TSTP Solution File: GRA010+1 by Fampire---1.3
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%------------------------------------------------------------------------------
% File : Fampire---1.3
% Problem : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : FlotterOnTPTP.pl -f oldtptp -s vampire -t %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 07:16:23 EDT 2022
% Result : Unknown 0.19s 0.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : FlotterOnTPTP.pl -f oldtptp -s vampire -t %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 23:25:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 cs: Command not found.
% 0.19/0.45
% 0.19/0.45 ERROR: Cannot translate to DFG with tptp4X
% 0.19/0.45 %--------------------------------------------------------------------------
% 0.19/0.45 % File : GRA010+1 : TPTP v8.0.0. Bugfixed v3.2.0.
% 0.19/0.45 % Domain : Graph Theory
% 0.19/0.45 % Problem : Maximal shortest path length in terms of triangles
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : In a complete graph, if there is a shortest path P from V1 to
% 0.19/0.45 % V2 with edges E1 and E2, E1 sequential to E2 means there is an
% 0.19/0.45 % edge E3 such that E1, E2, and E3 form a triangle, then the
% 0.19/0.45 % number of sequential pairs in P is the number of triangles
% 0.19/0.45 % in P.
% 0.19/0.45
% 0.19/0.45 % Refs :
% 0.19/0.45 % Source : [TPTP]
% 0.19/0.45 % Names :
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.29 v5.3.0, 0.30 v5.2.0, 0.20 v5.1.0, 0.29 v5.0.0, 0.25 v4.1.0, 0.30 v4.0.1, 0.35 v4.0.0, 0.33 v3.7.0, 0.25 v3.5.0, 0.26 v3.4.0, 0.32 v3.3.0, 0.29 v3.2.0
% 0.19/0.45
% 0.19/0.45 % Syntax : Number of formulae : 18 ( 1 unt; 0 def)
% 0.19/0.45 % Number of atoms : 97 ( 25 equ)
% 0.19/0.45 % Maximal formula atoms : 9 ( 5 avg)
% 0.19/0.45 % Number of connectives : 85 ( 6 ~; 3 |; 49 &)
% 0.19/0.45 % ( 3 <=>; 19 =>; 2 <=; 3 <~>)
% 0.19/0.45 % Maximal formula depth : 13 ( 9 avg)
% 0.19/0.45 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.45 % Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% 0.19/0.45 % Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 71 ( 60 !; 11 ?)
% 0.19/0.45 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.45
% 0.19/0.45 % Comments :
% 0.19/0.45 % Bugfixes : v3.2.0 - Bugfix to GRA001+0.ax
% 0.19/0.45 %--------------------------------------------------------------------------
% 0.19/0.45 %----Include axioms for directed graphs and paths
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 begin_problem(SomeProblem).
% 0.19/0.45 list_of_descriptions.
% 0.19/0.45 name({* BLAH *}).
% 0.19/0.45 author({* BLAH *}).
% 0.19/0.45 status(unknown).
% 0.19/0.45 description({* BLAH *}).
% 0.19/0.45 end_of_list.
% 0.19/0.45 list_of_symbols.
% 0.19/0.45 functions[(edges__dfg,0),(empty__dfg,0),(graph__dfg,0),(head_of__dfg,1),(length_of__dfg,1),(minus__dfg,2),(n1__dfg,0),(number_of_in__dfg,2),(path_cons__dfg,2),(sequential_pairs__dfg,0),(tail_of__dfg,1),(triangles__dfg,0)].
% 0.19/0.45 predicates[(complete__dfg,0),(edge__dfg,1),(in_path__dfg,2),(less_or_equal__dfg,2),(on_path__dfg,2),(path__dfg,3),(precedes__dfg,3),(sequential__dfg,2),(shortest_path__dfg,3),(triangle__dfg,3),(vertex__dfg,1)].
% 0.19/0.45 end_of_list.
% 0.19/0.45
% 0.19/0.45 list_of_formulae(axioms).
% 0.19/0.45
% 0.19/0.45 formula(
% 0.19/0.45 forall([E],
% 0.19/0.45 implies(
% 0.19/0.45 edge__dfg(E),
% 0.19/0.45 not(
% 0.19/0.45 equal(head_of__dfg(E),tail_of__dfg(E))))),
% 0.19/0.45 no_loops).
% 0.19/0.45
% 0.19/0.45 formula(
% 0.19/0.45 forall([E],
% 0.19/0.45 implies(
% 0.19/0.45 edge__dfg(E),
% 0.19/0.45 and(
% 0.19/0.45 vertex__dfg(head_of__dfg(E)),
% 0.19/0.45 vertex__dfg(tail_of__dfg(E))))),
% 0.19/0.45 edge_ends_are_vertices).
% 0.19/0.45
% 0.19/0.45 formula(
% 0.19/0.45 implies(
% 0.19/0.45 complete__dfg,
% 0.19/0.45 forall([V1,V2],
% 0.19/0.45 implies(
% 0.19/0.45 and(
% 0.19/0.45 vertex__dfg(V1),
% 0.19/0.45 and(
% 0.19/0.45 vertex__dfg(V2),
% 0.19/0.45 not(
% 0.19/0.45 equal(V1,V2)))),
% 0.19/0.45 exists([E],
% 0.19/0.45 and(
% 0.19/0.45 edge__dfg(E),
% 0.19/0.45 ERROR: (JJ misuse): Not a DFG connective
%------------------------------------------------------------------------------