%------------------------------------------------------------------------------
% File     : GEO259+1 : TPTP v7.4.0. Bugfixed v6.4.0.
% Domain   : Geometry (Constructive)
% Problem  : Betweeness
% Version  : [vPl98] axioms : Especial.
% English  :

% Refs     : [vPl98] von Plato (1998), A Constructive Theory of Ordered Aff
%          : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% Source   : [ILTP]
% Names    : Theorem 6.4.ii [vPl98]

% Status   : Theorem
% Rating   : 0.24 v7.4.0, 0.12 v7.3.0, 0.14 v7.2.0, 0.17 v7.1.0, 0.25 v7.0.0, 0.21 v6.4.0
% Syntax   : Number of formulae    :   32 (   7 unit)
%            Number of atoms       :  108 (   0 equality)
%            Maximal formula depth :   13 (   6 average)
%            Number of connectives :   93 (  17   ~;  24   |;  29   &)
%                                         (   5 <=>;  18  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :   12 (   0 propositional; 1-4 arity)
%            Number of functors    :    4 (   0 constant; 1-2 arity)
%            Number of variables   :   75 (   0 sgn;  75   !;   0   ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : FOF_THM_RFO_NEQ

% Comments : Definitions unfolded, hence Especial.
% Bugfixes : v6.4.0 - Bugfix in GEO007+1.ax, fixed conjecture.
%------------------------------------------------------------------------------
include('Axioms/GEO007+0.ax').
%------------------------------------------------------------------------------
fof(con,conjecture,(
    ! [L,A,B,C] :
      ( ( line(L)
        & distinct_points(A,C)
        & distinct_points(B,C)
        & distinct_points(A,B) )
     => ~ ( between_on_line(L,A,B,C)
          & between_on_line(L,B,A,C) ) ) )).

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