This article is the twentieth of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find criteria for effectively choosing between using and avoiding equality predicates. Since there exist inference rules (such as paramodulation) that enable an automated reasoning program to treat equality as ‘understood’, the discovery of such criteria would mark an important advance for the field. For evaluating a proposed solution to this research problem, we suggest possible test problems from group theory, ring theory, and Boolean algebra.