TPTP Axioms File: GEO006+2.ax


%------------------------------------------------------------------------------
% File     : GEO006+2 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Geometry (Constructive)
% Axioms   : Affine geometry
% Version  : [vPl95] axioms.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of formulae    :    3 (   2 unit)
%            Number of atoms       :    6 (   0 equality)
%            Maximal formula depth :    7 (   5 average)
%            Number of connectives :    5 (   2 ~  ;   2  |;   0  &)
%                                         (   0 <=>;   1 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    3 (   0 propositional; 2-2 arity)
%            Number of functors    :    1 (   0 constant; 2-2 arity)
%            Number of variables   :    7 (   0 singleton;   7 !;   0 ?)
%            Maximal term depth    :    2 (   1 average)
% SPC      : 

% Comments : Requires GEO006+0
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%----Axioms for constructed parallels
fof(cp1,axiom,(
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )).

fof(cp2,axiom,(
    ! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )).

%----Constructive uniqueness axiom for parallels
fof(cup1,axiom,(
    ! [X,Y,Z] :
      ( distinct_lines(Y,Z)
     => ( apart_point_and_line(X,Y)
        | apart_point_and_line(X,Z)
        | convergent_lines(Y,Z) ) ) )).

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