%--------------------------------------------------------------------------
% File     : GEO009-2 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Geometry
% Problem  : First inner connectivity property of betweenness
% Version  : [Qua89] axioms.
% English  : For all points x, y, z, and w, if y and w are between x and
%            z, then either y is between x and w or w is between x and y.

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
%          : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
%          : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% Source   : [TPTP]
% Names    :

% Status   : Unknown
% Rating   : 1.00 v2.0.0
% Syntax   : Number of clauses     :   22 (  10 unt;   5 nHn;  19 RR)
%            Number of literals    :   60 (   7 equ;  36 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-4 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-6 aty)
%            Number of variables   :   71 (   3 sgn)
% SPC      : CNF_UNK_RFO_SEQ_NHN

% Comments : Infinox says this has no finite (counter-) models.
%--------------------------------------------------------------------------
%----Include Tarski geometry axioms
include('Axioms/GEO002-0.ax').
%--------------------------------------------------------------------------
cnf(c_between_a_and_e,hypothesis,
    between(a,c,e) ).

cnf(d_between_a_and_e,hypothesis,
    between(a,d,e) ).

cnf(c_not_between_a_and_d,hypothesis,
    ~ between(a,c,d) ).

cnf(prove_d_between_a_and_c,negated_conjecture,
    ~ between(a,d,c) ).

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