%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 29.90s 4.80s % Output : Proof 79.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.19/0.35 % Computer : n028.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Sun Aug 27 03:46:23 EDT 2023 % 0.19/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 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 ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 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 % 2.99/1.11 Prover 1: Preprocessing ... % 2.99/1.11 Prover 4: Preprocessing ... % 3.36/1.14 Prover 6: Preprocessing ... % 3.36/1.14 Prover 5: Preprocessing ... % 3.36/1.14 Prover 2: Preprocessing ... % 3.36/1.15 Prover 0: Preprocessing ... % 3.36/1.15 Prover 3: Preprocessing ... % 7.32/1.77 Prover 1: Constructing countermodel ... % 7.82/1.80 Prover 6: Proving ... % 7.82/1.80 Prover 5: Proving ... % 7.82/1.81 Prover 3: Constructing countermodel ... % 7.82/1.83 Prover 2: Proving ... % 8.98/1.99 Prover 0: Proving ... % 8.98/2.04 Prover 4: Constructing countermodel ... % 29.90/4.79 Prover 5: proved (4156ms) % 29.90/4.80 % 29.90/4.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.90/4.80 % 30.49/4.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 30.49/4.81 Prover 3: stopped % 30.49/4.82 Prover 0: stopped % 30.49/4.82 Prover 6: stopped % 30.49/4.86 Prover 2: stopped % 30.49/4.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 30.49/4.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 30.49/4.86 Prover 7: Preprocessing ... % 30.49/4.86 Prover 8: Preprocessing ... % 30.49/4.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 30.49/4.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 31.02/4.93 Prover 10: Preprocessing ... % 31.02/4.96 Prover 11: Preprocessing ... % 31.02/4.99 Prover 10: Warning: ignoring some quantifiers % 31.02/4.99 Prover 13: Preprocessing ... % 31.02/5.01 Prover 10: Constructing countermodel ... % 31.02/5.04 Prover 8: Warning: ignoring some quantifiers % 31.02/5.05 Prover 8: Constructing countermodel ... % 31.02/5.07 Prover 10: gave up % 31.02/5.08 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 31.02/5.09 Prover 7: Warning: ignoring some quantifiers % 31.02/5.10 Prover 7: Constructing countermodel ... % 32.63/5.14 Prover 7: gave up % 32.63/5.14 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 32.90/5.15 Prover 13: Warning: ignoring some quantifiers % 32.90/5.16 Prover 16: Preprocessing ... % 32.90/5.17 Prover 13: Constructing countermodel ... % 33.13/5.19 Prover 19: Preprocessing ... % 33.13/5.20 Prover 11: Constructing countermodel ... % 33.67/5.25 Prover 16: Warning: ignoring some quantifiers % 33.67/5.27 Prover 16: Constructing countermodel ... % 34.23/5.37 Prover 19: Warning: ignoring some quantifiers % 34.64/5.38 Prover 19: Constructing countermodel ... % 68.07/10.01 Prover 13: stopped % 68.07/10.02 Prover 19: stopped % 78.26/11.24 Prover 16: Found proof (size 137) % 78.26/11.24 Prover 16: proved (6160ms) % 78.26/11.25 Prover 8: stopped % 78.26/11.25 Prover 11: stopped % 78.26/11.25 Prover 1: stopped % 78.26/11.25 Prover 4: stopped % 78.26/11.25 % 78.26/11.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 78.26/11.25 % 78.85/11.28 % SZS output start Proof for theBenchmark % 78.85/11.28 Assumptions after simplification: % 78.85/11.28 --------------------------------- % 78.85/11.28 % 78.85/11.28 (back_edge) % 78.85/11.31 ~ complete | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 78.85/11.31 $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.31 shortest_path(v0, v1, v4) | ~ precedes(v2, v3, v4) | ? [v5: $i] : ? [v6: % 78.85/11.31 $i] : ? [v7: $i] : (head_of(v7) = v6 & head_of(v3) = v5 & tail_of(v7) = % 78.85/11.31 v5 & tail_of(v2) = v6 & $i(v7) & $i(v6) & $i(v5) & edge(v7))) % 78.85/11.31 % 78.85/11.31 (edge_ends_are_vertices) % 78.85/11.31 ! [v0: $i] : ( ~ $i(v0) | ~ edge(v0) | ? [v1: $i] : ? [v2: $i] : % 78.85/11.31 (head_of(v0) = v1 & tail_of(v0) = v2 & $i(v2) & $i(v1) & vertex(v2) & % 78.85/11.31 vertex(v1))) % 78.85/11.31 % 78.85/11.31 (no_loops) % 78.85/11.31 ! [v0: $i] : ( ~ $i(v0) | ~ edge(v0) | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 78.85/11.31 v1) & head_of(v0) = v1 & tail_of(v0) = v2 & $i(v2) & $i(v1))) % 78.85/11.31 % 78.85/11.31 (on_path_properties) % 78.85/11.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 78.85/11.31 | ~ $i(v1) | ~ $i(v0) | ~ on_path(v3, v2) | ~ path(v0, v1, v2) | % 78.85/11.31 edge(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 78.85/11.31 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ on_path(v3, v2) | ~ % 78.85/11.31 path(v0, v1, v2) | ? [v4: $i] : ? [v5: $i] : (head_of(v3) = v4 & % 78.85/11.31 tail_of(v3) = v5 & $i(v5) & $i(v4) & in_path(v5, v2) & in_path(v4, v2))) % 78.85/11.31 % 78.85/11.31 (precedes_properties) % 78.85/11.