%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GRA002+4 : 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 4.32s 1.66s
% Output   : Proof 6.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRA002+4 : 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 02:48:56 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.54/0.61          ____       _                          
% 0.54/0.61    ___  / __ \_____(_)___  ________  __________
% 0.54/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.54/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.54/0.61  
% 0.54/0.61  A Theorem Prover for First-Order Logic
% 0.54/0.61  (ePrincess v.1.0)
% 0.54/0.61  
% 0.54/0.61  (c) Philipp Rümmer, 2009-2015
% 0.54/0.61  (c) Peter Backeman, 2014-2015
% 0.54/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.61  Bug reports to peter@backeman.se
% 0.54/0.61  
% 0.54/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.61  
% 0.54/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/1.01  Prover 0: Preprocessing ...
% 3.11/1.38  Prover 0: Warning: ignoring some quantifiers
% 3.11/1.41  Prover 0: Constructing countermodel ...
% 4.32/1.66  Prover 0: proved (997ms)
% 4.32/1.66  
% 4.32/1.66  No countermodel exists, formula is valid
% 4.32/1.66  % SZS status Theorem for theBenchmark
% 4.32/1.66  
% 4.32/1.66  Generating proof ... Warning: ignoring some quantifiers
% 6.31/2.08  found it (size 21)
% 6.31/2.08  
% 6.31/2.08  % SZS output start Proof for theBenchmark
% 6.31/2.08  Assumed formulas after preprocessing and simplification: 
% 6.31/2.08  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (minus(v4, n1) = v5 & number_of_in(triangles, graph) = v0 & length_of(v1) = v4 & shortest_path(v2, v3, v1) & complete &  ~ less_or_equal(v5, v0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (tail_of(v13) = v11) |  ~ (tail_of(v8) = v11) |  ~ (head_of(v9) = v12) |  ~ shortest_path(v6, v7, v10) |  ~ precedes(v8, v9, v10) |  ? [v14] : ( ~ (v14 = v12) & head_of(v13) = v14)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (tail_of(v8) = v11) |  ~ (head_of(v13) = v12) |  ~ (head_of(v9) = v12) |  ~ shortest_path(v6, v7, v10) |  ~ precedes(v8, v9, v10) |  ? [v14] : ( ~ (v14 = v11) & tail_of(v13) = v14)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (tail_of(v8) = v11) |  ~ (head_of(v9) = v12) |  ~ shortest_path(v6, v7, v10) |  ~ precedes(v9, v8, v10) |  ~ precedes(v8, v9, v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (length_of(v10) = v11) |  ~ (length_of(v8) = v9) |  ~ shortest_path(v6, v7, v8) |  ~ path(v6, v7, v10) | less_or_equal(v9, v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ precedes(v9, v8, v6) |  ~ precedes(v7, v8, v6) |  ~ sequential(v7, v9) |  ~ sequential(v7, v8) |  ~ path(v10, v11, v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ precedes(v9, v8, v6) |  ~ sequential(v7, v9) |  ~ on_path(v8, v6) |  ~ on_path(v7, v6) |  ~ path(v10, v11, v6) | precedes(v7, v8, v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (tail_of(v9) = v10) |  ~ on_path(v9, v8) |  ~ path(v6, v7, v8) | in_path(v10, v8)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (tail_of(v9) = v10) |  ~ on_path(v9, v8) |  ~ path(v6, v7, v8) | edge(v9)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (tail_of(v9) = v10) |  ~ on_path(v9, v8) |  ~ path(v6, v7, v8) |  ? [v11] : (head_of(v9) = v11 & in_path(v11, v8))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (head_of(v9) = v10) |  ~ on_path(v9, v8) |  ~ path(v6, v7, v8) | in_path(v10, v8)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (head_of(v9) = v10) |  ~ on_path(v9, v8) |  ~ path(v6, v7, v8) | edge(v9)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (head_of(v9) = v10) |  ~ on_path(v9, v8) |  ~ path(v6, v7, v8) |  ? [v11] : (tail_of(v9) = v11 & in_path(v11, v8))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ precedes(v7, v8, v6) |  ~ path(v9, v10, v6) | sequential(v7, v8) |  ? [v11] : (precedes(v11, v8, v6) & sequential(v7, v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ precedes(v7, v8, v6) |  ~ path(v9, v10, v6) | on_path(v8, v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ precedes(v7, v8, v6) |  ~ path(v9, v10, v6) | on_path(v7, v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ sequential(v7, v8) |  ~ on_path(v8, v6) |  ~ on_path(v7, v6) |  ~ path(v9, v10, v6) | precedes(v7, v8, v6)) &  ? [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (path_cons(v9, empty) = v10) |  ~ vertex(v8) |  ~ vertex(v7) |  ~ edge(v9) | path(v7, v8, v6) |  ? [v11] :  ? [v12] : (tail_of(v9) = v11 & head_of(v9) = v12 & ( ~ (v11 = v7) | ( ! [v13] : ( ~ (path_cons(v9, v13) = v6) |  ~ path(v12, v8, v13)) & ( ~ (v12 = v8) |  ~ (v10 = v6)))))) &  ? [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (head_of(v9) = v10) |  ~ vertex(v8) |  ~ vertex(v7) |  ~ edge(v9) | path(v7, v8, v6) |  ? [v11] :  ? [v12] : (path_cons(v9, empty) = v12 & tail_of(v9) = v11 & ( ~ (v11 = v7) | ( ! [v13] : ( ~ (path_cons(v9, v13) = v6) |  ~ path(v10, v8, v13)) & ( ~ (v12 = v6) |  ~ (v10 = v8)))))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (tail_of(v7) = v9) |  ~ (head_of(v6) = v8) |  ~ sequential(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (minus(v9, v8) = v7) |  ~ (minus(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (number_of_in(v9, v8) = v7) |  ~ (number_of_in(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (length_of(v8) = v9) |  ~ path(v6, v7, v8) | shortest_path(v6, v7, v8) |  ? [v10] :  ? [v11] : (length_of(v10) = v11 & path(v6, v7, v10) &  ~ less_or_equal(v9, v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (path_cons(v9, v8) = v7) |  ~ (path_cons(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (number_of_in(triangles, v6) = v9) |  ~ shortest_path(v7, v8, v6) | number_of_in(sequential_pairs, v6) = v9) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (number_of_in(triangles, v6) = v9) |  ~ path(v7, v8, v6) |  ? [v10] :  ? [v11] : ((v10 = v9 & number_of_in(sequential_pairs, v6) = v9) | (sequential(v10, v11) & on_path(v11, v6) & on_path(v10, v6) &  ! [v12] :  ~ triangle(v10, v11, v12)))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (number_of_in(sequential_pairs, v8) = v9) |  ~ path(v6, v7, v8) |  ? [v10] : (minus(v10, n1) = v9 & length_of(v8) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (number_of_in(sequential_pairs, v6) = v9) |  ~ shortest_path(v7, v8, v6) | number_of_in(triangles, v6) = v9) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (number_of_in(sequential_pairs, v6) = v9) |  ~ path(v7, v8, v6) |  ? [v10] :  ? [v11] : ((v10 = v9 & number_of_in(triangles, v6) = v9) | (sequential(v10, v11) & on_path(v11, v6) & on_path(v10, v6) &  ! [v12] :  ~ triangle(v10, v11, v12)))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (number_of_in(edges, v8) = v9) |  ~ path(v6, v7, v8) | length_of(v8) = v9) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (length_of(v8) = v9) |  ~ shortest_path(v6, v7, v8) | path(v6, v7, v8)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (length_of(v8) = v9) |  ~ path(v6, v7, v8) | number_of_in(edges, v8) = v9) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (length_of(v8) = v9) |  ~ path(v6, v7, v8) |  ? [v10] : (minus(v9, n1) = v10 & number_of_in(sequential_pairs, v8) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (tail_of(v7) = v9) |  ~ (head_of(v6) = v8) |  ~ sequential(v6, v7) | edge(v7)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (tail_of(v7) = v9) |  ~ (head_of(v6) = v8) |  ~ sequential(v6, v7) | edge(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ in_path(v9, v8) |  ~ path(v6, v7, v8) | vertex(v9)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ in_path(v9, v8) |  ~ path(v6, v7, v8) |  ? [v10] :  ? [v11] :  ? [v12] : (tail_of(v10) = v12 & head_of(v10) = v11 & on_path(v10, v8) & (v12 = v9 | v11 = v9))) &  ? [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (tail_of(v9) = v7) |  ~ vertex(v8) |  ~ vertex(v7) |  ~ edge(v9) | path(v7, v8, v6) |  ? [v10] :  ? [v11] : (path_cons(v9, empty) = v11 & head_of(v9) = v10 &  ! [v12] : ( ~ (path_cons(v9, v12) = v6) |  ~ path(v10, v8, v12)) & ( ~ (v11 = v6) |  ~ (v10 = v8)))) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (length_of(v8) = v7) |  ~ (length_of(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (tail_of(v8) = v7) |  ~ (tail_of(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (tail_of(v7) = v8) |  ~ (head_of(v6) = v8) |  ~ edge(v7) |  ~ edge(v6) | sequential(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (head_of(v8) = v7) |  ~ (head_of(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (number_of_in(v6, v7) = v8) |  ? [v9] : (number_of_in(v6, graph) = v9 & less_or_equal(v8, v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (length_of(v7) = v8) |  ~ shortest_path(v6, v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (tail_of(v6) = v8) |  ~ (head_of(v6) = v7) |  ~ sequential(v6, v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ triangle(v6, v7, v8) | sequential(v8, v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ triangle(v6, v7, v8) | sequential(v7, v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ triangle(v6, v7, v8) | sequential(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ triangle(v6, v7, v8) | edge(v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ triangle(v6, v7, v8) | edge(v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ triangle(v6, v7, v8) | edge(v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ sequential(v8, v6) |  ~ sequential(v7, v8) |  ~ sequential(v6, v7) |  ~ edge(v8) |  ~ edge(v7) |  ~ edge(v6) | triangle(v6, v7, v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ path(v6, v7, v8) | vertex(v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ path(v6, v7, v8) | vertex(v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ path(v6, v7, v8) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (path_cons(v9, empty) = v11 & tail_of(v9) = v6 & head_of(v9) = v10 & edge(v9) & ( ~ (v11 = v8) |  ~ (v10 = v7) |  ! [v14] : ( ~ (path_cons(v9, v14) = v8) |  ~ path(v7, v7, v14))) & ((v13 = v8 & path_cons(v9, v12) = v8 & path(v10, v7, v12)) | (v11 = v8 & v10 = v7)))) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ vertex(v7) |  ~ vertex(v6) |  ? [v8] :  ? [v9] :  ? [v10] : (tail_of(v8) = v10 & head_of(v8) = v9 & edge(v8) & ((v10 = v7 & v9 = v6) | (v10 = v6 & v9 = v7)))) &  ! [v6] :  ! [v7] : ( ~ (tail_of(v6) = v7) |  ~ edge(v6) | vertex(v7)) &  ! [v6] :  ! [v7] : ( ~ (tail_of(v6) = v7) |  ~ edge(v6) |  ? [v8] : ( ~ (v8 = v7) & head_of(v6) = v8)) &  ! [v6] :  ! [v7] : ( ~ (tail_of(v6) = v7) |  ~ edge(v6) |  ? [v8] : (head_of(v6) = v8 & vertex(v8))) &  ! [v6] :  ! [v7] : ( ~ (head_of(v6) = v7) |  ~ edge(v6) | vertex(v7)) &  ! [v6] :  ! [v7] : ( ~ (head_of(v6) = v7) |  ~ edge(v6) |  ? [v8] : ( ~ (v8 = v7) & tail_of(v6) = v8)) &  ! [v6] :  ! [v7] : ( ~ (head_of(v6) = v7) |  ~ edge(v6) |  ? [v8] : (tail_of(v6) = v8 & vertex(v8))))
% 6.53/2.13  | 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 yields:
% 6.53/2.13  | (1) minus(all_0_1_1, n1) = all_0_0_0 & number_of_in(triangles, graph) = all_0_5_5 & length_of(all_0_4_4) = all_0_1_1 & shortest_path(all_0_3_3, all_0_2_2, all_0_4_4) & complete &  ~ less_or_equal(all_0_0_0, all_0_5_5) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (tail_of(v7) = v5) |  ~ (tail_of(v2) = v5) |  ~ (head_of(v3) = v6) |  ~ shortest_path(v0, v1, v4) |  ~ precedes(v2, v3, v4) |  ? [v8] : ( ~ (v8 = v6) & head_of(v7) = v8)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (tail_of(v2) = v5) |  ~ (head_of(v7) = v6) |  ~ (head_of(v3) = v6) |  ~ shortest_path(v0, v1, v4) |  ~ precedes(v2, v3, v4) |  ? [v8] : ( ~ (v8 = v5) & tail_of(v7) = v8)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (tail_of(v2) = v5) |  ~ (head_of(v3) = v6) |  ~ shortest_path(v0, v1, v4) |  ~ precedes(v3, v2, v4) |  ~ precedes(v2, v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (length_of(v4) = v5) |  ~ (length_of(v2) = v3) |  ~ shortest_path(v0, v1, v2) |  ~ path(v0, v1, v4) | less_or_equal(v3, v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ precedes(v3, v2, v0) |  ~ precedes(v1, v2, v0) |  ~ sequential(v1, v3) |  ~ sequential(v1, v2) |  ~ path(v4, v5, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ precedes(v3, v2, v0) |  ~ sequential(v1, v3) |  ~ on_path(v2, v0) |  ~ on_path(v1, v0) |  ~ path(v4, v5, v0) | precedes(v1, v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (tail_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | in_path(v4, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (tail_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | edge(v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (tail_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) |  ? [v5] : (head_of(v3) = v5 & in_path(v5, v2))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | in_path(v4, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | edge(v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) |  ? [v5] : (tail_of(v3) = v5 & in_path(v5, v2))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ precedes(v1, v2, v0) |  ~ path(v3, v4, v0) | sequential(v1, v2) |  ? [v5] : (precedes(v5, v2, v0) & sequential(v1, v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ precedes(v1, v2, v0) |  ~ path(v3, v4, v0) | on_path(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ precedes(v1, v2, v0) |  ~ path(v3, v4, v0) | on_path(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ sequential(v1, v2) |  ~ on_path(v2, v0) |  ~ on_path(v1, v0) |  ~ path(v3, v4, v0) | precedes(v1, v2, v0)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (path_cons(v3, empty) = v4) |  ~ vertex(v2) |  ~ vertex(v1) |  ~ edge(v3) | path(v1, v2, v0) |  ? [v5] :  ? [v6] : (tail_of(v3) = v5 & head_of(v3) = v6 & ( ~ (v5 = v1) | ( ! [v7] : ( ~ (path_cons(v3, v7) = v0) |  ~ path(v6, v2, v7)) & ( ~ (v6 = v2) |  ~ (v4 = v0)))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ vertex(v2) |  ~ vertex(v1) |  ~ edge(v3) | path(v1, v2, v0) |  ? [v5] :  ? [v6] : (path_cons(v3, empty) = v6 & tail_of(v3) = v5 & ( ~ (v5 = v1) | ( ! [v7] : ( ~ (path_cons(v3, v7) = v0) |  ~ path(v4, v2, v7)) & ( ~ (v6 = v0) |  ~ (v4 = v2)))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (tail_of(v1) = v3) |  ~ (head_of(v0) = v2) |  ~ sequential(v0, v1)) &  ! [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 |  ~ (length_of(v2) = v3) |  ~ path(v0, v1, v2) | shortest_path(v0, v1, v2) |  ? [v4] :  ? [v5] : (length_of(v4) = v5 & path(v0, v1, v4) &  ~ less_or_equal(v3, v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (path_cons(v3, v2) = v1) |  ~ (path_cons(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(triangles, v0) = v3) |  ~ shortest_path(v1, v2, v0) | number_of_in(sequential_pairs, v0) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(triangles, v0) = v3) |  ~ path(v1, v2, v0) |  ? [v4] :  ? [v5] : ((v4 = v3 & number_of_in(sequential_pairs, v0) = v3) | (sequential(v4, v5) & on_path(v5, v0) & on_path(v4, v0) &  ! [v6] :  ~ triangle(v4, v5, v6)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(sequential_pairs, v2) = v3) |  ~ path(v0, v1, v2) |  ? [v4] : (minus(v4, n1) = v3 & length_of(v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(sequential_pairs, v0) = v3) |  ~ shortest_path(v1, v2, v0) | number_of_in(triangles, v0) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(sequential_pairs, v0) = v3) |  ~ path(v1, v2, v0) |  ? [v4] :  ? [v5] : ((v4 = v3 & number_of_in(triangles, v0) = v3) | (sequential(v4, v5) & on_path(v5, v0) & on_path(v4, v0) &  ! [v6] :  ~ triangle(v4, v5, v6)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(edges, v2) = v3) |  ~ path(v0, v1, v2) | length_of(v2) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (length_of(v2) = v3) |  ~ shortest_path(v0, v1, v2) | path(v0, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (length_of(v2) = v3) |  ~ path(v0, v1, v2) | number_of_in(edges, v2) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (length_of(v2) = v3) |  ~ path(v0, v1, v2) |  ? [v4] : (minus(v3, n1) = v4 & number_of_in(sequential_pairs, v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (tail_of(v1) = v3) |  ~ (head_of(v0) = v2) |  ~ sequential(v0, v1) | edge(v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (tail_of(v1) = v3) |  ~ (head_of(v0) = v2) |  ~ sequential(v0, v1) | edge(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ in_path(v3, v2) |  ~ path(v0, v1, v2) | vertex(v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ in_path(v3, v2) |  ~ path(v0, v1, v2) |  ? [v4] :  ? [v5] :  ? [v6] : (tail_of(v4) = v6 & head_of(v4) = v5 & on_path(v4, v2) & (v6 = v3 | v5 = v3))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (tail_of(v3) = v1) |  ~ vertex(v2) |  ~ vertex(v1) |  ~ edge(v3) | path(v1, v2, v0) |  ? [v4] :  ? [v5] : (path_cons(v3, empty) = v5 & head_of(v3) = v4 &  ! [v6] : ( ~ (path_cons(v3, v6) = v0) |  ~ path(v4, v2, v6)) & ( ~ (v5 = v0) |  ~ (v4 = v2)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (length_of(v2) = v1) |  ~ (length_of(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (tail_of(v2) = v1) |  ~ (tail_of(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (tail_of(v1) = v2) |  ~ (head_of(v0) = v2) |  ~ edge(v1) |  ~ edge(v0) | sequential(v0, v1)) &  ! [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))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (length_of(v1) = v2) |  ~ shortest_path(v0, v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (tail_of(v0) = v2) |  ~ (head_of(v0) = v1) |  ~ sequential(v0, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | sequential(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | sequential(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | sequential(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | edge(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | edge(v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | edge(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sequential(v2, v0) |  ~ sequential(v1, v2) |  ~ sequential(v0, v1) |  ~ edge(v2) |  ~ edge(v1) |  ~ edge(v0) | triangle(v0, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ path(v0, v1, v2) | vertex(v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ path(v0, v1, v2) | vertex(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ path(v0, v1, v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (path_cons(v3, empty) = v5 & tail_of(v3) = v0 & head_of(v3) = v4 & edge(v3) & ( ~ (v5 = v2) |  ~ (v4 = v1) |  ! [v8] : ( ~ (path_cons(v3, v8) = v2) |  ~ path(v1, v1, v8))) & ((v7 = v2 & path_cons(v3, v6) = v2 & path(v4, v1, v6)) | (v5 = v2 & v4 = v1)))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ vertex(v1) |  ~ vertex(v0) |  ? [v2] :  ? [v3] :  ? [v4] : (tail_of(v2) = v4 & head_of(v2) = v3 & edge(v2) & ((v4 = v1 & v3 = v0) | (v4 = v0 & v3 = v1)))) &  ! [v0] :  ! [v1] : ( ~ (tail_of(v0) = v1) |  ~ edge(v0) | vertex(v1)) &  ! [v0] :  ! [v1] : ( ~ (tail_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : ( ~ (v2 = v1) & head_of(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (tail_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : (head_of(v0) = v2 & vertex(v2))) &  ! [v0] :  ! [v1] : ( ~ (head_of(v0) = v1) |  ~ edge(v0) | vertex(v1)) &  ! [v0] :  ! [v1] : ( ~ (head_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : ( ~ (v2 = v1) & tail_of(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (head_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : (tail_of(v0) = v2 & vertex(v2)))
% 6.53/2.15  |
% 6.53/2.15  | Applying alpha-rule on (1) yields:
% 6.53/2.15  | (2) shortest_path(all_0_3_3, all_0_2_2, all_0_4_4)
% 6.70/2.15  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | edge(v2))
% 6.70/2.15  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (tail_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | edge(v3))
% 6.70/2.15  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | sequential(v1, v2))
% 6.70/2.15  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (number_of_in(v0, v1) = v2) |  ? [v3] : (number_of_in(v0, graph) = v3 & less_or_equal(v2, v3)))
% 6.70/2.15  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ precedes(v3, v2, v0) |  ~ precedes(v1, v2, v0) |  ~ sequential(v1, v3) |  ~ sequential(v1, v2) |  ~ path(v4, v5, v0))
% 6.70/2.15  | (8) minus(all_0_1_1, n1) = all_0_0_0
% 6.70/2.15  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ path(v0, v1, v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (path_cons(v3, empty) = v5 & tail_of(v3) = v0 & head_of(v3) = v4 & edge(v3) & ( ~ (v5 = v2) |  ~ (v4 = v1) |  ! [v8] : ( ~ (path_cons(v3, v8) = v2) |  ~ path(v1, v1, v8))) & ((v7 = v2 & path_cons(v3, v6) = v2 & path(v4, v1, v6)) | (v5 = v2 & v4 = v1))))
% 6.70/2.15  | (10)  ! [v0] :  ! [v1] : ( ~ (head_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : (tail_of(v0) = v2 & vertex(v2)))
% 6.70/2.15  | (11)  ! [v0] :  ! [v1] : ( ~ (tail_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : (head_of(v0) = v2 & vertex(v2)))
% 6.70/2.15  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ path(v0, v1, v2) | vertex(v0))
