When used to verify safety-critical properties of a software system, the answers provided by a CP-based constraint solver must be formally certied through trusted and faithful methodologies. In such cases, one has often to formally verify that a constraint system is unsatisable, as it is required to prove that no reachable states can violate the property to be ensured. Unfortunately, proving that a constraint system is unsatisable is much more complex for a CP-solver than checking a possible solution.