The Generalized Resolution Principle

The generalized resolution principle is a single inference principle which provides, by itself, a complete formulation of the quantifier-free first-order predicate calculus with equality. It is a natural generalization of the various versions and extensions of the resolution principle, each of which it includes as special cases; but in addition it supplies all of the inferential machinery which is needed in order to be able to treat the intended interpretation of the equality symbol as ‘built in’, and obviates the need to include special axioms of equality in the formulation of every theorem-proving problem which makes use of that notion.