Real-time logic (RTL) is useful for the verification of a safety assertion with respect to the specification of a real-time system. Since the satisfiability problem for RTL is undecidable, the systematic debugging of a real-time system appears impossible. This paper provides a first step towards this challenge. With RTL, each propositional formula corresponds to a verification condition. The number of truth assignments of a propositional formula helps to determine the timing constraints which should be added or modified to the system's specification. We have implemented a tool (called SDRTL) that is able to perform systematic debugging. The confidence of our approach is high as we have evaluated SDRTL on several existing industrial-based applications.