TPTP Axioms File: GEO002-1.ax


%--------------------------------------------------------------------------
% File     : GEO002-1 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Geometry (Tarskian)
% Axioms   : Colinearity axioms for the GEO002 geometry axioms
% Version  : [Qua89] axioms.
% English  :

% Refs     : [Tar59] Tarski (1959), What is Elementary Geometry?
%          : [MOW76] McCharen et al. (1976), Problems and Experiments for a
%          : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% Source   : [ANL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    4 (   1 non-Horn;   0 unit;   4 RR)
%            Number of atoms      :   10 (   0 equality)
%            Maximal clause size  :    4 (   2 average)
%            Number of predicates :    2 (   0 propositional; 3-3 arity)
%            Number of functors   :    0 (   0 constant; --- arity)
%            Number of variables  :   12 (   0 singleton)
%            Maximal term depth   :    1 (   1 average)
% SPC      : 

% Comments : Requires GEO002-0.ax
%          : This version differs from the originals only in the ordering
%            of betweenness arguments. The equivalence is obvious from the
%            symmetry of betweenness.
%--------------------------------------------------------------------------
cnf(colinearity1,axiom,
    ( ~ between(X,Y,Z)
    | colinear(X,Y,Z) )).

cnf(colinearity2,axiom,
    ( ~ between(Y,Z,X)
    | colinear(X,Y,Z) )).

cnf(colinearity3,axiom,
    ( ~ between(Z,X,Y)
    | colinear(X,Y,Z) )).

cnf(colinearity4,axiom,
    ( ~ colinear(X,Y,Z)
    | between(X,Y,Z)
    | between(Y,Z,X)
    | between(Z,X,Y) )).

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