % 26.86/4.50 | | | (34) at(all_37_3, all_37_2) = all_277_2 & at(all_37_4, all_37_2) = % 26.86/4.50 | | | all_277_1 & at_the_same_time(all_277_2, all_277_1) = all_277_0 & % 26.86/4.50 | | | once(all_277_0) = 0 & $i(all_277_0) & $i(all_277_1) & % 26.86/4.50 | | | $i(all_277_2) % 26.86/4.50 | | | % 26.86/4.50 | | | ALPHA: (34) implies: % 26.86/4.50 | | | (35) once(all_277_0) = 0 % 26.86/4.50 | | | (36) at_the_same_time(all_277_2, all_277_1) = all_277_0 % 26.86/4.50 | | | (37) at(all_37_4, all_37_2) = all_277_1 % 26.86/4.50 | | | (38) at(all_37_3, all_37_2) = all_277_2 % 26.86/4.50 | | | % 26.86/4.50 | | | BETA: splitting (33) gives: % 26.86/4.50 | | | % 26.86/4.50 | | | Case 1: % 26.86/4.50 | | | | % 26.86/4.50 | | | | (39) all_275_0 = 0 & once(all_252_1) = 0 % 26.86/4.50 | | | | % 26.86/4.50 | | | | ALPHA: (39) implies: % 26.86/4.50 | | | | (40) once(all_252_1) = 0 % 26.86/4.50 | | | | % 26.86/4.51 | | | | GROUND_INST: instantiating (4) with all_252_0, 0, all_252_1, simplifying % 26.86/4.51 | | | | with (27), (40) gives: % 26.86/4.51 | | | | (41) all_252_0 = 0 % 26.86/4.51 | | | | % 26.86/4.51 | | | | REDUCE: (24), (41) imply: % 26.86/4.51 | | | | (42) $false % 26.86/4.51 | | | | % 26.86/4.51 | | | | CLOSE: (42) is inconsistent. % 26.86/4.51 | | | | % 26.86/4.51 | | | Case 2: % 26.86/4.51 | | | | % 26.86/4.51 | | | | (43) ~ (all_275_1 = 0) & at_the_same_time(all_252_2, all_252_3) = % 26.86/4.51 | | | | all_275_2 & once(all_275_2) = all_275_1 & $i(all_275_2) % 26.86/4.51 | | | | % 26.86/4.51 | | | | ALPHA: (43) implies: % 26.86/4.51 | | | | (44) ~ (all_275_1 = 0) % 26.86/4.51 | | | | (45) once(all_275_2) = all_275_1 % 26.86/4.51 | | | | (46) at_the_same_time(all_252_2, all_252_3) = all_275_2 % 26.86/4.51 | | | | % 26.86/4.51 | | | | GROUND_INST: instantiating (6) with all_252_3, all_277_1, all_37_2, % 26.86/4.51 | | | | all_37_4, simplifying with (29), (37) gives: % 26.86/4.51 | | | | (47) all_277_1 = all_252_3 % 26.86/4.51 | | | | % 26.86/4.51 | | | | GROUND_INST: instantiating (6) with all_252_2, all_277_2, all_37_2, % 26.86/4.51 | | | | all_37_3, simplifying with (30), (38) gives: % 26.86/4.51 | | | | (48) all_277_2 = all_252_2 % 26.86/4.51 | | | | % 26.86/4.51 | | | | REDUCE: (36), (47), (48) imply: % 26.86/4.51 | | | | (49) at_the_same_time(all_252_2, all_252_3) = all_277_0 % 26.86/4.51 | | | | % 26.86/4.51 | | | | GROUND_INST: instantiating (5) with all_275_2, all_277_0, all_252_3, % 26.86/4.51 | | | | all_252_2, simplifying with (46), (49) gives: % 26.86/4.51 | | | | (50) all_277_0 = all_275_2 % 26.86/4.51 | | | | % 26.86/4.51 | | | | REDUCE: (35), (50) imply: % 26.86/4.51 | | | | (51) once(all_275_2) = 0 % 26.86/4.51 | | | | % 26.86/4.51 | | | | GROUND_INST: instantiating (4) with all_275_1, 0, all_275_2, simplifying % 26.86/4.51 | | | | with (45), (51) gives: % 26.86/4.51 | | | | (52) all_275_1 = 0 % 26.86/4.51 | | | | % 26.86/4.51 | | | | REDUCE: (44), (52) imply: % 26.86/4.51 | | | | (53) $false % 26.86/4.51 | | | | % 26.86/4.51 | | | | CLOSE: (53) is inconsistent. % 26.86/4.51 | | | | % 26.86/4.51 | | | End of split % 26.86/4.51 | | | % 26.86/4.51 | | End of split % 26.86/4.51 | | % 26.86/4.51 | Case 2: % 26.86/4.51 | | % 26.86/4.51 | | (54) all_37_1 = 0 & ~ (all_37_0 = 0) % 