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Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:18:21 AM UTC 2026

% Result   : Theorem 7.74s 3.36s
% Output   : Refutation 7.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   40 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :  236 (  62 equ;   0 cnn)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  687 (  19   ~;   6   |; 125   &; 472   @)
%                                         (   3 <=>;  57  =>;   2  <=;   3 <~>)
%            Maximal formula depth :   19 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;   8 con; 0-3 aty)
%            Number of variables   :  163 (   0   ^; 136   !;  27   ?; 163   :)

% Comments : 
%------------------------------------------------------------------------------
thf(complete_decl,type,
    complete: $o ).

thf(shortest_path_decl,type,
    shortest_path: $i > $i > $i > $o ).

thf(precedes_decl,type,
    precedes: $i > $i > $i > $o ).

thf(sequential_decl,type,
    sequential: $i > $i > $o ).

thf(triangle_decl,type,
    triangle: $i > $i > $i > $o ).

thf(path_decl,type,
    path: $i > $i > $i > $o ).

thf(vertex_decl,type,
    vertex: $i > $o ).

thf(edge_decl,type,
    edge: $i > $o ).

thf(tail_of_decl,type,
    tail_of: $i > $i ).

thf(head_of_decl,type,
    head_of: $i > $i ).

thf(path_cons_decl,type,
    path_cons: $i > $i > $i ).

thf(empty_decl,type,
    empty: $i ).

thf(in_path_decl,type,
    in_path: $i > $i > $o ).

thf(on_path_decl,type,
    on_path: $i > $i > $o ).

thf(number_of_in_decl,type,
    number_of_in: $i > $i > $i ).

thf(sequential_pairs_decl,type,
    sequential_pairs: $i ).

thf(minus_decl,type,
    minus: $i > $i > $i ).

thf(length_of_decl,type,
    length_of: $i > $i ).

thf(n1_decl,type,
    n1: $i ).

thf(less_or_equal_decl,type,
    less_or_equal: $i > $i > $o ).

thf(graph_decl,type,
    graph: $i ).

thf(edges_decl,type,
    edges: $i ).

thf(triangles_decl,type,
    triangles: $i ).

thf(8,axiom,
    ! [A: $i,B: $i] : ( graph @ ( A @ number_of_in ) @ ( B @ ( A @ number_of_in ) @ less_or_equal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).

thf(69,plain,
    ! [A: $i,B: $i] : ( graph @ ( A @ number_of_in ) @ ( B @ ( A @ number_of_in ) @ less_or_equal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( B @ path ) ) )
     => ! [D: $i,E: $i] :
          ( ( A @ ( E @ ( D @ precedes ) ) )
         => ( ( ( E @ ( D @ sequential ) )
            <~> ? [F: $i] :
                  ( ( A @ ( E @ ( F @ precedes ) ) )
                  & ( F @ ( D @ sequential ) ) ) )
            & ( A @ ( E @ on_path ) )
            & ( A @ ( D @ on_path ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_properties) ).

thf(142,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( B @ path ) ) )
     => ! [D: $i,E: $i] :
          ( ( A @ ( E @ ( D @ precedes ) ) )
         => ( ~ ( ( ? [F: $i] :
                      ( ( A @ ( E @ ( F @ precedes ) ) )
                      & ( F @ ( D @ sequential ) ) )
                 => ( E @ ( D @ sequential ) ) )
                & ( ( E @ ( D @ sequential ) )
                 => ? [F: $i] :
                      ( ( A @ ( E @ ( F @ precedes ) ) )
                      & ( F @ ( D @ sequential ) ) ) ) )
            & ( A @ ( E @ on_path ) )
            & ( A @ ( D @ on_path ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( B @ path ) ) )
     => ! [D: $i,E: $i] :
          ( ( A @ ( E @ ( D @ precedes ) ) )
         <= ( ( ? [F: $i] :
                  ( ( A @ ( E @ ( F @ precedes ) ) )
                  & ( F @ ( D @ sequential ) ) )
              | ( E @ ( D @ sequential ) ) )
            & ( A @ ( E @ on_path ) )
            & ( A @ ( D @ on_path ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_defn) ).

thf(121,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( B @ path ) ) )
     => ! [D: $i,E: $i] :
          ( ( ( ? [F: $i] :
                  ( ( A @ ( E @ ( F @ precedes ) ) )
                  & ( F @ ( D @ sequential ) ) )
              | ( E @ ( D @ sequential ) ) )
            & ( A @ ( E @ on_path ) )
            & ( A @ ( D @ on_path ) ) )
         => ( A @ ( E @ ( D @ precedes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ ( D @ ( C @ precedes ) ) )
        & ( E @ ( B @ ( A @ shortest_path ) ) ) )
     => ( ~ ( E @ ( C @ ( D @ precedes ) ) )
        & ~ ? [F: $i] :
              ( ( ( F @ head_of )
                = ( D @ head_of ) )
              & ( ( F @ tail_of )
                = ( C @ tail_of ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_properties) ).

