TPTP Problem File: GEO002-4.p
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%--------------------------------------------------------------------------
% File : GEO002-4 : TPTP v8.2.0. Released v1.1.0.
% Domain : Geometry
% Problem : For all points x and y, x is between x and y
% Version : [MOW76] axioms : Reduced > Incomplete.
% English :
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
% Source : [ANL]
% Names : Simple Theorem on Betweenness [Wos88]
% Status : Unsatisfiable
% Rating : 0.00 v6.1.0, 0.14 v6.0.0, 0.11 v5.5.0, 0.19 v5.4.0, 0.22 v5.3.0, 0.25 v5.2.0, 0.08 v5.1.0, 0.19 v5.0.0, 0.20 v4.0.1, 0.14 v3.4.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.4.0, 0.00 v2.3.0, 0.14 v2.2.1, 0.44 v2.2.0, 0.33 v2.1.0, 0.29 v2.0.0
% Syntax : Number of clauses : 8 ( 3 unt; 0 nHn; 6 RR)
% Number of literals : 17 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 3 usr; 0 prp; 2-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 29 ( 3 sgn)
% SPC : CNF_UNS_RFO_NEQ_HRN
% Comments :
%--------------------------------------------------------------------------
%----Include Tarski geometry axioms
% include('Axioms/GEO001-0.ax').
%--------------------------------------------------------------------------
cnf(transitivity_for_betweeness,axiom,
( ~ between(X,Y,V)
| ~ between(Y,Z,V)
| between(X,Y,Z) ) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,Z)
| equalish(X,Y) ) ).
cnf(outer_pasch1,axiom,
( ~ between(X,W,V)
| ~ between(Y,V,Z)
| between(X,outer_pasch(W,X,Y,Z,V),Y) ) ).
cnf(outer_pasch2,axiom,
( ~ between(X,W,V)
| ~ between(Y,V,Z)
| between(Z,W,outer_pasch(W,X,Y,Z,V)) ) ).
cnf(segment_construction1,axiom,
between(X,Y,extension(X,Y,W,V)) ).
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V) ).
%----Equality substitution axioms
cnf(between_substitution3,axiom,
( ~ equalish(X,Y)
| ~ between(W,Z,X)
| between(W,Z,Y) ) ).
cnf(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b) ).
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