%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 07:19:51 EDT 2022

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    9 (   2 unt;   0 def)
%            Number of atoms       :   48 (   7 equ)
%            Maximal formula atoms :    7 (   5 avg)
%            Number of connectives :   48 (   9   ~;   7   |;  21   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   9 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   2 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (   0 sgn  30   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(sequential_pairs_and_triangles,axiom,
    ! [P,V1,V2] :
      ( ( path(V1,V2,P)
        & ! [E1,E2] :
            ( ( on_path(E1,P)
              & on_path(E2,P)
              & sequential(E1,E2) )
           => ? [E3] : triangle(E1,E2,E3) ) )
     => number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ).

fof(complete_means_sequential_pairs_and_triangles,conjecture,
    ( complete
   => ! [P,V1,V2] :
        ( ( path(V1,V2,P)
          & ! [E1,E2] :
              ( ( on_path(E1,P)
                & on_path(E2,P)
                & sequential(E1,E2) )
             => ? [E3] : triangle(E1,E2,E3) ) )
       => number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ).

fof(subgoal_0,plain,
    ( complete
   => ! [P,V1,V2] :
        ( ( path(V1,V2,P)
          & ! [E1,E2] :
              ( ( on_path(E1,P)
                & on_path(E2,P)
                & sequential(E1,E2) )
             => ? [E3] : triangle(E1,E2,E3) ) )
       => number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
    inference(strip,[],[complete_means_sequential_pairs_and_triangles]) ).

fof(negate_0_0,plain,
    ~ ( complete
     => ! [P,V1,V2] :
          ( ( path(V1,V2,P)
            & ! [E1,E2] :
                ( ( on_path(E1,P)
                  & on_path(E2,P)
                  & sequential(E1,E2) )
               => ? [E3] : triangle(E1,E2,E3) ) )
         => number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( complete
    & ? [P] :
        ( number_of_in(sequential_pairs,P) != number_of_in(triangles,P)
        & ? [V1,V2] : path(V1,V2,P)
        & ! [E1,E2] :
            ( ~ on_path(E1,P)
            | ~ on_path(E2,P)
            | ~ sequential(E1,E2)
            | ? [E3] : triangle(E1,E2,E3) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [P] :
      ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
      | ? [E1,E2] :
          ( on_path(E1,P)
          & on_path(E2,P)
          & sequential(E1,E2)
          & ! [E3] : ~ triangle(E1,E2,E3) )
      | ! [V1,V2] : ~ path(V1,V2,P) ),
    inference(canonicalize,[],[sequential_pairs_and_triangles]) ).

fof(normalize_0_2,plain,
    ! [P] :
      ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
      | ? [E1,E2] :
          ( on_path(E1,P)
          & on_path(E2,P)
          & sequential(E1,E2)
          & ! [E3] : ~ triangle(E1,E2,E3) )
      | ! [V1,V2] : ~ path(V1,V2,P) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon May 30 23:16:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37  
% 0.12/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37  
%------------------------------------------------------------------------------