reached(X) :- in_hm(Z,X), vertex(Z), vertex(X).

in_hm(X,Y) | out_hm(X,Y) :- start(X), arc(X,Y).
in_hm(X,Y) | out_hm(X,Y) :- reached(X), arc(X,Y).

:- in_hm(X,Y), in_hm(X,Y1), Y != Y1, vertex(X), vertex(Y), vertex(Y1).
:- in_hm(X,Y), in_hm(X1,Y), X != X1, vertex(X), vertex(Y), vertex(X1).

:- arc(X,Z), not reached(X), vertex(Z), vertex(X).

start(0).