TPTP Axioms File: GEO006+6.ax


%------------------------------------------------------------------------------
% File     : GEO006+6 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :   10 (   0 equality)
%            Maximal formula depth :    5 (   5 average)
%            Number of connectives :   10 (   5   ~;   0   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=)
%                                         (   0 <~>;   0  ~|;   0  ~&)
%            Number of predicates  :   10 (   0 propositional; 2-2 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :   10 (   0 sgn;  10   !;   0   ?)
%            Maximal term depth    :    1 (   1 average)
% 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) ) )).

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