%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO083+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 : n025.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 23:21:19 EDT 2023 % Result : Theorem 7.73s 1.76s % Output : Proof 10.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO083+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n025.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 % 0.20/0.34 % CPULimit : 300 % 0.20/0.34 % WCLimit : 300 % 0.20/0.34 % DateTime : Wed Aug 30 00:22:55 EDT 2023 % 0.20/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.05/1.09 Prover 4: Preprocessing ... % 3.05/1.09 Prover 1: Preprocessing ... % 3.05/1.12 Prover 5: Preprocessing ... % 3.05/1.12 Prover 3: Preprocessing ... % 3.05/1.12 Prover 2: Preprocessing ... % 3.05/1.12 Prover 6: Preprocessing ... % 3.05/1.12 Prover 0: Preprocessing ... % 5.98/1.50 Prover 2: Proving ... % 5.98/1.51 Prover 5: Proving ... % 5.98/1.53 Prover 3: Warning: ignoring some quantifiers % 5.98/1.55 Prover 6: Proving ... % 5.98/1.55 Prover 3: Constructing countermodel ... % 6.63/1.57 Prover 1: Warning: ignoring some quantifiers % 6.80/1.59 Prover 1: Constructing countermodel ... % 7.73/1.76 Prover 3: proved (1111ms) % 7.73/1.76 % 7.73/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.73/1.76 % 7.73/1.76 Prover 2: stopped % 7.73/1.76 Prover 5: stopped % 8.20/1.78 Prover 6: stopped % 8.20/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.20/1.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.20/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.20/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.20/1.83 Prover 8: Preprocessing ... % 8.20/1.83 Prover 7: Preprocessing ... % 8.20/1.86 Prover 10: Preprocessing ... % 8.20/1.86 Prover 11: Preprocessing ... % 8.96/1.90 Prover 1: Found proof (size 41) % 8.96/1.90 Prover 1: proved (1266ms) % 8.96/1.91 Prover 10: Warning: ignoring some quantifiers % 8.96/1.92 Prover 7: Warning: ignoring some quantifiers % 8.96/1.92 Prover 10: Constructing countermodel ... % 9.24/1.92 Prover 10: stopped % 9.24/1.93 Prover 7: Constructing countermodel ... % 9.24/1.93 Prover 11: stopped % 9.24/1.93 Prover 7: stopped % 9.24/1.95 Prover 8: Warning: ignoring some quantifiers % 9.24/1.97 Prover 8: Constructing countermodel ... % 9.24/1.97 Prover 8: stopped % 9.24/1.98 Prover 4: Warning: ignoring some quantifiers % 9.24/2.02 Prover 4: Constructing countermodel ... % 9.79/2.03 Prover 4: stopped % 9.79/2.07 Prover 0: Proving ... % 9.79/2.07 Prover 0: stopped % 9.79/2.07 % 9.79/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.79/2.07 % 9.79/2.08 % SZS output start Proof for theBenchmark % 9.79/2.08 Assumptions after simplification: % 9.79/2.08 --------------------------------- % 9.79/2.08 % 9.79/2.08 (corollary_2_6_1) % 10.31/2.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.31/2.11 $i] : ? [v6: int] : ( ~ (v6 = 0) & meet(v3, v0, v2) = 0 & meet(v3, v0, v1) % 10.31/2.11 = 0 & sum(v0, v2) = v5 & sum(v0, v1) = v4 & part_of(v4, v5) = v6 & % 10.31/2.11 part_of(v1, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.31/2.11 % 10.31/2.11 (part_of_defn) % 10.31/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, v0) = v2) % 10.31/2.11 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 10.31/2.11 incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) & ! [v0: $i] % 10.31/2.11 : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: % 10.31/2.11 $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, v0) = v3) | ~ $i(v2) | % 10.31/2.11 ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4))) % 10.31/2.11 % 10.31/2.11 (sum_defn) % 10.31/2.12 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (sum(v1, % 10.31/2.12 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: % 10.31/2.12 any] : ? [v6: any] : ? [v7: any] : (incident_c(v4, v2) = v7 & % 10.31/2.12 incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) % 10.31/2.12 | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0: % 10.31/2.12 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1, v2) = v0) | ~ $i(v2) | ~ % 10.31/2.12 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 10.31/2.12 (incident_c(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] : ? [v6: int] : ( % 10.31/2.12 ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3, % 10.31/2.12 v1) = v5)) & ! [v3: $i] : ( ~ (incident_c(v3, v0) = 0) | ~ $i(v3) % 10.31/2.12 | ? [v4: any] : ? [v5: any] : (incident_c(v3, v2) = v5 & % 10.31/2.12 incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 10.31/2.12 % 10.31/2.12 (function-axioms) % 10.31/2.13 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.31/2.13 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, % 10.31/2.13 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 10.31/2.13 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ % 10.31/2.13 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.31/2.13 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.31/2.13 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : ! % 10.31/2.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ % 10.31/2.13 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.31/2.13 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3, % 10.31/2.13 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.31/2.13 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.31/2.13 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0: % 10.31/2.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.31/2.13 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.31/2.13 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~ % 10.31/2.13 (closed(v2) = v0)) % 10.31/2.13 % 10.31/2.13 Further assumptions not needed in the proof: % 10.31/2.13 -------------------------------------------- % 10.31/2.13 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn, % 10.31/2.13 inner_point_defn, meet_defn, open_defn % 10.31/2.13 % 10.31/2.13 Those formulas are unsatisfiable: % 10.31/2.13 --------------------------------- % 10.31/2.13 % 10.31/2.13 Begin of proof % 10.31/2.13 | % 10.31/2.13 | ALPHA: (part_of_defn) implies: % 10.31/2.13 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ % 10.31/2.13 | $i(v0) | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, % 10.31/2.13 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & % 10.31/2.13 | incident_c(v2, v1) = v4))) % 10.31/2.14 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, % 10.31/2.14 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 10.31/2.14 | ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & % 10.31/2.14 | $i(v3))) % 10.31/2.14 | % 10.31/2.14 | ALPHA: (sum_defn) implies: % 10.31/2.14 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1, v2) = v0) | ~ % 10.31/2.14 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = % 10.31/2.14 | 0 | ~ (incident_c(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] : ? % 10.31/2.14 | [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 % 10.31/2.14 | & incident_c(v3, v1) = v5)) & ! [v3: $i] : ( ~ (incident_c(v3, % 10.31/2.14 | v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : % 10.31/2.14 | (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4 % 10.31/2.14 | = 0))))) % 10.31/2.14 | % 10.31/2.14 | ALPHA: (function-axioms) implies: % 10.31/2.14 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.31/2.14 | ! [v3: $i] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ % 10.31/2.14 | (incident_c(v3, v2) = v0)) % 10.31/2.14 | % 10.31/2.14 | DELTA: instantiating (corollary_2_6_1) with fresh symbols all_19_0, all_19_1, % 10.31/2.14 | all_19_2, all_19_3, all_19_4, all_19_5, all_19_6 gives: % 10.31/2.14 | (5) ~ (all_19_0 = 0) & meet(all_19_3, all_19_6, all_19_4) = 0 & % 10.31/2.14 | meet(all_19_3, all_19_6, all_19_5) = 0 & sum(all_19_6, all_19_4) = % 10.31/2.14 | all_19_1 & sum(all_19_6, all_19_5) = all_19_2 & part_of(all_19_2, % 10.31/2.14 | all_19_1) = all_19_0 & part_of(all_19_5, all_19_4) = 0 & $i(all_19_1) % 10.31/2.14 | & $i(all_19_2) & $i(all_19_3) & $i(all_19_4) & $i(all_19_5) & % 10.31/2.14 | $i(all_19_6) % 10.31/2.14 | % 10.31/2.14 | ALPHA: (5) implies: % 10.31/2.14 | (6) ~ (all_19_0 = 0) % 10.31/2.14 | (7) $i(all_19_6) % 10.31/2.14 | (8) $i(all_19_5) % 10.31/2.14 | (9) $i(all_19_4) % 10.31/2.15 | (10) $i(all_19_2) % 10.31/2.15 | (11) $i(all_19_1) % 10.31/2.15 | (12) part_of(all_19_5, all_19_4) = 0 % 10.31/2.15 | (13) part_of(all_19_2, all_19_1) = all_19_0 % 10.31/2.15 | (14) sum(all_19_6, all_19_5) = all_19_2 % 10.31/2.15 | (15) sum(all_19_6, all_19_4) = all_19_1 % 10.31/2.15 | % 10.31/2.15 | GROUND_INST: instantiating (1) with all_19_4, all_19_5, simplifying with (8), % 10.31/2.15 | (9), (12) gives: % 10.31/2.15 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_4) = % 10.31/2.15 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0, % 10.31/2.15 | all_19_5) = v2)) % 10.31/2.15 | % 10.31/2.15 | GROUND_INST: instantiating (2) with all_19_1, all_19_2, all_19_0, simplifying % 10.31/2.15 | with (10), (11), (13) gives: % 10.31/2.15 | (17) all_19_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.31/2.15 | incident_c(v0, all_19_1) = v1 & incident_c(v0, all_19_2) = 0 & % 10.31/2.15 | $i(v0)) % 10.31/2.15 | % 10.31/2.15 | GROUND_INST: instantiating (3) with all_19_2, all_19_6, all_19_5, simplifying % 10.31/2.15 | with (7), (8), (10), (14) gives: % 10.31/2.15 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_2) = % 10.31/2.15 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~ % 10.31/2.15 | (v2 = 0) & incident_c(v0, all_19_5) = v3 & incident_c(v0, % 10.31/2.15 | all_19_6) = v2)) & ! [v0: $i] : ( ~ (incident_c(v0, all_19_2) = % 10.31/2.15 | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (incident_c(v0, % 10.31/2.15 | all_19_5) = v2 & incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 = % 10.31/2.15 | 0))) % 10.31/2.15 | % 10.31/2.15 | ALPHA: (18) implies: % 10.31/2.15 | (19) ! [v0: $i] : ( ~ (incident_c(v0, all_19_2) = 0) | ~ $i(v0) | ? [v1: % 10.31/2.15 | any] : ? [v2: any] : (incident_c(v0, all_19_5) = v2 & % 10.31/2.15 | incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 = 0))) % 10.31/2.15 | % 10.31/2.15 | GROUND_INST: instantiating (3) with all_19_1, all_19_6, all_19_4, simplifying % 10.31/2.15 | with (7), (9), (11), (15) gives: % 10.31/2.15 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_1) = % 10.31/2.15 