TSTP Solution File: GRA003+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GRA003+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 : n020.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 11.63s 2.32s
% Output : Proof 16.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.37 % Computer : n020.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun Aug 27 03:42:44 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.65 ________ _____
% 0.23/0.65 ___ __ \_________(_)________________________________
% 0.23/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.23/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.23/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.23/0.65
% 0.23/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.23/0.65 (2023-06-19)
% 0.23/0.65
% 0.23/0.65 (c) Philipp Rümmer, 2009-2023
% 0.23/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.23/0.65 Amanda Stjerna.
% 0.23/0.65 Free software under BSD-3-Clause.
% 0.23/0.65
% 0.23/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.23/0.65
% 0.23/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.23/0.66 Running up to 7 provers in parallel.
% 0.23/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.23/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.23/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.23/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.23/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.23/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.23/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.22/1.16 Prover 4: Preprocessing ...
% 3.22/1.17 Prover 1: Preprocessing ...
% 3.22/1.21 Prover 2: Preprocessing ...
% 3.22/1.21 Prover 5: Preprocessing ...
% 3.22/1.21 Prover 0: Preprocessing ...
% 3.22/1.21 Prover 6: Preprocessing ...
% 3.22/1.21 Prover 3: Preprocessing ...
% 7.71/1.77 Prover 1: Constructing countermodel ...
% 7.71/1.77 Prover 6: Proving ...
% 7.71/1.77 Prover 3: Constructing countermodel ...
% 7.71/1.78 Prover 5: Proving ...
% 7.71/1.82 Prover 2: Proving ...
% 8.79/1.96 Prover 4: Constructing countermodel ...
% 9.05/2.01 Prover 0: Proving ...
% 11.17/2.32 Prover 2: proved (1643ms)
% 11.63/2.32
% 11.63/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.63/2.32
% 11.63/2.32 Prover 0: proved (1652ms)
% 11.63/2.32
% 11.63/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.63/2.32
% 11.63/2.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.63/2.32 Prover 5: stopped
% 11.63/2.32 Prover 6: stopped
% 11.63/2.33 Prover 3: stopped
% 11.63/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.63/2.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.63/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.63/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.89/2.38 Prover 13: Preprocessing ...
% 11.89/2.39 Prover 7: Preprocessing ...
% 11.89/2.40 Prover 8: Preprocessing ...
% 11.89/2.40 Prover 10: Preprocessing ...
% 11.89/2.41 Prover 11: Preprocessing ...
% 13.29/2.56 Prover 10: Warning: ignoring some quantifiers
% 13.29/2.56 Prover 13: Warning: ignoring some quantifiers
% 13.47/2.57 Prover 7: Warning: ignoring some quantifiers
% 13.47/2.57 Prover 10: Constructing countermodel ...
% 13.47/2.58 Prover 8: Warning: ignoring some quantifiers
% 13.47/2.59 Prover 8: Constructing countermodel ...
% 13.47/2.60 Prover 7: Constructing countermodel ...
% 13.47/2.62 Prover 13: Constructing countermodel ...
% 13.90/2.64 Prover 10: gave up
% 13.90/2.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.90/2.68 Prover 7: gave up
% 13.90/2.68 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.90/2.74 Prover 16: Preprocessing ...
% 13.90/2.75 Prover 4: Found proof (size 126)
% 13.90/2.75 Prover 4: proved (2072ms)
% 13.90/2.75 Prover 13: stopped
% 13.90/2.75 Prover 8: stopped
% 13.90/2.75 Prover 1: stopped
% 13.90/2.76 Prover 19: Preprocessing ...
% 13.90/2.77 Prover 16: stopped
% 13.90/2.78 Prover 11: Constructing countermodel ...
% 14.76/2.79 Prover 11: stopped
% 15.35/2.87 Prover 19: Warning: ignoring some quantifiers
% 15.35/2.88 Prover 19: Constructing countermodel ...
% 15.35/2.88 Prover 19: stopped
% 15.35/2.88
% 15.35/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.35/2.88
% 15.56/2.91 % SZS output start Proof for theBenchmark
% 15.56/2.91 Assumptions after simplification:
% 15.56/2.91 ---------------------------------
% 15.56/2.91
% 15.56/2.91 (on_path_properties)
% 15.56/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 15.56/2.94 any] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~
% 15.56/2.94 (head_of(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 15.56/2.94 any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (on_path(v3, v2) = v6 &
% 15.56/2.94 in_path(v8, v2) = v9 & edge(v3) = v7 & tail_of(v3) = v8 & $i(v8) & ( ~ (v6
% 15.72/2.94 = 0) | (v9 = 0 & v7 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 15.72/2.94 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (in_path(v4, v2) =
% 15.72/2.94 v5) | ~ (path(v0, v1, v2) = 0) | ~ (tail_of(v3) = v4) | ~ $i(v3) | ~
% 15.72/2.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] :
% 15.72/2.94 ? [v9: any] : (on_path(v3, v2) = v6 & in_path(v8, v2) = v9 & head_of(v3) =
% 15.72/2.94 v8 & edge(v3) = v7 & $i(v8) & ( ~ (v6 = 0) | (v9 = 0 & v7 = 0 & v5 = 0))))
% 15.72/2.94 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 15.72/2.94 (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 15.72/2.94 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i]
% 15.72/2.94 : ? [v9: any] : (on_path(v3, v2) = v5 & in_path(v8, v2) = v9 & in_path(v6,
% 15.72/2.94 v2) = v7 & head_of(v3) = v6 & tail_of(v3) = v8 & $i(v8) & $i(v6) & ( ~
% 15.72/2.94 (v5 = 0) | (v9 = 0 & v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 15.72/2.94 ! [v2: $i] : ! [v3: $i] : ( ~ (on_path(v3, v2) = 0) | ~ (path(v0, v1, v2) =
% 15.72/2.94 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5:
% 15.72/2.94 $i] : (in_path(v5, v2) = 0 & in_path(v4, v2) = 0 & head_of(v3) = v4 &
% 15.72/2.94 edge(v3) = 0 & tail_of(v3) = v5 & $i(v5) & $i(v4)))
% 15.72/2.94
% 15.72/2.94 (path_properties)
% 15.72/2.94 $i(empty) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) =
% 15.72/2.94 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ?
% 15.72/2.94 [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : (path_cons(v3, empty)
% 15.72/2.94 = v5 & head_of(v3) = v4 & edge(v3) = 0 & tail_of(v3) = v0 & $i(v6) &
% 15.72/2.94 $i(v5) & $i(v4) & $i(v3) & ( ~ (v5 = v2) | ~ (v4 = v1) | ( ! [v9: $i] : (
% 15.72/2.94 ~ (path_cons(v3, v9) = v2) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 =
% 15.72/2.94 0) & path(v1, v1, v9) = v10)) & ! [v9: $i] : ( ~ (path(v1, v1,
% 15.72/2.94 v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v2) &
% 15.72/2.94 path_cons(v3, v9) = v10 & $i(v10))))) & ((v8 = v2 & v7 = 0 &
% 15.72/2.94 path_cons(v3, v6) = v2 & path(v4, v1, v6) = 0) | (v5 = v2 & v4 =
% 15.72/2.94 v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1,
% 15.72/2.94 v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (vertex(v1) = 0 &
% 15.72/2.94 vertex(v0) = 0))
% 15.72/2.94
% 15.72/2.94 (precedes_defn)
% 15.72/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 15.72/2.95 MultipleValueBool] : ! [v6: $i] : ( ~ (precedes(v6, v4, v0) = 0) | ~
% 15.72/2.95 (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v6) | ~
% 15.72/2.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ?
