%%  Vertex-cover problem 
%%  The graph is given as facts "vtx(X)." and "edge(X,Y)"
%%  and k is the upper bound for vertices in a cover. 
%%  The main predicate is "incover". Atom "incover}(X)"
%%  represents the fact that vertex X is in a vertex cover.

% Select at least one of the ends of an edge to be included in the cover
1 { incover(X), incover(Y) } :- edge(X,Y). 

% Eliminate models where k+1 or more vertices have been chosen
:- k+1 {incover(X):vtx(X) }.