Abstract
This article is the twenty-first of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find an inference rule that performs as paramodulation does, but with the focus on inequalities rather than on equalities. Since, too often, inequalities that are present in the input play a passive role during a reasoning program's attempt to complete an assignment, such an inference rule would markedly add to program effectiveness by giving inequalities the potential of playing a key role. For evaluating a proposed solution to this research problem, we suggest as possible test problems theorems from group theory and theorems from ring theory.
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