TSTP Solution File: GRA003+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 : 600s
% DateTime : Sat Jul 16 07:15:31 EDT 2022
% Result : Theorem 19.01s 5.10s
% Output : Proof 23.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 02:49:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.54/0.60 ____ _
% 0.54/0.60 ___ / __ \_____(_)___ ________ __________
% 0.54/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.60
% 0.54/0.60 A Theorem Prover for First-Order Logic
% 0.54/0.60 (ePrincess v.1.0)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2015
% 0.54/0.60 (c) Peter Backeman, 2014-2015
% 0.54/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.60 Bug reports to peter@backeman.se
% 0.54/0.60
% 0.54/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.60
% 0.54/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/0.97 Prover 0: Preprocessing ...
% 2.80/1.29 Prover 0: Warning: ignoring some quantifiers
% 3.05/1.32 Prover 0: Constructing countermodel ...
% 3.28/1.44 Prover 0: gave up
% 3.28/1.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.65/1.49 Prover 1: Preprocessing ...
% 4.44/1.64 Prover 1: Constructing countermodel ...
% 17.65/4.80 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 17.89/4.86 Prover 2: Preprocessing ...
% 18.56/5.01 Prover 2: Warning: ignoring some quantifiers
% 18.56/5.01 Prover 2: Constructing countermodel ...
% 19.01/5.10 Prover 2: proved (303ms)
% 19.01/5.10 Prover 1: stopped
% 19.01/5.10
% 19.01/5.10 No countermodel exists, formula is valid
% 19.01/5.10 % SZS status Theorem for theBenchmark
% 19.01/5.10
% 19.01/5.10 Generating proof ... Warning: ignoring some quantifiers
% 22.50/5.96 found it (size 144)
% 22.50/5.96
% 22.50/5.96 % SZS output start Proof for theBenchmark
% 22.50/5.96 Assumed formulas after preprocessing and simplification:
% 22.50/5.96 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (shortest_path(v0, v1, v4) = 0 & precedes(v2, v3, v4) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = 0 | ~ (path_cons(v14, v16) = v12) | ~ (path(v10, v11, v12) = v13) | ~ (head_of(v14) = v15) | ? [v17] : (( ~ (v17 = v10) & tail_of(v14) = v17) | ( ~ (v17 = 0) & path(v15, v11, v16) = v17) | ( ~ (v17 = 0) & vertex(v11) = v17) | ( ~ (v17 = 0) & vertex(v10) = v17) | ( ~ (v17 = 0) & edge(v14) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = 0 | ~ (path(v15, v11, v16) = 0) | ~ (path(v10, v11, v12) = v13) | ~ (head_of(v14) = v15) | ? [v17] : (( ~ (v17 = v12) & path_cons(v14, v16) = v17) | ( ~ (v17 = v10) & tail_of(v14) = v17) | ( ~ (v17 = 0) & vertex(v11) = v17) | ( ~ (v17 = 0) & vertex(v10) = v17) | ( ~ (v17 = 0) & edge(v14) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (shortest_path(v10, v11, v14) = 0) | ~ (tail_of(v12) = v15) | ~ (head_of(v13) = v16) | ? [v17] : (( ~ (v17 = 0) & precedes(v13, v12, v14) = v17 & ! [v18] : ( ~ (tail_of(v18) = v15) | ? [v19] : ( ~ (v19 = v16) & head_of(v18) = v19)) & ! [v18] : ( ~ (head_of(v18) = v16) | ? [v19] : ( ~ (v19 = v15) & tail_of(v18) = v19))) | ( ~ (v17 = 0) & precedes(v12, v13, v14) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (precedes(v16, v14, v10) = 0) | ~ (sequential(v13, v14) = v15) | ~ (path(v11, v12, v10) = 0) | ? [v17] : ((v17 = 0 & precedes(v13, v14, v10) = 0) | ( ~ (v17 = 0) & sequential(v13, v16) = v17) | ( ~ (v17 = 0) & on_path(v14, v10) = v17) | ( ~ (v17 = 0) & on_path(v13, v10) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (sequential(v13, v16) = 0) | ~ (sequential(v13, v14) = v15) | ~ (path(v11, v12, v10) = 0) | ? [v17] : ((v17 = 0 & precedes(v13, v14, v10) = 0) | ( ~ (v17 = 0) & precedes(v16, v14, v10) = v17) | ( ~ (v17 = 0) & on_path(v14, v10) = v17) | ( ~ (v17 = 0) & on_path(v13, v10) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (precedes(v13, v14, v10) = v15) | ~ (path(v11, v12, v10) = 0) | ? [v16] : (( ~ (v16 = 0) & sequential(v13, v14) = v16 & ! [v17] : ( ~ (precedes(v17, v14, v10) = 0) | ? [v18] : ( ~ (v18 = 0) & sequential(v13, v17) = v18)) & ! [v17] : ( ~ (sequential(v13, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & precedes(v17, v14, v10) = v18))) | ( ~ (v16 = 0) & on_path(v14, v10) = v16) | ( ~ (v16 = 0) & on_path(v13, v10) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (path_cons(v14, empty) = v15) | ~ (path(v10, v11, v12) = v13) | ? [v16] : (( ~ (v16 = v10) & tail_of(v14) = v16) | ( ~ (v16 = 0) & vertex(v11) = v16) | ( ~ (v16 = 0) & vertex(v10) = v16) | ( ~ (v16 = 0) & edge(v14) = v16) | (head_of(v14) = v16 & ! [v17] : ( ~ (path_cons(v14, v17) = v12) | ? [v18] : ( ~ (v18 = 0) & path(v16, v11, v17) = v18)) & ! [v17] : ( ~ (path(v16, v11, v17) = 0) | ? [v18] : ( ~ (v18 = v12) & path_cons(v14, v17) = v18)) & ( ~ (v16 = v11) | ~ (v15 = v12))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (shortest_path(v10, v11, v14) = 0) | ~ (precedes(v13, v12, v14) = v15) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & precedes(v12, v13, v14) = v16) | ( ~ (v15 = 0) & tail_of(v12) = v16 & head_of(v13) = v17 & ! [v18] : ( ~ (tail_of(v18) = v16) | ? [v19] : ( ~ (v19 = v17) & head_of(v18) = v19)) & ! [v18] : ( ~ (head_of(v18) = v17) | ? [v19] : ( ~ (v19 = v16) & tail_of(v18) = v19))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (sequential(v13, v14) = v15) | ~ (path(v11, v12, v10) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v17 = 0 & v16 = 0 & on_path(v14, v10) = 0 & on_path(v13, v10) = 0 & ( ~ (v15 = 0) | ( ! [v21] : ( ~ (precedes(v21, v14, v10) = 0) | ? [v22] : ( ~ (v22 = 0) & sequential(v13, v21) = v22)) & ! [v21] : ( ~ (sequential(v13, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & precedes(v21, v14, v10) = v22)))) & (v15 = 0 | (v20 = 0 & v19 = 0 & precedes(v18, v14, v10) = 0 & sequential(v13, v18) = 0))) | ( ~ (v16 = 0) & precedes(v13, v14, v10) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (in_path(v14, v12) = v15) | ~ (path(v10, v11, v12) = 0) | ~ (tail_of(v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v16 = 0 & v15 = 0 & in_path(v17, v12) = 0 & edge(v13) = 0 & head_of(v13) = v17) | ( ~ (v16 = 0) & on_path(v13, v12) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (in_path(v14, v12) = v15) | ~ (path(v10, v11, v12) = 0) | ~ (head_of(v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v16 = 0 & v15 = 0 & in_path(v17, v12) = 0 & tail_of(v13) = v17 & edge(v13) = 0) | ( ~ (v16 = 0) & on_path(v13, v12) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (path(v10, v11, v12) = 0) | ~ (vertex(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in_path(v13, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (path(v10, v11, v12) = v13) | ~ (tail_of(v14) = v10) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & vertex(v11) = v15) | ( ~ (v15 = 0) & vertex(v10) = v15) | ( ~ (v15 = 0) & edge(v14) = v15) | (head_of(v14) = v15 & ! [v17] : ( ~ (path_cons(v14, v17) = v12) | ? [v18] : ( ~ (v18 = 0) & path(v15, v11, v17) = v18)) & ! [v17] : ( ~ (path(v15, v11, v17) = 0) | ? [v18] : ( ~ (v18 = v12) & path_cons(v14, v17) = v18)) & ( ~ (v15 = v11) | ( ~ (v16 = v12) & path_cons(v14, empty) = v16))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (path(v10, v11, v12) = v13) | ~ (edge(v14) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = v10) & tail_of(v14) = v15) | ( ~ (v15 = 0) & vertex(v11) = v15) | ( ~ (v15 = 0) & vertex(v10) = v15) | (head_of(v14) = v15 & ! [v17] : ( ~ (path_cons(v14, v17) = v12) | ? [v18] : ( ~ (v18 = 0) & path(v15, v11, v17) = v18)) & ! [v17] : ( ~ (path(v15, v11, v17) = 0) | ? [v18] : ( ~ (v18 = v12) & path_cons(v14, v17) = v18)) & ( ~ (v15 = v11) | ( ~ (v16 = v12) & path_cons(v14, empty) = v16))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (path(v10, v11, v12) = v13) | ~ (head_of(v14) = v11) | ? [v15] : (( ~ (v15 = v12) & path_cons(v14, empty) = v15) | ( ~ (v15 = v10) & tail_of(v14) = v15) | ( ~ (v15 = 0) & vertex(v11) = v15) | ( ~ (v15 = 0) & vertex(v10) = v15) | ( ~ (v15 = 0) & edge(v14) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (triangle(v14, v13, v12) = v11) | ~ (triangle(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (shortest_path(v14, v13, v12) = v11) | ~ (shortest_path(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (precedes(v14, v13, v12) = v11) | ~ (precedes(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (path(v14, v13, v12) = v11) | ~ (path(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (shortest_path(v10, v11, v14) = 0) | ~ (precedes(v12, v13, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & precedes(v13, v12, v14) = v17 & tail_of(v12) = v15 & head_of(v13) = v16 & ! [v18] : ( ~ (tail_of(v18) = v15) | ? [v19] : ( ~ (v19 = v16) & head_of(v18) = v19)) & ! [v18] : ( ~ (head_of(v18) = v16) | ? [v19] : ( ~ (v19 = v15) & tail_of(v18) = v19)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (precedes(v13, v14, v10) = 0) | ~ (path(v11, v12, v10) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (on_path(v14, v10) = 0 & on_path(v13, v10) = 0 & ((v18 = 0 & v17 = 0 & precedes(v16, v14, v10) = 0 & sequential(v13, v16) = 0) | (v15 = 0 & sequential(v13, v14) = 0)) & (( ~ (v15 = 0) & sequential(v13, v14) = v15) | ( ! [v19] : ( ~ (precedes(v19, v14, v10) = 0) | ? [v20] : ( ~ (v20 = 0) & sequential(v13, v19) = v20)) & ! [v19] : ( ~ (sequential(v13, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & precedes(v19, v14, v10) = v20)))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sequential(v13, v14) = 0) | ~ (path(v11, v12, v10) = 0) | ? [v15] : ((v15 = 0 & precedes(v13, v14, v10) = 0) | ( ~ (v15 = 0) & on_path(v14, v10) = v15) | ( ~ (v15 = 0) & on_path(v13, v10) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (path(v10, v11, v12) = 0) | ~ (vertex(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v16 = 0 & on_path(v15, v12) = 0 & ((v17 = v13 & tail_of(v15) = v13) | (v17 = v13 & head_of(v15) = v13))) | ( ~ (v15 = 0) & in_path(v13, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (path(v10, v11, v12) = 