We present a new approach for solving temporal problems using Answer Set Programming (ASP), which exploits the automata representation of temporal specifications. This approach is then used to solve key problems from Process Mining. The contributions are manifold. Firstly, for the Temporal Logics community, it provides a tool to perform temporal reasoning. Secondly, for the ASP community, it offers a method to intuitively handle time. Finally, for the Process Mining community, it provides both tools and methods for analyzing event logs.