Download PDFOpen PDF in browser

AVATAR Modulo Theories

14 pagesPublished: September 29, 2016


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

BibTeX entry
  author    = {Giles Reger and Nikolaj Bjorner and Martin Suda and Andrei Voronkov},
  title     = {AVATAR Modulo Theories},
  booktitle = {GCAI 2016. 2nd Global Conference on Artificial Intelligence},
  editor    = {Christoph Benzm\textbackslash{}"uller and Geoff Sutcliffe and Raul Rojas},
  series    = {EPiC Series in Computing},
  volume    = {41},
  pages     = {39--52},
  year      = {2016},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/k6tp}}
Download PDFOpen PDF in browser