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CafeOBJ is a wide spectrum formal specification language based on multiple logical foundations: mainly initial and hidden algebra. A wide range of systems can be specified in CafeOBJ thanks to its multiple logical foundations. However, distributed real-time systems happen to be excluded from targets of CafeOBJ. The authors propose a method of modeling and verifying such systems based on CafeOBJ, together with timed evolution of UNITY computational models.