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 78.85/11.32 $i] : ( ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 78.85/11.32 | ~ precedes(v3, v2, v0) | ~ precedes(v1, v2, v0) | ~ sequential(v1, v3) % 78.85/11.32 | ~ sequential(v1, v2) | ~ path(v4, v5, v0)) & ! [v0: $i] : ! [v1: $i] : % 78.85/11.32 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 78.85/11.32 ~ $i(v1) | ~ $i(v0) | ~ precedes(v1, v2, v0) | ~ path(v3, v4, v0) | % 78.85/11.32 sequential(v1, v2) | ? [v5: $i] : ($i(v5) & precedes(v5, v2, v0) & % 78.85/11.32 sequential(v1, v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 78.85/11.32 $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 78.85/11.32 $i(v0) | ~ precedes(v1, v2, v0) | ~ path(v3, v4, v0) | on_path(v2, v0)) & % 78.85/11.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 78.85/11.32 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ precedes(v1, v2, % 78.85/11.32 v0) | ~ path(v3, v4, v0) | on_path(v1, v0)) % 78.85/11.32 % 78.85/11.32 (sequential_defn) % 78.85/11.33 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ edge(v1) | % 78.85/11.33 ~ edge(v0) | sequential(v0, v1) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) % 78.85/11.33 & head_of(v0) = v2 & tail_of(v1) = v3 & $i(v3) & $i(v2))) & ! [v0: $i] : % 78.85/11.33 ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sequential(v0, v1) | edge(v1)) & ! % 78.85/11.33 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sequential(v0, v1) | % 78.85/11.33 edge(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.33 sequential(v0, v1) | ? [v2: $i] : (head_of(v0) = v2 & tail_of(v1) = v2 & % 78.85/11.33 $i(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~ sequential(v0, v0)) % 78.85/11.33 % 78.85/11.33 (sequential_is_triangle) % 78.85/11.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v4) % 78.85/11.33 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & shortest_path(v0, v1, v4) & % 78.85/11.33 precedes(v2, v3, v4) & sequential(v2, v3) & complete & ! [v5: $i] : ( ~ % 78.85/11.33 $i(v5) | ~ triangle(v2, v3, v5))) % 78.85/11.33 % 78.85/11.33 (shortest_path_defn) % 78.85/11.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ $i(v2) | ~ $i(v1) | % 78.85/11.34 ~ $i(v0) | ~ path(v0, v1, v2) | shortest_path(v0, v1, v2) | ? [v3: $i] : % 78.85/11.34 ? [v4: $i] : ? [v5: $i] : (length_of(v4) = v5 & length_of(v2) = v3 & $i(v5) % 78.85/11.34 & $i(v4) & $i(v3) & path(v0, v1, v4) & ~ less_or_equal(v3, v5))) & ! % 78.85/11.34 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.34 shortest_path(v0, v1, v2) | path(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : % 78.85/11.34 ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ shortest_path(v0, v1, v2) % 78.85/11.34 | ? [v3: $i] : (length_of(v2) = v3 & $i(v3) & ! [v4: $i] : ( ~ $i(v4) | ~ % 78.85/11.34 path(v0, v1, v4) | ? [v5: $i] : (length_of(v4) = v5 & $i(v5) & % 78.85/11.34 less_or_equal(v3, v5))))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 78.85/11.34 ~ $i(v0) | ~ shortest_path(v0, v0, v1)) % 78.85/11.34 % 78.85/11.34 (shortest_path_properties) % 78.85/11.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 78.85/11.34 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.34 shortest_path(v0, v1, v4) | ~ precedes(v3, v2, v4) | ~ precedes(v2, v3, % 78.85/11.34 v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 78.85/11.34 : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.34 shortest_path(v0, v1, v4) | ~ precedes(v2, v3, v4) | ? [v5: $i] : ? [v6: % 78.85/11.34 $i] : (head_of(v3) = v6 & tail_of(v2) = v5 & $i(v6) & $i(v5) & ? [v7: $i] % 78.85/11.34 : ( ~ $i(v7) | ? [v8: $i] : ? [v9: $i] : (( ~ (v9 = v6) & head_of(v7) = % 78.85/11.34 v9 & $i(v9)) | ( ~ (v8 = v5) & tail_of(v7) = v8 & $i(v8)))))) % 78.85/11.34 % 78.85/11.34 (triangle_defn) % 78.85/11.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 78.85/11.35 ~ triangle(v0, v1, v2) | sequential(v2, v0)) & ! [v0: $i] : ! [v1: $i] : % 78.85/11.35 ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ triangle(v0, v1, v2) | % 78.85/11.35 sequential(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 78.85/11.35 ~ $i(v1) | ~ $i(v0) | ~ triangle(v0, v1, v2) | sequential(v0, v1)) & ! % 78.85/11.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.35 triangle(v0, v1, v2) | edge(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 78.85/11.35 ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ triangle(v0, v1, v2) | edge(v1)) & ! % 78.85/11.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.35 triangle(v0, v1, v2) | edge(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 78.85/11.35 ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sequential(v2, v0) | ~ sequential(v1, % 78.85/11.35 v2) | ~ sequential(v0, v1) | ~ edge(v2) | ~ edge(v1) | ~ edge(v0) | % 78.85/11.35 triangle(v0, v1, v2)) % 78.85/11.35 % 78.85/11.35 (function-axioms) % 78.85/11.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.85/11.35 (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 78.85/11.35 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ % 78.85/11.35 (number_of_in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.85/11.35 [v3: $i] : (v1 = v0 | ~ (path_cons(v3, v2) = v1) | ~ (path_cons(v3, v2) = % 78.85/11.