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This paper presents the techniques and results of a novel model-based test case generation approach that automatically derives test cases from UML state machines. Mutation testing is applied on the modeling level to generate test cases. We present the test case generation approach, discuss the tool chain, and present the properties of the generated test cases. The main contribution of this paper is an empirical study of a car alarm system where different strategies for killing mutants are compared. We present detailed figures on the effectiveness of the test case generation technique. Although UML serves as an input language, all techniques are grounded on solid foundations: we give UML state transition diagrams a formal semantics by mapping them to Back's action systems.