% 6.70/2.16  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (number_of_in(v3, v2) = v1) |  ~ (number_of_in(v3, v2) = v0))
% 6.70/2.16  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sequential(v2, v0) |  ~ sequential(v1, v2) |  ~ sequential(v0, v1) |  ~ edge(v2) |  ~ edge(v1) |  ~ edge(v0) | triangle(v0, v1, v2))
% 6.70/2.16  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | sequential(v0, v1))
% 6.70/2.16  | (16)  ! [v0] :  ! [v1] : ( ~ (head_of(v0) = v1) |  ~ edge(v0) | vertex(v1))
% 6.70/2.16  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ in_path(v3, v2) |  ~ path(v0, v1, v2) |  ? [v4] :  ? [v5] :  ? [v6] : (tail_of(v4) = v6 & head_of(v4) = v5 & on_path(v4, v2) & (v6 = v3 | v5 = v3)))
% 6.70/2.16  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3, v2) = v0))
% 6.70/2.16  | (19)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ vertex(v2) |  ~ vertex(v1) |  ~ edge(v3) | path(v1, v2, v0) |  ? [v5] :  ? [v6] : (path_cons(v3, empty) = v6 & tail_of(v3) = v5 & ( ~ (v5 = v1) | ( ! [v7] : ( ~ (path_cons(v3, v7) = v0) |  ~ path(v4, v2, v7)) & ( ~ (v6 = v0) |  ~ (v4 = v2))))))
% 6.70/2.16  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (tail_of(v1) = v3) |  ~ (head_of(v0) = v2) |  ~ sequential(v0, v1) | edge(v1))
% 6.70/2.16  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (tail_of(v2) = v5) |  ~ (head_of(v3) = v6) |  ~ shortest_path(v0, v1, v4) |  ~ precedes(v3, v2, v4) |  ~ precedes(v2, v3, v4))
% 6.70/2.16  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | edge(v1))
% 6.70/2.16  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (length_of(v2) = v3) |  ~ shortest_path(v0, v1, v2) | path(v0, v1, v2))
% 6.70/2.16  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (length_of(v2) = v1) |  ~ (length_of(v2) = v0))
% 6.70/2.16  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (length_of(v2) = v3) |  ~ path(v0, v1, v2) | number_of_in(edges, v2) = v3)
% 6.70/2.16  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ precedes(v1, v2, v0) |  ~ path(v3, v4, v0) | on_path(v2, v0))
% 6.70/2.16  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | in_path(v4, v2))
% 6.70/2.16  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ precedes(v3, v2, v0) |  ~ sequential(v1, v3) |  ~ on_path(v2, v0) |  ~ on_path(v1, v0) |  ~ path(v4, v5, v0) | precedes(v1, v2, v0))
% 6.70/2.16  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (tail_of(v2) = v5) |  ~ (head_of(v7) = v6) |  ~ (head_of(v3) = v6) |  ~ shortest_path(v0, v1, v4) |  ~ precedes(v2, v3, v4) |  ? [v8] : ( ~ (v8 = v5) & tail_of(v7) = v8))
% 6.70/2.16  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | edge(v3))
% 6.70/2.16  | (31) length_of(all_0_4_4) = all_0_1_1
% 6.70/2.16  | (32)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ vertex(v1) |  ~ vertex(v0) |  ? [v2] :  ? [v3] :  ? [v4] : (tail_of(v2) = v4 & head_of(v2) = v3 & edge(v2) & ((v4 = v1 & v3 = v0) | (v4 = v0 & v3 = v1))))
% 6.70/2.16  | (33)  ! [v0] :  ! [v1] : ( ~ (tail_of(v0) = v1) |  ~ edge(v0) | vertex(v1))
% 6.70/2.16  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | edge(v0))
% 6.70/2.16  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (length_of(v4) = v5) |  ~ (length_of(v2) = v3) |  ~ shortest_path(v0, v1, v2) |  ~ path(v0, v1, v4) | less_or_equal(v3, v5))
% 6.70/2.16  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ precedes(v1, v2, v0) |  ~ path(v3, v4, v0) | on_path(v1, v0))
% 6.70/2.16  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ triangle(v0, v1, v2) | sequential(v2, v0))
% 6.70/2.17  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(sequential_pairs, v0) = v3) |  ~ path(v1, v2, v0) |  ? [v4] :  ? [v5] : ((v4 = v3 & number_of_in(triangles, v0) = v3) | (sequential(v4, v5) & on_path(v5, v0) & on_path(v4, v0) &  ! [v6] :  ~ triangle(v4, v5, v6))))
% 6.70/2.17  | (39)  ~ less_or_equal(all_0_0_0, all_0_5_5)
% 6.70/2.17  | (40)  ! [v0] :  ! [v1] : ( ~ (head_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : ( ~ (v2 = v1) & tail_of(v0) = v2))
% 6.70/2.17  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (tail_of(v1) = v3) |  ~ (head_of(v0) = v2) |  ~ sequential(v0, v1))
