We propose a method for automatically discovering likely program invariants for persistent memory (PM), which is a type of fast and byte-addressable storage device that can retain data after power loss. The invariants, also called PM properties, specify which objects of the program should be made persistent and in what order. Our method relies on a combination of static and dynamic analysis techniques. Specifically, it relies on static analysis to compute dependence relations between LOAD/STORE instructions and instruments the information into the executable program. Then, it relies on dynamic analysis of the execution traces and counter-factual reasoning to infer invariants. With precisely computed dependence relations, these are true invariants, i.e., necessary conditions for the program to behave correctly through power loss and recovery; with imprecise dependence relations, these are likely invariants. We have evaluated our method on benchmark programs including eight persistent data structures and two distributed storage applications, Redis and Memcached. The results show that our method can infer PM properties quickly and these properties are of higher quality than those inferred by a state-of-the-art technique. We also demonstrate the usefulness of the inferred properties by leveraging them for bug detection, which significantly improves the performance of a state-of-the-art bug detection technique.