Cooperating Proof Attempts

  • Giles RegerEmail author
  • Dmitry Tishkovsky
  • Andrei Voronkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9195)


This paper introduces a pseudo-concurrent architecture for first-order saturation-based theorem provers with the eventual aim of developing it into a truly concurrent architecture. The motivation behind this architecture is two-fold. Firstly, first-order theorem provers have many configuration parameters and commonly utilise multiple strategies to solve problems. It is also common that one of these strategies will solve the problem quickly but it may have to wait for many other strategies to be tried first. The architecture we propose interleaves the execution of these strategies, increasing the likeliness that these ‘quick’ proofs will be found. Secondly, previous work has established the existence of a synergistic effect when allowing proof attempts to communicate by sharing information about their inferences or clauses. The recently introduced AVATAR approach to splitting uses a SAT solver to explore the clause search space. The new architecture considers sharing this SAT solver between proof attempts, allowing them to share information about pruned areas of the search space, thus preventing them from making unnecessary inferences. Experimental results, using hard problems from the TPTP library, show that interleaving can lead to problems being solved more quickly, and that sharing the SAT solver can lead to new problems being solved by the combined strategies that were never solved individually by any existing theorem prover.


Proof Attempt TPTP Library Parallel Theorem Prover Splitting Branches Saturation Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, Chap. 2, pp. 19–99. Elsevier Science, Amsterdam (2001)Google Scholar
  2. 2.
    Böhme, S., Nipkow, T.: Sledgehammer: judgement day. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 107–121. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  3. 3.
    Bonacina, M.: A taxonomy of parallel strategies for deduction. Ann. Math. Artif. Intell. 29(1–4), 223–257 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Denzinger, J., Kronenburg., M.: Planning for distributed theorem proving: the teamwork approach. In: Görz, G., Hölldobler, S. (eds.) KI 1996. LNCS, vol. 1137. Springer, Heidelberg (1996) Google Scholar
  5. 5.
    Denzinger, J., Kronenburg, M., Schulz, S.: DISCOUNT – a distributed and learning equational prover. J. Autom. Reasoning 18(2), 189–198 (1997)CrossRefGoogle Scholar
  6. 6.
    Ganzinger, H., Korovin, K.: New directions in instantiation-based theorem proving. In: Proceedings of LICS 2003, pp. 55–64 (2003)Google Scholar
  7. 7.
    Hoder, K., Voronkov, A.: The 481 ways to split a clause and deal with propositional variables. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 450–464. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  8. 8.
    Kovács, L., Voronkov, A.: First-order theorem proving and vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1–35. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  9. 9.
    Kühlwein, D., Schulz, S., Urban, J.: E-MaLeS 1.1. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 407–413. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  10. 10.
    Lusk, E., McCune, W.: Experiments with ROO: a parallel automated deduction system. In: Fronhöfer, B., Wrightson, G. (eds.) Dagstuhl Seminar 1990. LNCS, vol. 590. Springer, Heidelberg (1992) CrossRefGoogle Scholar
  11. 11.
    Reger, G., Suda, M., Voronkov, A.: Playing with AVATAR. In: Proceedings of CADE2015 (2015)Google Scholar
  12. 12.
    Riazanov, A., Voronkov, A.: Limited resource strategy in resolution theorem proving. J. Symb. Comp. 36(1–2), 101–115 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Schulz, S.: System description: E 1.8. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 735–743. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  14. 14.
    Schumann, J., Letz, R.: PARTHEO: a high-performance parallel theorem prover. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 40–56. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  15. 15.
    Slaney, J.K., Lusk, E.L.: Parallelizing the closure computation in automated deduction. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 28–39. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  16. 16.
  17. 17.
    Sutcliffe, G.: The design and implementation of a compositional competition-cooperation parallel ATP system. In: Proceedings IWIL-2, number MPI-I-2001-2-006 in MPI für Informatik, Research Report, pp. 92–102 (2001)Google Scholar
  18. 18.
    Sutcliffe, G.: The TPTP problem library and associated infrastructure. J. Autom. Reasoning 43(4), 337–362 (2009)CrossRefzbMATHGoogle Scholar
  19. 19.
    Sutcliffe, G., Suttner, C.: Evaluating general purpose automated theorem proving systems. Artif. Intell. 131(1–2), 39–54 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Suttner, C.B., Schumann, J.: Chapter 9 – Parallel automated theorem proving. In: Parallel Processing for Artificial Intelligence, vol. 14 of Machine Intelligence and Pattern Recognition, pp. 209–257. North-Holland (1994)Google Scholar
  21. 21.
    Tammet, T.: Gandalf. J. Autom. Reasoning 18(2), 199–204 (1997)CrossRefGoogle Scholar
  22. 22.
    Voronkov, A.: AVATAR: The architecture for first-order theorem provers. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 696–710. Springer, Heidelberg (2014) Google Scholar
  23. 23.
    Wolf, A., Fuchs, M.: Cooperative parallel automated theorem proving. Technical report SFB Bereicht 342/21/97, Technische Universität München (1997)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Giles Reger
    • 1
    Email author
  • Dmitry Tishkovsky
    • 1
  • Andrei Voronkov
    • 1
  1. 1.University of ManchesterManchesterUK

Personalised recommendations