%--------------------------------------------------------------------------
% File     : GEO006-3 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Geometry
% Problem  : Betweenness for 3 points on a line
% Version  : [Qua89] axioms : Augmented.
% English  : For any three distinct points x, y, and z, if y is between
%            x and z, then both x is not between y and z and z is not
%            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   : [Qua89]
% Names    : T6 [Qua89]

% Status   : Unsatisfiable
% Rating   : 0.10 v8.1.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.20 v5.3.0, 0.22 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0, 0.23 v4.0.1, 0.27 v3.7.0, 0.00 v3.5.0, 0.09 v3.4.0, 0.17 v3.3.0, 0.21 v3.2.0, 0.15 v3.1.0, 0.09 v2.7.0, 0.17 v2.6.0, 0.10 v2.5.0, 0.08 v2.4.0, 0.11 v2.2.1, 0.00 v2.1.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :   54 (  21 unt;  10 nHn;  37 RR)
%            Number of literals    :  125 (  30 equ;  65 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-4 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-6 aty)
%            Number of variables   :  170 (   9 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments : This presentation may have alternatives/be incorrect.
%--------------------------------------------------------------------------
%----Include Tarski geometry axioms
include('Axioms/GEO002-0.ax').
%----Include definition of reflection
include('Axioms/GEO002-2.ax').
%--------------------------------------------------------------------------
cnf(d1,axiom,
    equidistant(U,V,U,V) ).

cnf(d2,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(W,X,U,V) ) ).

cnf(d3,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(V,U,W,X) ) ).

cnf(d4_1,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(U,V,X,W) ) ).

cnf(d4_2,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(V,U,X,W) ) ).

cnf(d4_3,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(W,X,V,U) ) ).

cnf(d4_4,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(X,W,U,V) ) ).

cnf(d4_5,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(X,W,V,U) ) ).

cnf(d5,axiom,
    ( ~ equidistant(U,V,W,X)
    | ~ equidistant(W,X,Y,Z)
    | equidistant(U,V,Y,Z) ) ).

cnf(e1,axiom,
    V = extension(U,V,W,W) ).

cnf(b0,axiom,
    ( Y != extension(U,V,W,X)
    | between(U,V,Y) ) ).

cnf(r2_1,axiom,
    between(U,V,reflection(U,V)) ).

cnf(r2_2,axiom,
    equidistant(V,reflection(U,V),U,V) ).

cnf(r3_1,axiom,
    ( U != V
    | V = reflection(U,V) ) ).

cnf(r3_2,axiom,
    U = reflection(U,U) ).

cnf(r4,axiom,
    ( V != reflection(U,V)
    | U = V ) ).

cnf(d7,axiom,
    equidistant(U,U,V,V) ).

cnf(d8,axiom,
    ( ~ equidistant(U,V,U1,V1)
    | ~ equidistant(V,W,V1,W1)
    | ~ between(U,V,W)
    | ~ between(U1,V1,W1)
    | equidistant(U,W,U1,W1) ) ).

cnf(d9,axiom,
    ( ~ between(U,V,W)
    | ~ between(U,V,X)
    | ~ equidistant(V,W,V,X)
    | U = V
    | W = X ) ).

cnf(d10_1,axiom,
    ( ~ between(U,V,W)
    | U = V
    | W = extension(U,V,V,W) ) ).

cnf(d10_2,axiom,
    ( ~ equidistant(W,X,Y,Z)
    | extension(U,V,W,X) = extension(U,V,Y,Z)
    | U = V ) ).

cnf(d10_3,axiom,
    ( extension(U,V,U,V) = extension(U,V,V,U)
    | U = V ) ).

cnf(r5,axiom,
    equidistant(V,U,V,reflection(reflection(U,V),V)) ).

cnf(r6,axiom,
    U = reflection(reflection(U,V),V) ).

cnf(t3,axiom,
    between(U,V,V) ).

cnf(b1,axiom,
    ( ~ between(U,W,X)
    | U != X
    | between(V,W,X) ) ).

cnf(t1,axiom,
    ( ~ between(U,V,W)
    | between(W,V,U) ) ).

cnf(t2,axiom,
    between(U,U,V) ).

cnf(b2,axiom,
    ( ~ between(U,V,W)
    | ~ between(V,U,W)
    | U = V ) ).

cnf(b3,axiom,
    ( ~ between(U,V,W)
    | ~ between(U,W,V)
    | V = W ) ).

cnf(a_not_c,hypothesis,
    a != c ).

cnf(a_not_d,hypothesis,
    a != d ).

cnf(c_not_d,hypothesis,
    c != d ).

cnf(c_between_a_and_d,hypothesis,
    between(a,c,d) ).

cnf(prove_not_between_others,negated_conjecture,
    ( between(c,a,d)
    | between(a,d,c) ) ).

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