0) | ~ (edge(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v16 = 0 & v14 = 0 & in_path(v17, v12) = 0 & in_path(v15, v12) = 0 & tail_of(v13) = v17 & head_of(v13) = v15) | ( ~ (v15 = 0) & on_path(v13, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v11 = v10 | ~ (shortest_path(v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v16 = 0 & ~ (v18 = 0) & length_of(v15) = v17 & length_of(v12) = v14 & less_or_equal(v14, v17) = v18 & path(v10, v11, v15) = 0) | ( ~ (v14 = 0) & path(v10, v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (triangle(v10, v11, v12) = v13) | ? [v14] : (( ~ (v14 = 0) & sequential(v12, v10) = v14) | ( ~ (v14 = 0) & sequential(v11, v12) = v14) | ( ~ (v14 = 0) & sequential(v10, v11) = v14) | ( ~ (v14 = 0) & edge(v12) = v14) | ( ~ (v14 = 0) & edge(v11) = v14) | ( ~ (v14 = 0) & edge(v10) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (minus(v13, v12) = v11) | ~ (minus(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (number_of_in(v13, v12) = v11) | ~ (number_of_in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (less_or_equal(v13, v12) = v11) | ~ (less_or_equal(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sequential(v13, v12) = v11) | ~ (sequential(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (on_path(v13, v12) = v11) | ~ (on_path(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in_path(v13, v12) = v11) | ~ (in_path(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (path_cons(v13, v12) = v11) | ~ (path_cons(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (on_path(v13, v12) = 0) | ~ (path(v10, v11, v12) = 0) | ? [v14] : ? [v15] : (in_path(v15, v12) = 0 & in_path(v14, v12) = 0 & tail_of(v13) = v15 & edge(v13) = 0 & head_of(v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (in_path(v13, v12) = 0) | ~ (path(v10, v11, v12) = 0) | vertex(v13) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (in_path(v13, v12) = 0) | ~ (path(v10, v11, v12) = 0) | ? [v14] : ? [v15] : (on_path(v14, v12) = 0 & ((v15 = v13 & tail_of(v14) = v13) | (v15 = v13 & head_of(v14) = v13)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (path(v10, v11, v12) = v13) | ? [v14] : ((v13 = 0 & ~ (v11 = v10) & length_of(v12) = v14 & ! [v15] : ! [v16] : ( ~ (length_of(v15) = v16) | ? [v17] : ((v17 = 0 & less_or_equal(v14, v16) = 0) | ( ~ (v17 = 0) & path(v10, v11, v15) = v17))) & ! [v15] : ( ~ (path(v10, v11, v15) = 0) | ? [v16] : (length_of(v15) = v16 & less_or_equal(v14, v16) = 0))) | ( ~ (v14 = 0) & shortest_path(v10, v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = v10 | ~ (sequential(v10, v11) = v12) | ? [v13] : ? [v14] : (( ~ (v14 = v13) & tail_of(v11) = v14 & head_of(v10) = v13) | ( ~ (v13 = 0) & edge(v11) = v13) | ( ~ (v13 = 0) & edge(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (length_of(v12) = v11) | ~ (length_of(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (path(v10, v11, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & ~ (v17 = 0) & length_of(v14) = v16 & length_of(v12) = v13 & less_or_equal(v13, v16) = v17 & path(v10, v11, v14) = 0) | (v13 = 0 & shortest_path(v10, v11, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vertex(v12) = v11) | ~ (vertex(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (tail_of(v12) = v11) | ~ (tail_of(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (edge(v12) = v11) | ~ (edge(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (head_of(v12) = v11) | ~ (head_of(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (number_of_in(v10, v11) = v12) | ? [v13] : (number_of_in(v10, graph) = v13 & less_or_equal(v12, v13) = 0)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triangle(v10, v11, v12) = 0) | (sequential(v12, v10) = 0 & sequential(v11, v12) = 0 & sequential(v10, v11) = 0 & edge(v12) = 0 & edge(v11) = 0 & edge(v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (shortest_path(v10, v11, v12) = 0) | ? [v13] : (length_of(v12) = v13 & path(v10, v11, v12) = 0 & ! [v14] : ! [v15] : ( ~ (length_of(v14) = v15) | ? [v16] : ((v16 = 0 & less_or_equal(v13, v15) = 0) | ( ~ (v16 = 0) & path(v10, v11, v14) = v16))) & ! [v14] : ( ~ (path(v10, v11, v14) = 0) | ? [v15] : (length_of(v14) = v15 & less_or_equal(v13, v15) = 0)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (path(v11, v12, v10) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & sequential(v13, v14) = 0 & on_path(v14, v10) = 0 & on_path(v13, v10) = 0 & ! [v18] : ~ (triangle(v13, v14, v18) = 0)) | (v14 = v13 & number_of_in(triangles, v10) = v13 & number_of_in(sequential_pairs, v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (path(v10, v11, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (tail_of(v13) = v10 & edge(v13) = 0 & head_of(v13) = v14 & ( ~ (v14 = v11) | ( ~ (v15 = v12) & path_cons(v13, empty) = v15) | ( ! [v19] : ( ~ (path_cons(v13, v19) = v12) | ? [v20] : ( ~ (v20 = 0) & path(v11, v11, v19) = v20)) & ! [v19] : ( ~ (path(v11, v11, v19) = 0) | ? [v20] : ( ~ (v20 = v12) & path_cons(v13, v19) = v20)))) & ((v18 = v12 & v17 = 0 & path_cons(v13, v16) = v12 & path(v14, v11, v16) = 0) | (v15 = v12 & v14 = v11 & path_cons(v13, empty) = v12)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (path(v10, v11, v12) = 0) | ? [v13] : ? [v14] : (minus(v14, n1) = v13 & number_of_in(sequential_pairs, v12) = v13 & length_of(v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (path(v10, v11, v12) = 0) | ? [v13] : (number_of_in(edges, v12) = v13 & length_of(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (path(v10, v11, v12) = 0) | (vertex(v11) = 0 & vertex(v10) = 0)) & ! [v10] : ! [v11] : ~ (shortest_path(v10, v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (sequential(v10, v11) = 0) | ? [v12] : (tail_of(v11) = v12 & edge(v11) = 0 & edge(v10) = 0 & head_of(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (tail_of(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & vertex(v12) = 0 & vertex(v11) = 0 & head_of(v10) = v12) | ( ~ (v12 = 0) & edge(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (tail_of(v10) = v11) | ? [v12] : (( ~ (v12 = v11) & head_of(v10) = v12) | ( ~ (v12 = 0) & edge(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (head_of(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v12 = 0 & vertex(v13) = 0 & vertex(v11) = 0 & tail_of(v10) = v13) | ( ~ (v12 = 0) & edge(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (head_of(v10) = v11) | ? [v12] : (( ~ (v12 = v11) & tail_of(v10) = v12) | ( ~ (v12 = 0) & edge(v10) = v12))) & ! [v10] : ~ (sequential(v10, v10) = 0) & ! [v10] : ( ~ (edge(v10) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & tail_of(v10) = v12 & head_of(v10) = v11)) & ! [v10] : ( ~ (edge(v10) = 0) | ? [v11] : ? [v12] : (vertex(v12) = 0 & vertex(v11) = 0 & tail_of(v10) = v12 & head_of(v10) = v11)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : triangle(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : ? [v13] : shortest_path(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : ? [v13] : precedes(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : ? [v13] : path(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : minus(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : number_of_in(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : less_or_equal(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : sequential(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : on_path(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : in_path(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : path_cons(v11, v10) = v12 & ? [v10] : ? [v11] : length_of(v10) = v11 & ? [v10] : ? [v11] : vertex(v10) = v11 & ? [v10] : ? [v11] : tail_of(v10) = v11 & ? [v10] : ? [v11] : edge(v10) = v11 & ? [v10] : ? [v11] : head_of(v10) = v11 & (v3 = v2 | v1 = v0 | ( ~ (v9 = 0) & path(v0, v1, v4) = v9) | ( ~ (v8 = 0) & edge(v3) = v8) | ( ~ (v7 = 0) & edge(v2) = v7) | ( ~ (v6 = 0) & vertex(v1) = v6) | ( ~ (v5 = 0) & vertex(v0) = v5)) & ( ~ complete | ! [v10] : ! [v11] : (v11 = v10 | ~ (vertex(v11) = 0) | ~ (vertex(v10) = 0) | ? [v12] : ? [v13] : ? [v14] : (tail_of(v12) = v14 & edge(v12) = 0 & head_of(v12) = v13 & ((v14 = v11 & v13 = v10) | (v14 = v10 & v13 = v11))))))
% 23.10/6.02 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 23.10/6.02 | (1) shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0 & precedes(all_0_7_7, all_0_6_6, all_0_5_5) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = 0 | ~ (path_cons(v4, v6) = v2) | ~ (path(v0, v1, v2) = v3) | ~ (head_of(v4) = v5) | ? [v7] : (( ~ (v7 = v0) & tail_of(v4) = v7) | ( ~ (v7 = 0) & path(v5, v1, v6) = v7) | ( ~ (v7 = 0) & vertex(v1) = v7) | ( ~ (v7 = 0) & vertex(v0) = v7) | ( ~ (v7 = 0) & edge(v4) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = 0 | ~ (path(v5, v1, v6) = 0) | ~ (path(v0, v1, v2) = v3) | ~ (head_of(v4) = v5) | ? [v7] : (( ~ (v7 = v2) & path_cons(v4, v6) = v7) | ( ~ (v7 = v0) & tail_of(v4) = v7) | ( ~ (v7 = 0) & vertex(v1) = v7) | ( ~ (v7 = 0) & vertex(v0) = v7) | ( ~ (v7 = 0) & edge(v4) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (tail_of(v2) = v5) | ~ (head_of(v3) = v6) | ? [v7] : (( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & ! [v8] : ( ~ (tail_of(v8) = v5) | ? [v9] : ( ~ (v9 = v6) & head_of(v8) = v9)) & ! [v8] : ( ~ (head_of(v8) = v6) | ? [v9] : ( ~ (v9 = v5) & tail_of(v8) = v9))) | ( ~ (v7 = 0) & precedes(v2, v3, v4) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (precedes(v6, v4, v0) = 0) | ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v7] : ((v7 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v7 = 0) & sequential(v3, v6) = v7) | ( ~ (v7 = 0) & on_path(v4, v0) = v7) | ( ~ (v7 = 0) & on_path(v3, v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sequential(v3, v6) = 0) | ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v7] : ((v7 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v7 = 0) & precedes(v6, v4, v0) = v7) | ( ~ (v7 = 0) & on_path(v4, v0) = v7) | ( ~ (v7 = 0) & on_path(v3, v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v6] : (( ~ (v6 = 0) & sequential(v3, v4) = v6 & ! [v7] : ( ~ (precedes(v7, v4, v0) = 0) | ? [v8] : ( ~ (v8 = 0) & sequential(v3, v7) = v8)) & ! [v7] : ( ~ (sequential(v3, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & precedes(v7, v4, v0) = v8))) | ( ~ (v6 = 0) & on_path(v4, v0) = v6) | ( ~ (v6 = 0) & on_path(v3, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (path_cons(v4, empty) = v5) | ~ (path(v0, v1, v2) = v3) | ? [v6] : (( ~ (v6 = v0) & tail_of(v4) = v6) | ( ~ (v6 = 0) & vertex(v1) = v6) | ( ~ (v6 = 0) & vertex(v0) = v6) | ( ~ (v6 = 0) & edge(v4) = v6) | (head_of(v4) = v6 & ! [v7] : ( ~ (path_cons(v4, v7) = v2) | ? [v8] : ( ~ (v8 = 0) & path(v6, v1, v7) = v8)) & ! [v7] : ( ~ (path(v6, v1, v7) = 0) | ? [v8] : ( ~ (v8 = v2) & path_cons(v4, v7) = v8)) & ( ~ (v6 = v1) | ~ (v5 = v2))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v3, v2, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & precedes(v2, v3, v4) = v6) | ( ~ (v5 = 0) & tail_of(v2) = v6 & head_of(v3) = v7 & ! [v8] : ( ~ (tail_of(v8) = v6) | ? [v9] : ( ~ (v9 = v7) & head_of(v8) = v9)) & ! [v8] : ( ~ (head_of(v8) = v7) | ? [v9] : ( ~ (v9 = v6) & tail_of(v8) = v9))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v7 = 0 & v6 = 0 & on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & ( ~ (v5 = 0) | ( ! [v11] : ( ~ (precedes(v11, v4, v0) = 0) | ? [v12] : ( ~ (v12 = 0) & sequential(v3, v11) = v12)) & ! [v11] : ( ~ (sequential(v3, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & precedes(v11, v4, v0) = v12)))) & (v5 = 0 | (v10 = 0 & v9 = 0 & precedes(v8, v4, v0) = 0 & sequential(v3, v8) = 0))) | ( ~ (v6 = 0) & precedes(v3, v4, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~ (tail_of(v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & v5 = 0 & in_path(v7, v2) = 0 & edge(v3) = 0 & head_of(v3) = v7) | ( ~ (v6 = 0) & on_path(v3, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~ (head_of(v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & v5 = 0 & in_path(v7, v2) = 0 & tail_of(v3) = v7 & edge(v3) = 0) | ( ~ (v6 = 0) & on_path(v3, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (path(v0, v1, v2) = 0) | ~ (vertex(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & in_path(v3, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (path(v0, v1, v2) = v3) | ~ (tail_of(v4) = v0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & vertex(v1) = v5) | ( ~ (v5 = 0) & vertex(v0) = v5) | ( ~ (v5 = 0) & edge(v4) = v5) | (head_of(v4) = v5 & ! [v7] : ( ~ (path_cons(v4, v7) = v2) | ? [v8] : ( ~ (v8 = 0) & path(v5, v1, v7) = v8)) & ! [v7] : ( ~ (path(v5, v1, v7) = 0) | ? [v8] : ( ~ (v8 = v2) & path_cons(v4, v7) = v8)) & ( ~ (v5 = v1) | ( ~ (v6 = v2) & path_cons(v4, empty) = v6))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (path(v0, v1, v2) = v3) | ~ (edge(v4) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = v0) & tail_of(v4) = v5) | ( ~ (v5 = 0) & vertex(v1) = v5) | ( ~ (v5 = 0) & vertex(v0) = v5) | (head_of(v4) = v5 & ! [v7] : ( ~ (path_cons(v4, v7) = v2) | ? [v8] : ( ~ (v8 = 0) & path(v5, v1, v7) = v8)) & ! [v7] : ( ~ (path(v5, v1, v7) = 0) | ? [v8] : ( ~ (v8 = v2) & path_cons(v4, v7) = v8)) & ( ~ (v5 = v1) | ( ~ (v6 = v2) & path_cons(v4, empty) = v6))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (path(v0, v1, v2) = v3) | ~ (head_of(v4) = v1) | ? [v5] : (( ~ (v5 = v2) & path_cons(v4, empty) = v5) | ( ~ (v5 = v0) & tail_of(v4) = v5) | ( ~ (v5 = 0) & vertex(v1) = v5) | ( ~ (v5 = 0) & vertex(v0) = v5) | ( ~ (v5 = 0) & edge(v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ (triangle(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ (precedes(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & tail_of(v2) = v5 & head_of(v3) = v6 & ! [v8] : ( ~ (tail_of(v8) = v5) | ? [v9] : ( ~ (v9 = v6) & head_of(v8) = v9)) & ! [v8] : ( ~ (head_of(v8) = v6) | ? [v9] : ( ~ (v9 = v5) & tail_of(v8) = v9)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & ((v8 = 0 & v7 = 0 & precedes(v6, v4, v0) = 0 & sequential(v3, v6) = 0) | (v5 = 0 & sequential(v3, v4) = 0)) & (( ~ (v5 = 0) & sequential(v3, v4) = v5) | ( ! [v9] : ( ~ (precedes(v9, v4, v0) = 0) | ? [v10] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9] : ( ~ (sequential(v3, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sequential(v3, v4) = 0) | ~ (path(v1, v2, v0) = 0) | ? [v5] : ((v5 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v5 = 0) & on_path(v4, v0) = v5) | ( ~ (v5 = 0) & on_path(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (path(v0, v1, v2) = 0) | ~ (vertex(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & on_path(v5, v2) = 0 & ((v7 = v3 & tail_of(v5) = v3) | (v7 = v3 & head_of(v5) = v3))) | ( ~ (v5 = 0) & in_path(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & v4 = 0 & in_path(v7, v2) = 0 & in_path(v5, v2) = 0 & tail_of(v3) = v7 & head_of(v3) = v5) | ( ~ (v5 = 0) & on_path(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v1 = v0 | ~ (shortest_path(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & ~ (v8 = 0) & length_of(v5) = v7 & length_of(v2) = v4 & less_or_equal(v4, v7) = v8 & path(v0, v1, v5) = 0) | ( ~ (v4 = 0) & path(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (triangle(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sequential(v2, v0) = v4) | ( ~ (v4 = 0) & sequential(v1, v2) = v4) | ( ~ (v4 = 0) & sequential(v0, v1) = v4) | ( ~ (v4 = 0) & edge(v2) = v4) | ( ~ (v4 = 0) & edge(v1) = v4) | ( ~ (v4 = 0) & edge(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ (less_or_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (path_cons(v3, v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (on_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = 0) | ? [v4] : ? [v5] : (in_path(v5, v2) = 0 & in_path(v4, v2) = 0 & tail_of(v3) = v5 & edge(v3) = 0 & head_of(v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = 0) | vertex(v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = 0) | ? [v4] : ? [v5] : (on_path(v4, v2) = 0 & ((v5 = v3 & tail_of(v4) = v3) | (v5 = v3 & head_of(v4) = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (path(v0, v1, v2) = v3) | ? [v4] : ((v3 = 0 & ~ (v1 = v0) & length_of(v2) = v4 & ! [v5] : ! [v6] : ( ~ (length_of(v5) = v6) | ? [v7] : ((v7 = 0 & less_or_equal(v4, v6) = 0) | ( ~ (v7 = 0) & path(v0, v1, v5) = v7))) & ! [v5] : ( ~ (path(v0, v1, v5) = 0) | ? [v6] : (length_of(v5) = v6 & less_or_equal(v4, v6) = 0))) | ( ~ (v4 = 0) & shortest_path(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (sequential(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = v3) & tail_of(v1) = v4 & head_of(v0) = v3) | ( ~ (v3 = 0) & edge(v1) = v3) | ( ~ (v3 = 0) & edge(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (path(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v5 = 0 & ~ (v7 = 0) & length_of(v4) = v6 & length_of(v2) = v3 & less_or_equal(v3, v6) = v7 & path(v0, v1, v4) = 0) | (v3 = 0 & shortest_path(v0, v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (number_of_in(v0, v1) = v2) | ? [v3] : (number_of_in(v0, graph) = v3 & less_or_equal(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triangle(v0, v1, v2) = 0) | (sequential(v2, v0) = 0 & sequential(v1, v2) = 0 & sequential(v0, v1) = 0 & edge(v2) = 0 & edge(v1) = 0 & edge(v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (shortest_path(v0, v1, v2) = 0) | ? [v3] : (length_of(v2) = v3 & path(v0, v1, v2) = 0 & ! [v4] : ! [v5] : ( ~ (length_of(v4) = v5) | ? [v6] : ((v6 = 0 & less_or_equal(v3, v5) = 0) | ( ~ (v6 = 0) & path(v0, v1, v4) = v6))) & ! [v4] : ( ~ (path(v0, v1, v4) = 0) | ? [v5] : (length_of(v4) = v5 & less_or_equal(v3, v5) = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v1, v2, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & sequential(v3, v4) = 0 & on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & ! [v8] : ~ (triangle(v3, v4, v8) = 0)) | (v4 = v3 & number_of_in(triangles, v0) = v3 & number_of_in(sequential_pairs, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (tail_of(v3) = v0 & edge(v3) = 0 & head_of(v3) = v4 & ( ~ (v4 = v1) | ( ~ (v5 = v2) & path_cons(v3, empty) = v5) | ( ! [v9] : ( ~ (path_cons(v3, v9) = v2) | ? [v10] : ( ~ (v10 = 0) & path(v1, v1, v9) = v10)) & ! [v9] : ( ~ (path(v1, v1, v9) = 0) | ? [v10] : ( ~ (v10 = v2) & path_cons(v3, v9) = v10)))) & ((v8 = v2 & v7 = 0 & path_cons(v3, v6) = v2 & path(v4, v1, v6) = 0) | (v5 = v2 & v4 = v1 & path_cons(v3, empty) = v2)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & length_of(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | ? [v3] : (number_of_in(edges, v2) = v3 & length_of(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | (vertex(v1) = 0 & vertex(v0) = 0)) & ! [v0] : ! [v1] : ~ (shortest_path(v0, v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (sequential(v0, v1) = 0) | ? [v2] : (tail_of(v1) = v2 & edge(v1) = 0 & edge(v0) = 0 & head_of(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (tail_of(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & vertex(v2) = 0 & vertex(v1) = 0 & head_of(v0) = v2) | ( ~ (v2 = 0) & edge(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (tail_of(v0) = v1) | ? [v2] : (( ~ (v2 = v1) & head_of(v0) = v2) | ( ~ (v2 = 0) & edge(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (head_of(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & vertex(v3) = 0 & vertex(v1) = 0 & tail_of(v0) = v3) | ( ~ (v2 = 0) & edge(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (head_of(v0) = v1) | ? [v2] : (( ~ (v2 = v1) & tail_of(v0) = v2) | ( ~ (v2 = 0) & edge(v0) = v2))) & ! [v0] : ~ (sequential(v0, v0) = 0) & ! [v0] : ( ~ (edge(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & tail_of(v0) = v2 & head_of(v0) = v1)) & ! [v0] : ( ~ (edge(v0) = 