% 6.70/2.17  | (42) number_of_in(triangles, graph) = all_0_5_5
% 6.70/2.17  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (tail_of(v0) = v2) |  ~ (head_of(v0) = v1) |  ~ sequential(v0, v0))
% 6.70/2.17  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(edges, v2) = v3) |  ~ path(v0, v1, v2) | length_of(v2) = v3)
% 6.70/2.17  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (tail_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) | in_path(v4, v2))
% 6.70/2.17  | (46) complete
% 6.70/2.17  | (47)  ! [v0] :  ! [v1] : ( ~ (tail_of(v0) = v1) |  ~ edge(v0) |  ? [v2] : ( ~ (v2 = v1) & head_of(v0) = v2))
% 6.70/2.17  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (tail_of(v7) = v5) |  ~ (tail_of(v2) = v5) |  ~ (head_of(v3) = v6) |  ~ shortest_path(v0, v1, v4) |  ~ precedes(v2, v3, v4) |  ? [v8] : ( ~ (v8 = v6) & head_of(v7) = v8))
% 6.70/2.17  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ sequential(v1, v2) |  ~ on_path(v2, v0) |  ~ on_path(v1, v0) |  ~ path(v3, v4, v0) | precedes(v1, v2, v0))
% 6.70/2.17  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ path(v0, v1, v2) | vertex(v1))
% 6.70/2.17  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (path_cons(v3, v2) = v1) |  ~ (path_cons(v3, v2) = v0))
% 6.70/2.17  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (length_of(v2) = v3) |  ~ path(v0, v1, v2) |  ? [v4] : (minus(v3, n1) = v4 & number_of_in(sequential_pairs, v2) = v4))
% 6.70/2.17  | (53)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (tail_of(v3) = v1) |  ~ vertex(v2) |  ~ vertex(v1) |  ~ edge(v3) | path(v1, v2, v0) |  ? [v4] :  ? [v5] : (path_cons(v3, empty) = v5 & head_of(v3) = v4 &  ! [v6] : ( ~ (path_cons(v3, v6) = v0) |  ~ path(v4, v2, v6)) & ( ~ (v5 = v0) |  ~ (v4 = v2))))
% 6.70/2.17  | (54)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (head_of(v2) = v1) |  ~ (head_of(v2) = v0))
% 6.70/2.17  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (tail_of(v1) = v3) |  ~ (head_of(v0) = v2) |  ~ sequential(v0, v1) | edge(v0))
% 6.70/2.17  | (56)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (tail_of(v1) = v2) |  ~ (head_of(v0) = v2) |  ~ edge(v1) |  ~ edge(v0) | sequential(v0, v1))
% 6.70/2.17  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ precedes(v1, v2, v0) |  ~ path(v3, v4, v0) | sequential(v1, v2) |  ? [v5] : (precedes(v5, v2, v0) & sequential(v1, v5)))
% 6.70/2.17  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (length_of(v2) = v3) |  ~ path(v0, v1, v2) | shortest_path(v0, v1, v2) |  ? [v4] :  ? [v5] : (length_of(v4) = v5 & path(v0, v1, v4) &  ~ less_or_equal(v3, v5)))
% 6.70/2.17  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(sequential_pairs, v0) = v3) |  ~ shortest_path(v1, v2, v0) | number_of_in(triangles, v0) = v3)
% 6.70/2.17  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(triangles, v0) = v3) |  ~ shortest_path(v1, v2, v0) | number_of_in(sequential_pairs, v0) = v3)
% 6.70/2.17  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (tail_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) |  ? [v5] : (head_of(v3) = v5 & in_path(v5, v2)))
% 6.70/2.17  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (head_of(v3) = v4) |  ~ on_path(v3, v2) |  ~ path(v0, v1, v2) |  ? [v5] : (tail_of(v3) = v5 & in_path(v5, v2)))
% 6.70/2.18  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ in_path(v3, v2) |  ~ path(v0, v1, v2) | vertex(v3))
% 6.70/2.18  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(triangles, v0) = v3) |  ~ path(v1, v2, v0) |  ? [v4] :  ? [v5] : ((v4 = v3 & number_of_in(sequential_pairs, v0) = v3) | (sequential(v4, v5) & on_path(v5, v0) & on_path(v4, v0) &  ! [v6] :  ~ triangle(v4, v5, v6))))
% 6.70/2.18  | (65)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (length_of(v1) = v2) |  ~ shortest_path(v0, v0, v1))
% 6.70/2.18  | (66)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (tail_of(v2) = v1) |  ~ (tail_of(v2) = v0))
% 6.70/2.18  | (67)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (path_cons(v3, empty) = v4) |  ~ vertex(v2) |  ~ vertex(v1) |  ~ edge(v3) | path(v1, v2, v0) |  ? [v5] :  ? [v6] : (tail_of(v3) = v5 & head_of(v3) = v6 & ( ~ (v5 = v1) | ( ! [v7] : ( ~ (path_cons(v3, v7) = v0) |  ~ path(v6, v2, v7)) & ( ~ (v6 = v2) |  ~ (v4 = v0))))))
