%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 : Thu Aug 31 00:04:29 EDT 2023 % Result : Theorem 9.51s 2.09s % Output : Proof 12.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 03:17:54 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.66 ________ _____ % 0.21/0.66 ___ __ \_________(_)________________________________ % 0.21/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.66 % 0.21/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.66 (2023-06-19) % 0.21/0.66 % 0.21/0.66 (c) Philipp Rümmer, 2009-2023 % 0.21/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.66 Amanda Stjerna. % 0.21/0.66 Free software under BSD-3-Clause. % 0.21/0.66 % 0.21/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.66 % 0.21/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.67 Running up to 7 provers in parallel. % 0.21/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.43/1.21 Prover 4: Preprocessing ... % 3.43/1.22 Prover 1: Preprocessing ... % 3.43/1.26 Prover 0: Preprocessing ... % 3.43/1.26 Prover 6: Preprocessing ... % 3.43/1.26 Prover 5: Preprocessing ... % 3.43/1.26 Prover 3: Preprocessing ... % 3.43/1.26 Prover 2: Preprocessing ... % 7.51/1.82 Prover 6: Proving ... % 7.89/1.82 Prover 3: Constructing countermodel ... % 7.89/1.82 Prover 1: Constructing countermodel ... % 7.89/1.83 Prover 5: Proving ... % 8.10/1.88 Prover 2: Proving ... % 9.51/2.04 Prover 4: Constructing countermodel ... % 9.51/2.05 Prover 0: Proving ... % 9.51/2.09 Prover 3: proved (1411ms) % 9.51/2.09 % 9.51/2.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.51/2.10 % 9.51/2.10 Prover 0: stopped % 9.51/2.10 Prover 6: stopped % 9.51/2.10 Prover 5: stopped % 9.51/2.11 Prover 2: stopped % 9.51/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.51/2.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.51/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.51/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.01/2.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.01/2.16 Prover 8: Preprocessing ... % 10.01/2.16 Prover 11: Preprocessing ... % 10.47/2.17 Prover 7: Preprocessing ... % 10.47/2.17 Prover 10: Preprocessing ... % 10.47/2.19 Prover 13: Preprocessing ... % 11.35/2.28 Prover 10: Warning: ignoring some quantifiers % 11.35/2.31 Prover 10: Constructing countermodel ... % 11.35/2.31 Prover 1: Found proof (size 35) % 11.35/2.31 Prover 1: proved (1632ms) % 11.35/2.31 Prover 4: stopped % 11.35/2.32 Prover 10: stopped % 11.35/2.32 Prover 7: Warning: ignoring some quantifiers % 11.67/2.33 Prover 13: Warning: ignoring some quantifiers % 11.67/2.33 Prover 7: Constructing countermodel ... % 11.77/2.34 Prover 8: Warning: ignoring some quantifiers % 11.77/2.34 Prover 7: stopped % 11.77/2.35 Prover 8: Constructing countermodel ... % 11.77/2.35 Prover 13: Constructing countermodel ... % 11.77/2.36 Prover 8: stopped % 11.77/2.36 Prover 13: stopped % 11.77/2.41 Prover 11: Constructing countermodel ... % 12.19/2.42 Prover 11: stopped % 12.19/2.42 % 12.19/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.19/2.42 % 12.19/2.42 % SZS output start Proof for theBenchmark % 12.19/2.42 Assumptions after simplification: % 12.19/2.42 --------------------------------- % 12.19/2.42 % 12.19/2.42 (complete_means_sequential_pairs_and_triangles) % 12.19/2.45 $i(triangles) & $i(sequential_pairs) & complete & ? [v0: $i] : ? [v1: $i] : % 12.19/2.45 