% 15.72/2.95 [v8: any] : ? [v9: any] : (( ~ (v7 = 0) & sequential(v3, v6) = v7) |
% 15.72/2.95 (precedes(v3, v4, v0) = v9 & on_path(v4, v0) = v8 & on_path(v3, v0) = v7 &
% 15.72/2.95 ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 15.72/2.95 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: MultipleValueBool] : ! [v6:
% 15.72/2.95 $i] : ( ~ (sequential(v3, v6) = 0) | ~ (sequential(v3, v4) = v5) | ~
% 15.72/2.95 (path(v1, v2, v0) = 0) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 15.72/2.95 $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: any] : ? [v9: any] : (( ~ (v7 =
% 15.72/2.95 0) & precedes(v6, v4, v0) = v7) | (precedes(v3, v4, v0) = v9 &
% 15.72/2.95 on_path(v4, v0) = v8 & on_path(v3, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)
% 15.72/2.95 | v9 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 15.72/2.95 ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~
% 15.72/2.95 (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 15.72/2.95 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (sequential(v3, v4) =
% 15.72/2.95 v8 & on_path(v4, v0) = v7 & on_path(v3, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 15.72/2.95 0) | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~
% 15.72/2.95 $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10))
% 15.72/2.95 & ! [v9: $i] : ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10:
% 15.72/2.95 int] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10)))))) & ! [v0:
% 15.72/2.95 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.72/2.95 (sequential(v3, v4) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3)
% 15.72/2.95 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 15.72/2.95 any] : (precedes(v3, v4, v0) = v7 & on_path(v4, v0) = v6 & on_path(v3, v0)
% 15.72/2.95 = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))
% 15.72/2.95
% 15.72/2.95 (precedes_properties)
% 15.72/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 15.72/2.95 any] : ( ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4)
% 15.72/2.95 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 15.72/2.95 any] : ? [v8: any] : ? [v9: $i] : ? [v10: int] : ? [v11: int] :
% 15.72/2.95 (precedes(v3, v4, v0) = v6 & on_path(v4, v0) = v8 & on_path(v3, v0) = v7 &
% 15.72/2.95 $i(v9) & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0 & ( ~ (v5 = 0) | ( ! [v12: $i] :
% 15.72/2.95 ( ~ (precedes(v12, v4, v0) = 0) | ~ $i(v12) | ? [v13: int] : ( ~
% 15.72/2.95 (v13 = 0) & sequential(v3, v12) = v13)) & ! [v12: $i] : ( ~
% 15.72/2.95 (sequential(v3, v12) = 0) | ~ $i(v12) | ? [v13: int] : ( ~
% 15.72/2.95 (v13 = 0) & precedes(v12, v4, v0) = v13)))) & (v5 = 0 | (v11 =
% 15.72/2.95 0 & v10 = 0 & precedes(v9, v4, v0) = 0 & sequential(v3, v9) =
% 15.72/2.95 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 15.72/2.95 ! [v4: $i] : ( ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ~
% 15.72/2.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 15.72/2.95 [v6: $i] : ? [v7: int] : ? [v8: int] : (sequential(v3, v4) = v5 &
% 15.72/2.95 on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & $i(v6) & ( ~ (v5 = 0) | ( !
% 15.72/2.95 [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? [v10: int]
% 15.72/2.95 : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9: $i] : ( ~
% 15.72/2.95 (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0)
% 15.72/2.95 & precedes(v9, v4, v0) = v10)))) & (v5 = 0 | (v8 = 0 & v7 = 0 &
% 15.72/2.95 precedes(v6, v4, v0) = 0 & sequential(v3, v6) = 0))))
% 15.72/2.95
% 15.72/2.95 (shortest_path_defn)
% 15.72/2.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 |
% 15.72/2.96 ~ (shortest_path(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 15.72/2.96 [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9:
% 15.72/2.96 int] : (length_of(v2) = v5 & path(v0, v1, v2) = v4 & $i(v6) & $i(v5) & ( ~
% 15.72/2.96 (v4 = 0) | (v7 = 0 & ~ (v9 = 0) & length_of(v6) = v8 &
% 15.72/2.96 less_or_equal(v5, v8) = v9 & path(v0, v1, v6) = 0 & $i(v8))))) & !
% 15.72/2.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (path(v0, v1, v2) =
% 15.72/2.96 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] :
% 15.72/2.96 (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v5 & $i(v5) & ( ~ (v4 = 0)
% 15.72/2.96 | (v3 = 0 & ~ (v1 = v0) & ! [v6: $i] : ! [v7: $i] : ( ~
% 15.72/2.96 (length_of(v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: any] :
% 15.72/2.96 (less_or_equal(v5, v7) = v9 & path(v0, v1, v6) = v8 & ( ~ (v8 = 0) |
% 15.72/2.96 v9 = 0))) & ! [v6: $i] : ( ~ (path(v0, v1, v6) = 0) | ~ $i(v6)
% 15.72/2.96 | ? [v7: $i] : (length_of(v6) = v7 & less_or_equal(v5, v7) = 0 &
% 15.72/2.96 $i(v7))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 15.72/2.96 | ~ (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 15.72/2.96 $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8:
% 15.72/2.96 int] : (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v3 & $i(v5) &
% 15.72/2.96 $i(v3) & (v4 = 0 | (v6 = 0 & ~ (v8 = 0) & length_of(v5) = v7 &
% 15.72/2.96 less_or_equal(v3, v7) = v8 & path(v0, v1, v5) = 0 & $i(v7))))) & !
% 15.72/2.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, v2) = 0) |
% 15.72/2.96 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (length_of(v2) = v3 &
% 15.72/2.96 path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 15.72/2.96 (length_of(v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] :
% 15.72/2.96 (less_or_equal(v3, v5) = v7 & path(v0, v1, v4) = v6 & ( ~ (v6 = 0) | v7
% 15.72/2.96 = 0))) & ! [v4: $i] : ( ~ (path(v0, v1, v4) = 0) | ~ $i(v4) | ?
% 15.72/2.96 [v5: $i] : (length_of(v4) = v5 & less_or_equal(v3, v5) = 0 & $i(v5)))))
% 15.72/2.96 & ! [v0: $i] : ! [v1: $i] : ( ~ (shortest_path(v0, v0, v1) = 0) | ~ $i(v1)
% 15.72/2.96 | ~ $i(v0))
% 15.72/2.96
% 15.72/2.96 (shortest_path_properties)
% 15.72/2.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 15.72/2.96 $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (head_of(v3) =
% 15.72/2.96 v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 15.72/2.96 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (precedes(v3, v2, v4) =
% 15.72/2.96 v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = 0) | ( ~ (v8 = 0) & ! [v9: $i]
% 15.72/2.96 : ( ~ (head_of(v9) = v6) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v5) &
% 15.72/2.96 tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) =
% 15.72/2.96 v5) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) =
% 15.72/2.96 v10 & $i(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.72/2.96 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) |
% 15.72/2.96 ~ (precedes(v3, v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 15.72/2.96 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] :
% 15.72/2.96 (precedes(v2, v3, v4) = v6 & head_of(v3) = v8 & tail_of(v2) = v7 & $i(v8) &
% 15.72/2.96 $i(v7) & ( ~ (v6 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~ (head_of(v9) =
% 15.72/2.96 v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v7) & tail_of(v9) =
% 15.72/2.96 v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v7) | ~ $i(v9)
% 15.72/2.96 | ? [v10: $i] : ( ~ (v10 = v8) & head_of(v9) = v10 & $i(v10)))))))
% 15.72/2.96 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.72/2.96 (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | ~ $i(v4)
% 15.72/2.96 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i]
% 15.72/2.96 : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & head_of(v3) = v6
% 15.72/2.96 & tail_of(v2) = v5 & $i(v6) & $i(v5) & ! [v8: $i] : ( ~ (head_of(v8) =
% 15.72/2.96 v6) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v5) & tail_of(v8) = v9 &
% 15.72/2.96 $i(v9))) & ! [v8: $i] : ( ~ (tail_of(v8) = v5) | ~ $i(v8) | ? [v9:
% 15.72/2.96 $i] : ( ~ (v9 = v6) & head_of(v8) = v9 & $i(v9)))))
% 15.72/2.96
% 15.72/2.96 (vertices_and_edges)
% 15.72/2.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 15.72/2.96 any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 15.72/2.96 (shortest_path(v0, v1, v4) = 0 & precedes(v2, v3, v4) = 0 & path(v0, v1, v4) =
% 15.72/2.96 v9 & vertex(v1) = v6 & vertex(v0) = v5 & edge(v3) = v8 & edge(v2) = v7 &
% 15.72/2.96 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~
% 15.72/2.96 (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v3 = v2 | v1 = v0))
% 15.72/2.96
% 15.72/2.96 (function-axioms)
% 15.72/2.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.72/2.97 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~
% 15.72/2.97 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.72/2.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 15.72/2.97 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & !
% 15.72/2.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 15.72/2.97 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~
% 15.72/2.97 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.72/2.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 15.72/2.97 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 15.72/2.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~
% 15.72/2.97 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 15.72/2.97 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) =
% 15.72/2.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.72/2.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~
% 15.72/2.97 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.72/2.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.72/2.97 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0:
% 15.72/2.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.72/2.97 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0:
% 15.72/2.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.72/2.97 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0:
% 15.72/2.97 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3,
% 15.72/2.97 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 15.72/2.97 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) &
% 15.72/2.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 15.72/2.97 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1:
% 15.72/2.97 $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) =
% 15.72/2.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.72/2.97 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : !
