TPTP Problem File: GEO010-1.p
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%--------------------------------------------------------------------------
% File : GEO010-1 : TPTP v8.2.0. Bugfixed v2.5.0.
% Domain : Geometry
% Problem : Collinearity is invariant
% Version : [MOW76] axioms.
% English : For all points x, y, and z, if x, y, and z are collinear
% in one order, they are collinear in any order.
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% Source : [ANL]
% Names : T10 [MOW76]
% : t10.ver1.in [ANL]
% Status : Unsatisfiable
% Rating : 0.40 v8.2.0, 0.38 v8.1.0, 0.37 v7.5.0, 0.42 v7.4.0, 0.47 v7.3.0, 0.50 v7.1.0, 0.42 v7.0.0, 0.47 v6.4.0, 0.53 v6.3.0, 0.45 v6.2.0, 0.50 v6.1.0, 0.57 v6.0.0, 0.70 v5.5.0, 0.75 v5.4.0, 0.70 v5.3.0, 0.83 v5.2.0, 0.69 v5.1.0, 0.65 v5.0.0, 0.50 v4.1.0, 0.62 v4.0.1, 0.55 v3.7.0, 0.40 v3.5.0, 0.55 v3.4.0, 0.58 v3.3.0, 0.50 v3.2.0, 0.62 v3.1.0, 0.45 v2.7.0, 0.50 v2.5.0
% Syntax : Number of clauses : 26 ( 7 unt; 7 nHn; 23 RR)
% Number of literals : 80 ( 8 equ; 47 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 2-4 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-6 aty)
% Number of variables : 91 ( 3 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
% Bugfixes : v1.0.1 - Bug in GEO001-0.eq fixed.
% : v2.5.0 - Bug in GEO001-0.ax fixed.
%--------------------------------------------------------------------------
%----Include Tarski geometry axioms
include('Axioms/GEO001-0.ax').
%----Include Tarski geometry axioms for colinearity
include('Axioms/GEO001-1.ax').
%--------------------------------------------------------------------------
cnf(abc_colinear,hypothesis,
colinear(a,b,c) ).
cnf(prove_colinear_in_all_orders,negated_conjecture,
( ~ colinear(a,c,b)
| ~ colinear(b,a,c)
| ~ colinear(b,c,a)
| ~ colinear(c,a,b)
| ~ colinear(c,b,a) ) ).
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