%------------------------------------------------------------------------------
% File     : GRA117^1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Graph Theory
% Problem  : Ramsey number r(3,3) = 6
% 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_3_6 [Kal24]

% Status   : Unsatisfiable
% Rating   : 0.00 v9.3.0
% Syntax   : Number of formulae    :   25 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :   29 (  21 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   46 (  19   ~;  11   |;   0   &;  16   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    8 (   0   ^;   8   !;   0   ?;   8   :)
% SPC      : TH0_UNS_EQU_NAR_NDT

% Comments :
%------------------------------------------------------------------------------
thf(rtp,type,
    r: $i > $i > $o ).

thf(v0tp,type,
    v0: $i ).

thf(v1tp,type,
    v1: $i ).

thf(v2tp,type,
    v2: $i ).

thf(v3tp,type,
    v3: $i ).

thf(v4tp,type,
    v4: $i ).

thf(v5tp,type,
    v5: $i ).

thf(rsym,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( r @ X @ Y )
      | ( r @ Y @ X ) ) ).

thf(rno3cl,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( X = Y )
      | ( X = Z )
      | ( Y = Z )
      | ~ ( r @ X @ Y )
      | ~ ( r @ X @ Z )
      | ~ ( r @ Y @ Z ) ) ).

thf(rno3acl,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( X = Y )
      | ( X = Z )
      | ( Y = Z )
      | ( r @ X @ Y )
      | ( r @ X @ Z )
      | ( r @ Y @ Z ) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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