%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO112+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 23:21:29 EDT 2023 % Result : Theorem 7.25s 1.77s % Output : Proof 10.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO112+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n012.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Tue Aug 29 20:24:09 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.81/1.16 Prover 4: Preprocessing ... % 2.81/1.16 Prover 1: Preprocessing ... % 3.37/1.20 Prover 3: Preprocessing ... % 3.37/1.20 Prover 0: Preprocessing ... % 3.37/1.20 Prover 2: Preprocessing ... % 3.37/1.20 Prover 5: Preprocessing ... % 3.37/1.20 Prover 6: Preprocessing ... % 6.33/1.62 Prover 2: Proving ... % 6.33/1.62 Prover 5: Proving ... % 6.33/1.64 Prover 1: Warning: ignoring some quantifiers % 6.33/1.65 Prover 3: Warning: ignoring some quantifiers % 6.33/1.67 Prover 6: Proving ... % 6.33/1.67 Prover 1: Constructing countermodel ... % 6.33/1.67 Prover 3: Constructing countermodel ... % 7.25/1.77 Prover 3: proved (1109ms) % 7.25/1.77 % 7.25/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.25/1.77 % 7.25/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.25/1.77 Prover 5: stopped % 7.25/1.77 Prover 6: stopped % 7.25/1.77 Prover 2: stopped % 7.25/1.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.25/1.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.25/1.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.25/1.83 Prover 7: Preprocessing ... % 7.25/1.84 Prover 10: Preprocessing ... % 7.25/1.84 Prover 11: Preprocessing ... % 7.25/1.85 Prover 8: Preprocessing ... % 8.12/1.90 Prover 1: Found proof (size 29) % 8.12/1.90 Prover 1: proved (1242ms) % 8.12/1.91 Prover 7: Warning: ignoring some quantifiers % 8.12/1.92 Prover 10: Warning: ignoring some quantifiers % 8.12/1.92 Prover 7: Constructing countermodel ... % 8.12/1.93 Prover 7: stopped % 8.12/1.94 Prover 10: Constructing countermodel ... % 8.12/1.94 Prover 11: stopped % 8.12/1.95 Prover 10: stopped % 9.04/1.98 Prover 8: Warning: ignoring some quantifiers % 9.04/1.99 Prover 8: Constructing countermodel ... % 9.04/2.00 Prover 8: stopped % 9.58/2.07 Prover 4: Warning: ignoring some quantifiers % 9.77/2.10 Prover 4: Constructing countermodel ... % 9.77/2.11 Prover 4: stopped % 10.12/2.17 Prover 0: Proving ... % 10.12/2.18 Prover 0: stopped % 10.12/2.18 % 10.12/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.12/2.18 % 10.12/2.20 % SZS output start Proof for theBenchmark % 10.12/2.20 Assumptions after simplification: % 10.12/2.20 --------------------------------- % 10.12/2.20 % 10.12/2.20 (between_c_defn) % 10.44/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.44/2.24 | v3 = v1 | ~ (between_c(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.44/2.25 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (inner_point(v2, v5) = 0) | ~ $i(v5) % 10.44/2.25 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (end_point(v3, v5) = v8 & % 10.44/2.25 end_point(v1, v5) = v7 & part_of(v5, v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = % 10.44/2.25 0) | ~ (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 10.44/2.25 [v3: $i] : ( ~ (between_c(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 10.44/2.25 $i(v1) | ~ $i(v0) | ( ~ (v3 = v1) & ? [v4: $i] : (inner_point(v2, v4) = 0 % 10.44/2.25 & end_point(v3, v4) = 0 & end_point(v1, v4) = 0 & part_of(v4, v0) = 0 & % 10.44/2.25 $i(v4)))) % 10.44/2.25 % 10.44/2.25 (theorem_3_8_2) % 10.44/2.25 