TPTP Problem File: GEO114+1.p
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%--------------------------------------------------------------------------
% File : GEO114+1 : TPTP v8.2.0. Released v2.4.0.
% Domain : Geometry (Oriented curves)
% Problem : Basic property of orderings on linear structures 4
% Version : [EHK99] axioms.
% English : If P, Q and R are distinct and on c then one of the points is
% between the others wrt. c.
% Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source : [KE99]
% Names : Theorem 3.8 (4) [KE99]
% : T7 [EHK99]
% Status : Unknown
% Rating : 1.00 v2.4.0
% Syntax : Number of formulae : 18 ( 1 unt; 0 def)
% Number of atoms : 82 ( 14 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 72 ( 8 ~; 11 |; 30 &)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 0 prp; 1-4 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 62 ( 52 !; 10 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments :
%--------------------------------------------------------------------------
%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
%----Include axioms of betweenness for simple curves
include('Axioms/GEO004+1.ax').
%--------------------------------------------------------------------------
fof(theorem_3_8_4,conjecture,
! [C,P,Q,R] :
( ( incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q
& Q != R
& P != R )
=> ( between_c(C,P,Q,R)
| between_c(C,Q,P,R)
| between_c(C,P,R,Q) ) ) ).
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