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & % 12.19/2.45 number_of_in(triangles, v0) = v4 & number_of_in(sequential_pairs, v0) = v3 & % 12.19/2.45 path(v1, v2, v0) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: % 12.19/2.45 $i] : ! [v6: $i] : ( ~ (on_path(v6, v0) = 0) | ~ (on_path(v5, v0) = 0) | % 12.19/2.45 ~ $i(v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & sequential(v5, v6) = % 12.19/2.45 v7) | ? [v7: $i] : (triangle(v5, v6, v7) = 0 & $i(v7)))) % 12.19/2.45 % 12.19/2.45 (path_length_sequential_pairs) % 12.19/2.45 $i(n1) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.19/2.45 (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 12.19/2.45 ? [v4: $i] : (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & % 12.19/2.45 length_of(v2) = v4 & $i(v4) & $i(v3))) % 12.19/2.45 % 12.19/2.45 (sequential_pairs_and_triangles) % 12.19/2.46 $i(triangles) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 12.19/2.46 : ( ~ (path(v1, v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 12.19/2.46 : ? [v4: $i] : (sequential(v3, v4) = 0 & on_path(v4, v0) = 0 & on_path(v3, % 12.19/2.46 v0) = 0 & $i(v4) & $i(v3) & ! [v5: $i] : ( ~ (triangle(v3, v4, v5) = 0) % 12.19/2.46 | ~ $i(v5))) | ? [v3: $i] : (number_of_in(triangles, v0) = v3 & % 12.19/2.46 number_of_in(sequential_pairs, v0) = v3 & $i(v3))) % 12.19/2.46 % 12.19/2.46 (function-axioms) % 12.19/2.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.19/2.47 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ % 12.19/2.47 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.19/2.47 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.19/2.47 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & ! % 12.19/2.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.19/2.47 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ % 12.19/2.47 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.19/2.47 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.19/2.47 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 12.19/2.47 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ % 12.19/2.47 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.19/2.47 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = % 12.19/2.47 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.19/2.47 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ % 12.19/2.47 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.19/2.47 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.19/2.47 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0: % 12.19/2.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.19/2.47 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0: % 12.19/2.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.19/2.47 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0: % 12.19/2.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3, % 12.19/2.47 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 12.19/2.47 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & % 12.19/2.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 12.19/2.47 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1: % 12.19/2.47 $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = % 12.19/2.47 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.19/2.47 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : ! % 12.19/2.