Distributed systems depend on correct protocol implementations, but testing them remains complex due to concurrency and data-dependent behaviors. We explore the use of First-Order Linear Temporal Logic (FOLTL) for both offline and online monitoring, enabling precise specification of system properties over execution traces. While, in general, FOLTL is undecidable, recent advances in automated reasoning tools make reasoning in practical fragments feasible, opening new directions for validating real-world distributed systems. We present example specifications of real-world distributed protocols and outline research avenues that could facilitate the use of FOLTL fragments in testing such systems.