 
Summary: The Use of Lemmas in the Model Elimination Procedure
O.L. Astrachan and D.W. Loveland \Lambda
Department of Computer Science
Duke University
Durham, NC 277080129
9196606500
folajdwlg@cs.duke.edu
Abstract
When the Model Elimination (ME) procedure was first proposed, a notion of lemma was put
forth as a promising augmentation to the basic complete proof procedure. Here the lemmas that
are used are also discovered by the procedure in the same proof run. Several implementations of
ME now exist but only a 1970's implementation explicitly examined this lemma mechanism, with
indifferent results. We report on the successful use of lemmas using the METEOR implementa
tion of ME. Not only does the lemma device permit METEOR to obtain proofs not otherwise
obtainable by METEOR, or any other ME prover not using lemmas, but some wellknown chal
lenge problems are solved. We discuss several of these more difficult problems, including two
challenge problems for uniform generalpurpose provers, where METEOR was first in obtaining
the proof. The problems are not selected simply to show off the lemma device, but rather to
understand it better. Thus, we choose problems with widely different characteristics, including
one where very few lemmas are created automatically, the opposite of normal behavior. This