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = % 12.19/2.47 v0)) % 12.19/2.47 % 12.19/2.47 Further assumptions not needed in the proof: % 12.19/2.47 -------------------------------------------- % 12.19/2.47 complete_properties, edge_ends_are_vertices, graph_has_them_all, % 12.19/2.47 in_path_properties, length_defn, no_loops, on_path_properties, path_defn, % 12.19/2.47 path_properties, precedes_defn, precedes_properties, sequential_defn, % 12.19/2.47 shortest_path_defn, shortest_path_properties, triangle_defn % 12.19/2.47 % 12.19/2.47 Those formulas are unsatisfiable: % 12.19/2.47 --------------------------------- % 12.19/2.47 % 12.19/2.47 Begin of proof % 12.47/2.47 | % 12.47/2.47 | ALPHA: (path_length_sequential_pairs) implies: % 12.47/2.47 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) | % 12.47/2.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 12.47/2.47 | (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & % 12.47/2.47 | length_of(v2) = v4 & $i(v4) & $i(v3))) % 12.47/2.47 | % 12.47/2.47 | ALPHA: (sequential_pairs_and_triangles) implies: % 12.47/2.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v1, v2, v0) = 0) | % 12.47/2.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 12.47/2.47 | (sequential(v3, v4) = 0 & on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & % 12.47/2.47 | $i(v4) & $i(v3) & ! [v5: $i] : ( ~ (triangle(v3, v4, v5) = 0) | ~ % 12.47/2.47 | $i(v5))) | ? [v3: $i] : (number_of_in(triangles, v0) = v3 & % 12.47/2.47 | number_of_in(sequential_pairs, v0) = v3 & $i(v3))) % 12.47/2.47 | % 12.47/2.47 | ALPHA: (complete_means_sequential_pairs_and_triangles) implies: % 12.47/2.48 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( % 12.47/2.48 | ~ (v4 = v3) & number_of_in(triangles, v0) = v4 & % 12.47/2.48 | number_of_in(sequential_pairs, v0) = v3 & path(v1, v2, v0) = 0 & % 12.47/2.48 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: % 12.47/2.48 | $i] : ( ~ (on_path(v6, v0) = 0) | ~ (on_path(v5, v0) = 0) | ~ % 12.47/2.48 | $i(v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & sequential(v5, % 12.47/2.48 | v6) = v7) | ? [v7: $i] : (triangle(v5, v6, v7) = 0 & $i(v7)))) % 12.47/2.48 | % 12.47/2.48 | ALPHA: (function-axioms) implies: % 12.47/2.48 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.47/2.48 | ! [v3: $i] : (v1 = v0 | ~ (sequential(v3, v2) = v1) | ~ % 12.47/2.48 | (sequential(v3, v2) = v0)) % 12.47/2.48 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.47/2.48 | (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = v0)) % 12.47/2.48 | % 12.47/2.48 | DELTA: instantiating (3) with fresh symbols all_20_0, all_20_1, all_20_2, % 12.47/2.48 | all_20_3, all_20_4 gives: % 12.47/2.48 | (6) ~ (all_20_0 = all_20_1) & number_of_in(triangles, all_20_4) = all_20_0 % 12.47/2.48 | & number_of_in(sequential_pairs, all_20_4) = all_20_1 & path(all_20_3, % 12.47/2.48 | all_20_2, all_20_4) = 0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) % 12.47/2.48 | & $i(all_20_3) & $i(all_20_4) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.47/2.48 | (on_path(v1, all_20_4) = 0) | ~ (on_path(v0, all_20_4) = 0) | ~ % 12.47/2.48 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & sequential(v0, v1) % 12.47/2.48 | = v2) | ? [v2: $i] : (triangle(v0, v1, v2) = 0 & $i(v2))) % 12.47/2.48 | % 12.47/2.48 | ALPHA: (6) implies: % 12.47/2.48 | (7) ~ (all_20_0 = all_20_1) % 12.47/2.48 | (8) $i(all_20_4) % 12.47/2.48 | (9) $i(all_20_3) % 12.47/2.48 | (10) $i(all_20_2) % 12.47/2.48 | (11) path(all_20_3, all_20_2, all_20_4) = 0 % 12.47/2.48 | (12) number_of_in(sequential_pairs, all_20_4) = all_20_1 % 12.47/2.48 | (13) number_of_in(triangles, all_20_4) = all_20_0 % 12.47/2.48 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (on_path(v1, all_20_4) = 0) | ~ % 12.47/2.48 | (on_path(v0, all_20_4) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : % 12.47/2.48 | ( ~ (v2 = 0) & sequential(v0, v1) = v2) | ? [v2: $i] : % 12.47/2.48 | (triangle(v0, v1, v2) = 0 & $i(v2))) % 12.47/2.48 | % 12.47/2.48 | GROUND_INST: instantiating (2) with all_20_4, all_20_3, all_20_2, simplifying % 12.47/2.48 | with (8), (9), (10), (11) gives: % 12.47/2.48 | (15) ? [v0: $i] : ? [v1: $i] : (sequential(v0, v1) = 0 & on_path(v1, % 12.47/2.48 | all_20_4) = 0 & on_path(v0, all_20_4) = 0 & $i(v1) & $i(v0) & ! % 12.47/2.48 | [v2: $i] : ( ~ (triangle(v0, v1, v2) = 0) | ~ $i(v2))) | ? [v0: % 12.47/2.48 | $i] : (number_of_in(triangles, all_20_4) = v0 & % 12.47/2.48 | number_of_in(sequential_pairs, all_20_4) = v0 & $i(v0)) % 12.47/2.48 | % 12.47/2.48 | GROUND_INST: instantiating (1) with all_20_3, all_20_2, all_20_4, simplifying % 12.47/2.48 | with (8), (9), (10), (11) gives: % 12.47/2.48 | (16) ? [v0: $i] : ? [v1: $i] : (minus(v1, n1) = v0 & % 12.47/2.48 | number_of_in(sequential_pairs, all_20_4) = v0 & length_of(all_20_4) % 12.47/2.49 | = v1 & $i(v1) & $i(v0)) % 12.47/2.49 | % 12.47/2.49 | DELTA: instantiating (16) with fresh symbols all_38_0, all_38_1 gives: % 12.47/2.49 | (17) minus(all_38_0, n1) = all_38_1 & number_of_in(sequential_pairs, % 12.47/2.49 | all_20_4) = all_38_1 & length_of(all_20_4) = all_38_0 & $i(all_38_0) % 12.47/2.49 | & $i(all_38_1) % 12.47/2.49 | % 12.47/2.49 | ALPHA: (17) implies: % 12.47/2.49 | (18) number_of_in(sequential_pairs, all_20_4) = all_38_1 % 12.47/2.49 | % 12.47/2.49 | GROUND_INST: instantiating (5) with all_20_1, all_38_1, all_20_4, % 12.47/2.49 | sequential_pairs, simplifying with (12), (18) gives: % 12.47/2.49 | (19) all_38_1 = all_20_1 % 12.47/2.49 | % 12.47/2.49 | BETA: splitting (15) gives: % 12.47/2.49 | % 12.47/2.49 | Case 1: % 12.47/2.49 | | % 12.47/2.49 | | (20) ? [v0: $i] : ? [v1: $i] : (sequential(v0, v1) = 0 & on_path(v1, % 12.47/2.49 | | all_20_4) = 0 & on_path(v0, all_20_4) = 0 & $i(v1) & $i(v0) & ! % 12.47/2.49 | | [v2: $i] : ( ~ (triangle(v0, v1, v2) = 0) | ~ $i(v2))) % 12.47/2.49 | | % 12.47/2.49 | | DELTA: instantiating (20) with fresh symbols all_49_0, all_49_1 gives: % 12.47/2.49 | | (21) sequential(all_49_1, all_49_0) = 0 & on_path(all_49_0, all_20_4) = 0 % 12.47/2.49 | | & on_path(all_49_1, all_20_4) = 0 & $i(all_49_0) & $i(all_49_1) & ! % 12.47/2.49 | | [v0: $i] : ( ~ (triangle(all_49_1, all_49_0, v0) = 0) | ~ $i(v0)) % 12.47/2.49 | | % 12.47/2.49 | | ALPHA: (21) implies: % 12.47/2.49 | | (22) $i(all_49_1) % 12.47/2.49 | | (23) $i(all_49_0) % 12.47/2.49 | | (24) on_path(all_49_1, all_20_4) = 0 % 12.47/2.49 | | (25) on_path(all_49_0, all_20_4) = 0 % 12.47/2.49 | | (26) sequential(all_49_1, all_49_0) = 0 % 12.47/2.49 | | (27) ! [v0: $i] : ( ~ (triangle(all_49_1, all_49_0, v0) = 0) | ~ % 12.47/2.49 | | $i(v0)) % 12.47/2.49 | | % 12.47/2.49 | | GROUND_INST: instantiating (14) with all_49_1, all_49_0, simplifying with % 12.47/2.49 | | (22), (23), (24), (25) gives: % 12.47/2.49 | | (28) ? [v0: int] : ( ~ (v0 = 0) & sequential(all_49_1, all_49_0) = v0) | % 12.47/2.49 | | ? [v0: $i] : (triangle(all_49_1, all_49_0, v0) = 0 & $i(v0)) % 12.47/2.49 | | % 12.47/2.49 | | BETA: splitting (28) gives: % 12.47/2.49 | | % 12.47/2.49 | | Case 1: % 12.47/2.49 | | | % 12.47/2.49 | | | (29) ? [v0: int] : ( ~ (v0 = 0) & sequential(all_49_1, all_49_0) = v0) % 12.47/2.49 | | | % 12.47/2.49 | | | DELTA: instantiating (29) with fresh symbol all_66_0 gives: % 12.47/2.49 | | | (30) ~ (all_66_0 = 0) & sequential(all_49_1, all_49_0) = all_66_0 % 12.47/2.49 | | | % 12.47/2.49 | | | ALPHA: (30) implies: % 12.47/2.49 | | | (31) ~ (all_66_0 = 0) % 12.47/2.49 | | | (32) sequential(all_49_1, all_49_0) = all_66_0 % 12.47/2.49 | | | % 12.47/2.49 | | | GROUND_INST: instantiating (4) with 0, all_66_0, all_49_0, all_49_1, % 12.47/2.49 | | | simplifying with (26), (32) gives: % 12.47/2.49 | | | (33) all_66_0 = 0 % 12.47/2.49 | | | % 12.47/2.49 | | | REDUCE: (31), (33) imply: % 12.47/2.49 | | | (34) $false % 12.47/2.49 | | | % 12.47/2.49 | | | CLOSE: (34) is inconsistent. % 12.47/2.49 | | | % 12.47/2.49 | | Case 2: % 12.47/2.49 | | | % 12.47/2.49 | | | (35) ? [v0: $i] : (triangle(all_49_1, all_49_0, v0) = 0 & $i(v0)) % 12.47/2.49 | | | % 12.47/2.49 | | | DELTA: instantiating (35) with fresh symbol all_66_0 gives: % 12.47/2.49 | | | (36) triangle(all_49_1, all_49_0, all_66_0) = 0 & $i(all_66_0) % 12.47/2.49 | | | % 12.47/2.49 | | | ALPHA: (36) implies: % 12.47/2.49 | | | (37) $i(all_66_0) % 12.47/2.49 | | | (38) triangle(all_49_1, all_49_0, all_66_0) = 0 % 12.47/2.49 | | | % 12.47/2.49 | | | GROUND_INST: instantiating (27) with all_66_0, simplifying with (37), (38) % 12.47/2.49 | | | gives: % 12.47/2.49 | | | (39) $false % 12.47/2.49 | | | % 12.47/2.49 | | | CLOSE: (39) is inconsistent. % 12.47/2.50 | | | % 12.47/2.50 | | End of split % 12.47/2.50 | | % 12.47/2.50 | Case 2: % 12.47/2.50 | | % 12.47/2.50 | | (40) ? [v0: $i] : (number_of_in(triangles, all_20_4) = v0 & % 12.47/2.50 | | number_of_in(sequential_pairs, all_20_4) = v0 & $i(v0)) % 12.47/2.50 | | % 12.47/2.50 | | DELTA: instantiating (40) with fresh symbol all_49_0 gives: % 12.47/2.50 | | (41) number_of_in(triangles, all_20_4) = all_49_0 & % 12.47/2.50 | | number_of_in(sequential_pairs, all_20_4) = all_49_0 & $i(all_49_0) % 12.47/2.50 | | % 12.47/2.50 | | ALPHA: (41) implies: % 12.47/2.50 | | (42) number_of_in(sequential_pairs, all_20_4) = all_49_0 % 12.47/2.50 | | (43) number_of_in(triangles, all_20_4) = all_49_0 % 12.47/2.50 | | % 12.47/2.50 | | GROUND_INST: instantiating (5) with all_20_1, all_49_0, all_20_4, % 12.47/2.50 | | sequential_pairs, simplifying with (12), (42) gives: % 12.47/2.50 | | (44) all_49_0 = all_20_1 % 12.47/2.50 | | % 12.47/2.50 | | GROUND_INST: instantiating (5) with all_20_0, all_49_0, all_20_4, triangles, % 12.47/2.50 | | simplifying with (13), (43) gives: % 12.47/2.50 | | (45) all_49_0 = all_20_0 % 12.47/2.50 | | % 12.47/2.50 | | COMBINE_EQS: (44), (45) imply: % 12.47/2.50 | | (46) all_20_0 = all_20_1 % 12.47/2.50 | | % 12.47/2.50 | | REDUCE: (7), (46) imply: % 12.47/2.50 | | (47) $false % 12.47/2.50 | | % 12.47/2.50 | | CLOSE: (47) is inconsistent. % 12.47/2.50 | | % 12.47/2.50 | End of split % 12.47/2.50 | % 12.47/2.50 End of proof % 12.47/2.50 % SZS output end Proof for theBenchmark % 12.47/2.50 % 12.47/2.50 1838ms %------------------------------------------------------------------------------