0) | ? [v1] : ? [v2] : (vertex(v2) = 0 & vertex(v1) = 0 & tail_of(v0) = v2 & head_of(v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : triangle(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : shortest_path(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : precedes(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : path(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : minus(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : number_of_in(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : less_or_equal(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sequential(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : on_path(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in_path(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : path_cons(v1, v0) = v2 & ? [v0] : ? [v1] : length_of(v0) = v1 & ? [v0] : ? [v1] : vertex(v0) = v1 & ? [v0] : ? [v1] : tail_of(v0) = v1 & ? [v0] : ? [v1] : edge(v0) = v1 & ? [v0] : ? [v1] : head_of(v0) = v1 & (all_0_6_6 = all_0_7_7 | all_0_8_8 = all_0_9_9 | ( ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1) | ( ~ (all_0_2_2 = 0) & edge(all_0_7_7) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & vertex(all_0_8_8) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & vertex(all_0_9_9) = all_0_4_4)) & ( ~ complete | ! [v0] : ! [v1] : (v1 = v0 | ~ (vertex(v1) = 0) | ~ (vertex(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (tail_of(v2) = v4 & edge(v2) = 0 & head_of(v2) = v3 & ((v4 = v1 & v3 = v0) | (v4 = v0 & v3 = v1)))))
% 23.25/6.05 |
% 23.25/6.05 | Applying alpha-rule on (1) yields:
% 23.25/6.05 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (path(v0, v1, v2) = v3) | ~ (head_of(v4) = v1) | ? [v5] : (( ~ (v5 = v2) & path_cons(v4, empty) = v5) | ( ~ (v5 = v0) & tail_of(v4) = v5) | ( ~ (v5 = 0) & vertex(v1) = v5) | ( ~ (v5 = 0) & vertex(v0) = v5) | ( ~ (v5 = 0) & edge(v4) = v5)))
% 23.25/6.06 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~ (head_of(v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & v5 = 0 & in_path(v7, v2) = 0 & tail_of(v3) = v7 & edge(v3) = 0) | ( ~ (v6 = 0) & on_path(v3, v2) = v6)))
% 23.25/6.06 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (path(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v5 = 0 & ~ (v7 = 0) & length_of(v4) = v6 & length_of(v2) = v3 & less_or_equal(v3, v6) = v7 & path(v0, v1, v4) = 0) | (v3 = 0 & shortest_path(v0, v1, v2) = 0)))
% 23.25/6.06 | (5) ? [v0] : ? [v1] : length_of(v0) = v1
% 23.25/6.06 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v1, v2, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & sequential(v3, v4) = 0 & on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & ! [v8] : ~ (triangle(v3, v4, v8) = 0)) | (v4 = v3 & number_of_in(triangles, v0) = v3 & number_of_in(sequential_pairs, v0) = v3)))
% 23.25/6.06 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~ (tail_of(v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & v5 = 0 & in_path(v7, v2) = 0 & edge(v3) = 0 & head_of(v3) = v7) | ( ~ (v6 = 0) & on_path(v3, v2) = v6)))
% 23.25/6.06 | (8) ? [v0] : ? [v1] : ? [v2] : minus(v1, v0) = v2
% 23.25/6.06 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (path(v0, v1, v2) = v3) | ~ (edge(v4) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = v0) & tail_of(v4) = v5) | ( ~ (v5 = 0) & vertex(v1) = v5) | ( ~ (v5 = 0) & vertex(v0) = v5) | (head_of(v4) = v5 & ! [v7] : ( ~ (path_cons(v4, v7) = v2) | ? [v8] : ( ~ (v8 = 0) & path(v5, v1, v7) = v8)) & ! [v7] : ( ~ (path(v5, v1, v7) = 0) | ? [v8] : ( ~ (v8 = v2) & path_cons(v4, v7) = v8)) & ( ~ (v5 = v1) | ( ~ (v6 = v2) & path_cons(v4, empty) = v6)))))
% 23.25/6.06 | (10) ! [v0] : ! [v1] : ( ~ (sequential(v0, v1) = 0) | ? [v2] : (tail_of(v1) = v2 & edge(v1) = 0 & edge(v0) = 0 & head_of(v0) = v2))
% 23.25/6.06 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (on_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = 0) | ? [v4] : ? [v5] : (in_path(v5, v2) = 0 & in_path(v4, v2) = 0 & tail_of(v3) = v5 & edge(v3) = 0 & head_of(v3) = v4))
% 23.25/6.06 | (12) shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0
% 23.25/6.06 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (number_of_in(v0, v1) = v2) | ? [v3] : (number_of_in(v0, graph) = v3 & less_or_equal(v2, v3) = 0))
% 23.25/6.06 | (14) ! [v0] : ! [v1] : ( ~ (tail_of(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & vertex(v2) = 0 & vertex(v1) = 0 & head_of(v0) = v2) | ( ~ (v2 = 0) & edge(v0) = v2)))
% 23.25/6.06 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & length_of(v2) = v4))
% 23.25/6.06 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (triangle(v0, v1, v2) = 0) | (sequential(v2, v0) = 0 & sequential(v1, v2) = 0 & sequential(v0, v1) = 0 & edge(v2) = 0 & edge(v1) = 0 & edge(v0) = 0))
% 23.25/6.06 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v1 = v0 | ~ (shortest_path(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & ~ (v8 = 0) & length_of(v5) = v7 & length_of(v2) = v4 & less_or_equal(v4, v7) = v8 & path(v0, v1, v5) = 0) | ( ~ (v4 = 0) & path(v0, v1, v2) = v4)))
% 23.25/6.06 | (18) precedes(all_0_7_7, all_0_6_6, all_0_5_5) = 0
% 23.25/6.06 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = 0) | vertex(v3) = 0)
% 23.25/6.06 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0))
% 23.25/6.06 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ (triangle(v4, v3, v2) = v0))
% 23.25/6.06 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v7 = 0 & v6 = 0 & on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & ( ~ (v5 = 0) | ( ! [v11] : ( ~ (precedes(v11, v4, v0) = 0) | ? [v12] : ( ~ (v12 = 0) & sequential(v3, v11) = v12)) & ! [v11] : ( ~ (sequential(v3, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & precedes(v11, v4, v0) = v12)))) & (v5 = 0 | (v10 = 0 & v9 = 0 & precedes(v8, v4, v0) = 0 & sequential(v3, v8) = 0))) | ( ~ (v6 = 0) & precedes(v3, v4, v0) = v6)))
% 23.25/6.06 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = v0))
% 23.25/6.06 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (path_cons(v4, empty) = v5) | ~ (path(v0, v1, v2) = v3) | ? [v6] : (( ~ (v6 = v0) & tail_of(v4) = v6) | ( ~ (v6 = 0) & vertex(v1) = v6) | ( ~ (v6 = 0) & vertex(v0) = v6) | ( ~ (v6 = 0) & edge(v4) = v6) | (head_of(v4) = v6 & ! [v7] : ( ~ (path_cons(v4, v7) = v2) | ? [v8] : ( ~ (v8 = 0) & path(v6, v1, v7) = v8)) & ! [v7] : ( ~ (path(v6, v1, v7) = 0) | ? [v8] : ( ~ (v8 = v2) & path_cons(v4, v7) = v8)) & ( ~ (v6 = v1) | ~ (v5 = v2)))))
% 23.25/6.06 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0))
% 23.25/6.06 | (26) ! [v0] : ~ (sequential(v0, v0) = 0)
% 23.25/6.06 | (27) ? [v0] : ? [v1] : vertex(v0) = v1
% 23.25/6.06 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0))
% 23.25/6.06 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (sequential(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = v3) & tail_of(v1) = v4 & head_of(v0) = v3) | ( ~ (v3 = 0) & edge(v1) = v3) | ( ~ (v3 = 0) & edge(v0) = v3)))
% 23.25/6.06 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (precedes(v6, v4, v0) = 0) | ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v7] : ((v7 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v7 = 0) & sequential(v3, v6) = v7) | ( ~ (v7 = 0) & on_path(v4, v0) = v7) | ( ~ (v7 = 0) & on_path(v3, v0) = v7)))
% 23.25/6.06 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v6] : (( ~ (v6 = 0) & sequential(v3, v4) = v6 & ! [v7] : ( ~ (precedes(v7, v4, v0) = 0) | ? [v8] : ( ~ (v8 = 0) & sequential(v3, v7) = v8)) & ! [v7] : ( ~ (sequential(v3, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & precedes(v7, v4, v0) = v8))) | ( ~ (v6 = 0) & on_path(v4, v0) = v6) | ( ~ (v6 = 0) & on_path(v3, v0) = v6)))
% 23.25/6.07 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0))
% 23.25/6.07 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = v0))
% 23.25/6.07 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sequential(v3, v4) = 0) | ~ (path(v1, v2, v0) = 0) | ? [v5] : ((v5 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v5 = 0) & on_path(v4, v0) = v5) | ( ~ (v5 = 0) & on_path(v3, v0) = v5)))
% 23.25/6.07 | (35) ? [v0] : ? [v1] : ? [v2] : ? [v3] : triangle(v2, v1, v0) = v3
% 23.25/6.07 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (tail_of(v2) = v5) | ~ (head_of(v3) = v6) | ? [v7] : (( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & ! [v8] : ( ~ (tail_of(v8) = v5) | ? [v9] : ( ~ (v9 = v6) & head_of(v8) = v9)) & ! [v8] : ( ~ (head_of(v8) = v6) | ? [v9] : ( ~ (v9 = v5) & tail_of(v8) = v9))) | ( ~ (v7 = 0) & precedes(v2, v3, v4) = v7)))
% 23.25/6.07 | (37) ? [v0] : ? [v1] : tail_of(v0) = v1
% 23.25/6.07 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ (precedes(v4, v3, v2) = v0))
% 23.25/6.07 | (39) ? [v0] : ? [v1] : ? [v2] : in_path(v1, v0) = v2
% 23.25/6.07 | (40) ? [v0] : ? [v1] : ? [v2] : number_of_in(v1, v0) = v2
% 23.25/6.07 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = v0))
% 23.25/6.07 | (42) ! [v0] : ! [v1] : ~ (shortest_path(v0, v0, v1) = 0)
% 23.25/6.07 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0))
% 23.25/6.07 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & tail_of(v2) = v5 & head_of(v3) = v6 & ! [v8] : ( ~ (tail_of(v8) = v5) | ? [v9] : ( ~ (v9 = v6) & head_of(v8) = v9)) & ! [v8] : ( ~ (head_of(v8) = v6) | ? [v9] : ( ~ (v9 = v5) & tail_of(v8) = v9))))
% 23.25/6.07 | (45) ? [v0] : ? [v1] : head_of(v0) = v1
% 23.25/6.07 | (46) ? [v0] : ? [v1] : ? [v2] : ? [v3] : shortest_path(v2, v1, v0) = v3
% 23.25/6.07 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sequential(v3, v6) = 0) | ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ? [v7] : ((v7 = 0 & precedes(v3, v4, v0) = 0) | ( ~ (v7 = 0) & precedes(v6, v4, v0) = v7) | ( ~ (v7 = 0) & on_path(v4, v0) = v7) | ( ~ (v7 = 0) & on_path(v3, v0) = v7)))
% 23.25/6.07 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0))
