/* Learning min/2 - finding a minimal element of a list */
/* This task requires negative examples. Otherwise the membership
   reletion would be learnt. This is because memb/2 subsumes min/2,
   i.e. the minimal element of a list must be a member of the list. */

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

/* Positive examples of the target predicate */
min('[1,2,3]',1).
min('[3,2,1]',1).
min('[2,1,3]',1).
min('[2,3,1]',1).
min('[3,1,2]',1).
min('[2,3]',2).
min('[1,3]',1).
min('[3,1]',1).
min('[2,1]',1).
min('[1,2]',1).
min('[1]',1).
min('[2]',2).
min('[3]',3).

/* Negative examples of the target predicate */
neg(min('[3,2,1]',3)).
neg(min('[1,2]',2)).

/* Background knowledge */

less(1,2).
less(2,3).
less(1,3).

components('[1,2,3]',1,'[2,3]').
components('[3,2,1]',3,'[2,1]').
components('[2,3,1]',2,'[3,1]').
components('[1,3,2]',1,'[3,2]').
components('[2,1,3]',2,'[1,3]').
components('[3,1,2]',3,'[1,2]').
components('[2,3]',2,'[3]').
components('[3,2]',3,'[2]').
components('[1,3]',1,'[3]').
components('[3,1]',3,'[1]').
components('[2,1]',2,'[1]').
components('[1,2]',1,'[2]').
components('[1]',1,[]).
components('[2]',2,[]).
components('[3]',3,[]).