%------------------------------------------------------------------------------
% File     : GRA120+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Graph Theory
% Problem  : Ramsey number r(3,4) = 9
% Version  : Especial.
% English  : The Ramsey property that if an undirected graph has at least
%            R(m,n) vertices, then it must have either an m-clique or an
%            n-anticlique.

% Refs     : [Ram30] Ramsey (1930), On a Problem of Formal Logic
%          : [Kal24] Kalizyk (2024), Email to G. Sutcliffe
% Source   : [Kal24]
% Names    : r_3_4_9 [Kal24]

% Status   : Unsatisfiable
% Rating   : 0.43 v9.3.0
% Syntax   : Number of formulae    :   39 (  36 unt;   0 def)
%            Number of atoms       :   56 (  45 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :   57 (  40   ~;  17   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    9 (   9 usr;   9 con; 0-0 aty)
%            Number of variables   :    9 (   9   !;   0   ?)
% SPC      : FOF_UNS_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
fof(rsym,axiom,
    ! [X,Y] :
      ( ~ r(X,Y)
      | r(Y,X) ) ).

fof(rno3cl,axiom,
    ! [X,Y,Z] :
      ( X = Y
      | X = Z
      | Y = Z
      | ~ r(X,Y)
      | ~ r(X,Z)
      | ~ r(Y,Z) ) ).

fof(rno4acl,axiom,
    ! [X,Y,Z,W] :
      ( X = Y
      | X = Z
      | Y = Z
      | X = W
      | Y = W
      | Z = W
      | r(X,Y)
      | r(X,Z)
      | r(Y,Z)
      | r(X,W)
      | r(Y,W)
      | r(Z,W) ) ).

fof(v0nv1,axiom,
    v0 != v1 ).

fof(v0nv2,axiom,
    v0 != v2 ).

fof(v1nv2,axiom,
    v1 != v2 ).

fof(v0nv3,axiom,
    v0 != v3 ).

fof(v1nv3,axiom,
    v1 != v3 ).

fof(v2nv3,axiom,
    v2 != v3 ).

fof(v0nv4,axiom,
    v0 != v4 ).

fof(v1nv4,axiom,
    v1 != v4 ).

fof(v2nv4,axiom,
    v2 != v4 ).

fof(v3nv4,axiom,
    v3 != v4 ).

fof(v0nv5,axiom,
    v0 != v5 ).

fof(v1nv5,axiom,
    v1 != v5 ).

fof(v2nv5,axiom,
    v2 != v5 ).

fof(v3nv5,axiom,
    v3 != v5 ).

fof(v4nv5,axiom,
    v4 != v5 ).

fof(v0nv6,axiom,
    v0 != v6 ).

fof(v1nv6,axiom,
    v1 != v6 ).

fof(v2nv6,axiom,
    v2 != v6 ).

fof(v3nv6,axiom,
    v3 != v6 ).

fof(v4nv6,axiom,
    v4 != v6 ).

fof(v5nv6,axiom,
    v5 != v6 ).

fof(v0nv7,axiom,
    v0 != v7 ).

fof(v1nv7,axiom,
    v1 != v7 ).

fof(v2nv7,axiom,
    v2 != v7 ).

fof(v3nv7,axiom,
    v3 != v7 ).

fof(v4nv7,axiom,
    v4 != v7 ).

fof(v5nv7,axiom,
    v5 != v7 ).

fof(v6nv7,axiom,
    v6 != v7 ).

fof(v0nv8,axiom,
    v0 != v8 ).

fof(v1nv8,axiom,
    v1 != v8 ).

fof(v2nv8,axiom,
    v2 != v8 ).

fof(v3nv8,axiom,
    v3 != v8 ).

fof(v4nv8,axiom,
    v4 != v8 ).

fof(v5nv8,axiom,
    v5 != v8 ).

fof(v6nv8,axiom,
    v6 != v8 ).

fof(v7nv8,axiom,
    v7 != v8 ).

%------------------------------------------------------------------------------