% 15.72/2.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) =
% 15.72/2.97 v0))
% 15.72/2.97
% 15.72/2.97 Further assumptions not needed in the proof:
% 15.72/2.97 --------------------------------------------
% 15.72/2.97 complete_properties, edge_ends_are_vertices, graph_has_them_all,
% 15.72/2.97 in_path_properties, length_defn, no_loops, path_defn,
% 15.72/2.97 path_length_sequential_pairs, sequential_defn, sequential_pairs_and_triangles,
% 15.72/2.97 triangle_defn
% 15.72/2.97
% 15.72/2.97 Those formulas are unsatisfiable:
% 15.72/2.97 ---------------------------------
% 15.72/2.97
% 15.72/2.97 Begin of proof
% 15.72/2.97 |
% 15.72/2.97 | ALPHA: (path_properties) implies:
% 15.72/2.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) |
% 15.72/2.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (vertex(v1) = 0 & vertex(v0) = 0))
% 15.72/2.97 |
% 15.72/2.97 | ALPHA: (on_path_properties) implies:
% 15.72/2.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 15.72/2.97 | ( ~ (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ~ $i(v3) | ~ $i(v2)
% 15.72/2.97 | | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] :
% 15.72/2.97 | ? [v8: $i] : ? [v9: any] : (on_path(v3, v2) = v5 & in_path(v8, v2)
% 15.72/2.97 | = v9 & in_path(v6, v2) = v7 & head_of(v3) = v6 & tail_of(v3) = v8 &
% 15.72/2.97 | $i(v8) & $i(v6) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0 & v4 = 0))))
% 15.72/2.97 |
% 15.72/2.97 | ALPHA: (precedes_defn) implies:
% 15.72/2.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.72/2.97 | ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ (path(v1,
% 15.72/2.97 | v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 15.72/2.97 | $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (sequential(v3,
% 15.72/2.97 | v4) = v8 & on_path(v4, v0) = v7 & on_path(v3, v0) = v6 & ( ~ (v7
% 15.72/2.98 | = 0) | ~ (v6 = 0) | ( ~ (v8 = 0) & ! [v9: $i] : ( ~
% 15.72/2.98 | (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? [v10: int] : ( ~
% 15.72/2.98 | (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9: $i] : ( ~
% 15.72/2.98 | (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~
% 15.72/2.98 | (v10 = 0) & precedes(v9, v4, v0) = v10))))))
% 15.72/2.98 |
% 15.72/2.98 | ALPHA: (precedes_properties) implies:
% 15.72/2.98 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 15.72/2.98 | ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4)
% 15.72/2.98 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 15.72/2.98 | [v6: $i] : ? [v7: int] : ? [v8: int] : (sequential(v3, v4) = v5 &
% 15.72/2.98 | on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & $i(v6) & ( ~ (v5 = 0) |
% 15.72/2.98 | ( ! [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ?
% 15.72/2.98 | [v10: int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & !
% 15.72/2.98 | [v9: $i] : ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10:
% 15.72/2.98 | int] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10)))) & (v5
% 15.72/2.98 | = 0 | (v8 = 0 & v7 = 0 & precedes(v6, v4, v0) = 0 &
% 15.72/2.98 | sequential(v3, v6) = 0))))
% 15.72/2.98 |
% 15.72/2.98 | ALPHA: (shortest_path_defn) implies:
% 15.72/2.98 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1,
% 15.72/2.98 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 15.72/2.98 | (length_of(v2) = v3 & path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] :
% 15.72/2.98 | ! [v5: $i] : ( ~ (length_of(v4) = v5) | ~ $i(v4) | ? [v6: any] :
% 15.72/2.98 | ? [v7: any] : (less_or_equal(v3, v5) = v7 & path(v0, v1, v4) = v6
% 15.72/2.98 | & ( ~ (v6 = 0) | v7 = 0))) & ! [v4: $i] : ( ~ (path(v0, v1,
% 15.72/2.98 | v4) = 0) | ~ $i(v4) | ? [v5: $i] : (length_of(v4) = v5 &
% 15.72/2.98 | less_or_equal(v3, v5) = 0 & $i(v5)))))
% 15.72/2.98 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (path(v0,
% 15.72/2.98 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 15.72/2.98 | : ? [v5: $i] : (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v5
% 15.72/2.98 | & $i(v5) & ( ~ (v4 = 0) | (v3 = 0 & ~ (v1 = v0) & ! [v6: $i] : !
% 15.72/2.98 | [v7: $i] : ( ~ (length_of(v6) = v7) | ~ $i(v6) | ? [v8: any]
% 15.72/2.98 | : ? [v9: any] : (less_or_equal(v5, v7) = v9 & path(v0, v1,
% 15.72/2.98 | v6) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v6: $i] : ( ~
% 15.72/2.98 | (path(v0, v1, v6) = 0) | ~ $i(v6) | ? [v7: $i] :
% 15.72/2.98 | (length_of(v6) = v7 & less_or_equal(v5, v7) = 0 &
% 15.72/2.98 | $i(v7)))))))
% 15.72/2.98 |
% 15.72/2.98 | ALPHA: (shortest_path_properties) implies:
% 15.72/2.98 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 15.72/2.98 | ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) |
% 15.72/2.98 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 15.72/2.98 | $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2,
% 15.72/2.98 | v4) = v7 & head_of(v3) = v6 & tail_of(v2) = v5 & $i(v6) & $i(v5)
% 15.72/2.98 | & ! [v8: $i] : ( ~ (head_of(v8) = v6) | ~ $i(v8) | ? [v9: $i] :
% 15.72/2.98 | ( ~ (v9 = v5) & tail_of(v8) = v9 & $i(v9))) & ! [v8: $i] : ( ~
% 15.72/2.98 | (tail_of(v8) = v5) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v6) &
% 15.72/2.98 | head_of(v8) = v9 & $i(v9)))))
% 15.72/2.98 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.72/2.98 | ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v3,
% 15.72/2.98 | v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 15.72/2.98 | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (precedes(v2,
% 15.72/2.99 | v3, v4) = v6 & head_of(v3) = v8 & tail_of(v2) = v7 & $i(v8) &
% 15.72/2.99 | $i(v7) & ( ~ (v6 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~
% 15.72/2.99 | (head_of(v9) = v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 =
% 15.72/2.99 | v7) & tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~
% 15.72/2.99 | (tail_of(v9) = v7) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 =
% 15.72/2.99 | v8) & head_of(v9) = v10 & $i(v10)))))))
% 15.72/2.99 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.72/2.99 | ! [v5: $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~
% 15.72/2.99 | (head_of(v3) = v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) |
% 15.72/2.99 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] :
% 15.72/2.99 | (precedes(v3, v2, v4) = v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = 0)
% 15.72/2.99 | | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ (head_of(v9) = v6) | ~ $i(v9)
% 15.72/2.99 | | ? [v10: $i] : ( ~ (v10 = v5) & tail_of(v9) = v10 &
% 15.72/2.99 | $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v5) | ~
% 15.72/2.99 | $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) = v10 &
% 15.72/2.99 | $i(v10)))))))
% 15.72/2.99 |
% 15.72/2.99 | ALPHA: (function-axioms) implies:
% 15.72/2.99 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.72/2.99 | : (v1 = v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0))
% 15.72/2.99 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.72/2.99 | : ! [v3: $i] : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3,
% 15.72/2.99 | v2) = v0))
% 15.72/2.99 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.72/2.99 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (path(v4, v3, v2) = v1) |
% 15.72/2.99 | ~ (path(v4, v3, v2) = v0))
% 15.72/2.99 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.72/2.99 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) =
% 15.72/2.99 | v1) | ~ (precedes(v4, v3, v2) = v0))
% 15.72/2.99 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.72/2.99 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (shortest_path(v4, v3, v2)
% 15.72/2.99 | = v1) | ~ (shortest_path(v4, v3, v2) = v0))
% 15.72/2.99 |
% 15.72/2.99 | DELTA: instantiating (vertices_and_edges) with fresh symbols all_20_0,
