## 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      :

%------------------------------------------------------------------------------
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) ) )).

%------------------------------------------------------------------------------
```