A constraint satisfaction problem may be relationally consistent, have no empty domain or unsatisfiable constraint, and yet be unsatisfiable. There are however some cases in which this is not possible.
The first case is that of strongly relational m-consistent problem when the domains contain at most m elements.
This would imply that any problem with domains of size m that is stongly m-consistent, is satisfiable. However on the same page they mention 3-colorability. It is NP-complete and consists of binary constraints on variables with domain size 3. Generally it should be possible to achieve strong-3-consistency in about $O(n^3)$, so the above statement should be wrong as it implies P=NP. What did they mean to say when the wrote the above statement? Or am I interpreting it in a wrong way?