% 23.25/6.07 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (path(v0, v1, v2) = 0) | ~ (vertex(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & on_path(v5, v2) = 0 & ((v7 = v3 & tail_of(v5) = v3) | (v7 = v3 & head_of(v5) = v3))) | ( ~ (v5 = 0) & in_path(v3, v2) = v5)))
% 23.25/6.07 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | (vertex(v1) = 0 & vertex(v0) = 0))
% 23.25/6.07 | (51) ? [v0] : ? [v1] : ? [v2] : sequential(v1, v0) = v2
% 23.25/6.07 | (52) ? [v0] : ? [v1] : ? [v2] : less_or_equal(v1, v0) = v2
% 23.25/6.07 | (53) ? [v0] : ? [v1] : ? [v2] : on_path(v1, v0) = v2
% 23.25/6.07 | (54) ~ complete | ! [v0] : ! [v1] : (v1 = v0 | ~ (vertex(v1) = 0) | ~ (vertex(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (tail_of(v2) = v4 & edge(v2) = 0 & head_of(v2) = v3 & ((v4 = v1 & v3 = v0) | (v4 = v0 & v3 = v1))))
% 23.25/6.07 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0))
% 23.25/6.07 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & ((v8 = 0 & v7 = 0 & precedes(v6, v4, v0) = 0 & sequential(v3, v6) = 0) | (v5 = 0 & sequential(v3, v4) = 0)) & (( ~ (v5 = 0) & sequential(v3, v4) = v5) | ( ! [v9] : ( ~ (precedes(v9, v4, v0) = 0) | ? [v10] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9] : ( ~ (sequential(v3, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10))))))
% 23.25/6.07 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (path_cons(v3, v2) = v1) | ~ (path_cons(v3, v2) = v0))
% 23.25/6.07 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & v4 = 0 & in_path(v7, v2) = 0 & in_path(v5, v2) = 0 & tail_of(v3) = v7 & head_of(v3) = v5) | ( ~ (v5 = 0) & on_path(v3, v2) = v5)))
% 23.25/6.07 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (path(v0, v1, v2) = v3) | ? [v4] : ((v3 = 0 & ~ (v1 = v0) & length_of(v2) = v4 & ! [v5] : ! [v6] : ( ~ (length_of(v5) = v6) | ? [v7] : ((v7 = 0 & less_or_equal(v4, v6) = 0) | ( ~ (v7 = 0) & path(v0, v1, v5) = v7))) & ! [v5] : ( ~ (path(v0, v1, v5) = 0) | ? [v6] : (length_of(v5) = v6 & less_or_equal(v4, v6) = 0))) | ( ~ (v4 = 0) & shortest_path(v0, v1, v2) = v4)))
% 23.25/6.07 | (60) ! [v0] : ( ~ (edge(v0) = 0) | ? [v1] : ? [v2] : (vertex(v2) = 0 & vertex(v1) = 0 & tail_of(v0) = v2 & head_of(v0) = v1))
% 23.25/6.07 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = 0 | ~ (path_cons(v4, v6) = v2) | ~ (path(v0, v1, v2) = v3) | ~ (head_of(v4) = v5) | ? [v7] : (( ~ (v7 = v0) & tail_of(v4) = v7) | ( ~ (v7 = 0) & path(v5, v1, v6) = v7) | ( ~ (v7 = 0) & vertex(v1) = v7) | ( ~ (v7 = 0) & vertex(v0) = v7) | ( ~ (v7 = 0) & edge(v4) = v7)))
% 23.25/6.07 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | ? [v3] : (number_of_in(edges, v2) = v3 & length_of(v2) = v3))
% 23.25/6.07 | (63) ? [v0] : ? [v1] : ? [v2] : path_cons(v1, v0) = v2
% 23.25/6.07 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = 0 | ~ (path(v5, v1, v6) = 0) | ~ (path(v0, v1, v2) = v3) | ~ (head_of(v4) = v5) | ? [v7] : (( ~ (v7 = v2) & path_cons(v4, v6) = v7) | ( ~ (v7 = v0) & tail_of(v4) = v7) | ( ~ (v7 = 0) & vertex(v1) = v7) | ( ~ (v7 = 0) & vertex(v0) = v7) | ( ~ (v7 = 0) & edge(v4) = v7)))
% 23.25/6.07 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = 0) | ? [v4] : ? [v5] : (on_path(v4, v2) = 0 & ((v5 = v3 & tail_of(v4) = v3) | (v5 = v3 & head_of(v4) = v3))))
% 23.25/6.07 | (66) ? [v0] : ? [v1] : edge(v0) = v1
% 23.25/6.07 | (67) ! [v0] : ! [v1] : ( ~ (tail_of(v0) = v1) | ? [v2] : (( ~ (v2 = v1) & head_of(v0) = v2) | ( ~ (v2 = 0) & edge(v0) = v2)))
% 23.25/6.07 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0))
% 23.25/6.07 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v3, v2, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & precedes(v2, v3, v4) = v6) | ( ~ (v5 = 0) & tail_of(v2) = v6 & head_of(v3) = v7 & ! [v8] : ( ~ (tail_of(v8) = v6) | ? [v9] : ( ~ (v9 = v7) & head_of(v8) = v9)) & ! [v8] : ( ~ (head_of(v8) = v7) | ? [v9] : ( ~ (v9 = v6) & tail_of(v8) = v9)))))
% 23.25/6.08 | (70) ? [v0] : ? [v1] : ? [v2] : ? [v3] : precedes(v2, v1, v0) = v3
% 23.25/6.08 | (71) ! [v0] : ! [v1] : ( ~ (head_of(v0) = v1) | ? [v2] : (( ~ (v2 = v1) & tail_of(v0) = v2) | ( ~ (v2 = 0) & edge(v0) = v2)))
% 23.25/6.08 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (shortest_path(v0, v1, v2) = 0) | ? [v3] : (length_of(v2) = v3 & path(v0, v1, v2) = 0 & ! [v4] : ! [v5] : ( ~ (length_of(v4) = v5) | ? [v6] : ((v6 = 0 & less_or_equal(v3, v5) = 0) | ( ~ (v6 = 0) & path(v0, v1, v4) = v6))) & ! [v4] : ( ~ (path(v0, v1, v4) = 0) | ? [v5] : (length_of(v4) = v5 & less_or_equal(v3, v5) = 0))))
% 23.25/6.08 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (path(v0, v1, v2) = 0) | ~ (vertex(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & in_path(v3, v2) = v5))
% 23.25/6.08 | (74) ! [v0] : ! [v1] : ( ~ (head_of(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & vertex(v3) = 0 & vertex(v1) = 0 & tail_of(v0) = v3) | ( ~ (v2 = 0) & edge(v0) = v2)))
% 23.25/6.08 | (75) all_0_6_6 = all_0_7_7 | all_0_8_8 = all_0_9_9 | ( ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1) | ( ~ (all_0_2_2 = 0) & edge(all_0_7_7) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & vertex(all_0_8_8) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & vertex(all_0_9_9) = all_0_4_4)
% 23.25/6.08 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ (less_or_equal(v3, v2) = v0))
% 23.25/6.08 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (path(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (tail_of(v3) = v0 & edge(v3) = 0 & head_of(v3) = v4 & ( ~ (v4 = v1) | ( ~ (v5 = v2) & path_cons(v3, empty) = v5) | ( ! [v9] : ( ~ (path_cons(v3, v9) = v2) | ? [v10] : ( ~ (v10 = 0) & path(v1, v1, v9) = v10)) & ! [v9] : ( ~ (path(v1, v1, v9) = 0) | ? [v10] : ( ~ (v10 = v2) & path_cons(v3, v9) = v10)))) & ((v8 = v2 & v7 = 0 & path_cons(v3, v6) = v2 & path(v4, v1, v6) = 0) | (v5 = v2 & v4 = v1 & path_cons(v3, empty) = v2))))
% 23.25/6.08 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (triangle(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sequential(v2, v0) = v4) | ( ~ (v4 = 0) & sequential(v1, v2) = v4) | ( ~ (v4 = 0) & sequential(v0, v1) = v4) | ( ~ (v4 = 0) & edge(v2) = v4) | ( ~ (v4 = 0) & edge(v1) = v4) | ( ~ (v4 = 0) & edge(v0) = v4)))
% 23.25/6.08 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (path(v0, v1, v2) = v3) | ~ (tail_of(v4) = v0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & vertex(v1) = v5) | ( ~ (v5 = 0) & vertex(v0) = v5) | ( ~ (v5 = 0) & edge(v4) = v5) | (head_of(v4) = v5 & ! [v7] : ( ~ (path_cons(v4, v7) = v2) | ? [v8] : ( ~ (v8 = 0) & path(v5, v1, v7) = v8)) & ! [v7] : ( ~ (path(v5, v1, v7) = 0) | ? [v8] : ( ~ (v8 = v2) & path_cons(v4, v7) = v8)) & ( ~ (v5 = v1) | ( ~ (v6 = v2) & path_cons(v4, empty) = v6)))))
% 23.25/6.08 | (80) ! [v0] : ( ~ (edge(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & tail_of(v0) = v2 & head_of(v0) = v1))
% 23.25/6.08 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : path(v2, v1, v0) = v3
% 23.25/6.08 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0))
% 23.25/6.08 |
% 23.25/6.08 | Instantiating formula (72) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.08 | (83) ? [v0] : (length_of(all_0_5_5) = v0 & path(all_0_9_9, all_0_8_8, all_0_5_5) = 0 & ! [v1] : ! [v2] : ( ~ (length_of(v1) = v2) | ? [v3] : ((v3 = 0 & less_or_equal(v0, v2) = 0) | ( ~ (v3 = 0) & path(all_0_9_9, all_0_8_8, v1) = v3))) & ! [v1] : ( ~ (path(all_0_9_9, all_0_8_8, v1) = 0) | ? [v2] : (length_of(v1) = v2 & less_or_equal(v0, v2) = 0)))
% 23.25/6.08 |
% 23.25/6.08 | Instantiating formula (69) with 0, all_0_5_5, all_0_7_7, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, precedes(all_0_7_7, all_0_6_6, all_0_5_5) = 0, yields:
% 23.25/6.08 | (84) ? [v0] : ( ~ (v0 = 0) & precedes(all_0_6_6, all_0_7_7, all_0_5_5) = v0)
% 23.25/6.08 |
% 23.25/6.08 | Instantiating formula (44) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, precedes(all_0_7_7, all_0_6_6, all_0_5_5) = 0, yields:
% 23.25/6.08 | (85) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & precedes(all_0_6_6, all_0_7_7, all_0_5_5) = v2 & tail_of(all_0_7_7) = v0 & head_of(all_0_6_6) = v1 & ! [v3] : ( ~ (tail_of(v3) = v0) | ? [v4] : ( ~ (v4 = v1) & head_of(v3) = v4)) & ! [v3] : ( ~ (head_of(v3) = v1) | ? [v4] : ( ~ (v4 = v0) & tail_of(v3) = v4)))
% 23.25/6.08 |
% 23.25/6.08 | Instantiating (85) with all_40_0_57, all_40_1_58, all_40_2_59 yields:
% 23.25/6.08 | (86) ~ (all_40_0_57 = 0) & precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_40_0_57 & tail_of(all_0_7_7) = all_40_2_59 & head_of(all_0_6_6) = all_40_1_58 & ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))
% 23.25/6.08 |
% 23.25/6.08 | Applying alpha-rule on (86) yields:
% 23.25/6.08 | (87) ~ (all_40_0_57 = 0)
% 23.25/6.08 | (88) precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_40_0_57
% 23.25/6.08 | (89) head_of(all_0_6_6) = all_40_1_58
% 23.25/6.08 | (90) tail_of(all_0_7_7) = all_40_2_59
% 23.25/6.08 | (91) ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))
% 23.25/6.08 | (92) ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1))
% 23.25/6.08 |
% 23.25/6.08 | Instantiating (84) with all_43_0_60 yields:
% 23.25/6.08 | (93) ~ (all_43_0_60 = 0) & precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_43_0_60
% 23.25/6.08 |
% 23.25/6.08 | Applying alpha-rule on (93) yields:
% 23.25/6.08 | (94) ~ (all_43_0_60 = 0)
% 23.25/6.08 | (95) precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_43_0_60
% 23.25/6.08 |
% 23.25/6.08 | Instantiating (83) with all_45_0_61 yields:
% 23.25/6.08 | (96) length_of(all_0_5_5) = all_45_0_61 & path(all_0_9_9, all_0_8_8, all_0_5_5) = 0 & ! [v0] : ! [v1] : ( ~ (length_of(v0) = v1) | ? [v2] : ((v2 = 0 & less_or_equal(all_45_0_61, v1) = 0) | ( ~ (v2 = 0) & path(all_0_9_9, all_0_8_8, v0) = v2))) & ! [v0] : ( ~ (path(all_0_9_9, all_0_8_8, v0) = 0) | ? [v1] : (length_of(v0) = v1 & less_or_equal(all_45_0_61, v1) = 0))