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 10.44/2.25 = 0) & between_c(v0, v3, v2, v1) = v4 & between_c(v0, v1, v2, v3) = 0 & % 10.44/2.25 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.44/2.25 % 10.44/2.25 (function-axioms) % 10.44/2.25 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.44/2.25 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_c(v5, v4, v3, % 10.44/2.25 v2) = v1) | ~ (between_c(v5, v4, v3, v2) = v0)) & ! [v0: % 10.44/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.44/2.25 : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = % 10.44/2.25 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.44/2.26 $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ % 10.44/2.26 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.44/2.26 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.44/2.26 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : ! % 10.44/2.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ % 10.44/2.26 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.44/2.26 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3, % 10.44/2.26 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.44/2.26 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.44/2.26 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0: % 10.44/2.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.44/2.26 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.44/2.26 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~ % 10.44/2.26 (closed(v2) = v0)) % 10.44/2.26 % 10.44/2.26 Further assumptions not needed in the proof: % 10.44/2.26 -------------------------------------------- % 10.44/2.26 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn, % 10.44/2.26 inner_point_defn, meet_defn, open_defn, part_of_defn, sum_defn % 10.44/2.26 % 10.44/2.26 Those formulas are unsatisfiable: % 10.44/2.26 --------------------------------- % 10.44/2.26 % 10.44/2.26 Begin of proof % 10.44/2.26 | % 10.44/2.26 | ALPHA: (between_c_defn) implies: % 10.44/2.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.44/2.26 | (between_c(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 10.44/2.26 | ~ $i(v0) | ( ~ (v3 = v1) & ? [v4: $i] : (inner_point(v2, v4) = 0 & % 10.44/2.26 | end_point(v3, v4) = 0 & end_point(v1, v4) = 0 & part_of(v4, v0) = % 10.44/2.26 | 0 & $i(v4)))) % 10.70/2.26 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.70/2.26 | (v4 = 0 | v3 = v1 | ~ (between_c(v0, v1, v2, v3) = v4) | ~ $i(v3) | % 10.70/2.26 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (inner_point(v2, % 10.70/2.26 | v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] : ? [v8: % 10.70/2.26 | any] : (end_point(v3, v5) = v8 & end_point(v1, v5) = v7 & % 10.70/2.26 | part_of(v5, v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 10.70/2.26 | 0))))) % 10.70/2.26 | % 10.70/2.26 | ALPHA: (function-axioms) implies: % 10.70/2.27 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.70/2.27 | ! [v3: $i] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, % 10.70/2.27 | v2) = v0)) % 10.70/2.27 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.70/2.27 | ! [v3: $i] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ % 10.70/2.27 | (end_point(v3, v2) = v0)) % 10.70/2.27 | % 10.70/2.27 | DELTA: instantiating (theorem_3_8_2) with fresh symbols all_19_0, all_19_1, % 10.70/2.27 | all_19_2, all_19_3, all_19_4 gives: % 10.70/2.27 | (5) ~ (all_19_0 = 0) & between_c(all_19_4, all_19_1, all_19_2, all_19_3) = % 10.70/2.27 | all_19_0 & between_c(all_19_4, all_19_3, all_19_2, all_19_1) = 