E-KRHyper is a versatile theorem prover and model generator for firstorder logic that natively supports equality. Inequality of constants, however, has to be given by explicitly adding facts. As the amount of these facts grows quadratically in the number of these distinct constants, the knowledge base is blown up. This makes it harder for a human reader to focus on the actual problem, and impairs the reasoning process. We extend E-Hyper- underlying E-KRhyper tableau calculus to avoid this blow-up by implementing a native handling for inequality of constants. This is done by introducing the unique name assumption for a subset of the constants (the so called distinct object identifiers). The obtained calculus is shown to be sound and complete and is implemented into the E-KRHyper system. Synthetic benchmarks, situated in the theory of arrays, are used to back up the benefits of the new calculus.