% 23.25/6.08 |
% 23.25/6.08 | Applying alpha-rule on (96) yields:
% 23.25/6.08 | (97) length_of(all_0_5_5) = all_45_0_61
% 23.25/6.08 | (98) path(all_0_9_9, all_0_8_8, all_0_5_5) = 0
% 23.25/6.08 | (99) ! [v0] : ! [v1] : ( ~ (length_of(v0) = v1) | ? [v2] : ((v2 = 0 & less_or_equal(all_45_0_61, v1) = 0) | ( ~ (v2 = 0) & path(all_0_9_9, all_0_8_8, v0) = v2)))
% 23.25/6.08 | (100) ! [v0] : ( ~ (path(all_0_9_9, all_0_8_8, v0) = 0) | ? [v1] : (length_of(v0) = v1 & less_or_equal(all_45_0_61, v1) = 0))
% 23.25/6.08 |
% 23.25/6.08 | Instantiating formula (38) with all_0_6_6, all_0_7_7, all_0_5_5, all_40_0_57, all_43_0_60 and discharging atoms precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_43_0_60, precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_40_0_57, yields:
% 23.25/6.08 | (101) all_43_0_60 = all_40_0_57
% 23.25/6.08 |
% 23.25/6.08 | From (101) and (95) follows:
% 23.25/6.08 | (88) precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_40_0_57
% 23.25/6.08 |
% 23.25/6.08 | Instantiating formula (69) with all_40_0_57, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_40_0_57, yields:
% 23.25/6.08 | (103) ? [v0] : ? [v1] : (( ~ (v0 = 0) & precedes(all_0_7_7, all_0_6_6, all_0_5_5) = v0) | ( ~ (all_40_0_57 = 0) & tail_of(all_0_7_7) = v0 & head_of(all_0_6_6) = v1 & ! [v2] : ( ~ (tail_of(v2) = v0) | ? [v3] : ( ~ (v3 = v1) & head_of(v2) = v3)) & ! [v2] : ( ~ (head_of(v2) = v1) | ? [v3] : ( ~ (v3 = v0) & tail_of(v2) = v3))))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (56) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_5_5 and discharging atoms precedes(all_0_7_7, all_0_6_6, all_0_5_5) = 0, path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.09 | (104) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (on_path(all_0_6_6, all_0_5_5) = 0 & on_path(all_0_7_7, all_0_5_5) = 0 & ((v3 = 0 & v2 = 0 & precedes(v1, all_0_6_6, all_0_5_5) = 0 & sequential(all_0_7_7, v1) = 0) | (v0 = 0 & sequential(all_0_7_7, all_0_6_6) = 0)) & (( ~ (v0 = 0) & sequential(all_0_7_7, all_0_6_6) = v0) | ( ! [v4] : ( ~ (precedes(v4, all_0_6_6, all_0_5_5) = 0) | ? [v5] : ( ~ (v5 = 0) & sequential(all_0_7_7, v4) = v5)) & ! [v4] : ( ~ (sequential(all_0_7_7, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & precedes(v4, all_0_6_6, all_0_5_5) = v5)))))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (4) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.09 | (105) all_0_8_8 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v2 = 0 & ~ (v4 = 0) & length_of(v1) = v3 & length_of(all_0_5_5) = v0 & less_or_equal(v0, v3) = v4 & path(all_0_9_9, all_0_8_8, v1) = 0) | (v0 = 0 & shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (50) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.09 | (106) vertex(all_0_8_8) = 0 & vertex(all_0_9_9) = 0
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (106) yields:
% 23.25/6.09 | (107) vertex(all_0_8_8) = 0
% 23.25/6.09 | (108) vertex(all_0_9_9) = 0
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (59) with 0, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.09 | (109) ? [v0] : (( ~ (v0 = 0) & shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = v0) | ( ~ (all_0_8_8 = all_0_9_9) & length_of(all_0_5_5) = v0 & ! [v1] : ! [v2] : ( ~ (length_of(v1) = v2) | ? [v3] : ((v3 = 0 & less_or_equal(v0, v2) = 0) | ( ~ (v3 = 0) & path(all_0_9_9, all_0_8_8, v1) = v3))) & ! [v1] : ( ~ (path(all_0_9_9, all_0_8_8, v1) = 0) | ? [v2] : (length_of(v1) = v2 & less_or_equal(v0, v2) = 0))))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (92) with all_0_7_7 and discharging atoms tail_of(all_0_7_7) = all_40_2_59, yields:
% 23.25/6.09 | (110) ? [v0] : ( ~ (v0 = all_40_1_58) & head_of(all_0_7_7) = v0)
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (36) with all_40_1_58, all_40_2_59, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, tail_of(all_0_7_7) = all_40_2_59, head_of(all_0_6_6) = all_40_1_58, yields:
% 23.25/6.09 | (111) ? [v0] : (( ~ (v0 = 0) & precedes(all_0_6_6, all_0_7_7, all_0_5_5) = v0 & ! [v1] : ( ~ (tail_of(v1) = all_40_2_59) | ? [v2] : ( ~ (v2 = all_40_1_58) & head_of(v1) = v2)) & ! [v1] : ( ~ (head_of(v1) = all_40_1_58) | ? [v2] : ( ~ (v2 = all_40_2_59) & tail_of(v1) = v2))) | ( ~ (v0 = 0) & precedes(all_0_7_7, all_0_6_6, all_0_5_5) = v0))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (91) with all_0_6_6 and discharging atoms head_of(all_0_6_6) = all_40_1_58, yields:
% 23.25/6.09 | (112) ? [v0] : ( ~ (v0 = all_40_2_59) & tail_of(all_0_6_6) = v0)
% 23.25/6.09 |
% 23.25/6.09 | Instantiating (109) with all_59_0_63 yields:
% 23.25/6.09 | (113) ( ~ (all_59_0_63 = 0) & shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = all_59_0_63) | ( ~ (all_0_8_8 = all_0_9_9) & length_of(all_0_5_5) = all_59_0_63 & ! [v0] : ! [v1] : ( ~ (length_of(v0) = v1) | ? [v2] : ((v2 = 0 & less_or_equal(all_59_0_63, v1) = 0) | ( ~ (v2 = 0) & path(all_0_9_9, all_0_8_8, v0) = v2))) & ! [v0] : ( ~ (path(all_0_9_9, all_0_8_8, v0) = 0) | ? [v1] : (length_of(v0) = v1 & less_or_equal(all_59_0_63, v1) = 0)))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating (104) with all_63_0_68, all_63_1_69, all_63_2_70, all_63_3_71 yields:
% 23.25/6.09 | (114) on_path(all_0_6_6, all_0_5_5) = 0 & on_path(all_0_7_7, all_0_5_5) = 0 & ((all_63_0_68 = 0 & all_63_1_69 = 0 & precedes(all_63_2_70, all_0_6_6, all_0_5_5) = 0 & sequential(all_0_7_7, all_63_2_70) = 0) | (all_63_3_71 = 0 & sequential(all_0_7_7, all_0_6_6) = 0)) & (( ~ (all_63_3_71 = 0) & sequential(all_0_7_7, all_0_6_6) = all_63_3_71) | ( ! [v0] : ( ~ (precedes(v0, all_0_6_6, all_0_5_5) = 0) | ? [v1] : ( ~ (v1 = 0) & sequential(all_0_7_7, v0) = v1)) & ! [v0] : ( ~ (sequential(all_0_7_7, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & precedes(v0, all_0_6_6, all_0_5_5) = v1))))
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (114) yields:
% 23.25/6.09 | (115) on_path(all_0_6_6, all_0_5_5) = 0
% 23.25/6.09 | (116) on_path(all_0_7_7, all_0_5_5) = 0
% 23.25/6.09 | (117) (all_63_0_68 = 0 & all_63_1_69 = 0 & precedes(all_63_2_70, all_0_6_6, all_0_5_5) = 0 & sequential(all_0_7_7, all_63_2_70) = 0) | (all_63_3_71 = 0 & sequential(all_0_7_7, all_0_6_6) = 0)
% 23.25/6.09 | (118) ( ~ (all_63_3_71 = 0) & sequential(all_0_7_7, all_0_6_6) = all_63_3_71) | ( ! [v0] : ( ~ (precedes(v0, all_0_6_6, all_0_5_5) = 0) | ? [v1] : ( ~ (v1 = 0) & sequential(all_0_7_7, v0) = v1)) & ! [v0] : ( ~ (sequential(all_0_7_7, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & precedes(v0, all_0_6_6, all_0_5_5) = v1)))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating (103) with all_65_0_72, all_65_1_73 yields:
% 23.25/6.09 | (119) ( ~ (all_65_1_73 = 0) & precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_65_1_73) | ( ~ (all_40_0_57 = 0) & tail_of(all_0_7_7) = all_65_1_73 & head_of(all_0_6_6) = all_65_0_72 & ! [v0] : ( ~ (tail_of(v0) = all_65_1_73) | ? [v1] : ( ~ (v1 = all_65_0_72) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_65_0_72) | ? [v1] : ( ~ (v1 = all_65_1_73) & tail_of(v0) = v1)))
% 23.25/6.09 |
% 23.25/6.09 | Instantiating (110) with all_66_0_74 yields:
% 23.25/6.09 | (120) ~ (all_66_0_74 = all_40_1_58) & head_of(all_0_7_7) = all_66_0_74
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (120) yields:
% 23.25/6.09 | (121) ~ (all_66_0_74 = all_40_1_58)
% 23.25/6.09 | (122) head_of(all_0_7_7) = all_66_0_74
% 23.25/6.09 |
% 23.25/6.09 | Instantiating (112) with all_73_0_81 yields:
% 23.25/6.09 | (123) ~ (all_73_0_81 = all_40_2_59) & tail_of(all_0_6_6) = all_73_0_81
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (123) yields:
% 23.25/6.09 | (124) ~ (all_73_0_81 = all_40_2_59)
% 23.25/6.09 | (125) tail_of(all_0_6_6) = all_73_0_81
% 23.25/6.09 |
% 23.25/6.09 | Instantiating (111) with all_75_0_82 yields:
% 23.25/6.09 | (126) ( ~ (all_75_0_82 = 0) & precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_75_0_82 & ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))) | ( ~ (all_75_0_82 = 0) & precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_75_0_82)
% 23.25/6.09 |
% 23.25/6.09 +-Applying beta-rule and splitting (113), into two cases.
% 23.25/6.09 |-Branch one:
% 23.25/6.09 | (127) ~ (all_59_0_63 = 0) & shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = all_59_0_63
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (127) yields:
% 23.25/6.09 | (128) ~ (all_59_0_63 = 0)
% 23.25/6.09 | (129) shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = all_59_0_63
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (68) with all_0_9_9, all_0_8_8, all_0_5_5, all_59_0_63, 0 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = all_59_0_63, shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.09 | (130) all_59_0_63 = 0
% 23.25/6.09 |
% 23.25/6.09 | Equations (130) can reduce 128 to:
% 23.25/6.09 | (131) $false
% 23.25/6.09 |
% 23.25/6.09 |-The branch is then unsatisfiable
% 23.25/6.09 |-Branch two:
% 23.25/6.09 | (132) ~ (all_0_8_8 = all_0_9_9) & length_of(all_0_5_5) = all_59_0_63 & ! [v0] : ! [v1] : ( ~ (length_of(v0) = v1) | ? [v2] : ((v2 = 0 & less_or_equal(all_59_0_63, v1) = 0) | ( ~ (v2 = 0) & path(all_0_9_9, all_0_8_8, v0) = v2))) & ! [v0] : ( ~ (path(all_0_9_9, all_0_8_8, v0) = 0) | ? [v1] : (length_of(v0) = v1 & less_or_equal(all_59_0_63, v1) = 0))
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (132) yields:
% 23.25/6.09 | (133) ~ (all_0_8_8 = all_0_9_9)
% 23.25/6.09 | (134) length_of(all_0_5_5) = all_59_0_63
% 23.25/6.09 | (135) ! [v0] : ! [v1] : ( ~ (length_of(v0) = v1) | ? [v2] : ((v2 = 0 & less_or_equal(all_59_0_63, v1) = 0) | ( ~ (v2 = 0) & path(all_0_9_9, all_0_8_8, v0) = v2)))
% 23.25/6.09 | (136) ! [v0] : ( ~ (path(all_0_9_9, all_0_8_8, v0) = 0) | ? [v1] : (length_of(v0) = v1 & less_or_equal(all_59_0_63, v1) = 0))
% 23.25/6.09 |
% 23.25/6.09 +-Applying beta-rule and splitting (119), into two cases.