0 & % 10.70/2.27 | $i(all_19_1) & $i(all_19_2) & $i(all_19_3) & $i(all_19_4) % 10.70/2.27 | % 10.70/2.27 | ALPHA: (5) implies: % 10.70/2.27 | (6) ~ (all_19_0 = 0) % 10.70/2.27 | (7) $i(all_19_4) % 10.70/2.27 | (8) $i(all_19_3) % 10.70/2.27 | (9) $i(all_19_2) % 10.70/2.27 | (10) $i(all_19_1) % 10.70/2.27 | (11) between_c(all_19_4, all_19_3, all_19_2, all_19_1) = 0 % 10.70/2.27 | (12) between_c(all_19_4, all_19_1, all_19_2, all_19_3) = all_19_0 % 10.70/2.27 | % 10.70/2.27 | GROUND_INST: instantiating (1) with all_19_4, all_19_3, all_19_2, all_19_1, % 10.70/2.27 | simplifying with (7), (8), (9), (10), (11) gives: % 10.70/2.27 | (13) ~ (all_19_1 = all_19_3) & ? [v0: $i] : (inner_point(all_19_2, v0) = % 10.70/2.27 | 0 & end_point(all_19_1, v0) = 0 & end_point(all_19_3, v0) = 0 & % 10.70/2.27 | part_of(v0, all_19_4) = 0 & $i(v0)) % 10.70/2.27 | % 10.70/2.27 | ALPHA: (13) implies: % 10.70/2.27 | (14) ~ (all_19_1 = all_19_3) % 10.70/2.27 | (15) ? [v0: $i] : (inner_point(all_19_2, v0) = 0 & end_point(all_19_1, v0) % 10.70/2.27 | = 0 & end_point(all_19_3, v0) = 0 & part_of(v0, all_19_4) = 0 & % 10.70/2.27 | $i(v0)) % 10.70/2.27 | % 10.70/2.27 | GROUND_INST: instantiating (2) with all_19_4, all_19_1, all_19_2, all_19_3, % 10.70/2.27 | all_19_0, simplifying with (7), (8), (9), (10), (12) gives: % 10.70/2.27 | (16) all_19_0 = 0 | all_19_1 = all_19_3 | ! [v0: $i] : ( ~ % 10.70/2.27 | (inner_point(all_19_2, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 10.70/2.27 | any] : ? [v3: any] : (end_point(all_19_1, v0) = v2 & % 10.70/2.27 | end_point(all_19_3, v0) = v3 & part_of(v0, all_19_4) = v1 & ( ~ % 10.70/2.27 | (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) % 10.70/2.27 | % 10.70/2.27 | DELTA: instantiating (15) with fresh symbol all_30_0 gives: % 10.70/2.28 | (17) inner_point(all_19_2, all_30_0) = 0 & end_point(all_19_1, all_30_0) = % 10.70/2.28 | 0 & end_point(all_19_3, all_30_0) = 0 & part_of(all_30_0, all_19_4) = % 10.70/2.28 | 0 & $i(all_30_0) % 10.70/2.28 | % 10.70/2.28 | ALPHA: (17) implies: % 10.70/2.28 | (18) $i(all_30_0) % 10.70/2.28 | (19) part_of(all_30_0, all_19_4) = 0 % 10.70/2.28 | (20) end_point(all_19_3, all_30_0) = 0 % 10.70/2.28 | (21) end_point(all_19_1, all_30_0) = 0 % 10.70/2.28 | (22) inner_point(all_19_2, all_30_0) = 0 % 10.70/2.28 | % 10.70/2.28 | BETA: splitting (16) gives: % 10.70/2.28 | % 10.70/2.28 | Case 1: % 10.70/2.28 | | % 10.70/2.28 | | (23) all_19_0 = 0 % 10.70/2.28 | | % 10.70/2.28 | | REDUCE: (6), (23) imply: % 10.70/2.28 | | (24) $false % 10.70/2.28 | | % 10.70/2.28 | | CLOSE: (24) is inconsistent. % 10.70/2.28 | | % 10.70/2.28 | Case 2: % 10.70/2.28 | | % 10.70/2.28 | | (25) all_19_1 = all_19_3 | ! [v0: $i] : ( ~ (inner_point(all_19_2, v0) = % 10.70/2.28 | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.70/2.28 | | (end_point(all_19_1, v0) = v2 & end_point(all_19_3, v0) = v3 & % 10.70/2.28 | | part_of(v0, all_19_4) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 % 10.70/2.28 | | = 0)))) % 10.70/2.28 | | % 10.70/2.28 | | BETA: splitting (25) gives: % 10.70/2.28 | | % 10.70/2.28 | | Case 1: % 10.70/2.28 | | | % 10.70/2.28 | | | (26) all_19_1 = all_19_3 % 10.70/2.28 | | | % 10.70/2.28 | | | REDUCE: (14), (26) imply: % 10.70/2.28 | | | (27) $false % 10.70/2.28 | | | % 10.70/2.28 | | | CLOSE: (27) is inconsistent. % 10.70/2.28 | | | % 10.70/2.28 | | Case 2: % 10.70/2.28 | | | % 10.70/2.28 | | | (28) ! [v0: $i] : ( ~ (inner_point(all_19_2, v0) = 0) | ~ $i(v0) | ? % 10.70/2.28 | | | [v1: any] : ? [v2: any] : ? [v3: any] : (end_point(all_19_1, % 10.70/2.28 | | | v0) = v2 & end_point(all_19_3, v0) = v3 & part_of(v0, % 10.70/2.28 | | | all_19_4) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) % 10.70/2.28 | | | % 10.70/2.28 | | | GROUND_INST: instantiating (28) with all_30_0, simplifying with (18), (22) % 10.70/2.28 | | | gives: % 10.70/2.28 | | | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : (end_point(all_19_1, % 10.70/2.28 | | | all_30_0) = v1 & end_point(all_19_3, all_30_0) = v2 & % 10.70/2.28 | | | part_of(all_30_0, all_19_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 10.70/2.28 | | | ~ (v0 = 0))) % 10.70/2.28 | | | % 10.70/2.28 | | | DELTA: instantiating (29) with fresh symbols all_58_0, all_58_1, all_58_2 % 10.70/2.28 | | | gives: % 10.70/2.28 | | | (30) end_point(all_19_1, all_30_0) = all_58_1 & end_point(all_19_3, % 10.70/2.28 | | | all_30_0) = all_58_0 & part_of(all_30_0, all_19_4) = all_58_2 & % 10.70/2.28 | | | ( ~ (all_58_0 = 0) | ~ (all_58_1 = 0) | ~ (all_58_2 = 0)) % 10.70/2.28 | | | % 10.70/2.28 | | | ALPHA: (30) implies: % 10.70/2.28 | | | (31) part_of(all_30_0, all_19_4) = all_58_2 % 10.70/2.28 | | | (32) end_point(all_19_3, all_30_0) = all_58_0 % 10.70/2.28 | | | (33) end_point(all_19_1, all_30_0) = all_58_1 % 10.70/2.28 | | | (34) ~ (all_58_0 = 0) | ~ (all_58_1 = 0) | ~ (all_58_2 = 0) % 10.70/2.28 | | | % 10.70/2.28 | | | GROUND_INST: instantiating (3) with 0, all_58_2, all_19_4, all_30_0, % 10.70/2.28 | | | simplifying with (19), (31) gives: % 10.70/2.28 | | | (35) all_58_2 = 0 % 10.70/2.28 | | | % 10.70/2.29 | | | GROUND_INST: instantiating (4) with 0, all_58_0, all_30_0, all_19_3, % 10.70/2.29 | | | simplifying with (20), (32) gives: % 10.70/2.29 | | | (36) all_58_0 = 0 % 10.70/2.29 | | | % 10.70/2.29 | | | GROUND_INST: instantiating (4) with 0, all_58_1, all_30_0, all_19_1, % 10.70/2.29 | | | simplifying with (21), (33) gives: % 10.70/2.29 | | | (37) all_58_1 = 0 % 10.70/2.29 | | | % 10.70/2.29 | | | BETA: splitting (34) gives: % 10.70/2.29 | | | % 10.70/2.29 | | | Case 1: % 10.70/2.29 | | | | % 10.70/2.29 | | | | (38) ~ (all_58_0 = 0) % 10.70/2.29 | | | | % 10.70/2.29 | | | | REDUCE: (36), (38) imply: % 10.70/2.29 | | | | (39) $false % 10.70/2.29 | | | | % 10.70/2.29 | | | | CLOSE: (39) is inconsistent. % 10.70/2.29 | | | | % 10.70/2.29 | | | Case 2: % 10.70/2.29 | | | | % 10.70/2.29 | | | | (40) ~ (all_58_1 = 0) | ~ (all_58_2 = 0) % 10.70/2.29 | | | | % 10.70/2.29 | | | | BETA: splitting (40) gives: % 10.70/2.29 | | | | % 10.70/2.29 | | | | Case 1: % 10.70/2.29 | | | | | % 10.70/2.29 | | | | | (41) ~ (all_58_1 = 0) % 10.70/2.29 | | | | | % 10.70/2.29 | | | | | REDUCE: (37), (41) imply: % 10.70/2.29 | | | | | (42) $false % 10.70/2.29 | | | | | % 10.70/2.29 | | | | | CLOSE: (42) is inconsistent. % 10.70/2.29 | | | | | % 10.70/2.29 | | | | Case 2: % 10.70/2.29 | | | | | % 10.70/2.29 | | | | | (43) ~ (all_58_2 = 0) % 10.70/2.29 | | | | | % 10.70/2.29 | | | | | REDUCE: (35), (43) imply: % 10.70/2.29 | | | | | (44) $false % 10.70/2.29 | | | | | % 10.70/2.29 | | | | | CLOSE: (44) is inconsistent. % 10.70/2.29 | | | | | % 10.70/2.29 | | | | End of split % 10.70/2.29 | | | | % 10.70/2.29 | | | End of split % 10.70/2.29 | | | % 10.70/2.29 | | End of split % 10.70/2.29 | | % 10.70/2.29 | End of split % 10.70/2.29 | % 10.70/2.29 End of proof % 10.70/2.29 % SZS output end Proof for theBenchmark % 10.70/2.29 % 10.70/2.29 1651ms %------------------------------------------------------------------------------