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 78.85/11.35 (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 78.85/11.35 : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = v0)) & ! % 78.85/11.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ % 78.85/11.35 (tail_of(v2) = v0)) % 78.85/11.35 % 78.85/11.35 Further assumptions not needed in the proof: % 78.85/11.35 -------------------------------------------- % 78.85/11.35 complete_properties, graph_has_them_all, in_path_properties, length_defn, % 78.85/11.35 path_defn, path_length_sequential_pairs, path_properties, precedes_defn, % 78.85/11.35 sequential_pairs_and_triangles % 78.85/11.35 % 78.85/11.35 Those formulas are unsatisfiable: % 78.85/11.35 --------------------------------- % 78.85/11.35 % 78.85/11.35 Begin of proof % 78.85/11.35 | % 78.85/11.35 | ALPHA: (on_path_properties) implies: % 78.85/11.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 78.85/11.35 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ on_path(v3, v2) | ~ path(v0, v1, % 78.85/11.35 | v2) | ? [v4: $i] : ? [v5: $i] : (head_of(v3) = v4 & tail_of(v3) = % 78.85/11.35 | v5 & $i(v5) & $i(v4) & in_path(v5, v2) & in_path(v4, v2))) % 78.85/11.35 | % 78.85/11.35 | ALPHA: (sequential_defn) implies: % 78.85/11.35 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sequential(v0, % 78.85/11.35 | v1) | ? [v2: $i] : (head_of(v0) = v2 & tail_of(v1) = v2 & $i(v2))) % 78.85/11.36 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sequential(v0, % 78.85/11.36 | v1) | edge(v0)) % 78.85/11.36 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sequential(v0, % 78.85/11.36 | v1) | edge(v1)) % 78.85/11.36 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.36 | edge(v1) | ~ edge(v0) | sequential(v0, v1) | ? [v2: $i] : ? [v3: % 78.85/11.36 | $i] : ( ~ (v3 = v2) & head_of(v0) = v2 & tail_of(v1) = v3 & $i(v3) % 78.85/11.36 | & $i(v2))) % 78.85/11.36 | % 78.85/11.36 | ALPHA: (precedes_properties) implies: % 78.85/11.36 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 78.85/11.36 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.36 | precedes(v1, v2, v0) | ~ path(v3, v4, v0) | on_path(v1, v0)) % 78.85/11.36 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 78.85/11.36 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.36 | precedes(v1, v2, v0) | ~ path(v3, v4, v0) | on_path(v2, v0)) % 78.85/11.36 | % 78.85/11.36 | ALPHA: (shortest_path_defn) implies: % 78.85/11.36 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 78.85/11.36 | $i(v0) | ~ shortest_path(v0, v1, v2) | path(v0, v1, v2)) % 78.85/11.36 | % 78.85/11.36 | ALPHA: (shortest_path_properties) implies: % 78.85/11.36 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 78.85/11.36 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.36 | shortest_path(v0, v1, v4) | ~ precedes(v2, v3, v4) | ? [v5: $i] : % 78.85/11.36 | ? [v6: $i] : (head_of(v3) = v6 & tail_of(v2) = v5 & $i(v6) & $i(v5) & % 78.85/11.36 | ? [v7: $i] : ( ~ $i(v7) | ? [v8: $i] : ? [v9: $i] : (( ~ (v9 = % 78.85/11.36 | v6) & head_of(v7) = v9 & $i(v9)) | ( ~ (v8 = v5) & % 78.85/11.36 | tail_of(v7) = v8 & $i(v8)))))) % 78.85/11.36 | % 78.85/11.36 | ALPHA: (triangle_defn) implies: % 78.85/11.36 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 78.85/11.36 | $i(v0) | ~ sequential(v2, v0) | ~ sequential(v1, v2) | ~ % 78.85/11.36 | sequential(v0, v1) | ~ edge(v2) | ~ edge(v1) | ~ edge(v0) | % 78.85/11.36 | triangle(v0, v1, v2)) % 78.85/11.36 | % 78.85/11.36 | ALPHA: (function-axioms) implies: % 78.85/11.36 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = % 78.85/11.36 | v1) | ~ (tail_of(v2) = v0)) % 78.85/11.36 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = % 78.85/11.36 | v1) | ~ (head_of(v2) = v0)) % 78.85/11.36 | % 78.85/11.36 | DELTA: instantiating (sequential_is_triangle) with fresh symbols all_19_0, % 78.85/11.36 | all_19_1, all_19_2, all_19_3, all_19_4 gives: % 78.85/11.37 | (13) $i(all_19_0) & $i(all_19_1) & $i(all_19_2) & $i(all_19_3) & % 78.85/11.37 | $i(all_19_4) & shortest_path(all_19_4, all_19_3, all_19_0) & % 78.85/11.37 | precedes(all_19_2, all_19_1, all_19_0) & sequential(all_19_2, % 78.85/11.37 | all_19_1) & complete & ! [v0: $i] : ( ~ $i(v0) | ~ % 78.85/11.37 | triangle(all_19_2, all_19_1, v0)) % 78.85/11.37 | % 78.85/11.37 | ALPHA: (13) implies: % 78.85/11.37 | (14) complete % 78.85/11.37 | (15) sequential(all_19_2, all_19_1) % 78.85/11.37 | (16) precedes(all_19_2, all_19_1, all_19_0) % 78.85/11.37 | (17) shortest_path(all_19_4, all_19_3, all_19_0) % 78.85/11.37 | (18) $i(all_19_4) % 78.85/11.37 | (19) $i(all_19_3) % 78.85/11.37 | (20) $i(all_19_2) % 78.85/11.37 | (21) $i(all_19_1) % 78.85/11.37 | (22) $i(all_19_0) % 78.85/11.37 | (23) ! [v0: $i] : ( ~ $i(v0) | ~ triangle(all_19_2, all_19_1, v0)) % 78.85/11.37 | % 78.85/11.37 | BETA: splitting (back_edge) gives: % 78.85/11.37 | % 78.85/11.37 | Case 1: % 78.85/11.37 | | % 78.85/11.37 | | (24) ~ complete % 