When getting in MiniZinc the message:
WARNING: model inconsistency detected
That means that the Model is UNSATISFIABLE due to a specific constraint in some line of the Model, is there a way apart from commenting out the constraint that leads to the inconsistency to "relax" this constraint and Minizinc recalculates a solution?
(I copied my comment to a "formal" answer, so now you can accept the answer.)
In the newest MiniZinc version (v2.2.0) there is a solver - "findMUS" - that is for these kind of problems where it tries to identify the culprit.