TOBIAS is a combinatorial testing tool, aimed at the production of large test suites. In this paper, TOBIAS is applied to conformance tests for model-based specifications (expressed with assertions, pre and post-conditions) and associated implementations. The tool takes advantage of the executable character of VDM or JML assertions which provide an oracle for the testing process. Executing large test suites may require a lot of time. This paper shows how assertions can be exploited at generation time to filter the set of test cases, and at execution time to detect inconclusive test cases.