Theorem recycling for Theorem Proving

Abstract

In this paper we examine two cases where solutions to one system of constraints can be used or adapted to solutions to others, for free. We first revisit a method by Bromberger for lifting solutions to systems over linear real arithmetic to solutions over integers. We extend it by identifying several scenarios where solutions over reals can be directly used to establish solutions over integers. Our second case discusses model-based projection, which was introduced in two different places with different, dual, definitions. It turns out that one can typically use the same underlying engines to compute both versions of model based projection and we characterize when this is the case. We extend projection with model- based realization. When used for quantifier reasoning, it serves a complementary purpose than projection. While projection can be used for computing conflict clauses, realizers may be used for forward pruning.