78.85/11.37 | | % 78.85/11.37 | | PRED_UNIFY: (14), (24) imply: % 78.85/11.37 | | (25) $false % 78.85/11.37 | | % 78.85/11.37 | | CLOSE: (25) is inconsistent. % 78.85/11.37 | | % 78.85/11.37 | Case 2: % 78.85/11.37 | | % 78.85/11.38 | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 78.85/11.38 | | : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.85/11.38 | | shortest_path(v0, v1, v4) | ~ precedes(v2, v3, v4) | ? [v5: $i] % 78.85/11.38 | | : ? [v6: $i] : ? [v7: $i] : (head_of(v7) = v6 & head_of(v3) = v5 % 78.85/11.39 | | & tail_of(v7) = v5 & tail_of(v2) = v6 & $i(v7) & $i(v6) & $i(v5) % 78.85/11.39 | | & edge(v7))) % 78.85/11.39 | | % 78.85/11.39 | | GROUND_INST: instantiating (4) with all_19_2, all_19_1, simplifying with % 78.85/11.39 | | (15), (20), (21) gives: % 78.85/11.39 | | (27) edge(all_19_1) % 78.85/11.39 | | % 78.85/11.39 | | GROUND_INST: instantiating (3) with all_19_2, all_19_1, simplifying with % 78.85/11.39 | | (15), (20), (21) gives: % 78.85/11.39 | | (28) edge(all_19_2) % 78.85/11.39 | | % 78.85/11.39 | | GROUND_INST: instantiating (2) with all_19_2, all_19_1, simplifying with % 78.85/11.39 | | (15), (20), (21) gives: % 78.85/11.39 | | (29) ? [v0: $i] : (head_of(all_19_2) = v0 & tail_of(all_19_1) = v0 & % 78.85/11.39 | | $i(v0)) % 78.85/11.39 | | % 78.85/11.39 | | GROUND_INST: instantiating (26) with all_19_4, all_19_3, all_19_2, all_19_1, % 78.85/11.39 | | all_19_0, simplifying with (16), (17), (18), (19), (20), (21), % 78.85/11.39 | | (22) gives: % 78.85/11.39 | | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (head_of(v2) = v1 & % 78.85/11.39 | | head_of(all_19_1) = v0 & tail_of(v2) = v0 & tail_of(all_19_2) = v1 % 78.85/11.39 | | & $i(v2) & $i(v1) & $i(v0) & edge(v2)) % 78.85/11.39 | | % 78.85/11.39 | | GROUND_INST: instantiating (9) with all_19_4, all_19_3, all_19_2, all_19_1, % 78.85/11.39 | | all_19_0, simplifying with (16), (17), (18), (19), (20), (21), % 78.85/11.39 | | (22) gives: % 78.85/11.39 | | (31) ? [v0: $i] : ? [v1: $i] : (head_of(all_19_1) = v1 & % 78.85/11.39 | | tail_of(all_19_2) = v0 & $i(v1) & $i(v0) & ? [v2: $i] : ( ~ % 78.85/11.39 | | $i(v2) | ? [v3: $i] : ? [v4: $i] : (( ~ (v4 = v1) & % 78.85/11.39 | | head_of(v2) = v4 & $i(v4)) | ( ~ (v3 = v0) & tail_of(v2) = % 78.85/11.39 | | v3 & $i(v3))))) % 78.85/11.39 | | % 78.85/11.39 | | GROUND_INST: instantiating (8) with all_19_4, all_19_3, all_19_0, % 78.85/11.39 | | simplifying with (17), (18), (19), (22) gives: % 78.85/11.39 | | (32) path(all_19_4, all_19_3, all_19_0) % 78.85/11.39 | | % 78.85/11.39 | | DELTA: instantiating (29) with fresh symbol all_39_0 gives: % 78.85/11.39 | | (33) head_of(all_19_2) = all_39_0 & tail_of(all_19_1) = all_39_0 & % 78.85/11.39 | | $i(all_39_0) % 78.85/11.39 | | % 78.85/11.39 | | ALPHA: (33) implies: % 78.85/11.39 | | (34) tail_of(all_19_1) = all_39_0 % 78.85/11.39 | | (35) head_of(all_19_2) = all_39_0 % 78.85/11.39 | | % 78.85/11.39 | | DELTA: instantiating (30) with fresh symbols all_44_0, all_44_1, all_44_2 % 78.85/11.39 | | gives: % 78.85/11.39 | | (36) head_of(all_44_0) = all_44_1 & head_of(all_19_1) = all_44_2 & % 78.85/11.39 | | tail_of(all_44_0) = all_44_2 & tail_of(all_19_2) = all_44_1 & % 78.85/11.39 | | $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & edge(all_44_0) % 78.85/11.39 | | % 78.85/11.39 | | ALPHA: (36) implies: % 78.85/11.39 | | (37) edge(all_44_0) % 78.85/11.39 | | (38) $i(all_44_0) % 78.85/11.39 | | (39) tail_of(all_19_2) = all_44_1 % 78.85/11.39 | | (40) tail_of(all_44_0) = all_44_2 % 78.85/11.39 | | (41) head_of(all_19_1) = all_44_2 % 78.85/11.40 | | (42) head_of(all_44_0) = all_44_1 % 78.85/11.40 | | % 78.85/11.40 | | DELTA: instantiating (31) with fresh symbols all_46_0, all_46_1 gives: % 78.85/11.40 | | (43) head_of(all_19_1) = all_46_0 & tail_of(all_19_2) = all_46_1 & % 78.85/11.40 | | $i(all_46_0) & $i(all_46_1) & ? [v0: $i] : ( ~ $i(v0) | ? [v1: % 78.85/11.40 | | any] : ? [v2: any] : (( ~ (v2 = all_46_0) & head_of(v0) = v2 & % 78.85/11.40 | | $i(v2)) | ( ~ (v1 = all_46_1) & tail_of(v0) = v1 & $i(v1)))) % 78.85/11.40 | | % 78.85/11.40 | | ALPHA: (43) implies: % 78.85/11.40 | | (44) tail_of(all_19_2) = all_46_1 % 78.85/11.40 | | (45) head_of(all_19_1) = all_46_0 % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (11) with all_44_1, all_46_1, all_19_2, % 78.85/11.40 | | simplifying with (39), (44) gives: % 78.85/11.40 | | (46) all_46_1 = all_44_1 % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (12) with all_44_2, all_46_0, all_19_1, % 78.85/11.40 | | simplifying with (41), (45) gives: % 78.85/11.40 | | (47) all_46_0 = all_44_2 % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (no_loops) with all_19_2, simplifying with (20), % 78.85/11.40 | | (28) gives: % 78.85/11.40 | | (48) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & head_of(all_19_2) = v0 & % 78.85/11.40 | | tail_of(all_19_2) = v1 & $i(v1) & $i(v0)) % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (edge_ends_are_vertices) with all_19_2, % 78.85/11.40 | | simplifying