%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA004+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 : n019.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 00:04:27 EDT 2023 % Result : Theorem 14.48s 3.02s % Output : Proof 30.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Aug 27 03:54:58 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.69 ________ _____ % 0.19/0.69 ___ __ \_________(_)________________________________ % 0.19/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.69 % 0.19/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.69 (2023-06-19) % 0.19/0.69 % 0.19/0.69 (c) Philipp Rümmer, 2009-2023 % 0.19/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.69 Amanda Stjerna. % 0.19/0.69 Free software under BSD-3-Clause. % 0.19/0.69 % 0.19/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.69 % 0.19/0.69 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.72 Running up to 7 provers in parallel. % 0.19/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 3.24/1.25 Prover 4: Preprocessing ... % 3.24/1.25 Prover 1: Preprocessing ... % 3.24/1.28 Prover 5: Preprocessing ... % 3.24/1.28 Prover 2: Preprocessing ... % 3.24/1.28 Prover 3: Preprocessing ... % 3.24/1.28 Prover 0: Preprocessing ... % 3.24/1.28 Prover 6: Preprocessing ... % 7.77/1.93 Prover 3: Constructing countermodel ... % 7.87/1.94 Prover 1: Constructing countermodel ... % 7.87/1.95 Prover 6: Proving ... % 7.87/1.99 Prover 2: Proving ... % 7.87/1.99 Prover 5: Proving ... % 8.39/2.15 Prover 4: Constructing countermodel ... % 9.01/2.20 Prover 0: Proving ... % 14.48/3.02 Prover 5: proved (2284ms) % 14.48/3.02 % 14.48/3.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.48/3.02 % 14.48/3.02 Prover 3: stopped % 14.48/3.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.48/3.02 Prover 0: stopped % 14.48/3.03 Prover 6: stopped % 14.48/3.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.48/3.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.48/3.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.48/3.03 Prover 2: stopped % 14.48/3.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.28/3.11 Prover 13: Preprocessing ... % 16.43/3.13 Prover 8: Preprocessing ... % 16.43/3.13 Prover 7: Preprocessing ... % 16.43/3.13 Prover 11: Preprocessing ... % 16.43/3.14 Prover 10: Preprocessing ... % 17.21/3.23 Prover 8: Warning: ignoring some quantifiers % 17.21/3.24 Prover 13: Warning: ignoring some quantifiers % 17.21/3.24 Prover 8: Constructing countermodel ... % 17.21/3.28 Prover 13: Constructing countermodel ... % 17.21/3.29 Prover 7: Warning: ignoring some quantifiers % 17.73/3.30 Prover 7: Constructing countermodel ... % 17.73/3.30 Prover 10: Warning: ignoring some quantifiers % 17.73/3.31 Prover 10: Constructing countermodel ... % 17.73/3.34 Prover 10: gave up % 17.73/3.35 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.73/3.36 Prover 7: gave up % 17.73/3.37 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 18.39/3.39 Prover 16: Preprocessing ... % 18.55/3.41 Prover 19: Preprocessing ... % 18.71/3.44 Prover 11: Constructing countermodel ... % 18.71/3.48 Prover 16: Warning: ignoring some quantifiers % 18.71/3.48 Prover 16: Constructing countermodel ... % 18.71/3.57 Prover 19: Warning: ignoring some quantifiers % 18.71/3.57 Prover 19: Constructing countermodel ... % 29.65/4.96 Prover 11: Found proof (size 129) % 29.65/4.96 Prover 11: proved (1935ms) % 29.65/4.96 Prover 19: stopped % 29.65/4.96 Prover 4: stopped % 29.65/4.96 Prover 1: stopped % 29.65/4.96 Prover 13: stopped % 29.65/4.97 Prover 16: stopped % 29.65/4.97 Prover 8: stopped % 29.65/4.97 % 29.65/4.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.65/4.97 % 29.65/4.98 % SZS output start Proof for theBenchmark % 29.65/4.98 Assumptions after simplification: % 29.65/4.98 --------------------------------- % 29.65/4.98 % 29.65/4.98 (on_path_properties) % 29.65/5.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 29.65/5.01 any] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~ % 29.65/5.01 (head_of(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 29.65/5.01 int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ((v9 = 0 & v7 = 0 & v5 % 29.65/5.01 = 0 & in_path(v8, v2) = 0 & edge(v3) = 0 & tail_of(v3) = v8 & $i(v8)) | % 29.65/5.01 ( ~ (v6 = 0) & on_path(v3, v2) = v6))) & ! [v0: $i] : ! [v1: $i] : ! % 29.65/5.01 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (in_path(v4, v2) = % 29.65/5.01 v5) | ~ (path(v0, v1, v2) = 0) | ~ (tail_of(v3) = v4) | ~ $i(v3) | ~ % 29.65/5.01 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: $i] : % 29.65/5.01 ? [v9: int] : ((v9 = 0 & v7 = 0 & v5 = 0 & in_path(v8, v2) = 0 & % 29.65/5.01 head_of(v3) = v8 & edge(v3) = 0 & $i(v8)) | ( ~ (v6 = 0) & on_path(v3, % 29.65/5.01 v2) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 29.65/5.01 ! [v4: any] : ( ~ (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ~ $i(v3) | ~ % 29.65/5.01 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : % 29.65/5.01 ? [v8: $i] : ? [v9: int] : ((v9 = 0 & v7 = 0 & v4 = 0 & in_path(v8, v2) = % 29.65/5.01 0 & in_path(v6, v2) = 0 & head_of(v3) = v6 & tail_of(v3) = v8 & $i(v8) & % 29.65/5.01 $i(v6)) | ( ~ (v5 = 0) & on_path(v3, v2) = v5))) & ! [v0: $i] : ! [v1: % 29.65/5.01 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (on_path(v3, v2) = 0) | ~ (path(v0, % 29.65/5.01 v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 29.65/5.01 $i] : ? [v5: $i] : (in_path(v5, v2) = 0 & in_path(v4, v2) = 0 & % 29.65/5.01 head_of(v3) = v4 & edge(v3) = 0 & tail_of(v3) = v5 & $i(v5) & $i(v4))) % 29.65/5.01 % 29.65/5.01 (precedes_defn) % 29.65/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 29.65/5.02 MultipleValueBool] : ! [v6: $i] : ( ~ (precedes(v6, v4, v0) = 0) | ~ % 29.65/5.02 (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v6) | ~ % 29.65/5.02 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? % 29.65/5.02 [v8: int] : ? [v9: int] : ((v9 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v8 = % 29.65/5.02 0) & on_path(v4, v0) = v8) | ( ~ (v7 = 0) & sequential(v3, v6) = v7) | % 29.65/5.02 ( ~ (v7 = 0) & on_path(v3, v0) = v7))) & ! [v0: $i] : ! [v1: $i] : ! % 29.65/5.02 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: MultipleValueBool] : ! [v6: % 29.65/5.02 $i] : ( ~ (sequential(v3, v6) = 0) | ~ (sequential(v3, v4) = v5) | ~ % 29.65/5.02 (path(v1, v2, v0) = 0) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 29.65/5.02 $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = 0 & % 29.65/5.02 precedes(v3, v4, v0) = 0) | ( ~ (v8 = 0) & on_path(v4, v0) = v8) | ( ~ % 29.65/5.02 (v7 = 0) & precedes(v6, v4, v0) = v7) | ( ~ (v7 = 0) & on_path(v3, v0) = % 29.65/5.02 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 29.65/5.02 $i] : ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ (path(v1, % 29.65/5.02 v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 29.65/5.02 | ? [v6: int] : ? [v7: int] : ? [v8: int] : (( ~ (v8 = 0) & % 29.65/5.02 sequential(v3, v4) = v8 & ! [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | % 29.65/5.02 ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) % 29.65/5.02 & ! [v9: $i] : ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] % 29.65/5.02 : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10))) | ( ~ (v7 = 0) & % 29.65/5.02 on_path(v4, v0) = v7) | ( ~ (v6 = 0) & on_path(v3, v0) = v6))) & ! [v0: % 29.65/5.