Minimizing the number of clauses by renaming

Abstract

The problem of translating a formula into a “good” clause form is known to be a very important one in resolution automated theorem proving. Some theorems have such a huge clause form that it is practically impossible to prove them by resolution. Several methods exist to reduce clause forms, some applied before and some after translation. They are generally based on (local or non-local) simplifications. A method consisting in the creation and use of definitions, which we call renaming, has been developed in [5], [4] and [7]. Applying it in an exhaustive way was shown to yield a translation into clause form polynomial in size (see [7]). In this paper we investigate non exhaustive renamings in the purpose of minimizing the number of clauses. We obtain a translation which is shown to be polynomial in size, and optimal in number of clauses when the theorem contains no equivalence. An example shows that this translation is not necessarily optimal in presence of equivalence. Experiments with “challenge” examples show the practical efficiency of this translation.