% 6.70/2.18  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (number_of_in(sequential_pairs, v2) = v3) |  ~ path(v0, v1, v2) |  ? [v4] : (minus(v4, n1) = v3 & length_of(v2) = v4))
% 6.70/2.18  |
% 6.70/2.18  | Instantiating formula (6) with all_0_5_5, graph, triangles and discharging atoms number_of_in(triangles, graph) = all_0_5_5, yields:
% 6.70/2.18  | (69)  ? [v0] : (number_of_in(triangles, graph) = v0 & less_or_equal(all_0_5_5, v0))
% 6.70/2.18  |
% 6.70/2.18  | Instantiating formula (23) with all_0_1_1, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms length_of(all_0_4_4) = all_0_1_1, shortest_path(all_0_3_3, all_0_2_2, all_0_4_4), yields:
% 6.70/2.18  | (70) path(all_0_3_3, all_0_2_2, all_0_4_4)
% 6.70/2.18  |
% 6.70/2.18  | Instantiating (69) with all_15_0_9 yields:
% 6.70/2.18  | (71) number_of_in(triangles, graph) = all_15_0_9 & less_or_equal(all_0_5_5, all_15_0_9)
% 6.70/2.18  |
% 6.70/2.18  | Applying alpha-rule on (71) yields:
% 6.70/2.18  | (72) number_of_in(triangles, graph) = all_15_0_9
% 6.70/2.18  | (73) less_or_equal(all_0_5_5, all_15_0_9)
% 6.70/2.18  |
% 6.70/2.18  | Instantiating formula (13) with triangles, graph, all_15_0_9, all_0_5_5 and discharging atoms number_of_in(triangles, graph) = all_15_0_9, number_of_in(triangles, graph) = all_0_5_5, yields:
% 6.70/2.18  | (74) all_15_0_9 = all_0_5_5
% 6.70/2.18  |
% 6.70/2.18  | From (74) and (72) follows:
% 6.70/2.18  | (42) number_of_in(triangles, graph) = all_0_5_5
% 6.70/2.18  |
% 6.70/2.18  | Instantiating formula (52) with all_0_1_1, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms length_of(all_0_4_4) = all_0_1_1, path(all_0_3_3, all_0_2_2, all_0_4_4), yields:
% 6.70/2.18  | (76)  ? [v0] : (minus(all_0_1_1, n1) = v0 & number_of_in(sequential_pairs, all_0_4_4) = v0)
% 6.70/2.18  |
% 6.70/2.18  | Instantiating (76) with all_27_0_10 yields:
% 6.70/2.18  | (77) minus(all_0_1_1, n1) = all_27_0_10 & number_of_in(sequential_pairs, all_0_4_4) = all_27_0_10
% 6.70/2.18  |
% 6.70/2.18  | Applying alpha-rule on (77) yields:
% 6.70/2.18  | (78) minus(all_0_1_1, n1) = all_27_0_10
% 6.70/2.18  | (79) number_of_in(sequential_pairs, all_0_4_4) = all_27_0_10
% 6.70/2.18  |
% 6.70/2.18  | Instantiating formula (18) with all_0_1_1, n1, all_27_0_10, all_0_0_0 and discharging atoms minus(all_0_1_1, n1) = all_27_0_10, minus(all_0_1_1, n1) = all_0_0_0, yields:
% 6.70/2.19  | (80) all_27_0_10 = all_0_0_0
% 6.70/2.19  |
% 6.70/2.19  | From (80) and (79) follows:
% 6.70/2.19  | (81) number_of_in(sequential_pairs, all_0_4_4) = all_0_0_0
% 6.70/2.19  |
% 6.70/2.19  | Instantiating formula (59) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms number_of_in(sequential_pairs, all_0_4_4) = all_0_0_0, shortest_path(all_0_3_3, all_0_2_2, all_0_4_4), yields:
% 6.70/2.19  | (82) number_of_in(triangles, all_0_4_4) = all_0_0_0
% 6.70/2.19  |
% 6.70/2.19  | Instantiating formula (6) with all_0_0_0, all_0_4_4, triangles and discharging atoms number_of_in(triangles, all_0_4_4) = all_0_0_0, yields:
% 6.70/2.19  | (83)  ? [v0] : (number_of_in(triangles, graph) = v0 & less_or_equal(all_0_0_0, v0))
% 6.70/2.19  |
% 6.70/2.19  | Instantiating (83) with all_65_0_25 yields:
% 6.70/2.19  | (84) number_of_in(triangles, graph) = all_65_0_25 & less_or_equal(all_0_0_0, all_65_0_25)
% 6.70/2.19  |
% 6.70/2.19  | Applying alpha-rule on (84) yields:
% 6.70/2.19  | (85) number_of_in(triangles, graph) = all_65_0_25
% 6.70/2.19  | (86) less_or_equal(all_0_0_0, all_65_0_25)
% 6.70/2.19  |
% 6.70/2.19  | Instantiating formula (13) with triangles, graph, all_65_0_25, all_0_5_5 and discharging atoms number_of_in(triangles, graph) = all_65_0_25, number_of_in(triangles, graph) = all_0_5_5, yields:
% 6.70/2.19  | (87) all_65_0_25 = all_0_5_5
% 6.70/2.19  |
% 6.70/2.19  | From (87) and (86) follows:
% 6.70/2.19  | (88) less_or_equal(all_0_0_0, all_0_5_5)
% 6.70/2.19  |
% 6.70/2.19  | Using (88) and (39) yields:
% 6.70/2.19  | (89) $false
% 6.70/2.19  |
% 6.70/2.19  |-The branch is then unsatisfiable
% 6.70/2.19  % SZS output end Proof for theBenchmark
% 6.70/2.19  
% 6.70/2.19  1570ms
%------------------------------------------------------------------------------