thf(102,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ ( D @ ( C @ precedes ) ) )
        & ( E @ ( B @ ( A @ shortest_path ) ) ) )
     => ( ~ ( E @ ( C @ ( D @ precedes ) ) )
        & ~ ? [F: $i] :
              ( ( ( F @ head_of )
                = ( D @ head_of ) )
              & ( ( F @ tail_of )
                = ( C @ tail_of ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(1,conjecture,
    ( complete
   => ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( D @ ( C @ sequential ) )
          & ( E @ ( D @ ( C @ precedes ) ) )
          & ( E @ ( B @ ( A @ shortest_path ) ) ) )
       => ? [F: $i] : ( F @ ( D @ ( C @ triangle ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_is_triangle) ).

thf(2,negated_conjecture,
    ~ ( complete
     => ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
          ( ( ( D @ ( C @ sequential ) )
            & ( E @ ( D @ ( C @ precedes ) ) )
            & ( E @ ( B @ ( A @ shortest_path ) ) ) )
         => ? [F: $i] : ( F @ ( D @ ( C @ triangle ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(21,plain,
    ~ ( complete
     => ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
          ( ( ( D @ ( C @ sequential ) )
            & ( E @ ( D @ ( C @ precedes ) ) )
            & ( E @ ( B @ ( A @ shortest_path ) ) ) )
         => ? [F: $i] : ( F @ ( D @ ( C @ triangle ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ path ) ) )
     <= ( ? [D: $i] :
            ( ( ? [E: $i] :
                  ( ( C
                    = ( E @ ( D @ path_cons ) ) )
                  & ( E @ ( B @ ( D @ head_of @ path ) ) ) )
              | ( ( C
                  = ( empty @ ( D @ path_cons ) ) )
                & ( B
                  = ( D @ head_of ) ) ) )
            & ( A
              = ( D @ tail_of ) )
            & ( D @ edge ) )
        & ( B @ vertex )
        & ( A @ vertex ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_defn) ).

thf(53,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ? [D: $i] :
            ( ( ? [E: $i] :
                  ( ( C
                    = ( E @ ( D @ path_cons ) ) )
                  & ( E @ ( B @ ( D @ head_of @ path ) ) ) )
              | ( ( C
                  = ( empty @ ( D @ path_cons ) ) )
                & ( B
                  = ( D @ head_of ) ) ) )
            & ( A
              = ( D @ tail_of ) )
            & ( D @ edge ) )
        & ( B @ vertex )
        & ( A @ vertex ) )
     => ( C @ ( B @ ( A @ path ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ path ) ) )
     => ( ( C @ length_of )
        = ( C @ ( edges @ number_of_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',length_defn) ).

thf(71,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ path ) ) )
     => ( ( C @ length_of )
        = ( C @ ( edges @ number_of_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(12,axiom,
    ( complete
   => ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( E @ ( D @ ( C @ precedes ) ) )
          & ( E @ ( B @ ( A @ shortest_path ) ) ) )
       => ? [F: $i] :
            ( ( ( F @ head_of )
              = ( C @ tail_of ) )
            & ( ( F @ tail_of )
              = ( D @ head_of ) )
            & ( F @ edge ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',back_edge) ).

thf(81,plain,
    ( complete
   => ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( E @ ( D @ ( C @ precedes ) ) )
          & ( E @ ( B @ ( A @ shortest_path ) ) ) )
       => ? [F: $i] :
            ( ( ( F @ head_of )
              = ( C @ tail_of ) )
            & ( ( F @ tail_of )
              = ( D @ head_of ) )
            & ( F @ edge ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ path ) ) )
     => ( ( C @ ( sequential_pairs @ number_of_in ) )
        = ( n1 @ ( C @ length_of @ minus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).

thf(66,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ path ) ) )
     => ( ( C @ ( sequential_pairs @ number_of_in ) )
        = ( n1 @ ( C @ length_of @ minus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ triangle ) ) )
    <=> ( ( A @ ( C @ sequential ) )
        & ( C @ ( B @ sequential ) )
        & ( B @ ( A @ sequential ) )
        & ( C @ edge )
        & ( B @ edge )
        & ( A @ edge ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).