with (20), (28) gives: % 78.85/11.40 | | (49) ? [v0: $i] : ? [v1: $i] : (head_of(all_19_2) = v0 & % 78.85/11.40 | | tail_of(all_19_2) = v1 & $i(v1) & $i(v0) & vertex(v1) & % 78.85/11.40 | | vertex(v0)) % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (no_loops) with all_19_1, simplifying with (21), % 78.85/11.40 | | (27) gives: % 78.85/11.40 | | (50) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & head_of(all_19_1) = v0 & % 78.85/11.40 | | tail_of(all_19_1) = v1 & $i(v1) & $i(v0)) % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (edge_ends_are_vertices) with all_19_1, % 78.85/11.40 | | simplifying with (21), (27) gives: % 78.85/11.40 | | (51) ? [v0: $i] : ? [v1: $i] : (head_of(all_19_1) = v0 & % 78.85/11.40 | | tail_of(all_19_1) = v1 & $i(v1) & $i(v0) & vertex(v1) & % 78.85/11.40 | | vertex(v0)) % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (5) with all_19_1, all_44_0, simplifying with % 78.85/11.40 | | (21), (27), (37), (38) gives: % 78.85/11.40 | | (52) all_44_0 = all_19_1 | sequential(all_19_1, all_44_0) | ? [v0: $i] : % 78.85/11.40 | | ? [v1: $i] : ( ~ (v1 = v0) & head_of(all_19_1) = v0 & % 78.85/11.40 | | tail_of(all_44_0) = v1 & $i(v1) & $i(v0)) % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (5) with all_44_0, all_19_2, simplifying with % 78.85/11.40 | | (20), (28), (37), (38) gives: % 78.85/11.40 | | (53) all_44_0 = all_19_2 | sequential(all_44_0, all_19_2) | ? [v0: $i] : % 78.85/11.40 | | ? [v1: $i] : ( ~ (v1 = v0) & head_of(all_44_0) = v0 & % 78.85/11.40 | | tail_of(all_19_2) = v1 & $i(v1) & $i(v0)) % 78.85/11.40 | | % 78.85/11.40 | | GROUND_INST: instantiating (no_loops) with all_44_0, simplifying with (37), % 78.85/11.41 | | (38) gives: % 78.85/11.41 | | (54) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & head_of(all_44_0) = v0 & % 78.85/11.41 | | tail_of(all_44_0) = v1 & $i(v1) & $i(v0)) % 78.85/11.41 | | % 78.85/11.41 | | GROUND_INST: instantiating (edge_ends_are_vertices) with all_44_0, % 78.85/11.41 | | simplifying with (37), (38) gives: % 78.85/11.41 | | (55) ? [v0: $i] : ? [v1: $i] : (head_of(all_44_0) = v0 & % 78.85/11.41 | | tail_of(all_44_0) = v1 & $i(v1) & $i(v0) & vertex(v1) & % 78.85/11.41 | | vertex(v0)) % 78.85/11.41 | | % 78.85/11.41 | | GROUND_INST: instantiating (7) with all_19_0, all_19_2, all_19_1, all_19_4, % 78.85/11.41 | | all_19_3, simplifying with (16), (18), (19), (20), (21), (22), % 78.85/11.41 | | (32) gives: % 78.85/11.41 | | (56) on_path(all_19_1, all_19_0) % 78.85/11.41 | | % 78.85/11.41 | | GROUND_INST: instantiating (6) with all_19_0, all_19_2, all_19_1, all_19_4, % 78.85/11.41 | | all_19_3, simplifying with (16), (18), (19), (20), (21), (22), % 78.85/11.41 | | (32) gives: % 78.85/11.41 | | (57) on_path(all_19_2, all_19_0) % 78.85/11.41 | | % 78.85/11.41 | | DELTA: instantiating (50) with fresh symbols all_61_0, all_61_1 gives: % 78.85/11.41 | | (58) ~ (all_61_0 = all_61_1) & head_of(all_19_1) = all_61_1 & % 78.85/11.41 | | tail_of(all_19_1) = all_61_0 & $i(all_61_0) & $i(all_61_1) % 78.85/11.41 | | % 78.85/11.41 | | ALPHA: (58) implies: % 78.85/11.41 | | (59) ~ (all_61_0 = all_61_1) % 78.85/11.41 | | (60) tail_of(all_19_1) = all_61_0 % 78.85/11.41 | | (61) head_of(all_19_1) = all_61_1 % 78.85/11.41 | | % 78.85/11.41 | | DELTA: instantiating (48) with fresh symbols all_63_0, all_63_1 gives: % 78.85/11.41 | | (62) ~ (all_63_0 = all_63_1) & head_of(all_19_2) = all_63_1 & % 78.85/11.41 | | tail_of(all_19_2) = all_63_0 & $i(all_63_0) & $i(all_63_1) % 78.85/11.41 | | % 78.85/11.41 | | ALPHA: (62) implies: % 78.85/11.41 | | (63) ~ (all_63_0 = all_63_1) % 78.85/11.41 | | (64) tail_of(all_19_2) = all_63_0 % 78.85/11.41 | | (65) head_of(all_19_2) = all_63_1 % 78.85/11.41 | | % 78.85/11.41 | | DELTA: instantiating (54) with fresh symbols all_65_0, all_65_1 gives: % 78.85/11.41 | | (66) ~ (all_65_0 = all_65_1) & head_of(all_44_0) = all_65_1 & % 78.85/11.41 | | tail_of(all_44_0) = all_65_0 & $i(all_65_0) & $i(all_65_1) % 78.85/11.41 | | % 78.85/11.41 | | ALPHA: (66) implies: % 78.85/11.41 | | (67) tail_of(all_44_0) = all_65_0 % 78.85/11.41 | | (68) head_of(all_44_0) = all_65_1 % 78.85/11.41 | | % 78.85/11.41 | | DELTA: instantiating (49) with fresh symbols all_67_0, all_67_1 gives: % 78.85/11.41 | | (69) head_of(all_19_2) = all_67_1 & tail_of(all_19_2) = all_67_0 & % 78.85/11.41 | | $i(all_67_0) & $i(all_67_1) & vertex(all_67_0) & vertex(all_67_1) % 78.85/11.41 | | % 78.85/11.41 | | ALPHA: (69) implies: % 78.85/11.41 | | (70) tail_of(all_19_2) = all_67_0 % 78.85/11.41 | | (71) head_of(all_19_2) = all_67_1 % 78.85/11.41 | | % 78.85/11.41 | | DELTA: instantiating (51) with fresh symbols all_69_0, all_69_1 gives: % 78.85/11.41 | | (72) head_of(all_19_1) = all_69_1 & tail_of(all_19_1) = all_69_0 & % 78.85/11.41 | | $i(all_69_0) & $i(all_69_1) & vertex(all_69_0) & vertex(all_69_1) % 78.85/11.41 | | % 78.85/11.41 | | ALPHA: (72) implies: % 78.85/11.41 | | (73) tail_of(all_19_1) = all_69_0 % 78.85/11.41 | | (74) head_of(all_19_1) = all_69_1 % 78.85/11.41 | | % 78.85/11.41 | | DELTA: instantiating (55) with fresh symbols all_71_0, all_71_1 gives: % 78.85/11.41 | | (75) head_of(all_44_0) = all_71_1 & tail_of(all_44_0) = all_71_0 & % 78.85/11.41 | | $i(all_71_0) & $i(all_71_1) & vertex(all_71_0) & vertex(all_71_1) % 78.85/11.41 | | % 78.85/11.41 | | ALPHA: (75) implies: % 78.85/11.41 | | (76) tail_of(all_44_0) = all_71_0 % 78.85/11.41 | | (77) head_of(all_44_0) = all_71_1 % 78.85/11.41 | | % 78.85/11.41 | | GROUND_INST: instantiating (11) with all_44_1, all_67_0, all_19_2, % 78.85/11.42 | | simplifying with (39), (70) gives: % 78.85/11.42 | | (78) all_67_0 = all_44_1 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (11) with all_63_0, all_67_0, all_19_2, % 78.85/11.42 | | simplifying with (64), (70) gives: % 78.85/11.42 | | (79) all_67_0 = all_63_0 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (11) with all_39_0, all_69_0, all_19_1, % 78.85/11.42 | | simplifying with (34), (73) gives: % 78.85/11.42 | | (80) all_69_0 = all_39_0 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (11) with all_61_0, all_69_0, all_19_1, % 78.85/11.42 | | simplifying with (60), (73) gives: % 78.85/11.42 | | (81) all_69_0 = all_61_0 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (11) with all_44_2, all_71_0, all_44_0, % 78.85/11.42 | | simplifying with (40), (76) gives: % 78.85/11.42 | | (82) all_71_0 = all_44_2 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (11) with all_65_0, all_71_0, all_44_0, % 78.85/11.42 | | simplifying with (67), (76) gives: % 78.85/11.42 | | (83) all_71_0 = all_65_0 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (11) with all_61_0, all_71_0, all_19_1, % 78.85/11.42 | | simplifying with (60) gives: % 78.85/11.42 | | (84) all_71_0 = all_61_0 | ~ (tail_of(all_19_1) = all_71_0) % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (12) with all_39_0, all_67_1, all_19_2, % 78.85/11.42 | | simplifying with (35), (71) gives: % 78.85/11.42 | | (85) all_67_1 = all_39_0 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (12) with all_63_1, all_67_1, all_19_2, % 78.85/11.42 | | simplifying with (65), (71) gives: % 78.85/11.42 | | (86) all_67_1 = all_63_1 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (12) with all_44_2, all_69_1, all_19_1, % 78.85/11.42 | | simplifying with (41), (74) gives: % 78.85/11.42 | | (87) all_69_1 = all_44_2 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (12) with all_61_1, all_69_1, all_19_1, % 78.85/11.42 | | simplifying with (61), (74) gives: % 78.85/11.42 | | (88) all_69_1 = all_61_1 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (12) with all_44_1, all_71_1, all_44_0, % 78.85/11.42 | | simplifying with (42), (77) gives: % 78.85/11.42 | | (89) all_71_1 = all_44_1 % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (12) with all_39_0, all_71_1, all_19_2, % 78.85/11.42 | | simplifying with (35) gives: % 78.85/11.42 | | (90) all_71_1 = all_39_0 | ~ (head_of(all_19_2) = all_71_1) % 78.85/11.42 | | % 78.85/11.42 | | GROUND_INST: instantiating (12) with all_65_1, all_71_1, all_44_0, % 78.85/11.42 | | simplifying with (68), (77) gives: % 78.85/11.42 | | (91) all_71_1 = all_65_1 % 78.85/11.42 | | % 78.85/11.42 | | COMBINE_EQS: (82), (83) imply: % 78.85/11.42 | | (92) all_65_0 = all_44_2 % 78.85/11.42 | | % 78.85/11.42 | | COMBINE_EQS: (89), (91) imply: % 78.85/11.42 | | (93) all_65_1 = all_44_1 % 78.85/11.42 | | % 78.85/11.42 | | COMBINE_EQS: (80), (81) imply: % 78.85/11.42 | | (94) all_61_0 = all_39_0 % 78.85/11.42 | | % 78.85/11.42 | | SIMP: (94) implies: % 78.85/11.42 | | (95) all_61_0 = all_39_0 % 78.85/11.42 | | % 79.52/11.42 | | COMBINE_EQS: (87), (88) imply: % 79.52/11.42 | | (96) all_61_1 = all_44_2 % 79.52/11.42 | | % 79.52/11.42 | | COMBINE_EQS: (78), (79) imply: % 79.52/11.42 | | (97) all_63_0 = all_44_1 % 79.52/11.42 | | % 79.52/11.42 | | SIMP: (97) implies: % 79.52/11.42 | | (98) all_63_0 = all_44_1 % 79.52/11.42 | | % 79.52/11.42 | | COMBINE_EQS: (85), (86) imply: % 79.52/11.42 | | (99) all_63_1 = all_39_0 % 79.52/11.42 | | % 79.52/11.42 | | SIMP: (99) implies: % 79.52/11.42 | | (100) all_63_1 = all_39_0 % 79.52/11.42 | | % 79.52/11.43 | | REDUCE: (63), (98), (100) imply: % 79.52/11.43 | | (101) ~ (all_44_1 = all_39_0) % 79.52/11.43 | | % 79.52/11.43 | | REDUCE: (59), (95), (96) imply: % 79.52/11.43 | | (102) ~ (all_44_2 = all_39_0) % 79.52/11.43 | | % 79.52/11.43 | | SIMP: (102) implies: % 79.52/11.43 | | (103) ~ (all_44_2 = all_39_0) % 79.52/11.43 | | % 79.52/11.43 | | GROUND_INST: instantiating (1) with all_19_4, all_19_3, all_19_0, all_19_2, % 79.52/11.43 | | simplifying with (18), (19), (20), (22), (32), (57) gives: % 79.52/11.43 | | (104) ? [v0: $i] : ? [v1: $i] : (head_of(all_19_2) = v0 & % 79.52/11.43 | | tail_of(all_19_2) = v1 & $i(v1) & $i(v0) & in_path(v1, all_19_0) % 79.52/11.43 | | & in_path(v0, all_19_0)) % 79.52/11.43 | | % 79.52/11.43 | | GROUND_INST: instantiating (1) with all_19_4, all_19_3, all_19_0, all_19_1, % 79.52/11.43 | | simplifying