% 23.25/6.09 |-Branch one:
% 23.25/6.09 | (137) ~ (all_65_1_73 = 0) & precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_65_1_73
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (137) yields:
% 23.25/6.09 | (138) ~ (all_65_1_73 = 0)
% 23.25/6.09 | (139) precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_65_1_73
% 23.25/6.09 |
% 23.25/6.09 | Instantiating formula (38) with all_0_7_7, all_0_6_6, all_0_5_5, all_65_1_73, 0 and discharging atoms precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_65_1_73, precedes(all_0_7_7, all_0_6_6, all_0_5_5) = 0, yields:
% 23.25/6.09 | (140) all_65_1_73 = 0
% 23.25/6.09 |
% 23.25/6.09 | Equations (140) can reduce 138 to:
% 23.25/6.09 | (131) $false
% 23.25/6.09 |
% 23.25/6.09 |-The branch is then unsatisfiable
% 23.25/6.09 |-Branch two:
% 23.25/6.09 | (142) ~ (all_40_0_57 = 0) & tail_of(all_0_7_7) = all_65_1_73 & head_of(all_0_6_6) = all_65_0_72 & ! [v0] : ( ~ (tail_of(v0) = all_65_1_73) | ? [v1] : ( ~ (v1 = all_65_0_72) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_65_0_72) | ? [v1] : ( ~ (v1 = all_65_1_73) & tail_of(v0) = v1))
% 23.25/6.09 |
% 23.25/6.09 | Applying alpha-rule on (142) yields:
% 23.25/6.09 | (87) ~ (all_40_0_57 = 0)
% 23.25/6.09 | (144) ! [v0] : ( ~ (head_of(v0) = all_65_0_72) | ? [v1] : ( ~ (v1 = all_65_1_73) & tail_of(v0) = v1))
% 23.25/6.09 | (145) ! [v0] : ( ~ (tail_of(v0) = all_65_1_73) | ? [v1] : ( ~ (v1 = all_65_0_72) & head_of(v0) = v1))
% 23.25/6.10 | (146) tail_of(all_0_7_7) = all_65_1_73
% 23.25/6.10 | (147) head_of(all_0_6_6) = all_65_0_72
% 23.25/6.10 |
% 23.25/6.10 +-Applying beta-rule and splitting (126), into two cases.
% 23.25/6.10 |-Branch one:
% 23.25/6.10 | (148) ~ (all_75_0_82 = 0) & precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_75_0_82 & ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))
% 23.25/6.10 |
% 23.25/6.10 | Applying alpha-rule on (148) yields:
% 23.25/6.10 | (149) ~ (all_75_0_82 = 0)
% 23.25/6.10 | (150) precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_75_0_82
% 23.25/6.10 | (92) ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1))
% 23.25/6.10 | (91) ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))
% 23.25/6.10 |
% 23.25/6.10 +-Applying beta-rule and splitting (105), into two cases.
% 23.25/6.10 |-Branch one:
% 23.25/6.10 | (153) all_0_8_8 = all_0_9_9
% 23.25/6.10 |
% 23.25/6.10 | Equations (153) can reduce 133 to:
% 23.25/6.10 | (131) $false
% 23.25/6.10 |
% 23.25/6.10 |-The branch is then unsatisfiable
% 23.25/6.10 |-Branch two:
% 23.25/6.10 | (133) ~ (all_0_8_8 = all_0_9_9)
% 23.25/6.10 | (156) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v2 = 0 & ~ (v4 = 0) & length_of(v1) = v3 & length_of(all_0_5_5) = v0 & less_or_equal(v0, v3) = v4 & path(all_0_9_9, all_0_8_8, v1) = 0) | (v0 = 0 & shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0))
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (38) with all_0_6_6, all_0_7_7, all_0_5_5, all_75_0_82, all_40_0_57 and discharging atoms precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_75_0_82, precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_40_0_57, yields:
% 23.25/6.10 | (157) all_75_0_82 = all_40_0_57
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (41) with all_0_7_7, all_65_1_73, all_40_2_59 and discharging atoms tail_of(all_0_7_7) = all_65_1_73, tail_of(all_0_7_7) = all_40_2_59, yields:
% 23.25/6.10 | (158) all_65_1_73 = all_40_2_59
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (33) with all_0_6_6, all_65_0_72, all_40_1_58 and discharging atoms head_of(all_0_6_6) = all_65_0_72, head_of(all_0_6_6) = all_40_1_58, yields:
% 23.25/6.10 | (159) all_65_0_72 = all_40_1_58
% 23.25/6.10 |
% 23.25/6.10 | Equations (157) can reduce 149 to:
% 23.25/6.10 | (87) ~ (all_40_0_57 = 0)
% 23.25/6.10 |
% 23.25/6.10 | From (157) and (150) follows:
% 23.25/6.10 | (88) precedes(all_0_6_6, all_0_7_7, all_0_5_5) = all_40_0_57
% 23.25/6.10 |
% 23.25/6.10 | From (158) and (146) follows:
% 23.25/6.10 | (90) tail_of(all_0_7_7) = all_40_2_59
% 23.25/6.10 |
% 23.25/6.10 | From (159) and (147) follows:
% 23.25/6.10 | (89) head_of(all_0_6_6) = all_40_1_58
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (11) with all_0_6_6, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms on_path(all_0_6_6, all_0_5_5) = 0, path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.10 | (164) ? [v0] : ? [v1] : (in_path(v1, all_0_5_5) = 0 & in_path(v0, all_0_5_5) = 0 & tail_of(all_0_6_6) = v1 & edge(all_0_6_6) = 0 & head_of(all_0_6_6) = v0)
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (11) with all_0_7_7, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms on_path(all_0_7_7, all_0_5_5) = 0, path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.10 | (165) ? [v0] : ? [v1] : (in_path(v1, all_0_5_5) = 0 & in_path(v0, all_0_5_5) = 0 & tail_of(all_0_7_7) = v1 & edge(all_0_7_7) = 0 & head_of(all_0_7_7) = v0)
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (36) with all_40_1_58, all_73_0_81, all_0_5_5, all_0_6_6, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, tail_of(all_0_6_6) = all_73_0_81, head_of(all_0_6_6) = all_40_1_58, yields:
% 23.25/6.10 | (166) ? [v0] : (( ~ (v0 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = v0 & ! [v1] : ( ~ (tail_of(v1) = all_73_0_81) | ? [v2] : ( ~ (v2 = all_40_1_58) & head_of(v1) = v2)) & ! [v1] : ( ~ (head_of(v1) = all_40_1_58) | ? [v2] : ( ~ (v2 = all_73_0_81) & tail_of(v1) = v2))) | ( ~ (v0 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = v0))
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (36) with all_66_0_74, all_40_2_59, all_0_5_5, all_0_7_7, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms shortest_path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, tail_of(all_0_7_7) = all_40_2_59, head_of(all_0_7_7) = all_66_0_74, yields:
% 23.25/6.10 | (167) ? [v0] : (( ~ (v0 = 0) & precedes(all_0_7_7, all_0_7_7, all_0_5_5) = v0 & ! [v1] : ( ~ (tail_of(v1) = all_40_2_59) | ? [v2] : ( ~ (v2 = all_66_0_74) & head_of(v1) = v2)) & ! [v1] : ( ~ (head_of(v1) = all_66_0_74) | ? [v2] : ( ~ (v2 = all_40_2_59) & tail_of(v1) = v2))) | ( ~ (v0 = 0) & precedes(all_0_7_7, all_0_7_7, all_0_5_5) = v0))
% 23.25/6.10 |
% 23.25/6.10 | Instantiating (167) with all_131_0_111 yields:
% 23.25/6.10 | (168) ( ~ (all_131_0_111 = 0) & precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111 & ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_66_0_74) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_66_0_74) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))) | ( ~ (all_131_0_111 = 0) & precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111)
% 23.25/6.10 |
% 23.25/6.10 | Instantiating (166) with all_145_0_134 yields:
% 23.25/6.10 | (169) ( ~ (all_145_0_134 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134 & ! [v0] : ( ~ (tail_of(v0) = all_73_0_81) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_73_0_81) & tail_of(v0) = v1))) | ( ~ (all_145_0_134 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134)
% 23.25/6.10 |
% 23.25/6.10 | Instantiating (165) with all_150_0_143, all_150_1_144 yields:
% 23.25/6.10 | (170) in_path(all_150_0_143, all_0_5_5) = 0 & in_path(all_150_1_144, all_0_5_5) = 0 & tail_of(all_0_7_7) = all_150_0_143 & edge(all_0_7_7) = 0 & head_of(all_0_7_7) = all_150_1_144
% 23.25/6.10 |
% 23.25/6.10 | Applying alpha-rule on (170) yields:
% 23.25/6.10 | (171) edge(all_0_7_7) = 0
% 23.25/6.10 | (172) in_path(all_150_1_144, all_0_5_5) = 0
% 23.25/6.10 | (173) head_of(all_0_7_7) = all_150_1_144
% 23.25/6.10 | (174) in_path(all_150_0_143, all_0_5_5) = 0
% 23.25/6.10 | (175) tail_of(all_0_7_7) = all_150_0_143
% 23.25/6.10 |
% 23.25/6.10 | Instantiating (164) with all_152_0_145, all_152_1_146 yields:
% 23.25/6.10 | (176) in_path(all_152_0_145, all_0_5_5) = 0 & in_path(all_152_1_146, all_0_5_5) = 0 & tail_of(all_0_6_6) = all_152_0_145 & edge(all_0_6_6) = 0 & head_of(all_0_6_6) = all_152_1_146
% 23.25/6.10 |
% 23.25/6.10 | Applying alpha-rule on (176) yields:
% 23.25/6.10 | (177) in_path(all_152_0_145, all_0_5_5) = 0
% 23.25/6.10 | (178) edge(all_0_6_6) = 0
% 23.25/6.10 | (179) tail_of(all_0_6_6) = all_152_0_145
% 23.25/6.10 | (180) head_of(all_0_6_6) = all_152_1_146
% 23.25/6.10 | (181) in_path(all_152_1_146, all_0_5_5) = 0
% 23.25/6.10 |
% 23.25/6.10 +-Applying beta-rule and splitting (75), into two cases.
% 23.25/6.10 |-Branch one:
% 23.25/6.10 | (182) all_0_6_6 = all_0_7_7
% 23.25/6.10 |
% 23.25/6.10 | From (182) and (88) follows:
% 23.25/6.10 | (183) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_40_0_57
% 23.25/6.10 |
% 23.25/6.10 | From (182) and (18) follows:
% 23.25/6.10 | (184) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = 0
% 23.25/6.10 |
% 23.25/6.10 +-Applying beta-rule and splitting (168), into two cases.
% 23.25/6.10 |-Branch one:
% 23.25/6.10 | (185) ~ (all_131_0_111 = 0) & precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111 & ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_66_0_74) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_66_0_74) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))
% 23.25/6.10 |
% 23.25/6.10 | Applying alpha-rule on (185) yields:
% 23.25/6.10 | (186) ~ (all_131_0_111 = 0)
% 23.25/6.10 | (187) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111
% 23.25/6.10 | (188) ! [v0] : ( ~ (tail_of(v0) = all_40_2_59) | ? [v1] : ( ~ (v1 = all_66_0_74) & head_of(v0) = v1))
% 23.25/6.10 | (189) ! [v0] : ( ~ (head_of(v0) = all_66_0_74) | ? [v1] : ( ~ (v1 = all_40_2_59) & tail_of(v0) = v1))
% 23.25/6.10 |
% 23.25/6.10 +-Applying beta-rule and splitting (169), into two cases.