thf(152,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A @ ( C @ sequential ) )
          & ( C @ ( B @ sequential ) )
          & ( B @ ( A @ sequential ) )
          & ( C @ edge )
          & ( B @ edge )
          & ( A @ edge ) )
       => ( C @ ( B @ ( A @ triangle ) ) ) )
      & ( ( C @ ( B @ ( A @ triangle ) ) )
       => ( ( A @ ( C @ sequential ) )
          & ( C @ ( B @ sequential ) )
          & ( B @ ( A @ sequential ) )
          & ( C @ edge )
          & ( B @ edge )
          & ( A @ edge ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( A @ edge )
     => ( ( A @ head_of )
       != ( A @ tail_of ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_loops) ).

thf(78,plain,
    ! [A: $i] :
      ( ( A @ edge )
     => ( ( A @ head_of )
       != ( A @ tail_of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ path ) ) )
     => ( ? [D: $i] :
            ( ( ( ( C
                  = ( empty @ ( D @ path_cons ) ) )
                & ( B
                  = ( D @ head_of ) ) )
            <~> ? [E: $i] :
                  ( ( C
                    = ( E @ ( D @ path_cons ) ) )
                  & ( E @ ( B @ ( D @ head_of @ path ) ) ) ) )
            & ( A
              = ( D @ tail_of ) )
            & ( D @ edge ) )
        & ( B @ vertex )
        & ( A @ vertex ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_properties) ).

thf(29,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ path ) ) )
     => ( ? [D: $i] :
            ( ~ ( ( ? [E: $i] :
                      ( ( C
                        = ( E @ ( D @ path_cons ) ) )
                      & ( E @ ( B @ ( D @ head_of @ path ) ) ) )
                 => ( ( C
                      = ( empty @ ( D @ path_cons ) ) )
                    & ( B
                      = ( D @ head_of ) ) ) )
                & ( ( ( C
                      = ( empty @ ( D @ path_cons ) ) )
                    & ( B
                      = ( D @ head_of ) ) )
                 => ? [E: $i] :
                      ( ( C
                        = ( E @ ( D @ path_cons ) ) )
                      & ( E @ ( B @ ( D @ head_of @ path ) ) ) ) ) )
            & ( A
              = ( D @ tail_of ) )
            & ( D @ edge ) )
        & ( B @ vertex )
        & ( A @ vertex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( D @ on_path ) )
        & ( C @ ( B @ ( A @ path ) ) ) )
     => ( ( C @ ( D @ tail_of @ in_path ) )
        & ( C @ ( D @ head_of @ in_path ) )
        & ( D @ edge ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',on_path_properties) ).

thf(61,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( D @ on_path ) )
        & ( C @ ( B @ ( A @ path ) ) ) )
     => ( ( C @ ( D @ tail_of @ in_path ) )
        & ( C @ ( D @ head_of @ in_path ) )
        & ( D @ edge ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ sequential ) )
    <=> ( ( ( A @ head_of )
          = ( B @ tail_of ) )
        & ( A != B )
        & ( B @ edge )
        & ( A @ edge ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_defn) ).

thf(89,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( ( A @ head_of )
            = ( B @ tail_of ) )
          & ( A != B )
          & ( B @ edge )
          & ( A @ edge ) )
       => ( B @ ( A @ sequential ) ) )
      & ( ( B @ ( A @ sequential ) )
       => ( ( ( A @ head_of )
            = ( B @ tail_of ) )
          & ( A != B )
          & ( B @ edge )
          & ( A @ edge ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( A @ edge )
     => ( ( A @ tail_of @ vertex )
        & ( A @ head_of @ vertex ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',edge_ends_are_vertices) ).

thf(74,plain,
    ! [A: $i] :
      ( ( A @ edge )
     => ( ( A @ tail_of @ vertex )
        & ( A @ head_of @ vertex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ shortest_path ) ) )
    <=> ( ! [D: $i] :
            ( ( D @ ( B @ ( A @ path ) ) )
           => ( D @ length_of @ ( C @ length_of @ less_or_equal ) ) )
        & ( A != B )
        & ( C @ ( B @ ( A @ path ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).

thf(107,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ! [D: $i] :
              ( ( D @ ( B @ ( A @ path ) ) )
             => ( D @ length_of @ ( C @ length_of @ less_or_equal ) ) )
          & ( A != B )
          & ( C @ ( B @ ( A @ path ) ) ) )
       => ( C @ ( B @ ( A @ shortest_path ) ) ) )
      & ( ( C @ ( B @ ( A @ shortest_path ) ) )
       => ( ! [D: $i] :
              ( ( D @ ( B @ ( A @ path ) ) )
             => ( D @ length_of @ ( C @ length_of @ less_or_equal ) ) )
          & ( A != B )
          & ( C @ ( B @ ( A @ path ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(17,axiom,
    ( complete
   => ! [A: $i,B: $i] :
        ( ( ( A != B )
          & ( B @ vertex )
          & ( A @ vertex ) )
       => ? [C: $i] :
            ( ( ( ( B
                  = ( C @ tail_of ) )
                & ( A
                  = ( C @ head_of ) ) )
            <~> ( ( A
                  = ( C @ tail_of ) )
                & ( B
                  = ( C @ head_of ) ) ) )
            & ( C @ edge ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_properties) ).