% 15.72/2.99 | all_20_1, all_20_2, all_20_3, all_20_4, all_20_5, all_20_6, all_20_7,
% 15.72/2.99 | all_20_8, all_20_9 gives:
% 15.72/2.99 | (15) shortest_path(all_20_9, all_20_8, all_20_5) = 0 & precedes(all_20_7,
% 15.72/2.99 | all_20_6, all_20_5) = 0 & path(all_20_9, all_20_8, all_20_5) =
% 15.72/2.99 | all_20_0 & vertex(all_20_8) = all_20_3 & vertex(all_20_9) = all_20_4 &
% 15.72/2.99 | edge(all_20_6) = all_20_1 & edge(all_20_7) = all_20_2 & $i(all_20_5) &
% 15.72/2.99 | $i(all_20_6) & $i(all_20_7) & $i(all_20_8) & $i(all_20_9) & ( ~
% 15.72/2.99 | (all_20_0 = 0) | ~ (all_20_1 = 0) | ~ (all_20_2 = 0) | ~
% 15.72/2.99 | (all_20_3 = 0) | ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8
% 15.72/2.99 | = all_20_9)
% 15.72/2.99 |
% 15.72/2.99 | ALPHA: (15) implies:
% 15.72/2.99 | (16) $i(all_20_9)
% 15.72/2.99 | (17) $i(all_20_8)
% 15.72/2.99 | (18) $i(all_20_7)
% 15.72/2.99 | (19) $i(all_20_6)
% 15.72/2.99 | (20) $i(all_20_5)
% 15.72/2.99 | (21) edge(all_20_7) = all_20_2
% 15.72/2.99 | (22) edge(all_20_6) = all_20_1
% 15.72/2.99 | (23) vertex(all_20_9) = all_20_4
% 15.72/2.99 | (24) vertex(all_20_8) = all_20_3
% 15.72/2.99 | (25) path(all_20_9, all_20_8, all_20_5) = all_20_0
% 15.72/2.99 | (26) precedes(all_20_7, all_20_6, all_20_5) = 0
% 15.72/2.99 | (27) shortest_path(all_20_9, all_20_8, all_20_5) = 0
% 15.72/2.99 | (28) ~ (all_20_0 = 0) | ~ (all_20_1 = 0) | ~ (all_20_2 = 0) | ~
% 15.72/2.99 | (all_20_3 = 0) | ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8 =
% 15.72/2.99 | all_20_9
% 15.72/2.99 |
% 15.72/2.99 | GROUND_INST: instantiating (6) with all_20_9, all_20_8, all_20_5, all_20_0,
% 15.72/2.99 | simplifying with (16), (17), (20), (25) gives:
% 15.72/3.00 | (29) ? [v0: any] : ? [v1: $i] : (shortest_path(all_20_9, all_20_8,
% 15.72/3.00 | all_20_5) = v0 & length_of(all_20_5) = v1 & $i(v1) & ( ~ (v0 = 0)
% 15.72/3.00 | | (all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v2: $i] : ! [v3:
% 15.72/3.00 | $i] : ( ~ (length_of(v2) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 15.72/3.00 | [v5: any] : (less_or_equal(v1, v3) = v5 & path(all_20_9,
% 15.72/3.00 | all_20_8, v2) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2:
% 15.72/3.00 | $i] : ( ~ (path(all_20_9, all_20_8, v2) = 0) | ~ $i(v2) | ?
% 15.72/3.00 | [v3: $i] : (length_of(v2) = v3 & less_or_equal(v1, v3) = 0 &
% 15.72/3.00 | $i(v3))))))
% 15.72/3.00 |
% 15.72/3.00 | GROUND_INST: instantiating (7) with all_20_9, all_20_8, all_20_7, all_20_6,
% 15.72/3.00 | all_20_5, simplifying with (16), (17), (18), (19), (20), (26),
% 15.72/3.00 | (27) gives:
% 15.72/3.00 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 15.72/3.00 | precedes(all_20_6, all_20_7, all_20_5) = v2 & head_of(all_20_6) = v1
% 15.72/3.00 | & tail_of(all_20_7) = v0 & $i(v1) & $i(v0) & ! [v3: $i] : ( ~
% 15.72/3.00 | (head_of(v3) = v1) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v0) &
% 15.72/3.00 | tail_of(v3) = v4 & $i(v4))) & ! [v3: $i] : ( ~ (tail_of(v3) =
% 15.72/3.00 | v0) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & head_of(v3) = v4
% 15.72/3.00 | & $i(v4))))
% 15.72/3.00 |
% 15.72/3.00 | GROUND_INST: instantiating (8) with all_20_9, all_20_8, all_20_6, all_20_7,
% 15.72/3.00 | all_20_5, 0, simplifying with (16), (17), (18), (19), (20), (26),
% 15.72/3.00 | (27) gives:
% 15.72/3.00 | (31) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = 0) &
% 15.72/3.00 | precedes(all_20_6, all_20_7, all_20_5) = v0 & head_of(all_20_7) = v2
% 15.72/3.00 | & tail_of(all_20_6) = v1 & $i(v2) & $i(v1))
% 15.72/3.00 |
% 15.72/3.00 | GROUND_INST: instantiating (5) with all_20_9, all_20_8, all_20_5, simplifying
% 15.72/3.00 | with (16), (17), (20), (27) gives:
% 15.72/3.00 | (32) ? [v0: $i] : (length_of(all_20_5) = v0 & path(all_20_9, all_20_8,
% 15.72/3.00 | all_20_5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 15.72/3.00 | (length_of(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] :
% 15.72/3.00 | (less_or_equal(v0, v2) = v4 & path(all_20_9, all_20_8, v1) = v3 &
% 15.72/3.00 | ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (path(all_20_9,
% 15.72/3.00 | all_20_8, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (length_of(v1)
% 15.72/3.00 | = v2 & less_or_equal(v0, v2) = 0 & $i(v2))))
% 15.72/3.00 |
% 15.72/3.00 | DELTA: instantiating (31) with fresh symbols all_27_0, all_27_1, all_27_2
% 15.72/3.00 | gives:
% 15.72/3.00 | (33) ~ (all_27_2 = 0) & precedes(all_20_6, all_20_7, all_20_5) = all_27_2
% 15.72/3.00 | & head_of(all_20_7) = all_27_0 & tail_of(all_20_6) = all_27_1 &
% 15.72/3.00 | $i(all_27_0) & $i(all_27_1)
% 15.72/3.00 |
% 15.72/3.00 | ALPHA: (33) implies:
% 15.72/3.00 | (34) tail_of(all_20_6) = all_27_1
% 15.72/3.00 | (35) head_of(all_20_7) = all_27_0
% 15.72/3.00 | (36) precedes(all_20_6, all_20_7, all_20_5) = all_27_2
% 15.72/3.00 |
% 15.72/3.00 | DELTA: instantiating (32) with fresh symbol all_29_0 gives:
% 15.72/3.00 | (37) length_of(all_20_5) = all_29_0 & path(all_20_9, all_20_8, all_20_5) =
% 15.72/3.00 | 0 & $i(all_29_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (length_of(v0) =
% 15.72/3.00 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 15.72/3.00 | (less_or_equal(all_29_0, v1) = v3 & path(all_20_9, all_20_8, v0) =
% 15.72/3.00 | v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (path(all_20_9,
% 15.72/3.00 | all_20_8, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (length_of(v0) =
% 15.72/3.00 | v1 & less_or_equal(all_29_0, v1) = 0 & $i(v1)))
% 15.72/3.00 |
% 15.72/3.00 | ALPHA: (37) implies:
% 15.72/3.00 | (38) path(all_20_9, all_20_8, all_20_5) = 0
% 15.72/3.00 |
% 15.72/3.00 | DELTA: instantiating (30) with fresh symbols all_32_0, all_32_1, all_32_2
% 15.72/3.00 | gives:
% 15.72/3.00 | (39) ~ (all_32_0 = 0) & precedes(all_20_6, all_20_7, all_20_5) = all_32_0
% 15.72/3.00 | & head_of(all_20_6) = all_32_1 & tail_of(all_20_7) = all_32_2 &
% 15.72/3.00 | $i(all_32_1) & $i(all_32_2) & ! [v0: $i] : ( ~ (head_of(v0) =
% 15.72/3.00 | all_32_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_2) &
% 15.72/3.00 | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) =
% 15.72/3.00 | all_32_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_1) &
% 15.72/3.00 | head_of(v0) = v1 & $i(v1)))
% 15.72/3.00 |
% 15.72/3.00 | ALPHA: (39) implies:
% 15.72/3.00 | (40) ~ (all_32_0 = 0)
% 15.72/3.00 | (41) tail_of(all_20_7) = all_32_2
% 15.72/3.00 | (42) head_of(all_20_6) = all_32_1
% 15.72/3.00 | (43) precedes(all_20_6, all_20_7, all_20_5) = all_32_0
% 15.72/3.00 |
% 15.72/3.00 | DELTA: instantiating (29) with fresh symbols all_35_0, all_35_1 gives:
% 15.72/3.00 | (44) shortest_path(all_20_9, all_20_8, all_20_5) = all_35_1 &
% 15.72/3.00 | length_of(all_20_5) = all_35_0 & $i(all_35_0) & ( ~ (all_35_1 = 0) |
% 15.72/3.00 | (all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v0: $i] : ! [v1: $i]
% 15.72/3.00 | : ( ~ (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 15.72/3.00 | any] : (less_or_equal(all_35_0, v1) = v3 & path(all_20_9,
% 15.72/3.00 | all_20_8, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i]
% 15.72/3.00 | : ( ~ (path(all_20_9, all_20_8, v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 15.72/3.00 | : (length_of(v0) = v1 & less_or_equal(all_35_0, v1) = 0 &
% 15.72/3.01 | $i(v1)))))
% 15.72/3.01 |
% 15.72/3.01 | ALPHA: (44) implies:
% 15.72/3.01 | (45) shortest_path(all_20_9, all_20_8, all_20_5) = all_35_1
% 15.72/3.01 | (46) ~ (all_35_1 = 0) | (all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v0:
% 15.72/3.01 | $i] : ! [v1: $i] : ( ~ (length_of(v0) = v1) | ~ $i(v0) | ? [v2:
% 15.72/3.01 | any] : ? [v3: any] : (less_or_equal(all_35_0, v1) = v3 &
% 15.72/3.01 | path(all_20_9, all_20_8, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) &
% 15.72/3.01 | ! [v0: $i] : ( ~ (path(all_20_9, all_20_8, v0) = 0) | ~ $i(v0) | ?