with (18), (19), (21), (22), (32), (56) gives: % 79.52/11.43 | | (105) ? [v0: $i] : ? [v1: $i] : (head_of(all_19_1) = v0 & % 79.52/11.43 | | tail_of(all_19_1) = v1 & $i(v1) & $i(v0) & in_path(v1, all_19_0) % 79.52/11.43 | | & in_path(v0, all_19_0)) % 79.52/11.43 | | % 79.52/11.43 | | DELTA: instantiating (105) with fresh symbols all_86_0, all_86_1 gives: % 79.52/11.43 | | (106) head_of(all_19_1) = all_86_1 & tail_of(all_19_1) = all_86_0 & % 79.52/11.43 | | $i(all_86_0) & $i(all_86_1) & in_path(all_86_0, all_19_0) & % 79.52/11.43 | | in_path(all_86_1, all_19_0) % 79.52/11.43 | | % 79.52/11.43 | | ALPHA: (106) implies: % 79.52/11.43 | | (107) head_of(all_19_1) = all_86_1 % 79.52/11.43 | | % 79.52/11.43 | | DELTA: instantiating (104) with fresh symbols all_88_0, all_88_1 gives: % 79.52/11.43 | | (108) head_of(all_19_2) = all_88_1 & tail_of(all_19_2) = all_88_0 & % 79.52/11.43 | | $i(all_88_0) & $i(all_88_1) & in_path(all_88_0, all_19_0) & % 79.52/11.43 | | in_path(all_88_1, all_19_0) % 79.52/11.43 | | % 79.52/11.43 | | ALPHA: (108) implies: % 79.52/11.43 | | (109) tail_of(all_19_2) = all_88_0 % 79.52/11.43 | | % 79.52/11.43 | | BETA: splitting (84) gives: % 79.52/11.43 | | % 79.52/11.43 | | Case 1: % 79.52/11.43 | | | % 79.52/11.43 | | | (110) ~ (tail_of(all_19_1) = all_71_0) % 79.52/11.43 | | | % 79.52/11.43 | | | REDUCE: (82), (110) imply: % 79.52/11.43 | | | (111) ~ (tail_of(all_19_1) = all_44_2) % 79.52/11.43 | | | % 79.52/11.43 | | | BETA: splitting (90) gives: % 79.52/11.43 | | | % 79.52/11.43 | | | Case 1: % 79.52/11.43 | | | | % 79.52/11.43 | | | | (112) ~ (head_of(all_19_2) = all_71_1) % 79.52/11.43 | | | | % 79.52/11.43 | | | | REDUCE: (89), (112) imply: % 79.52/11.43 | | | | (113) ~ (head_of(all_19_2) = all_44_1) % 79.52/11.43 | | | | % 79.52/11.43 | | | | GROUND_INST: instantiating (11) with all_44_1, all_88_0, all_19_2, % 79.52/11.43 | | | | simplifying with (39), (109) gives: % 79.52/11.43 | | | | (114) all_88_0 = all_44_1 % 79.52/11.43 | | | | % 79.52/11.43 | | | | GROUND_INST: instantiating (12) with all_44_2, all_86_1, all_19_1, % 79.52/11.43 | | | | simplifying with (41), (107) gives: % 79.52/11.43 | | | | (115) all_86_1 = all_44_2 % 79.52/11.43 | | | | % 79.52/11.43 | | | | PRED_UNIFY: (40), (111) imply: % 79.52/11.43 | | | | (116) ~ (all_44_0 = all_19_1) % 79.52/11.43 | | | | % 79.52/11.43 | | | | PRED_UNIFY: (42), (113) imply: % 79.52/11.43 | | | | (117) ~ (all_44_0 = all_19_2) % 79.52/11.43 | | | | % 79.52/11.43 | | | | BETA: splitting (53) gives: % 79.52/11.43 | | | | % 79.52/11.43 | | | | Case 1: % 79.52/11.43 | | | | | % 79.52/11.43 | | | | | (118) sequential(all_44_0, all_19_2) % 79.52/11.43 | | | | | % 79.52/11.43 | | | | | BETA: splitting (52) gives: % 79.52/11.43 | | | | | % 79.52/11.43 | | | | | Case 1: % 79.52/11.43 | | | | | | % 79.52/11.43 | | | | | | (119) sequential(all_19_1, all_44_0) % 79.52/11.43 | | | | | | % 79.52/11.43 | | | | | | GROUND_INST: instantiating (10) with all_19_2, all_19_1, all_44_0, % 79.52/11.43 | | | | | | simplifying with (15), (20), (21), (27), (28), (37), % 79.52/11.43 | | | | | | (38), (118), (119) gives: % 79.52/11.43 | | | | | | (120) triangle(all_19_2, all_19_1, all_44_0) % 79.52/11.43 | | | | | | % 79.52/11.43 | | | | | | GROUND_INST: instantiating (23) with all_44_0, simplifying with % 79.52/11.43 | | | | | | (38), (120) gives: % 79.52/11.43 | | | | | | (121) $false % 79.52/11.43 | | | | | | % 79.52/11.43 | | | | | | CLOSE: (121) is inconsistent. % 79.52/11.43 | | | | | | % 79.52/11.43 | | | | | Case 2: % 79.52/11.43 | | | | | | % 79.52/11.44 | | | | | | (122) all_44_0 = all_19_1 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 79.52/11.44 | | | | | | v0) & head_of(all_19_1) = v0 & tail_of(all_44_0) = v1 & % 79.52/11.44 | | | | | | $i(v1) & $i(v0)) % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | BETA: splitting (122) gives: % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | Case 1: % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | (123) all_44_0 = all_19_1 % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | REDUCE: (116), (123) imply: % 79.52/11.44 | | | | | | | (124) $false % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | CLOSE: (124) is inconsistent. % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | Case 2: % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | (125) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 79.52/11.44 | | | | | | | head_of(all_19_1) = v0 & tail_of(all_44_0) = v1 & % 79.52/11.44 | | | | | | | $i(v1) & $i(v0)) % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | DELTA: instantiating (125) with fresh symbols all_141_0, all_141_1 % 79.52/11.44 | | | | | | | gives: % 79.52/11.44 | | | | | | | (126) ~ (all_141_0 = all_141_1) & head_of(all_19_1) = % 79.52/11.44 | | | | | | | all_141_1 & tail_of(all_44_0) = all_141_0 & $i(all_141_0) % 79.52/11.44 | | | | | | | & $i(all_141_1) % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | ALPHA: (126) implies: % 79.52/11.44 | | | | | | | (127) ~ (all_141_0 = all_141_1) % 79.52/11.44 | | | | | | | (128) tail_of(all_44_0) = all_141_0 % 79.52/11.44 | | | | | | | (129) head_of(all_19_1) = all_141_1 % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | GROUND_INST: instantiating (11) with all_44_2, all_141_0, % 79.52/11.44 | | | | | | | all_44_0, simplifying with (40), (128) gives: % 79.52/11.44 | | | | | | | (130) all_141_0 = all_44_2 % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | GROUND_INST: instantiating (12) with all_44_2, all_141_1, % 79.52/11.44 | | | | | | | all_19_1, simplifying with (41), (129) gives: % 79.52/11.44 | | | | | | | (131) all_141_1 = all_44_2 % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | REDUCE: (127), (130), (131) imply: % 79.52/11.44 | | | | | | | (132) $false % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | | CLOSE: (132) is inconsistent. % 79.52/11.44 | | | | | | | % 79.52/11.44 | | | | | | End of split % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | End of split % 79.52/11.44 | | | | | % 79.52/11.44 | | | | Case 2: % 79.52/11.44 | | | | | % 79.52/11.44 | | | | | (133) all_44_0 = all_19_2 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 79.52/11.44 | | | | | v0) & head_of(all_44_0) = v0 & tail_of(all_19_2) = v1 & % 79.52/11.44 | | | | | $i(v1) & $i(v0)) % 79.52/11.44 | | | | | % 79.52/11.44 | | | | | BETA: splitting (133) gives: % 79.52/11.44 | | | | | % 79.52/11.44 | | | | | Case 1: % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | (134) all_44_0 = all_19_2 % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | REDUCE: (117), (134) imply: % 79.52/11.44 | | | | | | (135) $false % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | CLOSE: (135) is inconsistent. % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | Case 2: % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | (136) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 79.52/11.44 | | | | | | head_of(all_44_0) = v0 & tail_of(all_19_2) = v1 & $i(v1) % 79.52/11.44 | | | | | | & $i(v0)) % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | DELTA: instantiating (136) with fresh symbols all_141_0, all_141_1 % 79.52/11.44 | | | | | | gives: % 79.52/11.44 | | | | | | (137) ~ (all_141_0 = all_141_1) & head_of(all_44_0) = all_141_1 % 79.52/11.44 | | | | | | & tail_of(all_19_2) = all_141_0 & $i(all_141_0) & % 79.52/11.44 | | | | | | $i(all_141_1) % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | ALPHA: (137) implies: % 79.52/11.44 | | | | | | (138) ~ (all_141_0 = all_141_1) % 79.52/11.44 | | | | | | (139) tail_of(all_19_2) = all_141_0 % 79.52/11.44 | | | | | | (140) head_of(all_44_0) = all_141_1 % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | GROUND_INST: instantiating (11) with all_44_1, all_141_0, all_19_2, % 79.52/11.44 | | | | | | simplifying with (39), (139) gives: % 79.52/11.44 | | | | | | (141) all_141_0 = all_44_1 % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | GROUND_INST: instantiating (12) with all_44_1, all_141_1, all_44_0, % 79.52/11.44 | | | | | | simplifying with (42), (140) gives: % 79.52/11.44 | | | | | | (142) all_141_1 = all_44_1 % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | REDUCE: (138), (141), (142) imply: % 79.52/11.44 | | | | | | (143) $false % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | | CLOSE: (143) is inconsistent. % 79.52/11.44 | | | | | | % 79.52/11.44 | | | | | End of split % 79.52/11.44 | | | | | % 79.52/11.44 | | | | End of split % 79.52/11.44 | | | | % 79.52/11.44 | | | Case 2: % 79.52/11.44 | | | | % 79.52/11.44 | | | | (144) all_71_1 = all_39_0 % 79.52/11.44 | | | | % 79.52/11.44 | | | | COMBINE_EQS: (89), (144) imply: % 79.52/11.44 | | | | (145) all_44_1 = all_39_0 % 79.52/11.44 | | | | % 79.52/11.44 | | | | REDUCE: (101), (145) imply: % 79.52/11.44 | | | | (146) $false % 79.52/11.44 | | | | % 79.52/11.44 | | | | CLOSE: (146) is inconsistent. % 79.52/11.44 | | | | % 79.52/11.44 | | | End of split % 79.52/11.44 | | | % 79.52/11.44 | | Case 2: % 79.52/11.44 | | | % 79.52/11.44 | | | (147) all_71_0 = all_61_0 % 79.52/11.44 | | | % 79.52/11.44 | | | COMBINE_EQS: (82), (147) imply: % 79.52/11.44 | | | (148) all_61_0 = all_44_2 % 79.52/11.44 | | | % 79.52/11.44 | | | SIMP: (148) implies: % 79.52/11.44 | | | (149) all_61_0 = all_44_2 % 79.52/11.44 | | | % 79.52/11.44 | | | COMBINE_EQS: (95), (149) imply: % 79.52/11.44 | | | (150) all_44_2 = all_39_0 % 79.52/11.44 | | | % 79.52/11.44 | | | SIMP: (150) implies: % 79.52/11.44 | | | (151) all_44_2 = all_39_0 % 79.52/11.44 | | | % 79.52/11.44 | | | REDUCE: (103), (151) imply: % 79.52/11.44 | | | (152) $false % 79.52/11.44 | | | % 79.52/11.44 | | | CLOSE: (152) is inconsistent. % 79.52/11.44 | | | % 79.52/11.44 | | End of split % 79.52/11.44 | | % 79.65/11.44 | End of split % 79.65/11.44 | % 79.65/11.44 End of proof % 79.65/11.44 % SZS output end Proof for theBenchmark % 79.65/11.44 % 79.65/11.44 10828ms %------------------------------------------------------------------------------