% guess the path
path(X,Y) v outPath(X,Y) :- edge(X,Y), reached(X).
:- start(X), path(_,X).

% each vertex in the path must have at most one
% incoming and one outcoming edge 
:- vtx(X), path(X,Y), path(X,Z), Y != Z.
:- vtx(X), path(X1,X), path(X2,X), X1 != X2.

% the path must feature all vertices
:- vtx(X), not reached(X).
reached(X) :- path(Y,X).
reached(X) :- start(X).