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 29.65/5.02 (sequential(v3, v4) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) % 29.65/5.02 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 29.65/5.02 int] : ((v7 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v6 = 0) & on_path(v4, % 29.65/5.02 v0) = v6) | ( ~ (v5 = 0) & on_path(v3, v0) = v5))) % 29.65/5.02 % 29.65/5.02 (precedes_properties) % 29.65/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 29.65/5.03 any] : ( ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) % 29.65/5.03 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: % 29.65/5.03 int] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : % 29.65/5.03 ($i(v9) & ((v8 = 0 & v7 = 0 & on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & ( % 29.65/5.03 ~ (v5 = 0) | ( ! [v12: $i] : ( ~ (precedes(v12, v4, v0) = 0) | ~ % 29.65/5.03 $i(v12) | ? [v13: int] : ( ~ (v13 = 0) & sequential(v3, v12) = % 29.65/5.03 v13)) & ! [v12: $i] : ( ~ (sequential(v3, v12) = 0) | ~ % 29.65/5.03 $i(v12) | ? [v13: int] : ( ~ (v13 = 0) & precedes(v12, v4, v0) % 29.65/5.03 = v13)))) & (v5 = 0 | (v11 = 0 & v10 = 0 & precedes(v9, v4, % 29.65/5.03 v0) = 0 & sequential(v3, v9) = 0))) | ( ~ (v6 = 0) & % 29.65/5.03 precedes(v3, v4, v0) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.65/5.03 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (precedes(v3, v4, v0) = 0) | ~ % 29.65/5.03 (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 29.65/5.03 $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : % 29.65/5.03 (on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & $i(v6) & ((v8 = 0 & v7 = 0 & % 29.65/5.03 precedes(v6, v4, v0) = 0 & sequential(v3, v6) = 0) | (v5 = 0 & % 29.65/5.03 sequential(v3, v4) = 0)) & (( ~ (v5 = 0) & sequential(v3, v4) = v5) | % 29.65/5.03 ( ! [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? [v10: % 29.65/5.03 int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9: $i] : % 29.65/5.03 ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = % 29.65/5.03 0) & precedes(v9, v4, v0) = v10)))))) % 29.65/5.03 % 29.65/5.03 (sequential_defn) % 29.65/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 29.65/5.03 (sequential(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 29.65/5.03 int] : ? [v5: $i] : ? [v6: $i] : (( ~ (v6 = v5) & head_of(v0) = v5 & % 29.65/5.03 tail_of(v1) = v6 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & edge(v1) = v4) | ( % 29.65/5.03 ~ (v3 = 0) & edge(v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.65/5.03 (sequential(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 29.65/5.03 (head_of(v0) = v2 & edge(v1) = 0 & edge(v0) = 0 & tail_of(v1) = v2 & % 29.65/5.03 $i(v2))) & ! [v0: $i] : ( ~ (sequential(v0, v0) = 0) | ~ $i(v0)) % 29.65/5.03 % 29.65/5.03 (shortest_path_defn) % 29.65/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 | % 29.65/5.03 ~ (shortest_path(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.65/5.03 [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: % 29.65/5.03 int] : ($i(v6) & ((v7 = 0 & ~ (v9 = 0) & length_of(v6) = v8 & % 29.65/5.03 length_of(v2) = v5 & less_or_equal(v5, v8) = v9 & path(v0, v1, v6) = 0 % 29.65/5.03 & $i(v8) & $i(v5)) | ( ~ (v4 = 0) & path(v0, v1, v2) = v4)))) & ! % 29.65/5.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (path(v0, v1, v2) = % 29.65/5.03 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : % 29.65/5.03 ((v3 = 0 & ~ (v1 = v0) & length_of(v2) = v5 & $i(v5) & ! [v6: $i] : ! % 29.65/5.03 [v7: $i] : ( ~ (length_of(v6) = v7) | ~ $i(v6) | ? [v8: int] : ? [v9: % 29.65/5.03 int] : ((v9 = 0 & less_or_equal(v5, v7) = 0) | ( ~ (v8 = 0) & % 29.65/5.03 path(v0, v1, v6) = v8))) & ! [v6: $i] : ( ~ (path(v0, v1, v6) = % 29.65/5.03 0) | ~ $i(v6) | ? [v7: $i] : (length_of(v6) = v7 & % 29.65/5.03 less_or_equal(v5, v7) = 0 & $i(v7)))) | ( ~ (v4 = 0) & % 29.65/5.03 shortest_path(v0, v1, v2) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.65/5.03 $i] : (v1 = v0 | ~ (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 29.65/5.03 $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: % 29.65/5.03 $i] : ? [v8: int] : ($i(v5) & ((v6 = 0 & ~ (v8 = 0) & length_of(v5) = v7 % 29.65/5.03 & length_of(v2) = v3 & less_or_equal(v3, v7) = v8 & path(v0, v1, v5) = % 29.65/5.03 0 & $i(v7) & $i(v3)) | (v4 = 0 & shortest_path(v0, v1, v2) = 0)))) & % 29.65/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, v2) = 0) | % 29.65/5.03 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (length_of(v2) = v3 & % 29.65/5.03 path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 29.65/5.03 (length_of(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ((v7 = % 29.65/5.03 0 & less_or_equal(v3, v5) = 0) | ( ~ (v6 = 0) & path(v0, v1, v4) = % 29.65/5.03 v6))) & ! [v4: $i] : ( ~ (path(v0, v1, v4) = 0) | ~ $i(v4) | ? % 29.65/5.03 [v5: $i] : (length_of(v4) = v5 & less_or_equal(v3, v5) = 0 & $i(v5))))) % 29.65/5.03 & ! [v0: $i] : ! [v1: $i] : ( ~ (shortest_path(v0, v0, v1) = 0) | ~ $i(v1) % 29.65/5.03 | ~ $i(v0)) % 29.65/5.03 % 29.65/5.03 (shortest_path_properties) % 30.39/5.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 30.39/5.04 $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (head_of(v3) = % 30.39/5.04 v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 30.39/5.04 $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : (( ~ (v8 = 0) & % 30.39/5.04 precedes(v3, v2, v4) = v8 & ! [v9: $i] : ( ~ (head_of(v9) = v6) | ~ % 30.39/5.04 $i(v9) | ? [v10: $i] : ( ~ (v10 = v5) & tail_of(v9) = v10 & $i(v10))) % 30.39/5.04 & ! [v9: $i] : ( ~ (tail_of(v9) = v5) | ~ $i(v9) | ? [v10: $i] : ( ~ % 30.39/5.04 (v10 = v6) & head_of(v9) = v10 & $i(v10)))) | ( ~ (v7 = 0) & % 30.39/5.04 precedes(v2, v3, v4) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 30.39/5.04 ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) % 30.39/5.04 | ~ (precedes(v3, v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 30.39/5.04 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : (( ~ (v6 = % 30.39/5.04 0) & precedes(v2, v3, v4) = v6) | ( ~ (v5 = 0) & head_of(v3) = v8 & % 30.39/5.04 tail_of(v2) = v7 & $i(v8) & $i(v7) & ! [v9: $i] : ( ~ (head_of(v9) = % 30.39/5.04 v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v7) & tail_of(v9) = v10 % 30.39/5.04 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v7) | ~ $i(v9) | ? % 30.39/5.04 [v10: $i] : ( ~ (v10 = v8) & head_of(v9) = v10 & $i(v10)))))) & ! % 30.39/5.04 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 30.39/5.04 (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | ~ $i(v4) % 30.39/5.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] % 30.39/5.04 : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & head_of(v3) = v6 % 30.39/5.04 & tail_of(v2) = v5 & $i(v6) & $i(v5) & ! [v8: $i] : ( ~ (head_of(v8) = % 30.39/5.04 v6) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v5) & tail_of(v8) = v9 & % 30.39/5.04 $i(v9))) & ! [v8: $i] : ( ~ (tail_of(v8) = v5) | ~ $i(v8) | ? [v9: % 30.39/5.04 $i] : ( ~ (v9 = v6) & head_of(v8) = v9 & $i(v9))))) % 30.39/5.04 % 30.39/5.04 (shortest_path_properties_lemma) % 30.39/5.