MARTE (abbreviated for Modeling and Analysis of Real-Time and Embedded systems) is a UML profile which provides a general modeling framework to design and analyze real-time embedded systems. CCSL (abbreviated for Clock Constraint Specification Language) is a formal language companion to MARTE, used to specify the constraints between the occurrences of events in real-time embedded systems. Many approaches have been proposed to the formal analysis of CCSL such as simulation and model checking. We propose in this paper an SMT-based approach to the formal analysis of CCSL. It is well-known that the SMT-based approach can effectively overcome the state-explosion problem for model checking, and can also be used for theorem proving. The latter feature allows us to prove the invalidity of CCSL constraints, which most of the existing approaches lack. We implement the proposed approach in a prototype tool clyzer on top of K framework and use Z3 as the underlying SMT solver.