Process mining is the set of techniques to retrieve a process model starting from available logging data. The discovered process model has to be analyzed to verify it respects the defined properties, i.e., the so-called compliance checking. Our aim is to use a model checking based approach to verify compliance. First, we propose an integrated-tool approach using existing tools as ProM (a framework supporting process mining techniques) and CADP (a formal verification environment). More precisely, the execution traces from a software system are extracted. Then, using the "Mine Transition System" plugin in ProM, we obtain a labelled transition system, that can be easily used to verify formal properties trough CADP. However, this choice presents the "state explosion" problem, i.e., models discovered through the classical process mining techniques tend to be large and complex. In order to solve this problem, another custom-made approach is shown, which accomplishes a pre- processing on the traces to obtain abstract traces, where abstraction is based on the set of temporal logic formulae specifying the system properties. Then, from the set of abstracted traces, we discover a system described in Lotos, a process algebra specification language; in this way we do not build an operational model for the system, but we produce only a language description from which a model checking environment will automatically obtain the reduced corresponding transition system. Real systems have been used as case studies to evaluate the proposed methodologies.