% 23.25/6.10 |-Branch one:
% 23.25/6.10 | (190) ~ (all_145_0_134 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134 & ! [v0] : ( ~ (tail_of(v0) = all_73_0_81) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_73_0_81) & tail_of(v0) = v1))
% 23.25/6.10 |
% 23.25/6.10 | Applying alpha-rule on (190) yields:
% 23.25/6.10 | (191) ~ (all_145_0_134 = 0)
% 23.25/6.10 | (192) precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134
% 23.25/6.10 | (193) ! [v0] : ( ~ (tail_of(v0) = all_73_0_81) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1))
% 23.25/6.10 | (194) ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_73_0_81) & tail_of(v0) = v1))
% 23.25/6.10 |
% 23.25/6.10 | From (182)(182) and (192) follows:
% 23.25/6.10 | (195) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_131_0_111, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, yields:
% 23.25/6.10 | (196) all_145_0_134 = all_131_0_111
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_40_0_57, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_40_0_57, yields:
% 23.25/6.10 | (197) all_145_0_134 = all_40_0_57
% 23.25/6.10 |
% 23.25/6.10 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, 0, all_131_0_111 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = 0, yields:
% 23.25/6.10 | (198) all_131_0_111 = 0
% 23.25/6.10 |
% 23.25/6.10 | Combining equations (196,197) yields a new equation:
% 23.25/6.10 | (199) all_131_0_111 = all_40_0_57
% 23.25/6.10 |
% 23.25/6.10 | Simplifying 199 yields:
% 23.25/6.10 | (200) all_131_0_111 = all_40_0_57
% 23.25/6.10 |
% 23.25/6.10 | Combining equations (198,200) yields a new equation:
% 23.25/6.10 | (201) all_40_0_57 = 0
% 23.25/6.10 |
% 23.25/6.10 | Equations (201) can reduce 87 to:
% 23.25/6.10 | (131) $false
% 23.25/6.10 |
% 23.25/6.10 |-The branch is then unsatisfiable
% 23.25/6.10 |-Branch two:
% 23.25/6.10 | (203) ~ (all_145_0_134 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134
% 23.25/6.10 |
% 23.25/6.10 | Applying alpha-rule on (203) yields:
% 23.25/6.10 | (191) ~ (all_145_0_134 = 0)
% 23.25/6.10 | (192) precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134
% 23.25/6.10 |
% 23.25/6.10 | From (182)(182) and (192) follows:
% 23.25/6.10 | (195) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_131_0_111, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, yields:
% 23.25/6.11 | (196) all_145_0_134 = all_131_0_111
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_40_0_57, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_40_0_57, yields:
% 23.25/6.11 | (197) all_145_0_134 = all_40_0_57
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, 0, all_131_0_111 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = 0, yields:
% 23.25/6.11 | (198) all_131_0_111 = 0
% 23.25/6.11 |
% 23.25/6.11 | Combining equations (196,197) yields a new equation:
% 23.25/6.11 | (199) all_131_0_111 = all_40_0_57
% 23.25/6.11 |
% 23.25/6.11 | Simplifying 199 yields:
% 23.25/6.11 | (200) all_131_0_111 = all_40_0_57
% 23.25/6.11 |
% 23.25/6.11 | Combining equations (198,200) yields a new equation:
% 23.25/6.11 | (201) all_40_0_57 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (201) can reduce 87 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (214) ~ (all_131_0_111 = 0) & precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (214) yields:
% 23.25/6.11 | (186) ~ (all_131_0_111 = 0)
% 23.25/6.11 | (187) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111
% 23.25/6.11 |
% 23.25/6.11 +-Applying beta-rule and splitting (169), into two cases.
% 23.25/6.11 |-Branch one:
% 23.25/6.11 | (190) ~ (all_145_0_134 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134 & ! [v0] : ( ~ (tail_of(v0) = all_73_0_81) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1)) & ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_73_0_81) & tail_of(v0) = v1))
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (190) yields:
% 23.25/6.11 | (191) ~ (all_145_0_134 = 0)
% 23.25/6.11 | (192) precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134
% 23.25/6.11 | (193) ! [v0] : ( ~ (tail_of(v0) = all_73_0_81) | ? [v1] : ( ~ (v1 = all_40_1_58) & head_of(v0) = v1))
% 23.25/6.11 | (194) ! [v0] : ( ~ (head_of(v0) = all_40_1_58) | ? [v1] : ( ~ (v1 = all_73_0_81) & tail_of(v0) = v1))
% 23.25/6.11 |
% 23.25/6.11 | From (182)(182) and (192) follows:
% 23.25/6.11 | (195) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_131_0_111, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, yields:
% 23.25/6.11 | (196) all_145_0_134 = all_131_0_111
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_40_0_57, all_131_0_111 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_40_0_57, yields:
% 23.25/6.11 | (200) all_131_0_111 = all_40_0_57
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, 0, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = 0, yields:
% 23.25/6.11 | (225) all_145_0_134 = 0
% 23.25/6.11 |
% 23.25/6.11 | Combining equations (196,225) yields a new equation:
% 23.25/6.11 | (226) all_131_0_111 = 0
% 23.25/6.11 |
% 23.25/6.11 | Simplifying 226 yields:
% 23.25/6.11 | (198) all_131_0_111 = 0
% 23.25/6.11 |
% 23.25/6.11 | Combining equations (198,200) yields a new equation:
% 23.25/6.11 | (201) all_40_0_57 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (201) can reduce 87 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (203) ~ (all_145_0_134 = 0) & precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (203) yields:
% 23.25/6.11 | (191) ~ (all_145_0_134 = 0)
% 23.25/6.11 | (192) precedes(all_0_6_6, all_0_6_6, all_0_5_5) = all_145_0_134
% 23.25/6.11 |
% 23.25/6.11 | From (182)(182) and (192) follows:
% 23.25/6.11 | (195) precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_131_0_111, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, yields:
% 23.25/6.11 | (196) all_145_0_134 = all_131_0_111
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, all_40_0_57, all_131_0_111 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_131_0_111, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_40_0_57, yields:
% 23.25/6.11 | (200) all_131_0_111 = all_40_0_57
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (38) with all_0_7_7, all_0_7_7, all_0_5_5, 0, all_145_0_134 and discharging atoms precedes(all_0_7_7, all_0_7_7, all_0_5_5) = all_145_0_134, precedes(all_0_7_7, all_0_7_7, all_0_5_5) = 0, yields:
% 23.25/6.11 | (225) all_145_0_134 = 0
% 23.25/6.11 |
% 23.25/6.11 | Combining equations (196,225) yields a new equation:
% 23.25/6.11 | (226) all_131_0_111 = 0
% 23.25/6.11 |
% 23.25/6.11 | Simplifying 226 yields:
% 23.25/6.11 | (198) all_131_0_111 = 0
% 23.25/6.11 |
% 23.25/6.11 | Combining equations (198,200) yields a new equation:
% 23.25/6.11 | (201) all_40_0_57 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (201) can reduce 87 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (241) ~ (all_0_6_6 = all_0_7_7)
% 23.25/6.11 | (242) all_0_8_8 = all_0_9_9 | ( ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1) | ( ~ (all_0_2_2 = 0) & edge(all_0_7_7) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & vertex(all_0_8_8) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & vertex(all_0_9_9) = all_0_4_4)
% 23.25/6.11 |
% 23.25/6.11 +-Applying beta-rule and splitting (242), into two cases.
% 23.25/6.11 |-Branch one:
% 23.25/6.11 | (153) all_0_8_8 = all_0_9_9
% 23.25/6.11 |
% 23.25/6.11 | Equations (153) can reduce 133 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (133) ~ (all_0_8_8 = all_0_9_9)
% 23.25/6.11 | (246) ( ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1) | ( ~ (all_0_2_2 = 0) & edge(all_0_7_7) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & vertex(all_0_8_8) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & vertex(all_0_9_9) = all_0_4_4)
% 23.25/6.11 |
% 23.25/6.11 +-Applying beta-rule and splitting (246), into two cases.
% 23.25/6.11 |-Branch one:
% 23.25/6.11 | (247) ( ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1) | ( ~ (all_0_2_2 = 0) & edge(all_0_7_7) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & vertex(all_0_8_8) = all_0_3_3)
% 23.25/6.11 |
% 23.25/6.11 +-Applying beta-rule and splitting (247), into two cases.
% 23.25/6.11 |-Branch one:
% 23.25/6.11 | (248) ( ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1) | ( ~ (all_0_2_2 = 0) & edge(all_0_7_7) = all_0_2_2)
% 23.25/6.11 |
% 23.25/6.11 +-Applying beta-rule and splitting (248), into two cases.
% 23.25/6.11 |-Branch one:
% 23.25/6.11 | (249) ( ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1)
% 23.25/6.11 |
% 23.25/6.11 +-Applying beta-rule and splitting (249), into two cases.
% 23.25/6.11 |-Branch one:
% 23.25/6.11 | (250) ~ (all_0_0_0 = 0) & path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (250) yields:
% 23.25/6.11 | (251) ~ (all_0_0_0 = 0)
% 23.25/6.11 | (252) path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (32) with all_0_9_9, all_0_8_8, all_0_5_5, all_0_0_0, 0 and discharging atoms path(all_0_9_9, all_0_8_8, all_0_5_5) = all_0_0_0, path(all_0_9_9, all_0_8_8, all_0_5_5) = 0, yields:
% 23.25/6.11 | (253) all_0_0_0 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (253) can reduce 251 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (255) ~ (all_0_1_1 = 0) & edge(all_0_6_6) = all_0_1_1
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (255) yields:
% 23.25/6.11 | (256) ~ (all_0_1_1 = 0)
% 23.25/6.11 | (257) edge(all_0_6_6) = all_0_1_1
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (25) with all_0_6_6, 0, all_0_1_1 and discharging atoms edge(all_0_6_6) = all_0_1_1, edge(all_0_6_6) = 0, yields:
% 23.25/6.11 | (258) all_0_1_1 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (258) can reduce 256 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (260) ~ (all_0_2_2 = 0) & edge(all_0_7_7) = all_0_2_2
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (260) yields:
% 23.25/6.11 | (261) ~ (all_0_2_2 = 0)
% 23.25/6.11 | (262) edge(all_0_7_7) = all_0_2_2
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (25) with all_0_7_7, 0, all_0_2_2 and discharging atoms edge(all_0_7_7) = all_0_2_2, edge(all_0_7_7) = 0, yields:
% 23.25/6.11 | (263) all_0_2_2 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (263) can reduce 261 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (265) ~ (all_0_3_3 = 0) & vertex(all_0_8_8) = all_0_3_3
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (265) yields:
% 23.25/6.11 | (266) ~ (all_0_3_3 = 0)
% 23.25/6.11 | (267) vertex(all_0_8_8) = all_0_3_3
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (20) with all_0_8_8, all_0_3_3, 0 and discharging atoms vertex(all_0_8_8) = all_0_3_3, vertex(all_0_8_8) = 0, yields:
% 23.25/6.11 | (268) all_0_3_3 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (268) can reduce 266 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (270) ~ (all_0_4_4 = 0) & vertex(all_0_9_9) = all_0_4_4
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (270) yields:
% 23.25/6.11 | (271) ~ (all_0_4_4 = 0)
% 23.25/6.11 | (272) vertex(all_0_9_9) = all_0_4_4
% 23.25/6.11 |
% 23.25/6.11 | Instantiating formula (20) with all_0_9_9, all_0_4_4, 0 and discharging atoms vertex(all_0_9_9) = all_0_4_4, vertex(all_0_9_9) = 0, yields:
% 23.25/6.11 | (273) all_0_4_4 = 0
% 23.25/6.11 |
% 23.25/6.11 | Equations (273) can reduce 271 to:
% 23.25/6.11 | (131) $false
% 23.25/6.11 |
% 23.25/6.11 |-The branch is then unsatisfiable
% 23.25/6.11 |-Branch two:
% 23.25/6.11 | (275) ~ (all_75_0_82 = 0) & precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_75_0_82
% 23.25/6.11 |
% 23.25/6.11 | Applying alpha-rule on (275) yields:
% 23.25/6.11 | (149) ~ (all_75_0_82 = 0)
% 23.25/6.12 | (277) precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_75_0_82
% 23.25/6.12 |
% 23.25/6.12 | Instantiating formula (38) with all_0_7_7, all_0_6_6, all_0_5_5, all_75_0_82, 0 and discharging atoms precedes(all_0_7_7, all_0_6_6, all_0_5_5) = all_75_0_82, precedes(all_0_7_7, all_0_6_6, all_0_5_5) = 0, yields:
% 23.25/6.12 | (278) all_75_0_82 = 0
% 23.25/6.12 |
% 23.25/6.12 | Equations (278) can reduce 149 to:
% 23.25/6.12 | (131) $false
% 23.25/6.12 |
% 23.25/6.12 |-The branch is then unsatisfiable
% 23.25/6.12 % SZS output end Proof for theBenchmark
% 23.25/6.12
% 23.25/6.12 5506ms
%------------------------------------------------------------------------------