Abstract

Lee and Plaisted recently developed a new automated theorem proving strategy called hyper-linking. As part of his dissertation, Lee developed a round-by-round implementation of the hyper-linking strategy, which competes well with other automated theorem provers on a wide range of theorem proving problems. However, Lee's round-by-round implementation of hyper-linking is not particularly well suited for the addition of special methods in support of equality. In this dissertation, we describe, as alternative to the round-by-round hyper-linking implementation of Lee, a smallest instance first implementation of hyper-linking which addresses many of the inefficiencies of round-by-round hyper-linking encountered when adding special methods in support of equality. Smallest instance first hyper-linking is based on the formalization of generating smallest clauses first, a heuristic widely used in other automated theorem provers. We prove both the soundness and logical completeness of smallest instance first hyper-linking and show that it always generates smallest clauses first under

Citations