Skip to main content
SpringerLink
Log in

ENIGMA: Efficient Learning-Based Inference Guiding Machine

  • Conference paper
  • First Online:
Intelligent Computer Mathematics (CICM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10383))

Included in the following conference series:

Abstract

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many previous proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, classifying a clause as useful or un-useful for the proof search. This learned classification is used to guide next proof searches prioritizing useful clauses among other generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E’s performance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We use E Prover 1.9.1 (http://www.eprover.org/).

  2. 2.

    We use .

  3. 3.

    AIM is a long-term and large-scale project [15] in applied automated deduction concerned with proving open algebraic conjectures by Kinyon and Veroff.

  4. 4.

    Different proof search settings (term orderings, rewriting settings, etc.) may largely change the proof search and make training examples incompatible. That is to say, a classifier trained on proofs produced with some proof search settings should be used only with the same settings. In our case, the proof search settings used to produce competition proofs are not known. Thus we resort to a single E prover strategy and generate compatible training data ourselves.

  5. 5.

    All the experiments were performed at Intel Xeon 2.3 GHz workstation.

  6. 6.

    We use Vampire 4.0 in CASC mode.

  7. 7.

    In an initial experiment, a simple nearest-neighbor selection of training problems for the learning further decreases the solving times and proves one more AIM problem unsolved by Prover9.

References

  1. Blanchette, J.C., Greenaway, D., Kaliszyk, C., Kühlwein, D., Urban, J.: A learning-based fact selector for Isabelle/HOL. J. Autom. Reasoning 57(3), 219–244 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blanchette, J.C., Kaliszyk, C., Paulson, L.C., Urban, J.: Hammering towards QED. J. Formalized Reasoning 9(1), 101–148 (2016)

    MathSciNet  Google Scholar 

  3. Boser, B.E., Guyon, I., Vapnik, V.: A training algorithm for optimal margin classifiers. In: COLT, pp. 144–152. ACM (1992)

    Google Scholar 

  4. Fan, R., Chang, K., Hsieh, C., Wang, X., Lin, C.: LIBLINEAR: A library for large linear classification. J. Mach. Learn. Res. 9, 1871–1874 (2008)

    MATH  Google Scholar 

  5. Färber, M., Kaliszyk, C., Urban, J.: Monte Carlo connection prover. CoRR, abs/1611.05990 (2016)

    Google Scholar 

  6. Gottlob, G., Sutcliffe, G., Voronkov, A. (eds.) Global Conference on Artificial Intelligence (GCAI 2015), Tbilisi, Georgia. EPiC Series in Computing, EasyChair, vol. 36, 16–19 October 2015

    Google Scholar 

  7. Gransden, T., Walkinshaw, N., Raman, R.: SEPIA: search for proofs using inferred automata. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS, vol. 9195, pp. 246–255. Springer, Cham (2015). doi:10.1007/978-3-319-21401-6_16

    Chapter  Google Scholar 

  8. Hsieh, C., Chang, K., Lin, C., Keerthi, S.S., Sundararajan, S.: A dual coordinate descent method for large-scale linear SVM. In: ICML, ACM International Conference Proceeding Series, vol. 307, pp. 408–415. ACM (2008)

    Google Scholar 

  9. Jakubuv, J., Urban, J.: BliStrTune: hierarchical invention of theorem proving strategies. In: Bertot, Y., Vafeiadis, V. (eds.) Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs (CPP 2017), Paris, France. pp. 43–52. ACM. 16–17 January 2017(2017)

    Google Scholar 

  10. Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. J. Autom. Reasoning 53(2), 173–213 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kaliszyk, C., Urban, J.: FEMaLeCoP: Fairly efficient machine learning connection prover. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds.) LPAR 2015. LNCS, vol. 9450, pp. 88–96. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48899-7_7

    Chapter  Google Scholar 

  12. Kaliszyk, C., Urban, J.: MizAR 40 for Mizar 40. J. Autom. Reasoning 55(3), 245–256 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kaliszyk, C., Urban, J., Vyskočil, J.: Machine learner for automated reasoning 0.4 and 0.5. CoRR, abs/1402.2359, 2014, Accepted to (PAAR 2014)

