%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA005+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 : n004.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 00:04:28 EDT 2023 % Result : Theorem 9.44s 2.18s % Output : Proof 13.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : GRA005+1 : TPTP v8.1.2. Bugfixed v3.2.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n004.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 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sun Aug 27 03:26:22 EDT 2023 % 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 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 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.27/1.19 Prover 4: Preprocessing ... % 3.27/1.20 Prover 1: Preprocessing ... % 3.81/1.27 Prover 3: Preprocessing ... % 3.81/1.27 Prover 6: Preprocessing ... % 3.81/1.27 Prover 2: Preprocessing ... % 3.81/1.27 Prover 0: Preprocessing ... % 3.81/1.27 Prover 5: Preprocessing ... % 8.10/1.95 Prover 1: Constructing countermodel ... % 8.10/1.96 Prover 3: Constructing countermodel ... % 8.10/1.98 Prover 6: Proving ... % 8.10/1.98 Prover 5: Proving ... % 8.10/1.99 Prover 2: Proving ... % 9.44/2.17 Prover 4: Constructing countermodel ... % 9.44/2.17 Prover 3: proved (1523ms) % 9.44/2.18 % 9.44/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.44/2.18 % 9.44/2.18 Prover 6: stopped % 9.44/2.18 Prover 2: stopped % 9.78/2.19 Prover 5: stopped % 9.78/2.19 Prover 0: Proving ... % 9.78/2.19 Prover 0: stopped % 9.78/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.78/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.78/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.78/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.78/2.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.23/2.28 Prover 8: Preprocessing ... % 10.23/2.29 Prover 7: Preprocessing ... % 10.23/2.29 Prover 10: Preprocessing ... % 10.23/2.29 Prover 11: Preprocessing ... % 10.61/2.31 Prover 13: Preprocessing ... % 11.55/2.48 Prover 10: Warning: ignoring some quantifiers % 11.87/2.50 Prover 8: Warning: ignoring some quantifiers % 11.87/2.50 Prover 13: Warning: ignoring some quantifiers % 11.87/2.51 Prover 8: Constructing countermodel ... % 11.87/2.51 Prover 10: Constructing countermodel ... % 11.87/2.51 Prover 7: Warning: ignoring some quantifiers % 11.87/2.52 Prover 13: Constructing countermodel ... % 11.87/2.53 Prover 7: Constructing countermodel ... % 12.35/2.61 Prover 4: Found proof (size 62) % 12.35/2.61 Prover 4: proved (1957ms) % 12.35/2.61 Prover 13: stopped % 12.35/2.61 Prover 8: stopped % 12.35/2.61 Prover 1: stopped % 12.35/2.61 Prover 10: stopped % 12.35/2.62 Prover 7: stopped % 12.35/2.66 Prover 11: Constructing countermodel ... % 12.35/2.67 Prover 11: stopped % 12.35/2.67 % 12.35/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.35/2.67 % 12.35/2.69 % SZS output start Proof for theBenchmark % 12.35/2.69 Assumptions after simplification: % 12.35/2.69 --------------------------------- % 12.35/2.69 % 12.35/2.69 (edge_ends_are_vertices) % 13.10/2.72 ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? [v2: any] % 13.10/2.72 : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (vertex(v4) = v5 & vertex(v1) % 13.10/2.72 = v3 & edge(v0) = v2 & tail_of(v0) = v4 & $i(v4) & ( ~ (v2 = 0) | (v5 = 0 % 13.10/2.72 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ % 13.10/2.72 $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 13.10/2.72 (vertex(v3) = v4 & vertex(v1) = v5 & head_of(v0) = v3 & edge(v0) = v2 & % 13.10/2.72 $i(v3) & ( ~ (v2 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ( ~ (edge(v0) % 13.10/2.72 = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (vertex(v2) = 0 & % 13.10/2.72 vertex(v1) = 0 & head_of(v0) = v1 & tail_of(v0) = v2 & $i(v2) & $i(v1))) % 13.10/2.72 % 13.10/2.72 (no_loops) % 13.10/2.72 ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? [v2: any] % 13.10/2.72 : ? [v3: $i] : (edge(v0) = v2 & tail_of(v0) = v3 & $i(v3) & ( ~ (v3 = v1) | % 13.10/2.72 ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ % 13.10/2.72 $i(v0) | ? [v2: any] : ? [v3: $i] : (head_of(v0) = v3 & edge(v0) = v2 & % 13.10/2.72 $i(v3) & ( ~ (v3 = v1) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (edge(v0) = 0) % 13.10/2.72 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & head_of(v0) = v1 & % 13.10/2.72 tail_of(v0) = v2 & $i(v2) & $i(v1))) % 13.10/2.72 % 13.10/2.72 (no_short_cut_edge) % 13.10/2.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.10/2.73 $i] : ? [v6: $i] : ? [v7: $i] : (shortest_path(v0, v1, v4) = 0 & % 13.10/2.73 precedes(v2, v3, v4) = 0 & head_of(v7) = v6 & head_of(v3) = v6 & edge(v7) = % 13.10/2.73 0 & tail_of(v7) = v5 & tail_of(v2) = v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) % 13.10/2.73 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.10/2.73 % 13.10/2.73 (shortest_path_properties) % 13.10/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.10/2.73 $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (head_of(v3) = % 13.10/2.73 v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 13.10/2.73 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (precedes(v3, v2, v4) = % 13.10/2.73 v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = 0) | ( ~ (v8 = 0) & ! [v9: $i] % 13.10/2.73 : ( ~ (head_of(v9) = v6) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v5) & % 13.10/2.73 tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = % 13.10/2.73 v5) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) = % 13.10/2.73 v10 & $i(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.10/2.73 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) | % 13.10/2.73 ~ (precedes(v3, v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 13.10/2.73 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 13.10/2.73 (precedes(v2, v3, v4) = v6 & head_of(v3) = v8 & tail_of(v2) = v7 & $i(v8) & % 13.10/2.73 $i(v7) & ( ~ (v6 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~ (head_of(v9) = % 13.10/2.73 v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v7) & tail_of(v9) = % 13.10/2.73 v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v7) | ~ $i(v9) % 13.10/2.73 | ? [v10: $i] : ( ~ (v10 = v8) & head_of(v9) = v10 & $i(v10))))))) % 13.10/2.73 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.10/2.73 (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | ~ $i(v4) % 13.10/2.73 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] % 13.10/2.73 : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & head_of(v3) = v6 % 13.10/2.73 & tail_of(v2) = v5 & $i(v6) & $i(v5) & ! [v8: $i] : ( ~ (head_of(v8) = % 13.10/2.73 v6) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v5) & tail_of(v8) = v9 & % 13.10/2.73 $i(v9))) & ! [v8: $i] : ( ~ (tail_of(v8) = v5) | ~ $i(v8) | ? [v9: % 13.10/2.73 $i] : ( ~ (v9 = v6) & head_of(v8) = v9 & $i(v9))))) % 13.10/2.73 % 13.10/2.73 (function-axioms) % 13.10/2.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.10/2.74 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ % 13.10/2.74 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.10/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 13.10/2.74 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & ! % 13.10/2.74 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.10/2.74 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ % 13.10/2.74 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.10/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 13.10/2.74 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 13.10/2.74 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ % 13.10/2.74 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.10/2.74 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = % 13.10/2.74 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.10/2.74 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ % 13.10/2.74 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.10/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.10/2.74 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0: % 13.10/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.10/2.74 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0: % 13.10/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.10/2.74 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0: % 13.10/2.74 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3, % 13.10/2.74 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 13.10/2.74 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & % 13.10/2.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 13.10/2.74 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1: % 13.10/2.74 $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = % 13.10/2.74 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.10/2.74 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : ! % 13.10/2.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = % 13.10/2.74 v0)) % 13.10/2.74 % 13.10/2.74 Further assumptions not needed in the proof: % 13.10/2.74 -------------------------------------------- % 13.10/2.74 complete_properties, graph_has_them_all, in_path_properties, length_defn, % 13.10/2.74 on_path_properties, path_defn, path_length_sequential_pairs, path_properties, % 13.10/2.74 precedes_defn, precedes_properties, sequential_defn, % 13.10/2.74 sequential_pairs_and_triangles, shortest_path_defn, triangle_defn % 13.10/2.74 % 13.10/2.74 Those formulas are unsatisfiable: % 13.10/2.74 --------------------------------- % 13.10/2.74 % 13.10/2.74 Begin of proof % 13.10/2.74 | % 13.10/2.74 | ALPHA: (no_loops) implies: % 13.37/2.74 | (1) ! [v0: $i] : ( ~ (edge(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 13.37/2.74 | $i] : ( ~ (v2 = v1) & head_of(v0) = v1 & tail_of(v0) = v2 & $i(v2) % 13.37/2.74 | & $i(v1))) % 13.37/2.74 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ $i(v0) | ? % 13.37/2.74 | [v2: any] : ? [v3: $i] : (head_of(v0) = v3 & edge(v0) = v2 & $i(v3) % 13.37/2.74 | & ( ~ (v3 = v1) | ~ (v2 = 0)))) % 13.37/2.75 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? % 13.37/2.75 | [v2: any] : ? [v3: $i] : (edge(v0) = v2 & tail_of(v0) = v3 & $i(v3) % 13.37/2.75 | & ( ~ (v3 = v1) | ~ (v2 = 0)))) % 13.37/2.75 | % 13.37/2.75 | ALPHA: (edge_ends_are_vertices) implies: % 13.37/2.75 | (4) ! [v0: $i] : ( ~ (edge(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 13.37/2.75 | $i] : (vertex(v2) = 0 & vertex(v1) = 0 & head_of(v0) = v1 & % 13.37/2.75 | tail_of(v0) = v2 & $i(v2) & $i(v1))) % 13.37/2.75 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ $i(v0) | ? % 13.37/2.75 | [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : (vertex(v3) = % 13.37/2.75 | v4 & vertex(v1) = v5 & head_of(v0) = v3 & edge(v0) = v2 & $i(v3) & % 13.37/2.75 | ( ~ (v2 = 0) | (v5 = 0 & v4 = 0)))) % 13.37/2.75 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? % 13.37/2.75 | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (vertex(v4) = % 13.37/2.75 | v5 & vertex(v1) = v3 & edge(v0) = v2 & tail_of(v0) = v4 & $i(v4) & % 13.37/2.75 | ( ~ (v2 = 0) | (v5 = 0 & v3 = 0)))) % 13.37/2.75 | % 13.37/2.75 | ALPHA: (shortest_path_properties) implies: % 13.37/2.75 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 13.37/2.75 | ! [v5: $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ % 13.37/2.75 | (head_of(v3) = v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 13.37/2.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 13.37/2.75 | (precedes(v3, v2, v4) = v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = 0) % 13.37/2.75 | | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ (head_of(v9) = v6) | ~ $i(v9) % 13.37/2.75 | | ? [v10: $i] : ( ~ (v10 = v5) & tail_of(v9) = v10 & % 13.37/2.75 | $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v5) | ~ % 13.37/2.75 | $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) = v10 & % 13.37/2.75 | $i(v10))))))) % 13.37/2.75 | % 13.37/2.75 | ALPHA: (function-axioms) implies: % 13.37/2.75 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = % 13.37/2.75 | v1) | ~ (tail_of(v2) = v0)) % 13.37/2.75 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = % 13.37/2.75 | v1) | ~ (head_of(v2) = v0)) % 13.37/2.75 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.37/2.75 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = % 13.37/2.75 | v1) | ~ (precedes(v4, v3, v2) = v0)) % 13.37/2.75 | % 13.37/2.75 | DELTA: instantiating (no_short_cut_edge) with fresh symbols all_20_0, % 13.37/2.75 | all_20_1, all_20_2, all_20_3, all_20_4, all_20_5, all_20_6, all_20_7 % 13.37/2.75 | gives: % 13.37/2.76 | (11) shortest_path(all_20_7, all_20_6, all_20_3) = 0 & precedes(all_20_5, % 13.37/2.76 | all_20_4, all_20_3) = 0 & head_of(all_20_0) = all_20_1 & % 13.37/2.76 | head_of(all_20_4) = all_20_1 & edge(all_20_0) = 0 & tail_of(all_20_0) % 13.37/2.76 | = all_20_2 & tail_of(all_20_5) = all_20_2 & $i(all_20_0) & % 13.37/2.76 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) & % 13.37/2.76 | $i(all_20_5) & $i(all_20_6) & $i(all_20_7) % 13.37/2.76 | % 13.37/2.76 | ALPHA: (11) implies: % 13.37/2.76 | (12) $i(all_20_7) % 13.37/2.76 | (13) $i(all_20_6) % 13.37/2.76 | (14) $i(all_20_5) % 13.37/2.76 | (15) $i(all_20_4) % 13.37/2.76 | (16) $i(all_20_3) % 13.37/2.76 | (17) $i(all_20_0) % 13.37/2.76 | (18) tail_of(all_20_5) = all_20_2 % 13.37/2.76 | (19) tail_of(all_20_0) = all_20_2 % 13.37/2.76 | (20) edge(all_20_0) = 0 % 13.37/2.76 | (21) head_of(all_20_4) = all_20_1 % 13.37/2.76 | (22) head_of(all_20_0) = all_20_1 % 13.37/2.76 | (23) precedes(all_20_5, all_20_4, all_20_3) = 0 % 13.37/2.76 | (24) shortest_path(all_20_7, all_20_6, all_20_3) = 0 % 13.37/2.76 | % 13.37/2.76 | GROUND_INST: instantiating (5) with all_20_0, all_20_2, simplifying with (17), % 13.37/2.76 | (19) gives: % 13.37/2.76 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (vertex(v1) % 13.37/2.76 | = v2 & vertex(all_20_2) = v3 & head_of(all_20_0) = v1 & % 13.37/2.76 | edge(all_20_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 13.37/2.76 | % 13.37/2.76 | GROUND_INST: instantiating (2) with all_20_0, all_20_2, simplifying with (17), % 13.37/2.76 | (19) gives: % 13.37/2.76 | (26) ? [v0: any] : ? [v1: $i] : (head_of(all_20_0) = v1 & edge(all_20_0) % 13.37/2.76 | = v0 & $i(v1) & ( ~ (v1 = all_20_2) | ~ (v0 = 0))) % 13.37/2.76 | % 