% Hamiltonian Cycle in DLV2 (ASP-Core-2 syntax)
node(1..5).
edge(1,2). edge(2,3). edge(3,4). edge(4,5). edge(5,1). edge(1,3). edge(2,4).

% Guess an in-subgraph
{in(X,Y)} :- edge(X,Y).

% Each node has exactly one outgoing in-edge
:- node(X), #count{Y : in(X,Y)} != 1.

% Each node has exactly one incoming in-edge
:- node(X), #count{Y : in(Y,X)} != 1.

% The in-subgraph is connected (reachability from node 1)
reached(1).
reached(Y) :- reached(X), in(X,Y).
:- node(X), not reached(X).