%------------------------------------------------------------------------------
% File     : TIM002_0 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Time
% Axioms   : Allens axioms for interval algebra
% Version  : [All83] axioms : Especial.
% English  : 

% Refs     : [All83] Allen (1983), Maintaining Knowledge about Temporal Int
% Source   : [ChatGPT]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :   21 (   1 unt;  13 typ;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :    9 (   1   ~;   0   |;   1   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   24 (  12   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  12 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   16 (  16   !;   0   ?;  16   :)
% SPC      : TF0_SAT_NEQ_NAR_NDT

% Comments : 
%------------------------------------------------------------------------------
tff(interval_type,type,
    interval: $tType ).

tff(before_type,type,
    before: ( interval * interval ) > $o ).

tff(after_type,type,
    after: ( interval * interval ) > $o ).

tff(meets_type,type,
    meets: ( interval * interval ) > $o ).

tff(met_by_type,type,
    met_by: ( interval * interval ) > $o ).

tff(overlaps_type,type,
    overlaps: ( interval * interval ) > $o ).

tff(overlapped_by_type,type,
    overlapped_by: ( interval * interval ) > $o ).

tff(starts_type,type,
    starts: ( interval * interval ) > $o ).

tff(started_by_type,type,
    started_by: ( interval * interval ) > $o ).

tff(during_type,type,
    during: ( interval * interval ) > $o ).

tff(contains_type,type,
    contains: ( interval * interval ) > $o ).

tff(finishes_type,type,
    finishes: ( interval * interval ) > $o ).

tff(finished_by_type,type,
    finished_by: ( interval * interval ) > $o ).

tff(before_after,axiom,
    ! [I: interval,J: interval] :
      ( before(I,J)
    <=> after(J,I) ) ).

tff(meets_metby,axiom,
    ! [I: interval,J: interval] :
      ( meets(I,J)
    <=> met_by(J,I) ) ).

tff(overlaps_inverse,axiom,
    ! [I: interval,J: interval] :
      ( overlaps(I,J)
    <=> overlapped_by(J,I) ) ).

tff(starts_inverse,axiom,
    ! [I: interval,J: interval] :
      ( starts(I,J)
    <=> started_by(J,I) ) ).

tff(during_inverse,axiom,
    ! [I: interval,J: interval] :
      ( during(I,J)
    <=> contains(J,I) ) ).

tff(finishes_inverse,axiom,
    ! [I: interval,J: interval] :
      ( finishes(I,J)
    <=> finished_by(J,I) ) ).

tff(before_irreflexive,axiom,
    ! [I: interval] : ~ before(I,I) ).

tff(before_transitive,axiom,
    ! [I: interval,J: interval,K: interval] :
      ( ( before(I,J)
        & before(J,K) )
     => before(I,K) ) ).

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