% 15.72/3.01 | [v1: $i] : (length_of(v0) = v1 & less_or_equal(all_35_0, v1) = 0 &
% 15.72/3.01 | $i(v1))))
% 15.72/3.01 |
% 15.72/3.01 | GROUND_INST: instantiating (12) with all_20_0, 0, all_20_5, all_20_8,
% 15.72/3.01 | all_20_9, simplifying with (25), (38) gives:
% 15.72/3.01 | (47) all_20_0 = 0
% 15.72/3.01 |
% 15.72/3.01 | GROUND_INST: instantiating (13) with all_27_2, all_32_0, all_20_5, all_20_7,
% 15.72/3.01 | all_20_6, simplifying with (36), (43) gives:
% 15.72/3.01 | (48) all_32_0 = all_27_2
% 15.72/3.01 |
% 15.72/3.01 | GROUND_INST: instantiating (14) with 0, all_35_1, all_20_5, all_20_8,
% 15.72/3.01 | all_20_9, simplifying with (27), (45) gives:
% 15.72/3.01 | (49) all_35_1 = 0
% 15.72/3.01 |
% 15.72/3.01 | REDUCE: (40), (48) imply:
% 15.72/3.01 | (50) ~ (all_27_2 = 0)
% 15.72/3.01 |
% 15.72/3.01 | BETA: splitting (46) gives:
% 15.72/3.01 |
% 15.72/3.01 | Case 1:
% 15.72/3.01 | |
% 15.72/3.01 | | (51) ~ (all_35_1 = 0)
% 15.72/3.01 | |
% 15.72/3.01 | | REDUCE: (49), (51) imply:
% 15.72/3.01 | | (52) $false
% 15.72/3.01 | |
% 15.72/3.01 | | CLOSE: (52) is inconsistent.
% 15.72/3.01 | |
% 15.72/3.01 | Case 2:
% 15.72/3.01 | |
% 15.72/3.01 | | (53) all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v0: $i] : ! [v1: $i]
% 15.72/3.01 | | : ( ~ (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any]
% 15.72/3.01 | | : (less_or_equal(all_35_0, v1) = v3 & path(all_20_9, all_20_8, v0)
% 15.72/3.01 | | = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 15.72/3.01 | | (path(all_20_9, all_20_8, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 15.72/3.01 | | (length_of(v0) = v1 & less_or_equal(all_35_0, v1) = 0 & $i(v1)))
% 15.72/3.01 | |
% 15.72/3.01 | | ALPHA: (53) implies:
% 15.72/3.01 | | (54) ~ (all_20_8 = all_20_9)
% 15.72/3.01 | |
% 15.72/3.01 | | GROUND_INST: instantiating (9) with all_20_9, all_20_8, all_20_7, all_20_7,
% 15.72/3.01 | | all_20_5, all_32_2, all_27_0, simplifying with (16), (17),
% 15.72/3.01 | | (18), (20), (27), (35), (41) gives:
% 15.72/3.01 | | (55) ? [v0: any] : ? [v1: any] : (precedes(all_20_7, all_20_7,
% 15.72/3.01 | | all_20_5) = v1 & precedes(all_20_7, all_20_7, all_20_5) = v0 & (
% 15.72/3.01 | | ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) =
% 15.72/3.01 | | all_27_0) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_32_2)
% 15.72/3.01 | | & tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~
% 15.72/3.01 | | (tail_of(v2) = all_32_2) | ~ $i(v2) | ? [v3: any] : ( ~
% 15.72/3.01 | | (v3 = all_27_0) & head_of(v2) = v3 & $i(v3))))))
% 15.72/3.01 | |
% 15.72/3.01 | | GROUND_INST: instantiating (9) with all_20_9, all_20_8, all_20_6, all_20_6,
% 15.72/3.01 | | all_20_5, all_27_1, all_32_1, simplifying with (16), (17),
% 15.72/3.01 | | (19), (20), (27), (34), (42) gives:
% 15.72/3.01 | | (56) ? [v0: any] : ? [v1: any] : (precedes(all_20_6, all_20_6,
% 15.72/3.01 | | all_20_5) = v1 & precedes(all_20_6, all_20_6, all_20_5) = v0 & (
% 15.72/3.01 | | ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) =
% 15.72/3.01 | | all_32_1) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_27_1)
% 15.72/3.01 | | & tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~
% 15.72/3.01 | | (tail_of(v2) = all_27_1) | ~ $i(v2) | ? [v3: any] : ( ~
% 15.72/3.01 | | (v3 = all_32_1) & head_of(v2) = v3 & $i(v3))))))
% 15.72/3.01 | |
% 15.72/3.01 | | GROUND_INST: instantiating (9) with all_20_9, all_20_8, all_20_7, all_20_6,
% 15.72/3.01 | | all_20_5, all_32_2, all_32_1, simplifying with (16), (17),
% 15.72/3.01 | | (18), (19), (20), (27), (41), (42) gives:
% 15.72/3.01 | | (57) ? [v0: any] : ? [v1: any] : (precedes(all_20_6, all_20_7,
% 15.72/3.01 | | all_20_5) = v1 & precedes(all_20_7, all_20_6, all_20_5) = v0 & (
% 15.72/3.01 | | ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) =
% 15.72/3.01 | | all_32_1) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_32_2)
% 15.72/3.01 | | & tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~
% 15.72/3.01 | | (tail_of(v2) = all_32_2) | ~ $i(v2) | ? [v3: any] : ( ~
% 15.72/3.01 | | (v3 = all_32_1) & head_of(v2) = v3 & $i(v3))))))
% 15.72/3.01 | |
% 15.72/3.02 | | GROUND_INST: instantiating (4) with all_20_5, all_20_9, all_20_8, all_20_7,
% 15.72/3.02 | | all_20_6, simplifying with (16), (17), (18), (19), (20), (26),
% 15.72/3.02 | | (38) gives:
% 15.72/3.02 | | (58) ? [v0: any] : ? [v1: $i] : ? [v2: int] : ? [v3: int] :
% 15.72/3.02 | | (sequential(all_20_7, all_20_6) = v0 & on_path(all_20_6, all_20_5) =
% 15.72/3.02 | | 0 & on_path(all_20_7, all_20_5) = 0 & $i(v1) & ( ~ (v0 = 0) | ( !