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 30.39/5.04 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 30.39/5.04 (shortest_path(v0, v1, v4) = 0 & precedes(v2, v3, v4) = 0 & head_of(v3) = v6 & % 30.39/5.04 $i(v8) & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v7 = v6 & % 30.39/5.04 head_of(v2) = v6) | (tail_of(v2) = v5 & $i(v5) & (v6 = v5 | (v10 = v6 & % 30.39/5.04 v9 = v5 & head_of(v8) = v6 & tail_of(v8) = v5))))) % 30.39/5.04 % 30.39/5.04 (function-axioms) % 30.39/5.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 30.39/5.04 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ % 30.39/5.04 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.39/5.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 30.39/5.04 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & ! % 30.39/5.04 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 30.39/5.04 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ % 30.39/5.04 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.39/5.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 30.39/5.04 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 30.39/5.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ % 30.39/5.04 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 30.39/5.04 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = % 30.39/5.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 30.39/5.04 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ % 30.39/5.04 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.39/5.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.39/5.04 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0: % 30.39/5.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 30.39/5.04 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0: % 30.39/5.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 30.39/5.04 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0: % 30.39/5.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3, % 30.39/5.04 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 30.39/5.04 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & % 30.39/5.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 30.39/5.04 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1: % 30.39/5.04 $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = % 30.39/5.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 30.39/5.04 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : ! % 30.39/5.04 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = % 30.39/5.04 v0)) % 30.39/5.04 % 30.39/5.04 Further assumptions not needed in the proof: % 30.39/5.04 -------------------------------------------- % 30.39/5.05 complete_properties, edge_ends_are_vertices, graph_has_them_all, % 30.39/5.05 in_path_properties, length_defn, no_loops, path_defn, % 30.39/5.05 path_length_sequential_pairs, path_properties, sequential_pairs_and_triangles, % 30.39/5.05 triangle_defn % 30.39/5.05 % 30.39/5.05 Those formulas are unsatisfiable: % 30.39/5.05 --------------------------------- % 30.39/5.05 % 30.39/5.05 Begin of proof % 30.39/5.05 | % 30.39/5.05 | ALPHA: (on_path_properties) implies: % 30.39/5.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 30.39/5.05 | (on_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = 0) | ~ $i(v3) | ~ % 30.39/5.05 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : % 30.39/5.05 | (in_path(v5, v2) = 0 & in_path(v4, v2) = 0 & head_of(v3) = v4 & % 30.39/5.05 | edge(v3) = 0 & tail_of(v3) = v5 & $i(v5) & $i(v4))) % 30.39/5.05 | % 30.39/5.05 | ALPHA: (sequential_defn) implies: % 30.39/5.05 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 30.39/5.05 | (sequential(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 30.39/5.05 | [v4: int] : ? [v5: $i] : ? [v6: $i] : (( ~ (v6 = v5) & head_of(v0) % 30.39/5.05 | = v5 & tail_of(v1) = v6 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & % 30.39/5.05 | edge(v1) = v4) | ( ~ (v3 = 0) & edge(v0) = v3))) % 30.39/5.05 | % 30.39/5.05 | ALPHA: (precedes_defn) implies: % 30.39/5.05 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 30.39/5.05 | ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ (path(v1, % 30.39/5.05 | v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 30.39/5.05 | $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : (( ~ (v8 = 0) & % 30.39/5.05 | sequential(v3, v4) = v8 & ! [v9: $i] : ( ~ (precedes(v9, v4, v0) % 30.39/5.05 | = 0) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & % 30.39/5.05 | sequential(v3, v9) = v10)) & ! [v9: $i] : ( ~ % 30.39/5.05 | (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 % 30.39/5.05 | = 0) & precedes(v9, v4, v0) = v10))) | ( ~ (v7 = 0) & % 30.39/5.05 | on_path(v4, v0) = v7) | ( ~ (v6 = 0) & on_path(v3, v0) = v6))) % 30.39/5.05 | % 30.39/5.05 | ALPHA: (precedes_properties) implies: % 30.39/5.05 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 30.39/5.05 | ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) % 30.39/5.05 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? % 30.39/5.05 | [v6: $i] : ? [v7: int] : ? [v8: int] : (on_path(v4, v0) = 0 & % 30.39/5.05 | on_path(v3, v0) = 0 & $i(v6) & ((v8 = 0 & v7 = 0 & precedes(v6, v4, % 30.39/5.05 | v0) = 0 & sequential(v3, v6) = 0) | (v5 = 0 & sequential(v3, % 30.39/5.05 | v4) = 0)) & (( ~ (v5 = 0) & sequential(v3, v4) = v5) | ( ! % 30.39/5.05 | [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? % 30.39/5.05 | [v10: int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! % 30.39/5.05 | [v9: $i] : ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: % 30.39/5.05 | int] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10)))))) % 30.39/5.05 | % 30.39/5.05 | ALPHA: (shortest_path_defn) implies: % 30.39/5.05 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, % 30.39/5.05 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 30.39/5.05 | (length_of(v2) = v3 & path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] : % 30.39/5.05 | ! [v5: $i] : ( ~ (length_of(v4) = v5) | ~ $i(v4) | ? [v6: int] : % 30.39/5.05 | ? [v7: int] : ((v7 = 0 & less_or_equal(v3, v5) = 0) | ( ~ (v6 = % 30.39/5.05 | 0) & path(v0, v1, v4) = v6))) & ! [v4: $i] : ( ~ (path(v0, % 30.39/5.05 | v1, v4) = 0) | ~ $i(v4) | ? [v5: $i] : (length_of(v4) = v5 % 30.39/5.05 | & less_or_equal(v3, v5) = 0 & $i(v5))))) % 30.39/5.05 | % 30.39/5.05 | ALPHA: (shortest_path_properties) implies: % 30.39/5.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 30.39/5.06 | ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | % 30.39/5.06 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 30.39/5.06 | $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2, % 30.39/5.06 | v4) = v7 & head_of(v3) = v6 & tail_of(v2) = v5 & $i(v6) & $i(v5) % 30.39/5.06 | & ! [v8: $i] : ( ~ (head_of(v8) = v6) | ~ $i(v8) | ? [v9: $i] : % 30.39/5.06 | ( ~ (v9 = v5) & tail_of(v8) = v9 & $i(v9))) & ! [v8: $i] : ( ~ % 30.39/5.06 | (tail_of(v8) = v5) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v6) & % 30.39/5.06 | head_of(v8) = v9 & $i(v9))))) % 30.39/5.06 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 30.39/5.06 | ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v3, % 30.39/5.06 | v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 30.39/5.06 | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : (( ~ (v6 = 0) & % 30.39/5.06 | precedes(v2, v3, v4) = v6) | ( ~ (v5 = 0) & head_of(v3) = v8 & % 30.39/5.06 | tail_of(v2) = v7 & $i(v8) & $i(v7) & ! [v9: $i] : ( ~ % 30.39/5.06 | (head_of(v9) = v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v7) % 30.39/5.06 | & tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ % 30.39/5.06 | (tail_of(v9) = v7) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v8) % 30.39/5.06 | & head_of(v9) = v10 & $i(v10)))))) % 30.39/5.06 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 30.39/5.06 | ! [v5: $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ % 30.39/5.06 | (head_of(v3) = v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 30.39/5.