TPTP Problem File: GEO024-3.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : GEO024-3 : TPTP v8.2.0. Released v1.0.0.
% Domain : Geometry
% Problem : All null segments are congruent
% Version : [Qua89] axioms : Augmented.
% English :
% Refs : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% Source : [Qua89]
% Names : D7 [Qua89]
% Status : Unsatisfiable
% Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.3.0, 0.09 v6.2.0, 0.00 v5.5.0, 0.05 v5.3.0, 0.11 v5.2.0, 0.06 v5.0.0, 0.00 v3.3.0, 0.07 v3.2.0, 0.00 v2.5.0, 0.08 v2.4.0, 0.00 v2.0.0
% Syntax : Number of clauses : 36 ( 13 unt; 5 nHn; 27 RR)
% Number of literals : 86 ( 15 equ; 47 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 : 11 ( 11 usr; 5 con; 0-6 aty)
% Number of variables : 126 ( 6 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : In [Qua89] the previous problem (D6) is omitted.
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%----Include Tarski geometry axioms
include('Axioms/GEO002-0.ax').
%----Include definition of reflection
include('Axioms/GEO002-2.ax').
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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(prove_congruence,negated_conjecture,
~ equidistant(u,u,v,v) ).
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