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AVATAR Modulo Theories

14 pagesPublished: September 29, 2016

Abstract

This paper introduces a new technique for reasoning with quantifiers and theories. Traditionally, first-order theorem provers (ATPs) are well suited to reasoning with first-order problems containing many quantifiers and satisfiability modulo theories (SMT) solvers are well suited to reasoning with first-order problems in ground theories such as arithmetic. A recent development in first-order theorem proving has been the AVATAR architecture which uses a SAT solver to guide proof search based on a propositional abstraction of the first-order clause space. The approach turns a single proof search into a sequence of proof searches on (much) smaller sub-problems. This work extends the AVATAR approach to use a SMT solver in place of the SAT solver, with the effect that the first-order solver only needs to consider ground-theory-consistent sub-problems. The new architecture has been implemented using the Vampire theorem prover and Z3 SMT solver. Our experimental results, and the results of recent competitions, show that such a combination can be highly effective.

Keyphrases: automated reasoning, first-order logic, Satisfiability Modulo Theories, theorem proving, Vampire, Z3

In: Christoph Benzmüller, Geoff Sutcliffe and Raul Rojas (editors). GCAI 2016. 2nd Global Conference on Artificial Intelligence, vol 41, pages 39--52

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