The problem of choosing between using and avoiding equality predicates

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.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.