Induction in Saturation-Based Proof Search

Abstract

Many applications of theorem proving, for example programverification and analysis, require first-order reasoning with both quantifiers and theories such as arithmetic and datatypes. There is no completeprocedure for reasoning in such theories but the state-of-the-art in automatedtheorem proving is still able to reason effectively with real-worldproblems from this rich domain. In this paper we introduce a missingpart of the puzzle: automated induction inside a saturation-based theoremprover. Our goal is to incorporate lightweight automated inductionin a way that complements the saturation-based approach, allowing us tosolve problems requiring a combination of first-order reasoning, theoryreasoning, and inductive reasoning. We implement a number of techniquesand heuristics and evaluate them within the Vampire theoremprover. Our results show that these new techniques enjoy practical successon real-world problems