Because processes run concurrently in multitask systems, the size of the state space grows exponentially. Therefore, it is not straightforward to formally verify that such systems enjoy desired properties. Real-time constrains make the formal verification more challenging. In this paper, we propose the following to address the challenge: (1) a way to model multitask real-time systems as observational transition systems (OTSs), a kind of state transition systems, (2) a way to describe their specifications in CafeOBJ, an algebraic specification language, and (3) a way to verify that such systems enjoy desired properties based on such formal specifications by writing proof scores, proof plans, in CafeOBJ. As a case study, we model Fischer's protocol, a well-known real-time mutual exclusion protocol, as an OTS, describe its specification in CafeOBJ, and verify that the protocol enjoys the mutual exclusion property when an arbitrary number of processes participates in the protocol^*.