% 15.72/3.02 | | [v4: $i] : ( ~ (precedes(v4, all_20_6, all_20_5) = 0) | ~
% 15.72/3.02 | | $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & sequential(all_20_7,
% 15.72/3.02 | | v4) = v5)) & ! [v4: $i] : ( ~ (sequential(all_20_7, v4)
% 15.72/3.02 | | = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 15.72/3.02 | | precedes(v4, all_20_6, all_20_5) = v5)))) & (v0 = 0 | (v3
% 15.72/3.02 | | = 0 & v2 = 0 & precedes(v1, all_20_6, all_20_5) = 0 &
% 15.72/3.02 | | sequential(all_20_7, v1) = 0)))
% 15.72/3.02 | |
% 15.72/3.02 | | GROUND_INST: instantiating (2) with all_20_9, all_20_8, all_20_5, all_20_6,
% 15.72/3.02 | | all_20_1, simplifying with (16), (17), (19), (20), (22), (38)
% 15.72/3.02 | | gives:
% 15.72/3.02 | | (59) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 15.72/3.02 | | any] : (on_path(all_20_6, all_20_5) = v0 & in_path(v3, all_20_5) =
% 15.72/3.02 | | v4 & in_path(v1, all_20_5) = v2 & head_of(all_20_6) = v1 &
% 15.72/3.02 | | tail_of(all_20_6) = v3 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0
% 15.72/3.02 | | & v2 = 0 & all_20_1 = 0)))
% 15.72/3.02 | |
% 15.72/3.02 | | GROUND_INST: instantiating (2) with all_20_9, all_20_8, all_20_5, all_20_7,
% 15.72/3.02 | | all_20_2, simplifying with (16), (17), (18), (20), (21), (38)
% 15.72/3.02 | | gives:
% 15.72/3.02 | | (60) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 15.72/3.02 | | any] : (on_path(all_20_7, all_20_5) = v0 & in_path(v3, all_20_5) =
% 15.72/3.02 | | v4 & in_path(v1, all_20_5) = v2 & head_of(all_20_7) = v1 &
% 15.72/3.02 | | tail_of(all_20_7) = v3 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0
% 15.72/3.02 | | & v2 = 0 & all_20_2 = 0)))
% 15.72/3.02 | |
% 15.72/3.02 | | GROUND_INST: instantiating (1) with all_20_9, all_20_8, all_20_5,
% 15.72/3.02 | | simplifying with (16), (17), (20), (38) gives:
% 15.72/3.02 | | (61) vertex(all_20_8) = 0 & vertex(all_20_9) = 0
% 15.72/3.02 | |
% 15.72/3.02 | | ALPHA: (61) implies:
% 15.72/3.02 | | (62) vertex(all_20_9) = 0
% 15.72/3.02 | | (63) vertex(all_20_8) = 0
% 15.72/3.02 | |
% 15.72/3.02 | | GROUND_INST: instantiating (3) with all_20_5, all_20_9, all_20_8, all_20_6,
% 15.72/3.02 | | all_20_7, all_27_2, simplifying with (16), (17), (18), (19),
% 15.72/3.02 | | (20), (36), (38) gives:
% 15.72/3.02 | | (64) all_27_2 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 15.72/3.02 | | (sequential(all_20_6, all_20_7) = v2 & on_path(all_20_6, all_20_5) =
% 15.72/3.02 | | v0 & on_path(all_20_7, all_20_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)
% 15.72/3.02 | | | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ (precedes(v3, all_20_7,
% 15.72/3.02 | | all_20_5) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0)
% 15.72/3.02 | | & sequential(all_20_6, v3) = v4)) & ! [v3: $i] : ( ~
% 15.72/3.02 | | (sequential(all_20_6, v3) = 0) | ~ $i(v3) | ? [v4: int] :
% 15.72/3.02 | | ( ~ (v4 = 0) & precedes(v3, all_20_7, all_20_5) = v4)))))
% 15.72/3.02 | |
% 15.72/3.02 | | GROUND_INST: instantiating (8) with all_20_9, all_20_8, all_20_7, all_20_6,
% 15.72/3.02 | | all_20_5, all_27_2, simplifying with (16), (17), (18), (19),
% 15.72/3.02 | | (20), (27), (36) gives:
% 15.72/3.02 | | (65) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (precedes(all_20_7,
% 15.72/3.02 | | all_20_6, all_20_5) = v0 & head_of(all_20_6) = v2 &
% 15.72/3.02 | | tail_of(all_20_7) = v1 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ~
% 15.72/3.02 | | (all_27_2 = 0) & ! [v3: $i] : ( ~ (head_of(v3) = v2) | ~
% 15.72/3.02 | | $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & tail_of(v3) = v4 &
% 15.72/3.02 | | $i(v4))) & ! [v3: $i] : ( ~ (tail_of(v3) = v1) | ~
% 15.72/3.02 | | $i(v3) | ? [v4: $i] : ( ~ (v4 = v2) & head_of(v3) = v4 &
% 15.72/3.02 | | $i(v4))))))
% 15.72/3.02 | |
% 15.72/3.02 | | DELTA: instantiating (60) with fresh symbols all_86_0, all_86_1, all_86_2,
% 15.72/3.02 | | all_86_3, all_86_4 gives:
% 15.72/3.02 | | (66) on_path(all_20_7, all_20_5) = all_86_4 & in_path(all_86_1, all_20_5)
% 15.72/3.02 | | = all_86_0 & in_path(all_86_3, all_20_5) = all_86_2 &
% 15.72/3.02 | | head_of(all_20_7) = all_86_3 & tail_of(all_20_7) = all_86_1 &
% 15.72/3.02 | | $i(all_86_1) & $i(all_86_3) & ( ~ (all_86_4 = 0) | (all_86_0 = 0 &
% 15.72/3.02 | | all_86_2 = 0 & all_20_2 = 0))
% 15.72/3.02 | |
% 15.72/3.02 | | ALPHA: (66) implies:
% 15.72/3.02 | | (67) on_path(all_20_7, all_20_5) = all_86_4
% 15.72/3.02 | | (68) ~ (all_86_4 = 0) | (all_86_0 = 0 & all_86_2 = 0 & all_20_2 = 0)
% 15.72/3.02 | |
% 15.72/3.02 | | DELTA: instantiating (59) with fresh symbols all_90_0, all_90_1, all_90_2,
% 15.72/3.02 | | all_90_3, all_90_4 gives:
% 15.72/3.02 | | (69) on_path(all_20_6, all_20_5) = all_90_4 & in_path(all_90_1, all_20_5)
% 15.72/3.02 | | = all_90_0 & in_path(all_90_3, all_20_5) = all_90_2 &
% 15.72/3.02 | | head_of(all_20_6) = all_90_3 & tail_of(all_20_6) = all_90_1 &
% 15.72/3.02 | | $i(all_90_1) & $i(all_90_3) & ( ~ (all_90_4 = 0) | (all_90_0 = 0 &
% 15.72/3.02 | | all_90_2 = 0 & all_20_1 = 0))
% 15.72/3.02 | |
% 15.72/3.02 | | ALPHA: (69) implies:
% 15.72/3.02 | | (70) on_path(all_20_6, all_20_5) = all_90_4
% 15.72/3.02 | | (71) ~ (all_90_4 = 0) | (all_90_0 = 0 & all_90_2 = 0 & all_20_1 = 0)
% 15.72/3.02 | |
% 15.72/3.02 | | DELTA: instantiating (55) with fresh symbols all_94_0, all_94_1 gives:
% 15.72/3.02 | | (72) precedes(all_20_7, all_20_7, all_20_5) = all_94_0 &
% 15.72/3.02 | | precedes(all_20_7, all_20_7, all_20_5) = all_94_1 & ( ~ (all_94_1 =
% 15.72/3.02 | | 0) | ( ~ (all_94_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) =
% 15.72/3.02 | | all_27_0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_2) &
% 15.72/3.02 | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0)
% 15.72/3.02 | | = all_32_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_27_0)
% 15.72/3.02 | | & head_of(v0) = v1 & $i(v1)))))
% 15.72/3.02 | |
% 15.72/3.02 | | ALPHA: (72) implies:
% 15.72/3.02 | | (73) precedes(all_20_7, all_20_7, all_20_5) = all_94_1
% 15.72/3.02 | | (74) precedes(all_20_7, all_20_7, all_20_5) = all_94_0
% 15.72/3.02 | |
% 15.72/3.02 | | DELTA: instantiating (57) with fresh symbols all_96_0, all_96_1 gives:
% 15.72/3.02 | | (75) precedes(all_20_6, all_20_7, all_20_5) = all_96_0 &
% 15.72/3.02 | | precedes(all_20_7, all_20_6, all_20_5) = all_96_1 & ( ~ (all_96_1 =
% 15.72/3.02 | | 0) | ( ~ (all_96_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) =
% 15.72/3.02 | | all_32_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_2) &
% 15.72/3.02 | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0)
% 15.72/3.02 | | = all_32_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_1)
% 15.72/3.02 | | & head_of(v0) = v1 & $i(v1)))))
% 15.72/3.02 | |
% 15.72/3.02 | | ALPHA: (75) implies:
% 15.72/3.02 | | (76) precedes(all_20_7, all_20_6, all_20_5) = all_96_1
% 15.72/3.02 | | (77) precedes(all_20_6, all_20_7, all_20_5) = all_96_0
% 15.72/3.02 | |
% 15.72/3.02 | | DELTA: instantiating (56) with fresh symbols all_98_0, all_98_1 gives:
% 15.72/3.02 | | (78) precedes(all_20_6, all_20_6, all_20_5) = all_98_0 &
% 15.72/3.02 | | precedes(all_20_6, all_20_6, all_20_5) = all_98_1 & ( ~ (all_98_1 =
% 15.72/3.02 | | 0) | ( ~ (all_98_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) =
% 15.72/3.02 | | all_32_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_27_1) &
% 15.72/3.02 | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0)