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : (( ~ % 30.39/5.06 | (v8 = 0) & precedes(v3, v2, v4) = v8 & ! [v9: $i] : ( ~ % 30.39/5.06 | (head_of(v9) = v6) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v5) % 30.39/5.06 | & tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ % 30.39/5.06 | (tail_of(v9) = v5) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) % 30.39/5.06 | & head_of(v9) = v10 & $i(v10)))) | ( ~ (v7 = 0) & % 30.39/5.06 | precedes(v2, v3, v4) = v7))) % 30.39/5.06 | % 30.39/5.06 | ALPHA: (function-axioms) implies: % 30.39/5.06 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = % 30.39/5.06 | v1) | ~ (tail_of(v2) = v0)) % 30.39/5.06 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 30.39/5.06 | : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) % 30.39/5.06 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = % 30.39/5.06 | v1) | ~ (head_of(v2) = v0)) % 30.39/5.06 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 30.39/5.06 | : ! [v3: $i] : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, % 30.39/5.06 | v2) = v0)) % 30.39/5.06 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 30.39/5.06 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = % 30.39/5.06 | v1) | ~ (precedes(v4, v3, v2) = v0)) % 30.39/5.06 | % 30.39/5.06 | DELTA: instantiating (shortest_path_properties_lemma) with fresh symbols % 30.39/5.06 | all_20_0, all_20_1, all_20_2, all_20_3, all_20_4, all_20_5, all_20_6, % 30.39/5.06 | all_20_7, all_20_8, all_20_9, all_20_10 gives: % 30.39/5.07 | (14) shortest_path(all_20_10, all_20_9, all_20_6) = 0 & precedes(all_20_8, % 30.39/5.07 | all_20_7, all_20_6) = 0 & head_of(all_20_7) = all_20_4 & % 30.39/5.07 | $i(all_20_2) & $i(all_20_4) & $i(all_20_6) & $i(all_20_7) & % 30.39/5.07 | $i(all_20_8) & $i(all_20_9) & $i(all_20_10) & ((all_20_3 = all_20_4 & % 30.39/5.07 | head_of(all_20_8) = all_20_4) | (tail_of(all_20_8) = all_20_5 & % 30.39/5.07 | $i(all_20_5) & (all_20_4 = all_20_5 | (all_20_0 = all_20_4 & % 30.39/5.07 | all_20_1 = all_20_5 & head_of(all_20_2) = all_20_4 & % 30.39/5.07 | tail_of(all_20_2) = all_20_5)))) % 30.39/5.07 | % 30.39/5.07 | ALPHA: (14) implies: % 30.39/5.07 | (15) $i(all_20_10) % 30.39/5.07 | (16) $i(all_20_9) % 30.39/5.07 | (17) $i(all_20_8) % 30.39/5.07 | (18) $i(all_20_7) % 30.39/5.07 | (19) $i(all_20_6) % 30.39/5.07 | (20) $i(all_20_2) % 30.39/5.07 | (21) head_of(all_20_7) = all_20_4 % 30.39/5.07 | (22) precedes(all_20_8, all_20_7, all_20_6) = 0 % 30.39/5.07 | (23) shortest_path(all_20_10, all_20_9, all_20_6) = 0 % 30.39/5.07 | (24) (all_20_3 = all_20_4 & head_of(all_20_8) = all_20_4) | % 30.39/5.07 | (tail_of(all_20_8) = all_20_5 & $i(all_20_5) & (all_20_4 = all_20_5 | % 30.39/5.07 | (all_20_0 = all_20_4 & all_20_1 = all_20_5 & head_of(all_20_2) = % 30.39/5.07 | all_20_4 & tail_of(all_20_2) = all_20_5))) % 30.39/5.07 | % 30.39/5.07 | GROUND_INST: instantiating (6) with all_20_10, all_20_9, all_20_8, all_20_7, % 30.39/5.07 | all_20_6, simplifying with (15), (16), (17), (18), (19), (22), % 30.39/5.07 | (23) gives: % 30.39/5.07 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 30.39/5.07 | precedes(all_20_7, all_20_8, all_20_6) = v2 & head_of(all_20_7) = v1 % 30.39/5.07 | & tail_of(all_20_8) = v0 & $i(v1) & $i(v0) & ! [v3: $i] : ( ~ % 30.39/5.07 | (head_of(v3) = v1) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v0) & % 30.39/5.07 | tail_of(v3) = v4 & $i(v4))) & ! [v3: $i] : ( ~ (tail_of(v3) = % 30.39/5.07 | v0) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & head_of(v3) = v4 % 30.39/5.07 | & $i(v4)))) % 30.39/5.07 | % 30.93/5.07 | GROUND_INST: instantiating (7) with all_20_10, all_20_9, all_20_7, all_20_8, % 30.93/5.07 | all_20_6, 0, simplifying with (15), (16), (17), (18), (19), (22), % 30.93/5.07 | (23) gives: % 30.93/5.07 | (26) ? [v0: int] : ( ~ (v0 = 0) & precedes(all_20_7, all_20_8, all_20_6) = % 30.93/5.07 | v0) % 30.93/5.07 | % 30.93/5.07 | GROUND_INST: instantiating (5) with all_20_10, all_20_9, all_20_6, simplifying % 30.93/5.07 | with (15), (16), (19), (23) gives: % 30.93/5.07 | (27) ? [v0: $i] : (length_of(all_20_6) = v0 & path(all_20_10, all_20_9, % 30.93/5.07 | all_20_6) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 30.93/5.07 | (length_of(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: int] : % 30.93/5.07 | ((v4 = 0 & less_or_equal(v0, v2) = 0) | ( ~ (v3 = 0) & % 30.93/5.07 | path(all_20_10, all_20_9, v1) = v3))) & ! [v1: $i] : ( ~ % 30.93/5.07 | (path(all_20_10, all_20_9, v1) = 0) | ~ $i(v1) | ? [v2: $i] : % 30.93/5.07 | (length_of(v1) = v2 & less_or_equal(v0, v2) = 0 & $i(v2)))) % 30.93/5.07 | % 30.93/5.07 | DELTA: instantiating (26) with fresh symbol all_27_0 gives: % 30.93/5.07 | (28) ~ (all_27_0 = 0) & precedes(all_20_7, all_20_8, all_20_6) = all_27_0 % 30.93/5.07 | % 30.93/5.07 | ALPHA: (28) implies: % 30.93/5.07 | (29) precedes(all_20_7, all_20_8, all_20_6) = all_27_0 % 30.93/5.07 | % 30.93/5.07 | DELTA: instantiating (27) with fresh symbol all_31_0 gives: % 30.93/5.07 | (30) length_of(all_20_6) = all_31_0 & path(all_20_10, all_20_9, all_20_6) = % 30.93/5.07 | 0 & $i(all_31_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (length_of(v0) = % 30.93/5.07 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 30.93/5.07 | less_or_equal(all_31_0, v1) = 0) | ( ~ (v2 = 0) & % 30.93/5.07 | path(all_20_10, all_20_9, v0) = v2))) & ! [v0: $i] : ( ~ % 30.93/5.07 | (path(all_20_10, all_20_9, v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 30.93/5.07 | (length_of(v0) = v1 & less_or_equal(all_31_0, v1) = 0 & $i(v1))) % 30.93/5.07 | % 30.93/5.07 | ALPHA: (30) implies: % 30.93/5.07 | (31) path(all_20_10, all_20_9, all_20_6) = 0 % 30.93/5.07 | % 30.93/5.07 | DELTA: instantiating (25) with fresh symbols all_34_0, all_34_1, all_34_2 % 30.93/5.07 | gives: % 30.93/5.07 | (32) ~ (all_34_0 = 0) & precedes(all_20_7, all_20_8, all_20_6) = all_34_0 % 30.93/5.07 | & head_of(all_20_7) = all_34_1 & tail_of(all_20_8) = all_34_2 & % 30.93/5.07 | $i(all_34_1) & $i(all_34_2) & ! [v0: $i] : ( ~ (head_of(v0) = % 30.93/5.07 | all_34_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_34_2) & % 30.93/5.07 | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = % 30.93/5.07 | all_34_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_34_1) & % 30.93/5.07 | head_of(v0) = v1 & $i(v1))) % 30.93/5.07 | % 30.93/5.07 | ALPHA: (32) implies: % 30.93/5.07 | (33) tail_of(all_20_8) = all_34_2 % 30.93/5.07 | (34) head_of(all_20_7) = all_34_1 % 30.93/5.08 | (35) precedes(all_20_7, all_20_8, all_20_6) = all_34_0 % 30.93/5.08 | (36) ! [v0: $i] : ( ~ (tail_of(v0) = all_34_2) | ~ $i(v0) | ? [v1: any] % 30.93/5.08 | : ( ~ (v1 = all_34_1) & head_of(v0) = v1 & $i(v1))) % 30.93/5.08 | % 30.93/5.08 | GROUND_INST: instantiating (11) with all_20_4, all_34_1, all_20_7, simplifying % 30.93/5.08 | with (21), (34) gives: % 30.93/5.08 | (37) all_34_1 = all_20_4 % 30.93/5.08 | % 30.93/5.08 | GROUND_INST: instantiating (13) with all_27_0, all_34_0, all_20_6, all_20_8, % 30.93/5.08 | all_20_7, simplifying with (29), (35) gives: % 30.93/5.08 | (38) all_34_0 = all_27_0 % 30.93/5.08 | % 30.93/5.08 | GROUND_INST: instantiating (8) with all_20_10, all_20_9, all_20_8, all_20_7, % 30.93/5.08 | all_20_6, all_34_2, all_20_4, simplifying with (15), (16), (17), % 30.93/5.08 | (18), (19), (21), (23), (33) gives: % 30.93/5.08 | (39) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & precedes(all_20_7, % 30.93/5.08 | all_20_8, all_20_6) = v1 & ! [v2: $i] : ( ~ (head_of(v2) = % 30.93/5.08 | all_20_4) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_34_2) & % 30.93/5.08 | tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~ (tail_of(v2) = % 30.93/5.08 | all_34_2) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_20_4) & % 30.93/5.08 | head_of(v2) = v3 & $i(v3)))) | ( ~ (v0 = 0) & % 30.93/5.08 | precedes(all_20_8, all_20_7, all_20_6) = v0)) % 30.93/5.08 | % 30.93/5.08 | GROUND_INST: instantiating (36) with all_20_8, simplifying with (17), (33) % 30.93/5.08 | gives: % 30.93/5.08 | (40) ? [v0: any] : ( ~ (v0 = all_34_1) & head_of(all_20_8) = v0 & $i(v0)) % 30.93/5.08 | % 30.93/5.08 | GROUND_INST: instantiating (4) with all_20_6, all_20_10, all_20_9, all_20_8, % 30.93/5.08 | all_20_7, simplifying with (15), (16), (17), (18), (19), (22), % 30.93/5.08 | (31) gives: % 30.93/5.08 | (41) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : % 30.93/5.08 | (on_path(all_20_7, all_20_6) = 0 & on_path(all_20_8, all_20_6) = 0 & % 30.93/5.08 | $i(v1) & ((v3 = 0 & v2 = 0 & precedes(v1, all_20_7, all_20_6) = 0 & % 30.93/5.08 | sequential(all_20_8, v1) = 0) | (v0 = 0 & sequential(all_20_8, % 30.93/5.08 | all_20_7) = 0)) & (( ~ (v0 = 0) & sequential(all_20_8, % 30.93/5.08 | all_20_7) = v0) | ( ! [v4: $i] : ( ~ (precedes(v4, all_20_7, % 30.93/5.08 | all_20_6) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 30.93/5.08 | sequential(all_20_8, v4) = v5)) & ! [v4: $i] : ( ~ % 30.93/5.08 | (sequential(all_20_8, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( % 30.93/5.08 | ~ (v5 = 0) & precedes(v4, all_20_7, all_20_6) = v5))))) % 30.93/5.08 | % 30.93/5.08 | GROUND_INST: instantiating (3) with all_20_6, all_20_10, all_20_9, all_20_7, % 30.93/5.08 | all_20_8, all_27_0, simplifying with (15), (16), (17), (18), % 30.93/5.08 | (19), (29), (31) gives: % 30.93/5.08 | (42) all_27_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ (v2 = % 30.93/5.08 | 0) & sequential(all_20_7, all_20_8) = v2 & ! [v3: $i] : ( ~ % 30.93/5.08 | (precedes(v3, all_20_8, all_20_6) = 0) | ~ $i(v3) | ? [v4: % 30.93/5.08 | int] : ( ~ (v4 = 0) & sequential(all_20_7, v3) = v4)) & ! % 30.93/5.08 | [v3: $i] : ( ~ (sequential(all_20_7, v3) = 0) | ~ $i(v3) | ? % 30.93/5.08 | [v4: int] : ( ~ (v4 = 0) & precedes(v3, all_20_8, all_20_6) = % 30.93/5.08 | v4))) | ( ~ (v1 = 0) & on_path(all_20_8, all_20_6) = v1) | ( ~ % 30.93/5.08 | (v0 = 0) & on_path(all_20_7, all_20_6) = v0)) % 30.93/5.08 | % 30.93/5.08 | GROUND_INST: instantiating (7) with all_20_10, all_20_9, all_20_8, all_20_7, % 30.93/5.08 | all_20_6, all_27_0, simplifying with (15), (16), (17), (18), % 30.93/5.08 | (19), (23), (29) gives: % 30.93/5.08 | (43) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 30.93/5.08 | precedes(all_20_8, all_20_7, all_20_6) = v0) | ( ~ (all_27_0 = 0) % 30.93/5.08 | & head_of(all_20_7) = v2 & tail_of(all_20_8) = v1 & $i(v2) & % 30.93/5.08 | $i(v1) & ! [v3: $i] : ( ~ (head_of(v3) = v2) | ~ $i(v3) | ? % 30.93/5.08 | [v4: $i] : ( ~ (v4 = v1) & tail_of(v3) = v4 & $i(v4))) & ! [v3: % 30.93/5.08 | $i] : ( ~ (tail_of(v3) = v1) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 % 30.93/5.08 | = v2) & head_of(v3) = v4 & $i(v4))))) % 30.93/5.08 | % 30.93/5.08 | DELTA: instantiating (40) with fresh symbol all_51_0 gives: % 30.93/5.10 | (44) ~ (all_51_0 = all_34_1) & head_of(all_20_8) = all_51_0 & $i(all_51_0) % 30.93/5.10 | % 30.93/5.10 | ALPHA: (44) implies: % 30.93/5.10 | (45) ~ (all_51_0 = all_34_1) % 30.93/5.10 | (46) head_of(all_20_8) = all_51_0 % 30.93/5.10 | % 30.93/5.10 | DELTA: instantiating (39) with fresh symbols all_60_0, all_60_1 gives: % 30.93/5.10 | (47) ( ~ (all_60_0 = 0) & precedes(all_20_7, all_20_8, all_20_6) = all_60_0 % 30.93/5.10 | & ! [v0: $i] : ( ~ (head_of(v0) = all_20_4) | ~ $i(v0) | ? [v1: % 30.93/5.10 | any] : ( ~ (v1 = all_34_2) & tail_of(v0) = v1 & $i(v1))) & ! % 30.93/5.10 | [v0: $i] : ( ~ (tail_of(v0) = all_34_2) | ~ $i(v0) | ? [v1: any] : % 30.93/5.10 | ( ~ (v1 = all_20_4) & head_of(v0) = v1 & $i(v1)))) | ( ~ (all_60_1 % 30.93/5.10 | = 0) & precedes(all_20_8, all_20_7, all_20_6) = all_60_1) % 30.93/5.10 | % 30.93/5.10 | DELTA: instantiating (43) with fresh symbols all_62_0, all_62_1, all_62_2 % 30.93/5.10 | gives: % 30.93/5.10 | (48) ( ~ (all_62_2 = 0) & precedes(all_20_8, all_20_7, all_20_6) = % 30.93/5.10 | all_62_2) | ( ~ (all_27_0 = 0) & head_of(all_20_7) = all_62_0 & % 30.93/5.10 | tail_of(all_20_8) = all_62_1 & $i(all_62_0) & $i(all_62_1) & ! [v0: % 30.93/5.10 | $i] : ( ~ (head_of(v0) = all_62_0) | ~ $i(v0) | ? [v1: any] : ( % 30.93/5.10 | ~ (v1 = all_62_1) & tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : % 30.93/5.10 | ( ~ (tail_of(v0) = all_62_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 30.93/5.10 | all_62_0) & head_of(v0) = v1 & $i(v1)))) % 30.93/5.10 | % 30.93/5.10 | DELTA: instantiating (41) with fresh symbols all_63_0, all_63_1, all_63_2, % 30.93/5.10 | all_63_3 gives: % 30.93/5.10 | (49) on_path(all_20_7, all_20_6) = 0 & on_path(all_20_8, all_20_6) = 0 & % 30.93/5.10 | $i(all_63_2) & ((all_63_0 = 0 & all_63_1 = 0 & precedes(all_63_2, % 30.93/5.10 | all_20_7, all_20_6) = 0 & sequential(all_20_8, all_63_2) = 0) | % 30.93/5.10 | (all_63_3 = 0 & sequential(all_20_8, all_20_7) = 0)) & (( ~ % 30.93/5.10 | (all_63_3 = 0) & sequential(all_20_8, all_20_7) = all_63_3) | ( ! % 30.93/5.10 | [v0: $i] : ( ~ (precedes(v0, all_20_7, all_20_6) = 0) | ~ $i(v0) % 30.93/5.10 | | ? [v1: int] : ( ~ (v1 = 0) & sequential(all_20_8, v0) = v1)) % 30.93/5.10 | & ! [v0: $i] : ( ~ (sequential(all_20_8, v0) = 0) | ~ $i(v0) | % 30.93/5.10 | ? [v1: int] : ( ~ (v1 = 0) & precedes(v0, all_20_7, all_20_6) = % 30.93/5.10 | v1)))) % 30.93/5.10 | % 30.93/5.10 | ALPHA: (49) implies: % 30.93/5.10 | (50) on_path(all_20_8, all_20_6) = 0 % 30.93/5.10 | (51) on_path(all_20_7, all_20_6) = 0 % 30.93/5.10 | % 30.93/5.10 | REDUCE: (37), (45) imply: % 30.93/5.10 | (52) ~ (all_51_0 = all_20_4) % 30.93/5.10 | % 30.93/5.10 | BETA: splitting (24) gives: % 30.93/5.10 | % 30.93/5.10 | Case 1: % 30.93/5.10 | | % 30.93/5.10 | | (53) all_20_3 = all_20_4 & head_of(all_20_8) = all_20_4 % 30.93/5.10 | | % 30.93/5.10 | | ALPHA: (53) implies: % 30.93/5.10 | | (54) head_of(all_20_8) = all_20_4 % 30.93/5.10 | | % 30.93/5.10 | | GROUND_INST: instantiating (11) with all_20_4, all_51_0, all_20_8, % 30.93/5.10 | | simplifying with (46), (54) gives: % 30.93/5.10 | | (55) all_51_0 = all_20_4 % 30.93/5.10 | | % 30.93/5.10 | | REDUCE: (52), (55) imply: % 30.93/5.10 | | (56) $false % 30.93/5.10 | | % 30.93/5.10 | | CLOSE: (56) is inconsistent. % 30.93/5.10 | | % 30.93/5.11 | Case 2: % 30.93/5.11 | | % 30.93/5.11 | | (57) tail_of(all_20_8) = all_20_5 & $i(all_20_5) & (all_20_4 = all_20_5 | % 30.93/5.11 | | (all_20_0 = all_20_4 & all_20_1 = all_20_5 & head_of(all_20_2) = % 30.93/5.11 | | all_20_4 & tail_of(all_20_2) = all_20_5)) % 30.93/5.11 | | % 30.93/5.11 | | ALPHA: (57) implies: % 30.93/5.11 | | (58) tail_of(all_20_8) = all_20_5 % 30.93/5.11 | | (59) all_20_4 = all_20_5 | (all_20_0 = all_20_4 & all_20_1 = all_20_5 & % 30.93/5.11 | | head_of(all_20_2) = all_20_4 & tail_of(all_20_2) = all_20_5) % 30.93/5.11 | | % 30.93/5.11 | | BETA: splitting (48) gives: % 30.93/5.11 | | % 30.93/5.11 | | Case 1: % 30.93/5.11 | | | % 30.93/5.11 | | | (60) ~ (all_62_2 = 0) & precedes(all_20_8, all_20_7, all_20_6) = % 30.93/5.11 | | | all_62_2 % 30.93/5.11 | | | % 30.93/5.11 | | | ALPHA: (60) implies: % 30.93/5.11 | | | (61) ~ (all_62_2 = 0) % 30.93/5.11 | | | (62) precedes(all_20_8, all_20_7, all_20_6) = all_62_2 % 30.93/5.11 | | | % 30.93/5.11 | | | GROUND_INST: instantiating (13) with 0, all_62_2, all_20_6, all_20_7, % 30.93/5.11 | | | all_20_8, simplifying with (22), (62) gives: % 30.93/5.11 | | | (63) all_62_2 = 0 % 30.93/5.11 | | | % 30.93/5.11 | | | REDUCE: (61), (63) imply: % 30.93/5.11 | | | (64) $false % 30.93/5.11 | | | % 30.93/5.11 | | | CLOSE: (64) is inconsistent. % 30.93/5.11 | | | % 30.93/5.11 | | Case 2: % 30.93/5.11 | | | % 30.93/5.11 | | | (65) ~ (all_27_0 = 0) & head_of(all_20_7) = all_62_0 & % 30.93/5.11 | | | tail_of(all_20_8) = all_62_1 & $i(all_62_0) & $i(all_62_1) & ! % 30.93/5.11 | | | [v0: $i] : ( ~ (head_of(v0) = all_62_0) | ~ $i(v0) | ? [v1: any] % 30.93/5.11 | | | : ( ~ (v1 = all_62_1) & tail_of(v0) = v1 & $i(v1))) & ! [v0: % 30.93/5.11 | | | $i] : ( ~ (tail_of(v0) = all_62_1) | ~ $i(v0) | ? [v1: any] : % 30.93/5.11 | | | ( ~ (v1 = all_62_0) & head_of(v0) = v1 & $i(v1))) % 30.93/5.11 | | | % 30.93/5.11 | | | ALPHA: (65) implies: % 30.93/5.11 | | | (66) ~ (all_27_0 = 0) % 30.93/5.11 | | | (67) tail_of(all_20_8) = all_62_1 % 30.93/5.11 | | | (68) head_of(all_20_7) = all_62_0 % 30.93/5.11 | | | % 30.93/5.11 | | | BETA: splitting (42) gives: % 30.93/5.11 | | | % 30.93/5.11 | | | Case 1: % 30.93/5.11 | | | | % 30.93/5.11 | | | | (69) all_27_0 = 0 % 30.93/5.11 | | | | % 30.93/5.11 | | | | REDUCE: (66), (69) imply: % 30.93/5.11 | | | | (70) $false % 30.93/5.11 | | | | % 30.93/5.11 | | | | CLOSE: (70) is inconsistent. % 30.93/5.11 | | | | % 30.93/5.11 | | | Case 2: % 30.93/5.11 | | | | % 30.93/5.11 | | | | (71) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ (v2 = 0) & % 30.93/5.11 | | | | sequential(all_20_7, all_20_8) = v2 & ! [v3: $i] : ( ~ % 30.93/5.11 | | | | (precedes(v3, all_20_8, all_20_6) = 0) | ~ $i(v3) | ? % 30.93/5.11 | | | | [v4: int] : ( ~ (v4 = 0) & sequential(all_20_7, v3) = v4)) % 30.93/5.11 | | | | & ! [v3: $i] : ( ~ (sequential(all_20_7, v3) = 0) | ~ % 30.93/5.11 | | | | $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & precedes(v3, % 30.93/5.11 | | | | all_20_8, all_20_6) = v4))) | ( ~ (v1 = 0) & % 30.93/5.11 | | | | on_path(all_20_8, all_20_6) = v1) | ( ~ (v0 = 0) & % 30.93/5.11 | | | | on_path(all_20_7, all_20_6) = v0)) % 30.93/5.11 | | | | % 30.93/5.11 | | | | DELTA: instantiating (71) with fresh symbols all_91_0, all_91_1, % 30.93/5.11 | | | | all_91_2 gives: % 30.93/5.11 | | | | (72) ( ~ (all_91_0 = 0) & sequential(all_20_7, all_20_8) = all_91_0 & % 30.93/5.11 | | | | ! [v0: $i] : ( ~ (precedes(v0, all_20_8, all_20_6) = 0) | ~ % 30.93/5.11 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & sequential(all_20_7, % 30.93/5.11 | | | | v0) = v1)) & ! [v0: $i] : ( ~ (sequential(all_20_7, v0) % 30.93/5.11 | | | | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 30.93/5.11 | | | | precedes(v0, all_20_8, all_20_6) = v1))) | ( ~ (all_91_1 = % 30.93/5.11 | | | | 0) & on_path(all_20_8, all_20_6) = all_91_1) | ( ~ (all_91_2 % 30.93/5.11 | | | | = 0) & on_path(all_20_7, all_20_6) = all_91_2) % 30.93/5.11 | | | | % 30.93/5.11 | | | | BETA: splitting (72) gives: % 30.93/5.11 | | | | % 30.93/5.11 | | | | Case 1: % 30.93/5.11 | | | | | % 30.93/5.11 | | | | | (73) ~ (all_91_0 = 0) & sequential(all_20_7, all_20_8) = all_91_0 % 30.93/5.11 | | | | | & ! [v0: $i] : ( ~ (precedes(v0, all_20_8, all_20_6) = 0) | % 30.93/5.11 | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 30.93/5.11 | | | | | sequential(all_20_7, v0) = v1)) & ! [v0: $i] : ( ~ % 30.93/5.11 | | | | | (sequential(all_20_7, v0) = 0) | ~ $i(v0) | ? [v1: int] : % 30.93/5.11 | | | | | ( ~ (v1 = 0) & precedes(v0, all_20_8, all_20_6) = v1)) % 30.93/5.11 | | | | | % 30.93/5.11 | | | | | ALPHA: (73) implies: % 30.93/5.11 | | | | | (74) ~ (all_91_0 = 0) % 30.93/5.11 | | | | | (75) sequential(all_20_7, all_20_8) = all_91_0 % 30.93/5.11 | | | | | % 30.93/5.11 | | | | | BETA: splitting (47) gives: % 30.93/5.11 | | | | | % 30.93/5.11 | | | | | Case 1: % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | (76) ~ (all_60_0 = 0) & precedes(all_20_7, all_20_8, all_20_6) = % 30.93/5.11 | | | | | | all_60_0 & ! [v0: $i] : ( ~ (head_of(v0) = all_20_4) | ~ % 30.93/5.11 | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_34_2) & tail_of(v0) % 30.93/5.11 | | | | | | = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = % 30.93/5.11 | | | | | | all_34_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 30.93/5.11 | | | | | | all_20_4) & head_of(v0) = v1 & $i(v1))) % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | ALPHA: (76) implies: % 30.93/5.11 | | | | | | (77) ~ (all_60_0 = 0) % 30.93/5.11 | | | | | | (78) precedes(all_20_7, all_20_8, all_20_6) = all_60_0 % 30.93/5.11 | | | | | | (79) ! [v0: $i] : ( ~ (head_of(v0) = all_20_4) | ~ $i(v0) | ? % 30.93/5.11 | | | | | | [v1: any] : ( ~ (v1 = all_34_2) & tail_of(v0) = v1 & % 30.93/5.11 | | | | | | $i(v1))) % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | GROUND_INST: instantiating (9) with all_34_2, all_62_1, all_20_8, % 30.93/5.11 | | | | | | simplifying with (33), (67) gives: % 30.93/5.11 | | | | | | (80) all_62_1 = all_34_2 % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | GROUND_INST: instantiating (9) with all_20_5, all_62_1, all_20_8, % 30.93/5.11 | | | | | | simplifying with (58), (67) gives: % 30.93/5.11 | | | | | | (81) all_62_1 = all_20_5 % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | GROUND_INST: instantiating (11) with all_20_4, all_62_0, all_20_7, % 30.93/5.11 | | | | | | simplifying with (21), (68) gives: % 30.93/5.11 | | | | | | (82) all_62_0 = all_20_4 % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | GROUND_INST: instantiating (13) with all_27_0, all_60_0, all_20_6, % 30.93/5.11 | | | | | | all_20_8, all_20_7, simplifying with (29), (78) gives: % 30.93/5.11 | | | | | | (83) all_60_0 = all_27_0 % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | COMBINE_EQS: (80), (81) imply: % 30.93/5.11 | | | | | | (84) all_34_2 = all_20_5 % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | SIMP: (84) implies: % 30.93/5.11 | | | | | | (85) all_34_2 = all_20_5 % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | GROUND_INST: instantiating (1) with all_20_10, all_20_9, all_20_6, % 30.93/5.11 | | | | | | all_20_8, simplifying with (15), (16), (17), (19), % 30.93/5.11 | | | | | | (31), (50) gives: % 30.93/5.11 | | | | | | (86) ? [v0: $i] : ? [v1: $i] : (in_path(v1, all_20_6) = 0 & % 30.93/5.11 | | | | | | in_path(v0, all_20_6) = 0 & head_of(all_20_8) = v0 & % 30.93/5.11 | | | | | | edge(all_20_8) = 0 & tail_of(all_20_8) = v1 & $i(v1) & % 30.93/5.11 | | | | | | $i(v0)) % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | GROUND_INST: instantiating (1) with all_20_10, all_20_9, all_20_6, % 30.93/5.11 | | | | | | all_20_7, simplifying with (15), (16), (18), (19), % 30.93/5.11 | | | | | | (31), (51) gives: % 30.93/5.11 | | | | | | (87) ? [v0: $i] : ? [v1: $i] : (in_path(v1, all_20_6) = 0 & % 30.93/5.11 | | | | | | in_path(v0, all_20_6) = 0 & head_of(all_20_7) = v0 & % 30.93/5.11 | | | | | | edge(all_20_7) = 0 & tail_of(all_20_7) = v1 & $i(v1) & % 30.93/5.11 | | | | | | $i(v0)) % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | GROUND_INST: instantiating (2) with all_20_7, all_20_8, all_91_0, % 30.93/5.11 | | | | | | simplifying with (17), (18), (75) gives: % 30.93/5.11 | | | | | | (88) all_91_0 = 0 | all_20_7 = all_20_8 | ? [v0: int] : ? [v1: % 30.93/5.11 | | | | | | int] : ? [v2: $i] : ? [v3: $i] : (( ~ (v3 = v2) & % 30.93/5.11 | | | | | | head_of(all_20_7) = v2 & tail_of(all_20_8) = v3 & $i(v3) % 30.93/5.11 | | | | | | & $i(v2)) | ( ~ (v1 = 0) & edge(all_20_8) = v1) | ( ~ % 30.93/5.11 | | | | | | (v0 = 0) & edge(all_20_7) = v0)) % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | DELTA: instantiating (87) with fresh symbols all_134_0, all_134_1 % 30.93/5.11 | | | | | | gives: % 30.93/5.11 | | | | | | (89) in_path(all_134_0, all_20_6) = 0 & in_path(all_134_1, % 30.93/5.11 | | | | | | all_20_6) = 0 & head_of(all_20_7) = all_134_1 & % 30.93/5.11 | | | | | | edge(all_20_7) = 0 & tail_of(all_20_7) = all_134_0 & % 30.93/5.11 | | | | | | $i(all_134_0) & $i(all_134_1) % 30.93/5.11 | | | | | | % 30.93/5.11 | | | | | | ALPHA: (89) implies: % 30.93/5.12 | | | | | | (90) edge(all_20_7) = 0 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | DELTA: instantiating (86) with fresh symbols all_136_0, all_136_1 % 30.93/5.12 | | | | | | gives: % 30.93/5.12 | | | | | | (91) in_path(all_136_0, all_20_6) = 0 & in_path(all_136_1, % 30.93/5.12 | | | | | | all_20_6) = 0 & head_of(all_20_8) = all_136_1 & % 30.93/5.12 | | | | | | edge(all_20_8) = 0 & tail_of(all_20_8) = all_136_0 & % 30.93/5.12 | | | | | | $i(all_136_0) & $i(all_136_1) % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | ALPHA: (91) implies: % 30.93/5.12 | | | | | | (92) edge(all_20_8) = 0 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | BETA: splitting (59) gives: % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | Case 1: % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | (93) all_20_4 = all_20_5 % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | REDUCE: (21), (93) imply: % 30.93/5.12 | | | | | | | (94) head_of(all_20_7) = all_20_5 % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | BETA: splitting (88) gives: % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | Case 1: % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | | (95) all_91_0 = 0 % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | | REDUCE: (74), (95) imply: % 30.93/5.12 | | | | | | | | (96) $false % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | | CLOSE: (96) is inconsistent. % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | Case 2: % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | | (97) all_20_7 = all_20_8 | ? [v0: int] : ? [v1: int] : ? % 30.93/5.12 | | | | | | | | [v2: $i] : ? [v3: $i] : (( ~ (v3 = v2) & % 30.93/5.12 | | | | | | | | head_of(all_20_7) = v2 & tail_of(all_20_8) = v3 & % 30.93/5.12 | | | | | | | | $i(v3) & $i(v2)) | ( ~ (v1 = 0) & edge(all_20_8) = % 30.93/5.12 | | | | | | | | v1) | ( ~ (v0 = 0) & edge(all_20_7) = v0)) % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | | BETA: splitting (97) gives: % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | | Case 1: % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | (98) all_20_7 = all_20_8 % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | REDUCE: (29), (98) imply: % 30.93/5.12 | | | | | | | | | (99) precedes(all_20_8, all_20_8, all_20_6) = all_27_0 % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | REDUCE: (22), (98) imply: % 30.93/5.12 | | | | | | | | | (100) precedes(all_20_8, all_20_8, all_20_6) = 0 % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_27_0, all_20_6, % 30.93/5.12 | | | | | | | | | all_20_8, all_20_8, simplifying with (99), (100) % 30.93/5.12 | | | | | | | | | gives: % 30.93/5.12 | | | | | | | | | (101) all_27_0 = 0 % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | REDUCE: (66), (101) imply: % 30.93/5.12 | | | | | | | | | (102) $false % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | CLOSE: (102) is inconsistent. % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | Case 2: % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | (103) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: % 30.93/5.12 | | | | | | | | | $i] : (( ~ (v3 = v2) & head_of(all_20_7) = v2 & % 30.93/5.12 | | | | | | | | | tail_of(all_20_8) = v3 & $i(v3) & $i(v2)) | ( ~ % 30.93/5.12 | | | | | | | | | (v1 = 0) & edge(all_20_8) = v1) | ( ~ (v0 = 0) & % 30.93/5.12 | | | | | | | | | edge(all_20_7) = v0)) % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_308_0, % 30.93/5.12 | | | | | | | | | all_308_1, all_308_2, all_308_3 gives: % 30.93/5.12 | | | | | | | | | (104) ( ~ (all_308_0 = all_308_1) & head_of(all_20_7) = % 30.93/5.12 | | | | | | | | | all_308_1 & tail_of(all_20_8) = all_308_0 & % 30.93/5.12 | | | | | | | | | $i(all_308_0) & $i(all_308_1)) | ( ~ (all_308_2 = % 30.93/5.12 | | | | | | | | | 0) & edge(all_20_8) = all_308_2) | ( ~ (all_308_3 % 30.93/5.12 | | | | | | | | | = 0) & edge(all_20_7) = all_308_3) % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | BETA: splitting (104) gives: % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | | Case 1: % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | (105) ~ (all_308_0 = all_308_1) & head_of(all_20_7) = % 30.93/5.12 | | | | | | | | | | all_308_1 & tail_of(all_20_8) = all_308_0 & % 30.93/5.12 | | | | | | | | | | $i(all_308_0) & $i(all_308_1) % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | ALPHA: (105) implies: % 30.93/5.12 | | | | | | | | | | (106) ~ (all_308_0 = all_308_1) % 30.93/5.12 | | | | | | | | | | (107) tail_of(all_20_8) = all_308_0 % 30.93/5.12 | | | | | | | | | | (108) head_of(all_20_7) = all_308_1 % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | GROUND_INST: instantiating (9) with all_20_5, all_308_0, % 30.93/5.12 | | | | | | | | | | all_20_8, simplifying with (58), (107) gives: % 30.93/5.12 | | | | | | | | | | (109) all_308_0 = all_20_5 % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | GROUND_INST: instantiating (11) with all_20_5, all_308_1, % 30.93/5.12 | | | | | | | | | | all_20_7, simplifying with (94), (108) gives: % 30.93/5.12 | | | | | | | | | | (110) all_308_1 = all_20_5 % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | REDUCE: (106), (109), (110) imply: % 30.93/5.12 | | | | | | | | | | (111) $false % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | CLOSE: (111) is inconsistent. % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | Case 2: % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | (112) ( ~ (all_308_2 = 0) & edge(all_20_8) = all_308_2) | % 