So you say the CLP(FD) doesn't find a solution. Do you
mean it terminates with "no" or do you mean it doesn't
terminate?
The problem looks like a Hamiltonian path problem. It
could be that the search needs exponential time, and simply
doesn't terminate in practical time.
In this particular case, giving restrictions like symmetry
breaking heuristics, could in fact reduce the search time!
For example from your starting point, you could fix the search
in 2 directions, the other directions can be derived later.
So if the answer is "No", this means too many restrictions.
If the answer is that it doesn't terminate, this means not
enough restrictions or impossible to practically solve.
Despite all the brute force you put into searching a path,
it might later turn out that a solution is systematic. Or
you might get the idea by yourself.
Bye