% 15.72/3.02 | | = all_27_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_1)
% 15.72/3.02 | | & head_of(v0) = v1 & $i(v1)))))
% 15.72/3.02 | |
% 15.72/3.02 | | ALPHA: (78) implies:
% 15.72/3.02 | | (79) precedes(all_20_6, all_20_6, all_20_5) = all_98_1
% 15.72/3.03 | | (80) precedes(all_20_6, all_20_6, all_20_5) = all_98_0
% 15.72/3.03 | |
% 15.72/3.03 | | DELTA: instantiating (65) with fresh symbols all_100_0, all_100_1, all_100_2
% 15.72/3.03 | | gives:
% 15.72/3.03 | | (81) precedes(all_20_7, all_20_6, all_20_5) = all_100_2 &
% 15.72/3.03 | | head_of(all_20_6) = all_100_0 & tail_of(all_20_7) = all_100_1 &
% 15.72/3.03 | | $i(all_100_0) & $i(all_100_1) & ( ~ (all_100_2 = 0) | ( ~ (all_27_2
% 15.72/3.03 | | = 0) & ! [v0: $i] : ( ~ (head_of(v0) = all_100_0) | ~ $i(v0)
% 15.72/3.03 | | | ? [v1: any] : ( ~ (v1 = all_100_1) & tail_of(v0) = v1 &
% 15.72/3.03 | | $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = all_100_1) | ~
% 15.72/3.03 | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_100_0) & head_of(v0) =
% 15.72/3.03 | | v1 & $i(v1)))))
% 15.72/3.03 | |
% 15.72/3.03 | | ALPHA: (81) implies:
% 15.72/3.03 | | (82) precedes(all_20_7, all_20_6, all_20_5) = all_100_2
% 15.72/3.03 | |
% 15.72/3.03 | | DELTA: instantiating (58) with fresh symbols all_102_0, all_102_1,
% 15.72/3.03 | | all_102_2, all_102_3 gives:
% 15.72/3.03 | | (83) sequential(all_20_7, all_20_6) = all_102_3 & on_path(all_20_6,
% 15.72/3.03 | | all_20_5) = 0 & on_path(all_20_7, all_20_5) = 0 & $i(all_102_2) &
% 15.72/3.03 | | ( ~ (all_102_3 = 0) | ( ! [v0: $i] : ( ~ (precedes(v0, all_20_6,
% 15.72/3.03 | | all_20_5) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 15.72/3.03 | | sequential(all_20_7, v0) = v1)) & ! [v0: $i] : ( ~
% 15.72/3.03 | | (sequential(all_20_7, v0) = 0) | ~ $i(v0) | ? [v1: int] : (
% 15.72/3.03 | | ~ (v1 = 0) & precedes(v0, all_20_6, all_20_5) = v1)))) &
% 15.72/3.03 | | (all_102_3 = 0 | (all_102_0 = 0 & all_102_1 = 0 &
% 15.72/3.03 | | precedes(all_102_2, all_20_6, all_20_5) = 0 &
% 15.72/3.03 | | sequential(all_20_7, all_102_2) = 0))
% 15.72/3.03 | |
% 15.72/3.03 | | ALPHA: (83) implies:
% 15.72/3.03 | | (84) on_path(all_20_7, all_20_5) = 0
% 15.72/3.03 | | (85) on_path(all_20_6, all_20_5) = 0
% 15.72/3.03 | |
% 15.72/3.03 | | BETA: splitting (64) gives:
% 15.72/3.03 | |
% 15.72/3.03 | | Case 1:
% 15.72/3.03 | | |
% 15.72/3.03 | | | (86) all_27_2 = 0
% 15.72/3.03 | | |
% 15.72/3.03 | | | REDUCE: (50), (86) imply:
% 15.72/3.03 | | | (87) $false
% 15.72/3.03 | | |
% 15.72/3.03 | | | CLOSE: (87) is inconsistent.
% 15.72/3.03 | | |
% 15.72/3.03 | | Case 2:
% 15.72/3.03 | | |
% 15.72/3.03 | | | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sequential(all_20_6,
% 15.72/3.03 | | | all_20_7) = v2 & on_path(all_20_6, all_20_5) = v0 &
% 15.72/3.03 | | | on_path(all_20_7, all_20_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 15.72/3.03 | | | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ (precedes(v3, all_20_7,
% 15.72/3.03 | | | all_20_5) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 =
% 15.72/3.03 | | | 0) & sequential(all_20_6, v3) = v4)) & ! [v3: $i] : (
% 15.72/3.03 | | | ~ (sequential(all_20_6, v3) = 0) | ~ $i(v3) | ? [v4:
% 15.72/3.03 | | | int] : ( ~ (v4 = 0) & precedes(v3, all_20_7, all_20_5) =
% 15.72/3.03 | | | v4)))))
% 15.72/3.03 | | |
% 15.72/3.03 | | | DELTA: instantiating (88) with fresh symbols all_115_0, all_115_1,
% 15.72/3.03 | | | all_115_2 gives:
% 15.72/3.03 | | | (89) sequential(all_20_6, all_20_7) = all_115_0 & on_path(all_20_6,
% 15.72/3.03 | | | all_20_5) = all_115_2 & on_path(all_20_7, all_20_5) = all_115_1
% 15.72/3.03 | | | & ( ~ (all_115_1 = 0) | ~ (all_115_2 = 0) | ( ~ (all_115_0 = 0) &
% 15.72/3.03 | | | ! [v0: $i] : ( ~ (precedes(v0, all_20_7, all_20_5) = 0) | ~
% 15.72/3.03 | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & sequential(all_20_6,
% 15.72/3.03 | | | v0) = v1)) & ! [v0: $i] : ( ~ (sequential(all_20_6, v0)
% 15.72/3.03 | | | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 15.72/3.03 | | | precedes(v0, all_20_7, all_20_5) = v1))))
% 15.72/3.03 | | |
% 15.72/3.03 | | | ALPHA: (89) implies:
% 15.72/3.03 | | | (90) on_path(all_20_7, all_20_5) = all_115_1
% 15.72/3.03 | | | (91) on_path(all_20_6, all_20_5) = all_115_2
% 15.72/3.03 | | |
% 15.72/3.03 | | | GROUND_INST: instantiating (10) with all_20_4, 0, all_20_9, simplifying
% 15.72/3.03 | | | with (23), (62) gives:
% 15.72/3.03 | | | (92) all_20_4 = 0
% 15.72/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (10) with all_20_3, 0, all_20_8, simplifying
% 16.18/3.03 | | | with (24), (63) gives:
% 16.18/3.03 | | | (93) all_20_3 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (11) with all_86_4, all_115_1, all_20_5,
% 16.18/3.03 | | | all_20_7, simplifying with (67), (90) gives:
% 16.18/3.03 | | | (94) all_115_1 = all_86_4
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (11) with 0, all_115_1, all_20_5, all_20_7,
% 16.18/3.03 | | | simplifying with (84), (90) gives:
% 16.18/3.03 | | | (95) all_115_1 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (11) with all_90_4, all_115_2, all_20_5,
% 16.18/3.03 | | | all_20_6, simplifying with (70), (91) gives:
% 16.18/3.03 | | | (96) all_115_2 = all_90_4
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (11) with 0, all_115_2, all_20_5, all_20_6,
% 16.18/3.03 | | | simplifying with (85), (91) gives:
% 16.18/3.03 | | | (97) all_115_2 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_94_1, all_94_0, all_20_5,
% 16.18/3.03 | | | all_20_7, all_20_7, simplifying with (73), (74) gives:
% 16.18/3.03 | | | (98) all_94_0 = all_94_1
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (13) with 0, all_100_2, all_20_5, all_20_6,
% 16.18/3.03 | | | all_20_7, simplifying with (26), (82) gives:
% 16.18/3.03 | | | (99) all_100_2 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_96_1, all_100_2, all_20_5,
% 16.18/3.03 | | | all_20_6, all_20_7, simplifying with (76), (82) gives:
% 16.18/3.03 | | | (100) all_100_2 = all_96_1
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_27_2, all_96_0, all_20_5,
% 16.18/3.03 | | | all_20_7, all_20_6, simplifying with (36), (77) gives:
% 16.18/3.03 | | | (101) all_96_0 = all_27_2
% 16.18/3.03 | | |
% 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_98_1, all_98_0, all_20_5,
% 16.18/3.03 | | | all_20_6, all_20_6, simplifying with (79), (80) gives:
% 16.18/3.03 | | | (102) all_98_0 = all_98_1
% 16.18/3.03 | | |
% 16.18/3.03 | | | COMBINE_EQS: (94), (95) imply:
% 16.18/3.03 | | | (103) all_86_4 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | SIMP: (103) implies:
% 16.18/3.03 | | | (104) all_86_4 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | COMBINE_EQS: (96), (97) imply:
% 16.18/3.03 | | | (105) all_90_4 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | COMBINE_EQS: (99), (100) imply:
% 16.18/3.03 | | | (106) all_96_1 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | SIMP: (106) implies:
% 16.18/3.03 | | | (107) all_96_1 = 0
% 16.18/3.03 | | |
% 16.18/3.03 | | | BETA: splitting (68) gives:
% 16.18/3.03 | | |
% 16.18/3.03 | | | Case 1:
% 16.18/3.03 | | | |
% 16.18/3.03 | | | | (108) ~ (all_86_4 = 0)
% 16.18/3.03 | | | |
% 16.18/3.03 | | | | REDUCE: (104), (108) imply:
% 16.18/3.03 | | | | (109) $false
% 16.18/3.03 | | | |
% 16.18/3.03 | | | | CLOSE: (109) is inconsistent.
