%------------------------------------------------------------------------------
% File     : GEO006+6 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Geometry (Constructive)
% Axioms   : Geometry definitions
% Version  : [vPl95] axioms.
% English  :

% Refs     : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
% Source   : [ILTP]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    5 (   0 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   10 (   5   ~;   0   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   10 (  10 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   10 (  10   !;   0   ?)
% SPC      : 

% Comments : Requires GEO006+[0-5]
%------------------------------------------------------------------------------
fof(ax1,axiom,
    ! [X,Y] :
      ( equal_points(X,Y)
    <=> ~ distinct_points(X,Y) ) ).

fof(ax2,axiom,
    ! [X,Y] :
      ( equal_lines(X,Y)
    <=> ~ distinct_lines(X,Y) ) ).

fof(a3,axiom,
    ! [X,Y] :
      ( parallel_lines(X,Y)
    <=> ~ convergent_lines(X,Y) ) ).

fof(a4,axiom,
    ! [X,Y] :
      ( incident_point_and_line(X,Y)
    <=> ~ apart_point_and_line(X,Y) ) ).

fof(a5,axiom,
    ! [X,Y] :
      ( orthogonal_lines(X,Y)
    <=> ~ unorthogonal_lines(X,Y) ) ).

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