30.93/5.12 | | | | | | | | | | ( ~ (all_308_3 = 0) & edge(all_20_7) = all_308_3) % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | BETA: splitting (112) gives: % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | Case 1: % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | (113) ~ (all_308_2 = 0) & edge(all_20_8) = all_308_2 % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | ALPHA: (113) implies: % 30.93/5.12 | | | | | | | | | | | (114) ~ (all_308_2 = 0) % 30.93/5.12 | | | | | | | | | | | (115) edge(all_20_8) = all_308_2 % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_308_2, all_20_8, % 30.93/5.12 | | | | | | | | | | | simplifying with (92), (115) gives: % 30.93/5.12 | | | | | | | | | | | (116) all_308_2 = 0 % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | REDUCE: (114), (116) imply: % 30.93/5.12 | | | | | | | | | | | (117) $false % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | CLOSE: (117) is inconsistent. % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | Case 2: % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | (118) ~ (all_308_3 = 0) & edge(all_20_7) = all_308_3 % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | ALPHA: (118) implies: % 30.93/5.12 | | | | | | | | | | | (119) ~ (all_308_3 = 0) % 30.93/5.12 | | | | | | | | | | | (120) edge(all_20_7) = all_308_3 % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_308_3, all_20_7, % 30.93/5.12 | | | | | | | | | | | simplifying with (90), (120) gives: % 30.93/5.12 | | | | | | | | | | | (121) all_308_3 = 0 % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | REDUCE: (119), (121) imply: % 30.93/5.12 | | | | | | | | | | | (122) $false % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | | CLOSE: (122) is inconsistent. % 30.93/5.12 | | | | | | | | | | | % 30.93/5.12 | | | | | | | | | | End of split % 30.93/5.12 | | | | | | | | | | % 30.93/5.12 | | | | | | | | | End of split % 30.93/5.12 | | | | | | | | | % 30.93/5.12 | | | | | | | | End of split % 30.93/5.12 | | | | | | | | % 30.93/5.12 | | | | | | | End of split % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | Case 2: % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | (123) all_20_0 = all_20_4 & all_20_1 = all_20_5 & % 30.93/5.12 | | | | | | | head_of(all_20_2) = all_20_4 & tail_of(all_20_2) = % 30.93/5.12 | | | | | | | all_20_5 % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | ALPHA: (123) implies: % 30.93/5.12 | | | | | | | (124) tail_of(all_20_2) = all_20_5 % 30.93/5.12 | | | | | | | (125) head_of(all_20_2) = all_20_4 % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | GROUND_INST: instantiating (79) with all_20_2, simplifying with % 30.93/5.12 | | | | | | | (20), (125) gives: % 30.93/5.12 | | | | | | | (126) ? [v0: any] : ( ~ (v0 = all_34_2) & tail_of(all_20_2) = % 30.93/5.12 | | | | | | | v0 & $i(v0)) % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | DELTA: instantiating (126) with fresh symbol all_327_0 gives: % 30.93/5.12 | | | | | | | (127) ~ (all_327_0 = all_34_2) & tail_of(all_20_2) = all_327_0 % 30.93/5.12 | | | | | | | & $i(all_327_0) % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | ALPHA: (127) implies: % 30.93/5.12 | | | | | | | (128) ~ (all_327_0 = all_34_2) % 30.93/5.12 | | | | | | | (129) tail_of(all_20_2) = all_327_0 % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | REDUCE: (85), (128) imply: % 30.93/5.12 | | | | | | | (130) ~ (all_327_0 = all_20_5) % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | GROUND_INST: instantiating (9) with all_20_5, all_327_0, all_20_2, % 30.93/5.12 | | | | | | | simplifying with (124), (129) gives: % 30.93/5.12 | | | | | | | (131) all_327_0 = all_20_5 % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | REDUCE: (130), (131) imply: % 30.93/5.12 | | | | | | | (132) $false % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | | CLOSE: (132) is inconsistent. % 30.93/5.12 | | | | | | | % 30.93/5.12 | | | | | | End of split % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | Case 2: % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | (133) ~ (all_60_1 = 0) & precedes(all_20_8, all_20_7, all_20_6) % 30.93/5.12 | | | | | | = all_60_1 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | ALPHA: (133) implies: % 30.93/5.12 | | | | | | (134) ~ (all_60_1 = 0) % 30.93/5.12 | | | | | | (135) precedes(all_20_8, all_20_7, all_20_6) = all_60_1 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | GROUND_INST: instantiating (13) with 0, all_60_1, all_20_6, % 30.93/5.12 | | | | | | all_20_7, all_20_8, simplifying with (22), (135) gives: % 30.93/5.12 | | | | | | (136) all_60_1 = 0 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | REDUCE: (134), (136) imply: % 30.93/5.12 | | | | | | (137) $false % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | CLOSE: (137) is inconsistent. % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | End of split % 30.93/5.12 | | | | | % 30.93/5.12 | | | | Case 2: % 30.93/5.12 | | | | | % 30.93/5.12 | | | | | (138) ( ~ (all_91_1 = 0) & on_path(all_20_8, all_20_6) = all_91_1) % 30.93/5.12 | | | | | | ( ~ (all_91_2 = 0) & on_path(all_20_7, all_20_6) = % 30.93/5.12 | | | | | all_91_2) % 30.93/5.12 | | | | | % 30.93/5.12 | | | | | BETA: splitting (138) gives: % 30.93/5.12 | | | | | % 30.93/5.12 | | | | | Case 1: % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | (139) ~ (all_91_1 = 0) & on_path(all_20_8, all_20_6) = all_91_1 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | ALPHA: (139) implies: % 30.93/5.12 | | | | | | (140) ~ (all_91_1 = 0) % 30.93/5.12 | | | | | | (141) on_path(all_20_8, all_20_6) = all_91_1 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | GROUND_INST: instantiating (12) with 0, all_91_1, all_20_6, % 30.93/5.12 | | | | | | all_20_8, simplifying with (50), (141) gives: % 30.93/5.12 | | | | | | (142) all_91_1 = 0 % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | REDUCE: (140), (142) imply: % 30.93/5.12 | | | | | | (143) $false % 30.93/5.12 | | | | | | % 30.93/5.12 | | | | | | CLOSE: (143) is inconsistent. % 30.93/5.12 | | | | | | % 30.93/5.13 | | | | | Case 2: % 30.93/5.13 | | | | | | % 30.93/5.13 | | | | | | (144) ~ (all_91_2 = 0) & on_path(all_20_7, all_20_6) = all_91_2 % 30.93/5.13 | | | | | | % 30.93/5.13 | | | | | | ALPHA: (144) implies: % 30.93/5.13 | | | | | | (145) ~ (all_91_2 = 0) % 30.93/5.13 | | | | | | (146) on_path(all_20_7, all_20_6) = all_91_2 % 30.93/5.13 | | | | | | % 30.93/5.13 | | | | | | GROUND_INST: instantiating (12) with 0, all_91_2, all_20_6, % 30.93/5.13 | | | | | | all_20_7, simplifying with (51), (146) gives: % 30.93/5.13 | | | | | | (147) all_91_2 = 0 % 30.93/5.13 | | | | | | % 30.93/5.13 | | | | | | REDUCE: (145), (147) imply: % 30.93/5.13 | | | | | | (148) $false % 30.93/5.13 | | | | | | % 30.93/5.13 | | | | | | CLOSE: (148) is inconsistent. % 30.93/5.13 | | | | | | % 30.93/5.13 | | | | | End of split % 30.93/5.13 | | | | | % 30.93/5.13 | | | | End of split % 30.93/5.13 | | | | % 30.93/5.13 | | | End of split % 30.93/5.13 | | | % 30.93/5.13 | | End of split % 30.93/5.13 | | % 30.93/5.13 | End of split % 30.93/5.13 | % 30.93/5.13 End of proof % 30.93/5.13 % SZS output end Proof for theBenchmark % 30.93/5.13 % 30.93/5.13 4435ms %------------------------------------------------------------------------------