*Gerald E. Peterson*

This is a summary of the methods and results of a longer paper of the same name which will appear elsewhere. The main result is that an automatic theorem proving system consisting of resolution, paramodulation, factoring, equality reversal, simplification and subsumption removal is complete in first-order logic with equality. When restricted to sets of equality units, the resulting system is very much like the Knuth-Bendix procedure. The completeness of resolution and paramodulation without the functionally reflexive axioms is a corollary. The methods used are based upon the familiar ideas of reduction and semantic trees, and should be helpful in showing that other theorem proving systems with equality are complete.

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