% 16.18/3.03 | | | |
% 16.18/3.03 | | | Case 2:
% 16.18/3.03 | | | |
% 16.18/3.03 | | | | (110) all_86_0 = 0 & all_86_2 = 0 & all_20_2 = 0
% 16.18/3.03 | | | |
% 16.18/3.03 | | | | ALPHA: (110) implies:
% 16.18/3.03 | | | | (111) all_20_2 = 0
% 16.18/3.03 | | | |
% 16.18/3.03 | | | | BETA: splitting (71) gives:
% 16.18/3.03 | | | |
% 16.18/3.03 | | | | Case 1:
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | | (112) ~ (all_90_4 = 0)
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | | REDUCE: (105), (112) imply:
% 16.18/3.03 | | | | | (113) $false
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | | CLOSE: (113) is inconsistent.
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | Case 2:
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | | (114) all_90_0 = 0 & all_90_2 = 0 & all_20_1 = 0
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | | ALPHA: (114) implies:
% 16.18/3.03 | | | | | (115) all_20_1 = 0
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | | BETA: splitting (28) gives:
% 16.18/3.03 | | | | |
% 16.18/3.03 | | | | | Case 1:
% 16.18/3.03 | | | | | |
% 16.18/3.03 | | | | | | (116) ~ (all_20_0 = 0)
% 16.18/3.03 | | | | | |
% 16.18/3.03 | | | | | | REDUCE: (47), (116) imply:
% 16.18/3.03 | | | | | | (117) $false
% 16.18/3.03 | | | | | |
% 16.18/3.04 | | | | | | CLOSE: (117) is inconsistent.
% 16.18/3.04 | | | | | |
% 16.18/3.04 | | | | | Case 2:
% 16.18/3.04 | | | | | |
% 16.18/3.04 | | | | | | (118) ~ (all_20_1 = 0) | ~ (all_20_2 = 0) | ~ (all_20_3 = 0) |
% 16.18/3.04 | | | | | | ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8 =
% 16.18/3.04 | | | | | | all_20_9
% 16.18/3.04 | | | | | |
% 16.18/3.04 | | | | | | BETA: splitting (118) gives:
% 16.18/3.04 | | | | | |
% 16.18/3.04 | | | | | | Case 1:
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | | (119) ~ (all_20_1 = 0)
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | | REDUCE: (115), (119) imply:
% 16.18/3.04 | | | | | | | (120) $false
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | | CLOSE: (120) is inconsistent.
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | Case 2:
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | | (121) ~ (all_20_2 = 0) | ~ (all_20_3 = 0) | ~ (all_20_4 = 0)
% 16.18/3.04 | | | | | | | | all_20_6 = all_20_7 | all_20_8 = all_20_9
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | | BETA: splitting (121) gives:
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | | Case 1:
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | | (122) ~ (all_20_2 = 0)
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | | REDUCE: (111), (122) imply:
% 16.18/3.04 | | | | | | | | (123) $false
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | | CLOSE: (123) is inconsistent.
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | Case 2:
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | | (124) ~ (all_20_3 = 0) | ~ (all_20_4 = 0) | all_20_6 =
% 16.18/3.04 | | | | | | | | all_20_7 | all_20_8 = all_20_9
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | | BETA: splitting (124) gives:
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | | Case 1:
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | | (125) ~ (all_20_3 = 0)
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | | REDUCE: (93), (125) imply:
% 16.18/3.04 | | | | | | | | | (126) $false
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | | CLOSE: (126) is inconsistent.
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | Case 2:
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | | (127) ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8 =
% 16.18/3.04 | | | | | | | | | all_20_9
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | | BETA: splitting (127) gives:
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | | Case 1:
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | (128) ~ (all_20_4 = 0)
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | REDUCE: (92), (128) imply:
% 16.18/3.04 | | | | | | | | | | (129) $false
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | CLOSE: (129) is inconsistent.
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | Case 2:
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | (130) all_20_6 = all_20_7 | all_20_8 = all_20_9
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | BETA: splitting (130) gives:
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | Case 1:
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | (131) all_20_6 = all_20_7
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | REDUCE: (79), (131) imply:
% 16.18/3.04 | | | | | | | | | | | (132) precedes(all_20_7, all_20_7, all_20_5) = all_98_1
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | REDUCE: (36), (131) imply:
% 16.18/3.04 | | | | | | | | | | | (133) precedes(all_20_7, all_20_7, all_20_5) = all_27_2
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | REDUCE: (26), (131) imply:
% 16.18/3.04 | | | | | | | | | | | (134) precedes(all_20_7, all_20_7, all_20_5) = 0
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_94_1, 0, all_20_5,
% 16.18/3.04 | | | | | | | | | | | all_20_7, all_20_7, simplifying with (73), (134)
% 16.18/3.04 | | | | | | | | | | | gives:
% 16.18/3.04 | | | | | | | | | | | (135) all_94_1 = 0
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_94_1, all_98_1,
% 16.18/3.04 | | | | | | | | | | | all_20_5, all_20_7, all_20_7, simplifying with
% 16.18/3.04 | | | | | | | | | | | (73), (132) gives:
% 16.18/3.04 | | | | | | | | | | | (136) all_98_1 = all_94_1
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_27_2, all_98_1,
% 16.18/3.04 | | | | | | | | | | | all_20_5, all_20_7, all_20_7, simplifying with
% 16.18/3.04 | | | | | | | | | | | (132), (133) gives:
% 16.18/3.04 | | | | | | | | | | | (137) all_98_1 = all_27_2
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | COMBINE_EQS: (136), (137) imply:
% 16.18/3.04 | | | | | | | | | | | (138) all_94_1 = all_27_2
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | SIMP: (138) implies:
% 16.18/3.04 | | | | | | | | | | | (139) all_94_1 = all_27_2
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | COMBINE_EQS: (135), (139) imply:
% 16.18/3.04 | | | | | | | | | | | (140) all_27_2 = 0
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | REDUCE: (50), (140) imply:
% 16.18/3.04 | | | | | | | | | | | (141) $false
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | Case 2:
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | (142) all_20_8 = all_20_9
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | REDUCE: (54), (142) imply:
% 16.18/3.04 | | | | | | | | | | | (143) $false
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | | CLOSE: (143) is inconsistent.
% 16.18/3.04 | | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | | End of split
% 16.18/3.04 | | | | | | | | | |
% 16.18/3.04 | | | | | | | | | End of split
% 16.18/3.04 | | | | | | | | |
% 16.18/3.04 | | | | | | | | End of split
% 16.18/3.04 | | | | | | | |
% 16.18/3.04 | | | | | | | End of split
% 16.18/3.04 | | | | | | |
% 16.18/3.04 | | | | | | End of split
% 16.18/3.04 | | | | | |
% 16.18/3.04 | | | | | End of split
% 16.18/3.04 | | | | |
% 16.18/3.04 | | | | End of split
% 16.18/3.04 | | | |
% 16.18/3.04 | | | End of split
% 16.18/3.04 | | |
% 16.18/3.04 | | End of split
% 16.18/3.04 | |
% 16.18/3.04 | End of split
% 16.18/3.04 |
% 16.18/3.04 End of proof
% 16.18/3.04 % SZS output end Proof for theBenchmark
% 16.18/3.04
% 16.18/3.04 2392ms
%------------------------------------------------------------------------------