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~ % 10.31/2.15 | (v2 = 0) & incident_c(v0, all_19_4) = v3 & incident_c(v0, % 10.31/2.15 | all_19_6) = v2)) & ! [v0: $i] : ( ~ (incident_c(v0, all_19_1) = % 10.31/2.15 | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (incident_c(v0, % 10.31/2.15 | all_19_4) = v2 & incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 = % 10.31/2.15 | 0))) % 10.31/2.15 | % 10.31/2.15 | ALPHA: (20) implies: % 10.31/2.16 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_1) = % 10.31/2.16 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~ % 10.31/2.16 | (v2 = 0) & incident_c(v0, all_19_4) = v3 & incident_c(v0, % 10.31/2.16 | all_19_6) = v2)) % 10.31/2.16 | % 10.31/2.16 | BETA: splitting (17) gives: % 10.31/2.16 | % 10.31/2.16 | Case 1: % 10.31/2.16 | | % 10.31/2.16 | | (22) all_19_0 = 0 % 10.31/2.16 | | % 10.31/2.16 | | REDUCE: (6), (22) imply: % 10.31/2.16 | | (23) $false % 10.31/2.16 | | % 10.31/2.16 | | CLOSE: (23) is inconsistent. % 10.31/2.16 | | % 10.31/2.16 | Case 2: % 10.31/2.16 | | % 10.31/2.16 | | (24) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_19_1) % 10.31/2.16 | | = v1 & incident_c(v0, all_19_2) = 0 & $i(v0)) % 10.31/2.16 | | % 10.31/2.16 | | DELTA: instantiating (24) with fresh symbols all_38_0, all_38_1 gives: % 10.31/2.16 | | (25) ~ (all_38_0 = 0) & incident_c(all_38_1, all_19_1) = all_38_0 & % 10.31/2.16 | | incident_c(all_38_1, all_19_2) = 0 & $i(all_38_1) % 10.31/2.16 | | % 10.31/2.16 | | ALPHA: (25) implies: % 10.31/2.16 | | (26) ~ (all_38_0 = 0) % 10.31/2.16 | | (27) $i(all_38_1) % 10.31/2.16 | | (28) incident_c(all_38_1, all_19_2) = 0 % 10.31/2.16 | | (29) incident_c(all_38_1, all_19_1) = all_38_0 % 10.31/2.16 | | % 10.31/2.16 | | GROUND_INST: instantiating (19) with all_38_1, simplifying with (27), (28) % 10.31/2.16 | | gives: % 10.31/2.16 | | (30) ? [v0: any] : ? [v1: any] : (incident_c(all_38_1, all_19_5) = v1 & % 10.31/2.16 | | incident_c(all_38_1, all_19_6) = v0 & (v1 = 0 | v0 = 0)) % 10.31/2.16 | | % 10.31/2.16 | | GROUND_INST: instantiating (21) with all_38_1, all_38_0, simplifying with % 10.31/2.16 | | (27), (29) gives: % 10.31/2.16 | | (31) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 10.31/2.16 | | 0) & incident_c(all_38_1, all_19_4) = v1 & incident_c(all_38_1, % 10.31/2.16 | | all_19_6) = v0) % 10.31/2.16 | | % 10.31/2.16 | | DELTA: instantiating (30) with fresh symbols all_45_0, all_45_1 gives: % 10.31/2.16 | | (32) incident_c(all_38_1, all_19_5) = all_45_0 & incident_c(all_38_1, % 10.31/2.16 | | all_19_6) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0) % 10.31/2.16 | | % 10.31/2.16 | | ALPHA: (32) implies: % 10.31/2.16 | | (33) incident_c(all_38_1, all_19_6) = all_45_1 % 10.31/2.16 | | (34) incident_c(all_38_1, all_19_5) = all_45_0 % 10.31/2.16 | | (35) all_45_0 = 0 | all_45_1 = 0 % 10.31/2.16 | | % 10.31/2.16 | | BETA: splitting (31) gives: % 10.31/2.16 | | % 10.31/2.16 | | Case 1: % 10.31/2.16 | | | % 10.31/2.16 | | | (36) all_38_0 = 0 % 10.31/2.16 | | | % 10.31/2.16 | | | REDUCE: (26), (36) imply: % 10.31/2.16 | | | (37) $false % 10.31/2.16 | | | % 10.31/2.16 | | | CLOSE: (37) is inconsistent. % 10.31/2.16 | | | % 10.31/2.16 | | Case 2: % 10.31/2.16 | | | % 10.31/2.16 | | | (38) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 10.31/2.16 | | | incident_c(all_38_1, all_19_4) = v1 & incident_c(all_38_1, % 10.31/2.16 | | | all_19_6) = v0) % 10.31/2.16 | | | % 10.31/2.16 | | | DELTA: instantiating (38) with