Extension Rule in First Order Logic

The extension rule (ER) is a new method for theorem proving, which is potentially a complementary method to resolution-based methods. But the first-order ER method is incomplete. We improve the first-order ER approach by (a) revise the definition of the potential blockage, give a complete first-order ER algorithm, (b) increasing the case M-satisfiability by giving a bound M, so as to make the ER method more useful for theorem proving and logic programming, and (c) accelerating it through invoking the more efficient proposition ER method. We also prove the soundness and completeness of the improved first-order ER algorithm and report some preliminary computational results.