26.86/4.51 | | % 26.86/4.51 | | ALPHA: (54) implies: % 26.86/4.51 | | (55) all_37_1 = 0 % 26.86/4.51 | | (56) ~ (all_37_0 = 0) % 26.86/4.51 | | % 26.86/4.51 | | REDUCE: (11), (55) imply: % 26.86/4.51 | | (57) connect(all_37_4, all_37_3, all_37_2) = 0 % 26.86/4.51 | | % 26.86/4.51 | | BETA: splitting (15) gives: % 26.86/4.51 | | % 26.86/4.51 | | Case 1: % 26.86/4.51 | | | % 26.86/4.51 | | | (58) all_37_0 = 0 % 26.86/4.51 | | | % 26.86/4.51 | | | REDUCE: (56), (58) imply: % 26.86/4.51 | | | (59) $false % 26.86/4.51 | | | % 26.86/4.51 | | | CLOSE: (59) is inconsistent. % 26.86/4.51 | | | % 26.86/4.51 | | Case 2: % 26.86/4.51 | | | % 26.86/4.51 | | | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 26.86/4.51 | | | 0) & at(all_37_3, all_37_2) = v0 & at(all_37_4, all_37_2) = v1 % 26.86/4.51 | | | & at_the_same_time(v0, v1) = v2 & once(v2) = v3 & $i(v2) & % 26.86/4.51 | | | $i(v1) & $i(v0)) % 26.86/4.51 | | | % 26.86/4.51 | | | DELTA: instantiating (60) with fresh symbols all_252_0, all_252_1, % 26.86/4.51 | | | all_252_2, all_252_3 gives: % 26.86/4.51 | | | (61) ~ (all_252_0 = 0) & at(all_37_3, all_37_2) = all_252_3 & % 26.86/4.51 | | | at(all_37_4, all_37_2) = all_252_2 & at_the_same_time(all_252_3, % 26.86/4.51 | | | all_252_2) = all_252_1 & once(all_252_1) = all_252_0 & % 26.86/4.51 | | | $i(all_252_1) & $i(all_252_2) & $i(all_252_3) % 26.86/4.51 | | | % 26.86/4.51 | | | ALPHA: (61) implies: % 27.34/4.51 | | | (62) ~ (all_252_0 = 0) % 27.34/4.51 | | | (63) $i(all_252_3) % 27.34/4.51 | | | (64) $i(all_252_2) % 27.34/4.51 | | | (65) once(all_252_1) = all_252_0 % 27.34/4.51 | | | (66) at_the_same_time(all_252_3, all_252_2) = all_252_1 % 27.34/4.51 | | | (67) at(all_37_4, all_37_2) = all_252_2 % 27.34/4.51 | | | (68) at(all_37_3, all_37_2) = all_252_3 % 27.34/4.51 | | | % 27.34/4.52 | | | GROUND_INST: instantiating (1) with all_37_4, all_37_3, all_37_2, % 27.34/4.52 | | | simplifying with (8), (9), (10), (57) gives: % 27.34/4.52 | | | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (at(all_37_3, all_37_2) % 27.34/4.52 | | | = v1 & at(all_37_4, all_37_2) = v0 & at_the_same_time(v0, v1) = % 27.34/4.52 | | | v2 & once(v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 27.34/4.52 | | | % 27.34/4.52 | | | GROUND_INST: instantiating (3) with all_252_2, all_252_3, all_252_1, % 27.34/4.52 | | | simplifying with (63), (64), (66) gives: % 27.34/4.52 | | | (70) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 27.34/4.52 | | | once(all_252_1) = 0) | ( ~ (v1 = 0) & % 27.34/4.52 | | | at_the_same_time(all_252_2, all_252_3) = v0 & once(v0) = v1 & % 27.34/4.52 | | | $i(v0))) % 27.34/4.52 | | | % 27.34/4.52 | | | DELTA: instantiating (70) with fresh symbols all_275_0, all_275_1, % 27.34/4.52 | | | all_275_2 gives: % 27.34/4.52 | | | (71) (all_275_0 = 0 & once(all_252_1) = 0) | ( ~ (all_275_1 = 0) & % 27.34/4.52 | | | at_the_same_time(all_252_2, all_252_3) = all_275_2 & % 27.34/4.52 | | | once(all_275_2) = all_275_1 & $i(all_275_2)) % 27.34/4.52 | | | % 27.34/4.52 | | | DELTA: instantiating (69) with fresh symbols all_277_0, all_277_1, % 27.34/4.52 | | | all_277_2 gives: % 27.34/4.52 | | | (72) at(all_37_3, all_37_2) = all_277_1 & at(all_37_4, all_37_2) = % 27.34/4.52 | | | all_277_2 & at_the_same_time(all_277_2, all_277_1) = all_277_0 & % 27.34/4.52 | | | once(all_277_0) = 0 & $i(all_277_0) & $i(all_277_1) & % 27.34/4.52 | | | $i(all_277_2) % 27.34/4.52 | | | % 27.34/4.52 | | | ALPHA: (72) implies: % 27.34/4.52 | | | (73) once(all_277_0) = 0 % 27.34/4.52 | | | (74) at_the_same_time(all_277_2, all_277_1) = all_277_0 % 27.34/4.52 | | | (75) at(all_37_4, all_37_2) = all_277_2 % 27.34/4.52 | | | (76) at(all_37_3, all_37_2) = all_277_1 % 27.34/4.52 | | | % 27.34/4.52 | | | BETA: splitting (71) gives: % 27.34/4.52 | | | % 27.34/4.52 | | | Case 1: % 27.34/4.52 | | | | % 27.34/4.52 | | | | (77) all_275_0 = 0 & once(all_252_1) = 0 % 27.34/4.52 | | | | % 27.34/4.52 | | | | ALPHA: (77) implies: % 27.34/4.52 | | | | (78) once(all_252_1) = 0 % 27.34/4.52 | | | | % 27.34/4.52 | | | | GROUND_INST: instantiating (4) with all_252_0, 0, all_252_1, simplifying % 27.34/4.52 | | | | with (65), (78) gives: % 27.34/4.52 | | | | (79) all_252_0 = 0 % 27.34/4.52 | | | | % 27.34/4.52 | | | | REDUCE: (62), (79) imply: % 27.34/4.52 | | | | (80) $false % 27.34/4.52 | | | | % 27.34/4.52 | | | | CLOSE: (80) is inconsistent. % 27.34/4.52 | | | | % 27.34/4.52 | | | Case 2: % 27.34/4.52 | | | | % 27.34/4.52 | | | | (81) ~ (all_275_1 = 0) & at_the_same_time(all_252_2, all_252_3) = % 27.34/4.52 | | | | all_275_2 & once(all_275_2) = all_275_1 & $i(all_275_2) % 27.34/4.52 | | | | % 27.34/4.52 | | | | ALPHA: (81) implies: % 27.34/4.52 | | | | (82) ~ (all_275_1 = 0) % 27.34/4.52 | | | | (83) once(all_275_2) = all_275_1 % 27.34/4.52 | | | | (84) at_the_same_time(all_252_2, all_252_3) = all_275_2 % 27.34/4.52 | | | | % 27.34/4.52 | | | | GROUND_INST: instantiating (6) with all_252_2, all_277_2, all_37_2, % 27.34/4.52 | | | | all_37_4, simplifying with (67), (75) gives: % 27.34/4.52 | | | | (85) all_277_2 = all_252_2 % 27.34/4.52 | | | | % 27.34/4.52 | | | | GROUND_INST: instantiating (6) with all_252_3, all_277_1, all_37_2, % 27.34/4.52 | | | | all_37_3, simplifying with (68), (76) gives: % 27.34/4.52 | | | | (86) all_277_1 = all_252_3 % 27.34/4.52 | | | | % 27.34/4.52 | | | | REDUCE: (74), (85), (86) imply: % 27.34/4.52 | | | | (87) at_the_same_time(all_252_2, all_252_3) = all_277_0 % 27.34/4.52 | | | | % 27.34/4.52 | | | | GROUND_INST: instantiating (5) with all_275_2, all_277_0, all_252_3, % 27.34/4.52 | | | | all_252_2, simplifying with (84), (87) gives: % 27.34/4.52 | | | | (88) all_277_0 = all_275_2 % 27.34/4.52 | | | | % 27.34/4.52 | | | | REDUCE: (73), (88) imply: % 27.34/4.52 | | | | (89) once(all_275_2) = 0 % 27.34/4.52 | | | | % 27.34/4.52 | | | | GROUND_INST: instantiating (4) with all_275_1, 0, all_275_2, simplifying % 27.34/4.52 | | | | with (83), (89) gives: % 27.34/4.52 | | | | (90) all_275_1 = 0 % 27.34/4.52 | | | | % 27.34/4.52 | | | | REDUCE: (82), (90) imply: % 27.34/4.53 | | | | (91) $false % 27.34/4.53 | | | | % 27.34/4.53 | | | | CLOSE: (91) is inconsistent. % 27.34/4.53 | | | | % 27.34/4.53 | | | End of split % 27.34/4.53 | | | % 27.34/4.53 | | End of split % 27.34/4.53 | | % 27.34/4.53 | End of split % 27.34/4.53 | % 27.34/4.53 End of proof % 27.34/4.53 % SZS output end Proof for theBenchmark % 27.34/4.53 % 27.34/4.53 3904ms %------------------------------------------------------------------------------