%--------------------------------------------------------------------------
% File     : GEO004-3 : TPTP v8.2.0. Released v2.4.0.
% Domain   : Geometry (Oriented curves)
% Axioms   : Trajectories
% Version  : [EHK99] axioms.
% English  :

% Refs     : [KE99]  Kulik & Eschenbach (1999), A Geometry of Oriented Curv
%          : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source   : [EHK99]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :   14 (   1 unt;   0 nHn;  12 RR)
%            Number of literals    :   29 (   1 equ;  16 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   0 prp; 1-3 aty)
%            Number of functors    :    5 (   5 usr;   0 con; 1-2 aty)
%            Number of variables   :   34 (   2 sgn)
% SPC      : 

% Comments : Requires GEO004-0.ax GEO004-1.ax GEO004-2.ax
%          : Created by tptp2X -f tptp -t clausify:otter GEO004+3.ax
%--------------------------------------------------------------------------
cnf(connect_defn_1,axiom,
    ( ~ connect(A,B,C)
    | once(at_the_same_time(at(A,C),at(B,C))) ) ).

cnf(connect_defn_2,axiom,
    ( ~ once(at_the_same_time(at(A,B),at(C,B)))
    | connect(A,C,B) ) ).

cnf(symmetry_of_at_the_same_time_3,axiom,
    ( ~ once(at_the_same_time(A,B))
    | once(at_the_same_time(B,A)) ) ).

cnf(symmetry_of_at_the_same_time_4,axiom,
    ( ~ once(at_the_same_time(A,B))
    | once(at_the_same_time(B,A)) ) ).

cnf(assciativity_of_at_the_same_time_5,axiom,
    ( ~ once(at_the_same_time(at_the_same_time(A,B),C))
    | once(at_the_same_time(A,at_the_same_time(B,C))) ) ).

cnf(assciativity_of_at_the_same_time_6,axiom,
    ( ~ once(at_the_same_time(A,at_the_same_time(B,C)))
    | once(at_the_same_time(at_the_same_time(A,B),C)) ) ).

cnf(idempotence_of_at_the_same_time_7,axiom,
    ( ~ once(A)
    | once(at_the_same_time(A,A)) ) ).

cnf(conjunction_at_the_same_time_8,axiom,
    ( ~ once(at_the_same_time(A,B))
    | once(A) ) ).

cnf(conjunction_at_the_same_time_9,axiom,
    ( ~ once(at_the_same_time(A,B))
    | once(B) ) ).

cnf(at_on_trajectory_10,axiom,
    ( ~ once(at(A,B))
    | incident_o(B,trajectory_of(A)) ) ).

cnf(at_on_trajectory_11,axiom,
    ( ~ incident_o(A,trajectory_of(B))
    | once(at(B,A)) ) ).

cnf(trajectories_are_oriented_curves_12,axiom,
    trajectory_of(A) = ax3_sk1(A) ).

cnf(homogeneous_behaviour_13,axiom,
    ( ~ once(at_the_same_time(at(A,B),at(C,D)))
    | ~ once(at_the_same_time(at(A,E),at(C,F)))
    | ~ ordered_by(trajectory_of(A),B,E)
    | ~ ordered_by(trajectory_of(C),F,D) ) ).

cnf(localization_14,axiom,
    ( ~ once(A)
    | once(at_the_same_time(A,at(B,ax3_sk2(B,A)))) ) ).

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