fresh symbols all_51_0, all_51_1 gives: % 10.31/2.17 | | | (39) ~ (all_51_0 = 0) & ~ (all_51_1 = 0) & incident_c(all_38_1, % 10.31/2.17 | | | all_19_4) = all_51_0 & incident_c(all_38_1, all_19_6) = all_51_1 % 10.31/2.17 | | | % 10.31/2.17 | | | ALPHA: (39) implies: % 10.31/2.17 | | | (40) ~ (all_51_1 = 0) % 10.31/2.17 | | | (41) ~ (all_51_0 = 0) % 10.31/2.17 | | | (42) incident_c(all_38_1, all_19_6) = all_51_1 % 10.31/2.17 | | | (43) incident_c(all_38_1, all_19_4) = all_51_0 % 10.31/2.17 | | | % 10.31/2.17 | | | GROUND_INST: instantiating (4) with all_45_1, all_51_1, all_19_6, % 10.31/2.17 | | | all_38_1, simplifying with (33), (42) gives: % 10.31/2.17 | | | (44) all_51_1 = all_45_1 % 10.31/2.17 | | | % 10.31/2.17 | | | REDUCE: (40), (44) imply: % 10.31/2.17 | | | (45) ~ (all_45_1 = 0) % 10.31/2.17 | | | % 10.31/2.17 | | | BETA: splitting (35) gives: % 10.31/2.17 | | | % 10.31/2.17 | | | Case 1: % 10.31/2.17 | | | | % 10.31/2.17 | | | | (46) all_45_0 = 0 % 10.31/2.17 | | | | % 10.31/2.17 | | | | REDUCE: (34), (46) imply: % 10.31/2.17 | | | | (47) incident_c(all_38_1, all_19_5) = 0 % 10.31/2.17 | | | | % 10.31/2.17 | | | | GROUND_INST: instantiating (16) with all_38_1, all_51_0, simplifying % 10.31/2.17 | | | | with (27), (43) gives: % 10.31/2.17 | | | | (48) all_51_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 10.31/2.17 | | | | incident_c(all_38_1, all_19_5) = v0) % 10.31/2.17 | | | | % 10.31/2.17 | | | | BETA: splitting (48) gives: % 10.31/2.17 | | | | % 10.31/2.17 | | | | Case 1: % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | (49) all_51_0 = 0 % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | REDUCE: (41), (49) imply: % 10.31/2.17 | | | | | (50) $false % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | CLOSE: (50) is inconsistent. % 10.31/2.17 | | | | | % 10.31/2.17 | | | | Case 2: % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_38_1, all_19_5) = % 10.31/2.17 | | | | | v0) % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | DELTA: instantiating (51) with fresh symbol all_74_0 gives: % 10.31/2.17 | | | | | (52) ~ (all_74_0 = 0) & incident_c(all_38_1, all_19_5) = all_74_0 % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | ALPHA: (52) implies: % 10.31/2.17 | | | | | (53) ~ (all_74_0 = 0) % 10.31/2.17 | | | | | (54) incident_c(all_38_1, all_19_5) = all_74_0 % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | GROUND_INST: instantiating (4) with 0, all_74_0, all_19_5, all_38_1, % 10.31/2.17 | | | | | simplifying with (47), (54) gives: % 10.31/2.17 | | | | | (55) all_74_0 = 0 % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | REDUCE: (53), (55) imply: % 10.31/2.17 | | | | | (56) $false % 10.31/2.17 | | | | | % 10.31/2.17 | | | | | CLOSE: (56) is inconsistent. % 10.31/2.17 | | | | | % 10.31/2.17 | | | | End of split % 10.31/2.17 | | | | % 10.31/2.17 | | | Case 2: % 10.31/2.17 | | | | % 10.31/2.17 | | | | (57) all_45_1 = 0 % 10.31/2.17 | | | | % 10.31/2.17 | | | | REDUCE: (45), (57) imply: % 10.31/2.17 | | | | (58) $false % 10.31/2.17 | | | | % 10.31/2.17 | | | | CLOSE: (58) is inconsistent. % 10.31/2.17 | | | | % 10.31/2.17 | | | End of split % 10.31/2.17 | | | % 10.31/2.17 | | End of split % 10.31/2.17 | | % 10.31/2.17 | End of split % 10.31/2.17 | % 10.31/2.17 End of proof % 10.65/2.17 % SZS output end Proof for theBenchmark % 10.65/2.17 % 10.65/2.17 1558ms %------------------------------------------------------------------------------