/* Learning memb/2 with non-ground background knowledge */
/* Due to implementation reasons lists are not allowed as
   predicate agruments. However at a deeper level this is ok */

background([memb/2,components/3]).
propositional([]).

/* Examples of the target predicate */
memb(a(1),a([1,2,3])).
memb(a(3),a([1,2,3])).
memb(a(3),a([2,3])).
memb(a(1),a([1,2])).
memb(a(1),a([1,3])).
memb(a(1),a([1])).
memb(a(1),a([1,2,3])).
memb(a(2),a([1,2,3])).
memb(a(3),a([1,3])).
memb(a(3),a([3])).
memb(a(2),a([2,3])).

/* Background knowledge for 3-element ordered lists */
components(a([Head|Tail]),a(Head),a(Tail)) :-
    sublist([Head|Tail],[1,2,3]).

sublist([H|T],[H|V]) :- sublist(T,V).
sublist(T,[_|V]) :- !, sublist(T,V).
sublist([],_).