thf(126,plain,
    ( complete
   => ! [A: $i,B: $i] :
        ( ( ( A != B )
          & ( B @ vertex )
          & ( A @ vertex ) )
       => ? [C: $i] :
            ( ~ ( ( ( ( A
                      = ( C @ tail_of ) )
                    & ( B
                      = ( C @ head_of ) ) )
                 => ( ( B
                      = ( C @ tail_of ) )
                    & ( A
                      = ( C @ head_of ) ) ) )
                & ( ( ( B
                      = ( C @ tail_of ) )
                    & ( A
                      = ( C @ head_of ) ) )
                 => ( ( A
                      = ( C @ tail_of ) )
                    & ( B
                      = ( C @ head_of ) ) ) ) )
            & ( C @ edge ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( D @ in_path ) )
        & ( C @ ( B @ ( A @ path ) ) ) )
     => ( ? [E: $i] :
            ( ( ( D
                = ( E @ tail_of ) )
              | ( D
                = ( E @ head_of ) ) )
            & ( C @ ( E @ on_path ) ) )
        & ( D @ vertex ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_path_properties) ).

thf(47,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( D @ in_path ) )
        & ( C @ ( B @ ( A @ path ) ) ) )
     => ( ? [E: $i] :
            ( ( ( D
                = ( E @ tail_of ) )
              | ( D
                = ( E @ head_of ) ) )
            & ( C @ ( E @ on_path ) ) )
        & ( D @ vertex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i,E: $i] :
            ( ( ( E @ ( D @ sequential ) )
              & ( A @ ( E @ on_path ) )
              & ( A @ ( D @ on_path ) ) )
           => ? [F: $i] : ( F @ ( E @ ( D @ triangle ) ) ) )
        & ( A @ ( C @ ( B @ path ) ) ) )
     => ( ( A @ ( sequential_pairs @ number_of_in ) )
        = ( A @ ( triangles @ number_of_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).

thf(163,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i,E: $i] :
            ( ( ( E @ ( D @ sequential ) )
              & ( A @ ( E @ on_path ) )
              & ( A @ ( D @ on_path ) ) )
           => ? [F: $i] : ( F @ ( E @ ( D @ triangle ) ) ) )
        & ( A @ ( C @ ( B @ path ) ) ) )
     => ( ( A @ ( sequential_pairs @ number_of_in ) )
        = ( A @ ( triangles @ number_of_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(512,plain,
    $false,
    inference(e,[status(thm)],[69,142,121,102,21,53,71,81,66,152,78,29,61,89,74,107,126,47,163]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40  % Computer : n005.cluster.edu
% 0.14/0.40  % Model    : x86_64 x86_64
% 0.14/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40  % Memory   : 8046.5625MB
% 0.14/0.40  % OS       : Linux 6.8.0-71-generic
% 0.14/0.40  % CPULimit : 300
% 0.14/0.40  % WCLimit  : 300
% 0.14/0.40  % DateTime : Fri Sep 25 13:47:32 UTC 2026
% 0.14/0.40  % CPUTime  : 
% 0.14/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.45/1.21  % [INFO] 	 Parsing done (214ms). 
% 1.45/1.23  % [INFO] 	 Running in sequential loop mode. 
% 2.19/1.63  % [INFO] 	 eprover registered as external prover. 
% 2.19/1.64  % [INFO] 	 Scanning for conjecture ... 
% 2.40/1.75  % [INFO] 	 Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ... 
% 2.57/1.84  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 2.80/1.91  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.80/1.92  % [INFO] 	 Type checking passed. 
% 2.80/1.93  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 7.74/3.36  % External prover 'e' found a proof!
% 7.74/3.36  % [INFO] 	 Killing All external provers ... 
% 7.74/3.36  % Time passed: 2811ms (effective reasoning time: 2126ms)
% 7.74/3.36  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.74/3.36  % Axioms used in derivation (18): path_defn, sequential_defn, back_edge, graph_has_them_all, path_properties, sequential_pairs_and_triangles, edge_ends_are_vertices, no_loops, length_defn, triangle_defn, complete_properties, shortest_path_defn, in_path_properties, precedes_properties, on_path_properties, path_length_sequential_pairs, shortest_path_properties, precedes_defn
% 7.74/3.36  % No. of inferences in proof: 40
% 7.74/3.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2811 ms resp. 2126 ms w/o parsing
% 7.74/3.39  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.74/3.39  % [INFO] 	 Killing All external provers ... 
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