%------------------------------------------------------------------------------
% 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   : 0.00 v9.3.0
% Syntax   : Number of formulae    :   49 (  36 unt;  10 typ;   0 def)
%            Number of atoms       :   56 (  45 equ;   0 cnn)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :   79 (  40   ~;  17   |;   0   &;  22   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :    9 (   0   ^;   9   !;   0   ?;   9   :)
% 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(v6tp,type,
    v6: $i ).

thf(v7tp,type,
    v7: $i ).

thf(v8tp,type,
    v8: $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(rno4acl,axiom,
    ! [X: $i,Y: $i,Z: $i,W: $i] :
      ( ( X = Y )
      | ( X = Z )
      | ( X = W )
      | ( Y = Z )
      | ( Y = W )
      | ( Z = W )
      | ( r @ X @ Y )
      | ( r @ X @ Z )
      | ( r @ X @ W )
      | ( r @ Y @ Z )
      | ( r @ Y @ W )
      | ( r @ Z @ W ) ) ).

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 ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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