13.37/2.76 | GROUND_INST: instantiating (1) with all_20_0, simplifying with (17), (20) % 13.37/2.76 | gives: % 13.37/2.76 | (27) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & head_of(all_20_0) = v0 & % 13.37/2.76 | tail_of(all_20_0) = v1 & $i(v1) & $i(v0)) % 13.37/2.76 | % 13.37/2.76 | GROUND_INST: instantiating (4) with all_20_0, simplifying with (17), (20) % 13.37/2.76 | gives: % 13.37/2.76 | (28) ? [v0: $i] : ? [v1: $i] : (vertex(v1) = 0 & vertex(v0) = 0 & % 13.37/2.76 | head_of(all_20_0) = v0 & tail_of(all_20_0) = v1 & $i(v1) & $i(v0)) % 13.37/2.76 | % 13.37/2.76 | GROUND_INST: instantiating (6) with all_20_0, all_20_1, simplifying with (17), % 13.37/2.76 | (22) gives: % 13.37/2.76 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : (vertex(v2) % 13.37/2.76 | = v3 & vertex(all_20_1) = v1 & edge(all_20_0) = v0 & % 13.37/2.77 | tail_of(all_20_0) = v2 & $i(v2) & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0))) % 13.37/2.77 | % 13.37/2.77 | GROUND_INST: instantiating (3) with all_20_0, all_20_1, simplifying with (17), % 13.37/2.77 | (22) gives: % 13.37/2.77 | (30) ? [v0: any] : ? [v1: $i] : (edge(all_20_0) = v0 & tail_of(all_20_0) % 13.37/2.77 | = v1 & $i(v1) & ( ~ (v1 = all_20_1) | ~ (v0 = 0))) % 13.37/2.77 | % 13.37/2.77 | GROUND_INST: instantiating (7) with all_20_7, all_20_6, all_20_5, all_20_4, % 13.37/2.77 | all_20_3, all_20_2, all_20_1, simplifying with (12), (13), (14), % 13.37/2.77 | (15), (16), (18), (21), (24) gives: % 13.37/2.77 | (31) ? [v0: any] : ? [v1: any] : (precedes(all_20_4, all_20_5, all_20_3) % 13.37/2.77 | = v1 & precedes(all_20_5, all_20_4, all_20_3) = v0 & ( ~ (v0 = 0) | % 13.37/2.77 | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) = all_20_1) | ~ % 13.37/2.77 | $i(v2) | ? [v3: any] : ( ~ (v3 = all_20_2) & tail_of(v2) = v3 % 13.37/2.77 | & $i(v3))) & ! [v2: $i] : ( ~ (tail_of(v2) = all_20_2) | ~ % 13.37/2.77 | $i(v2) | ? [v3: any] : ( ~ (v3 = all_20_1) & head_of(v2) = v3 % 13.37/2.77 | & $i(v3)))))) % 13.37/2.77 | % 13.37/2.77 | DELTA: instantiating (30) with fresh symbols all_27_0, all_27_1 gives: % 13.37/2.77 | (32) edge(all_20_0) = all_27_1 & tail_of(all_20_0) = all_27_0 & % 13.37/2.77 | $i(all_27_0) & ( ~ (all_27_0 = all_20_1) | ~ (all_27_1 = 0)) % 13.37/2.77 | % 13.37/2.77 | ALPHA: (32) implies: % 13.37/2.77 | (33) tail_of(all_20_0) = all_27_0 % 13.37/2.77 | % 13.37/2.77 | DELTA: instantiating (27) with fresh symbols all_31_0, all_31_1 gives: % 13.37/2.77 | (34) ~ (all_31_0 = all_31_1) & head_of(all_20_0) = all_31_1 & % 13.37/2.77 | tail_of(all_20_0) = all_31_0 & $i(all_31_0) & $i(all_31_1) % 13.37/2.77 | % 13.37/2.77 | ALPHA: (34) implies: % 13.37/2.77 | (35) tail_of(all_20_0) = all_31_0 % 13.37/2.77 | (36) head_of(all_20_0) = all_31_1 % 13.37/2.77 | % 13.37/2.77 | DELTA: instantiating (26) with fresh symbols all_33_0, all_33_1 gives: % 13.37/2.77 | (37) head_of(all_20_0) = all_33_0 & edge(all_20_0) = all_33_1 & % 13.37/2.77 | $i(all_33_0) & ( ~ (all_33_0 = all_20_2) | ~ (all_33_1 = 0)) % 13.37/2.77 | % 13.37/2.77 | ALPHA: (37) implies: % 13.37/2.77 | (38) head_of(all_20_0) = all_33_0 % 13.37/2.77 | % 13.37/2.77 | DELTA: instantiating (28) with fresh symbols all_39_0, all_39_1 gives: % 13.37/2.77 | (39) vertex(all_39_0) = 0 & vertex(all_39_1) = 0 & head_of(all_20_0) = % 13.37/2.77 | all_39_1 & tail_of(all_20_0) = all_39_0 & $i(all_39_0) & $i(all_39_1) % 13.37/2.77 | % 13.37/2.77 | ALPHA: (39) implies: % 13.37/2.77 | (40) tail_of(all_20_0) = all_39_0 % 13.37/2.77 | (41) head_of(all_20_0) = all_39_1 % 13.37/2.77 | % 13.37/2.77 | DELTA: instantiating (29) with fresh symbols all_45_0, all_45_1, all_45_2, % 13.37/2.77 | all_45_3 gives: % 13.37/2.77 | (42) vertex(all_45_1) = all_45_0 & vertex(all_20_1) = all_45_2 & % 13.37/2.77 | edge(all_20_0) = all_45_3 & tail_of(all_20_0) = all_45_1 & % 13.37/2.77 | $i(all_45_1) & ( ~ (all_45_3 = 0) | (all_45_0 = 0 & all_45_2 = 0)) % 13.37/2.77 | % 13.37/2.77 | ALPHA: (42) implies: % 13.37/2.77 | (43) tail_of(all_20_0) = all_45_1 % 13.37/2.77 | % 13.37/2.77 | DELTA: instantiating (25) with fresh symbols all_47_0, all_47_1, all_47_2, % 13.37/2.77 | all_47_3 gives: % 13.37/2.77 | (44) vertex(all_47_2) = all_47_1 & vertex(all_20_2) = all_47_0 & % 13.37/2.77 | head_of(all_20_0) = all_47_2 & edge(all_20_0) = all_47_3 & % 13.37/2.77 | $i(all_47_2) & ( ~ (all_47_3 = 0) | (all_47_0 = 0 & all_47_1 = 0)) % 13.37/2.77 | % 13.37/2.77 | ALPHA: (44) implies: % 13.37/2.77 | (45) head_of(all_20_0) = all_47_2 % 13.37/2.78 | % 13.37/2.78 | DELTA: instantiating (31) with fresh symbols all_49_0, all_49_1 gives: % 13.37/2.78 | (46) precedes(all_20_4, all_20_5, all_20_3) = all_49_0 & precedes(all_20_5, % 13.37/2.78 | all_20_4, all_20_3) = all_49_1 & ( ~ (all_49_1 = 0) | ( ~ (all_49_0 % 13.37/2.78 | = 0) & ! [v0: $i] : ( ~ (head_of(v0) = all_20_1) | ~ $i(v0) | % 13.37/2.78 | ? [v1: any] : ( ~ (v1 = all_20_2) & tail_of(v0) = v1 & $i(v1))) % 13.37/2.78 | & ! [v0: $i] : ( ~ (tail_of(v0) = all_20_2) | ~ $i(v0) | ? [v1: % 13.37/2.78 | any] : ( ~ (v1 = all_20_1) & head_of(v0) = v1 & $i(v1))))) % 13.37/2.78 | % 13.37/2.78 | ALPHA: (46) implies: % 13.37/2.78 | (47) precedes(all_20_5, all_20_4, all_20_3) = all_49_1 % 13.37/2.78 | (48) ~ (all_49_1 = 0) | ( ~ (all_49_0 = 0) & ! [v0: $i] : ( ~ % 13.37/2.78 | (head_of(v0) = all_20_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 13.37/2.78 | all_20_2) & tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ % 13.37/2.78 | (tail_of(v0) = all_20_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 13.37/2.78 | all_20_1) & head_of(v0) = v1 & $i(v1)))) % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (8) with all_31_0, all_39_0, all_20_0, simplifying % 13.37/2.78 | with (35), (40) gives: % 13.37/2.78 | (49) all_39_0 = all_31_0 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (8) with all_27_0, all_39_0, all_20_0, simplifying % 13.37/2.78 | with (33), (40) gives: % 13.37/2.78 | (50) all_39_0 = all_27_0 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (8) with all_20_2, all_45_1, all_20_0, simplifying % 13.37/2.78 | with (19), (43) gives: % 13.37/2.78 | (51) all_45_1 = all_20_2 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (8) with all_39_0, all_45_1, all_20_0, simplifying % 13.37/2.78 | with (40), (43) gives: % 13.37/2.78 | (52) all_45_1 = all_39_0 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (9) with all_31_1, all_39_1, all_20_0, simplifying % 13.37/2.78 | with (36), (41) gives: % 13.37/2.78 | (53) all_39_1 = all_31_1 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (9) with all_20_1, all_47_2, all_20_0, simplifying % 13.37/2.78 | with (22), (45) gives: % 13.37/2.78 | (54) all_47_2 = all_20_1 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (9) with all_39_1, all_47_2, all_20_0, simplifying % 13.37/2.78 | with (41), (45) gives: % 13.37/2.78 | (55) all_47_2 = all_39_1 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (9) with all_33_0, all_47_2, all_20_0, simplifying % 13.37/2.78 | with (38), (45) gives: % 13.37/2.78 | (56) all_47_2 = all_33_0 % 13.37/2.78 | % 13.37/2.78 | GROUND_INST: instantiating (10) with 0, all_49_1, all_20_3, all_20_4, % 13.37/2.78 | all_20_5, simplifying with (23), (47) gives: % 13.37/2.78 | (57) all_49_1 = 0 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (55), (56) imply: % 13.37/2.78 | (58) all_39_1 = all_33_0 % 13.37/2.78 | % 13.37/2.78 | SIMP: (58) implies: % 13.37/2.78 | (59) all_39_1 = all_33_0 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (54), (56) imply: % 13.37/2.78 | (60) all_33_0 = all_20_1 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (51), (52) imply: % 13.37/2.78 | (61) all_39_0 = all_20_2 % 13.37/2.78 | % 13.37/2.78 | SIMP: (61) implies: % 13.37/2.78 | (62) all_39_0 = all_20_2 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (49), (62) imply: % 13.37/2.78 | (63) all_31_0 = all_20_2 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (49), (50) imply: % 13.37/2.78 | (64) all_31_0 = all_27_0 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (53), (59) imply: % 13.37/2.78 | (65) all_33_0 = all_31_1 % 13.37/2.78 | % 13.37/2.78 | SIMP: (65) implies: % 13.37/2.78 | (66) all_33_0 = all_31_1 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (60), (66) imply: % 13.37/2.78 | (67) all_31_1 = all_20_1 % 13.37/2.78 | % 13.37/2.78 | SIMP: (67) implies: % 13.37/2.78 | (68) all_31_1 = all_20_1 % 13.37/2.78 | % 13.37/2.78 | COMBINE_EQS: (63), (64) imply: % 13.37/2.78 | (69) all_27_0 = all_20_2 % 13.37/2.78 | % 13.37/2.79 | SIMP: (69) implies: % 13.37/2.79 | (70) all_27_0 = all_20_2 % 13.37/2.79 | % 13.37/2.79 | BETA: splitting (48) gives: % 13.37/2.79 | % 13.37/2.79 | Case 1: % 13.37/2.79 | | % 13.37/2.79 | | (71) ~ (all_49_1 = 0) % 13.37/2.79 | | % 13.37/2.79 | | REDUCE: (57), (71) imply: % 13.37/2.79 | | (72) $false % 13.37/2.79 | | % 13.37/2.79 | | CLOSE: (72) is inconsistent. % 13.37/2.79 | | % 13.37/2.79 | Case 2: % 13.37/2.79 | | % 13.37/2.79 | | (73) ~ (all_49_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) = all_20_1) | ~ % 13.37/2.79 | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_20_2) & tail_of(v0) = v1 & % 13.37/2.79 | | $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = all_20_2) | ~ % 13.37/2.79 | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_20_1) & head_of(v0) = v1 & % 13.37/2.79 | | $i(v1))) % 13.37/2.79 | | % 13.37/2.79 | | ALPHA: (73) implies: % 13.37/2.79 | | (74) ! [v0: $i] : ( ~ (head_of(v0) = all_20_1) | ~ $i(v0) | ? [v1: % 13.37/2.79 | | any] : ( ~ (v1 = all_20_2) & tail_of(v0) = v1 & $i(v1))) % 13.37/2.79 | | % 13.37/2.79 | | GROUND_INST: instantiating (74) with all_20_0, simplifying with (17), (22) % 13.37/2.79 | | gives: % 13.37/2.79 | | (75) ? [v0: any] : ( ~ (v0 = all_20_2) & tail_of(all_20_0) = v0 & % 13.37/2.79 | | $i(v0)) % 13.37/2.79 | | % 13.37/2.79 | | DELTA: instantiating (75) with fresh symbol all_84_0 gives: % 13.37/2.79 | | (76) ~ (all_84_0 = all_20_2) & tail_of(all_20_0) = all_84_0 & % 13.37/2.79 | | $i(all_84_0) % 13.37/2.79 | | % 13.37/2.79 | | ALPHA: (76) implies: % 13.37/2.79 | | (77) ~ (all_84_0 = all_20_2) % 13.37/2.79 | | (78) tail_of(all_20_0) = all_84_0 % 13.37/2.79 | | % 13.37/2.79 | | GROUND_INST: instantiating (8) with all_20_2, all_84_0, all_20_0, % 13.37/2.79 | | simplifying with (19), (78) gives: % 13.37/2.79 | | (79) all_84_0 = all_20_2 % 13.37/2.79 | | % 13.37/2.79 | | REDUCE: (77), (79) imply: % 13.37/2.79 | | (80) $false % 13.37/2.79 | | % 13.37/2.79 | | CLOSE: (80) is inconsistent. % 13.37/2.79 | | % 13.37/2.79 | End of split % 13.37/2.79 | % 13.37/2.79 End of proof % 13.37/2.79 % SZS output end Proof for theBenchmark % 13.37/2.79 % 13.37/2.79 2167ms %------------------------------------------------------------------------------