    Google Scholar 

  14. Kaliszyk, C., Urban, J., Vyskočil, J.: Efficient semantic features for automated reasoning over large theories. In: Yang, Q., Wooldridge, M. (eds.) IJCAI 2015, pp. 3084–3090. AAAI Press (2015)

    Google Scholar 

  15. Kinyon, M., Veroff, R., Vojtěchovský, P.: Loops with Abelian inner mapping groups: an application of automated deduction. In: Bonacina, M.P., Stickel, M.E. (eds.) Automated Reasoning and Mathematics. LNCS, vol. 7788, pp. 151–164. Springer, Heidelberg (2013). doi:10.1007/978-3-642-36675-8_8

    Chapter  Google Scholar 

  16. 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). doi:10.1007/978-3-642-39799-8_1

    Chapter  Google Scholar 

  17. Kühlwein, D., Urban, J.: MaLeS: A framework for automatic tuning of automated theorem provers. J. Autom. Reasoning 55(2), 91–116 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lin, C., Weng, R.C., Keerthi, S.S.: Trust region newton method for logistic regression. J. Mach. Learn. Res. 9, 627–650 (2008)

    MathSciNet  MATH  Google Scholar 

  19. Otten, J., Bibel, W.: leanCoP: lean connection-based theorem proving. J. Symb. Comput. 36(1–2), 139–161 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Schäfer, S., Schulz, S.: Breeding theorem proving heuristics with genetic algorithms. In: Gottlob et al. [6], pp. 263–274

    Google Scholar 

  21. Schulz, S.: E - A Brainiac Theorem Prover. AI Commun. 15(2–3), 111–126 (2002)

    MATH  Google Scholar 

  22. Sutcliffe, G.: The 8th IJCAR automated theorem proving system competition - CASC-J8. AI Commun. 29(5), 607–619 (2016)

    Article  MathSciNet  Google Scholar 

  23. Urban, J.: BliStr: The Blind Strategymaker. In: Gottlob et al. [6], pp. 312–319

    Google Scholar 

  24. Urban, J., Sutcliffe, G., Pudlák, P., Vyskočil, J.: MaLARea SG1 - Machine learner for automated reasoning with semantic guidance. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS, vol. 5195, pp. 441–456. Springer, Heidelberg (2008). doi:10.1007/978-3-540-71070-7_37

    Chapter  Google Scholar 

  25. Urban, J., Vyskočil, J., Štěpánek, P.: MaLeCoP machine learning connection prover. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 263–277. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22119-4_21

    Chapter  Google Scholar 

Download references

Acknowledgments

We thank Stephan Schulz for his open and modular implementation of E and its many features that allowed us to do this work. We also thank the Machine Learning Group at National Taiwan University for making LIBLINEAR openly available. This work was supported by the ERC Consolidator grant no. 649043 AI4REASON.

Author information

Authors and Affiliations

  1. Czech Technical University in Prague, Prague, Czech Republic

    Jan Jakubův & Josef Urban

Authors
  1. Jan Jakubův
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Josef Urban
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan Jakubův .

Editor information

Editors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Herman Geuvers

  2. Coventry University, Coventry, United Kingdom

    Matthew England

  3. National University of Sciences and Technology, Islamabad, Pakistan

    Osman Hasan

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. FIZ Karlsruhe, Berlin, Germany

    Olaf Teschke

The E Prover Strategy Used in Experiments

The E Prover Strategy Used in Experiments

The following fixed E strategy \(S_0\), described by its command line arguments, was used in the experiments:

figure a

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Jakubův, J., Urban, J. (2017). ENIGMA: Efficient Learning-Based Inference Guiding Machine. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds) Intelligent Computer Mathematics. CICM 2017. Lecture Notes in Computer Science(), vol 10383. Springer, Cham. https://doi.org/10.1007/978-3-319-62075-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-62075-6_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62074-9

  • Online ISBN: 978-3-319-62075-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation