ENIGMA: Efficient Learning-Based Inference Guiding Machine

  • Jan JakubůvEmail author
  • Josef Urban
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10383)


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.



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.

Supplementary material


  1. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blanchette, J.C., Kaliszyk, C., Paulson, L.C., Urban, J.: Hammering towards QED. J. Formalized Reasoning 9(1), 101–148 (2016)MathSciNetGoogle Scholar
  3. 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. 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)zbMATHGoogle Scholar
  5. 5.
    Färber, M., Kaliszyk, C., Urban, J.: Monte Carlo connection prover. CoRR, abs/1611.05990 (2016)Google Scholar
  6. 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 2015Google Scholar
  7. 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 CrossRefGoogle Scholar
  8. 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. 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. 10.
    Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. J. Autom. Reasoning 53(2), 173–213 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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 CrossRefGoogle Scholar
  12. 12.
    Kaliszyk, C., Urban, J.: MizAR 40 for Mizar 40. J. Autom. Reasoning 55(3), 245–256 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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. 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. 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 CrossRefGoogle Scholar
  16. 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 CrossRefGoogle Scholar
  17. 17.
    Kühlwein, D., Urban, J.: MaLeS: A framework for automatic tuning of automated theorem provers. J. Autom. Reasoning 55(2), 91–116 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Lin, C., Weng, R.C., Keerthi, S.S.: Trust region newton method for logistic regression. J. Mach. Learn. Res. 9, 627–650 (2008)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Otten, J., Bibel, W.: leanCoP: lean connection-based theorem proving. J. Symb. Comput. 36(1–2), 139–161 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Schäfer, S., Schulz, S.: Breeding theorem proving heuristics with genetic algorithms. In: Gottlob et al. [6], pp. 263–274Google Scholar
  21. 21.
    Schulz, S.: E - A Brainiac Theorem Prover. AI Commun. 15(2–3), 111–126 (2002)zbMATHGoogle Scholar
  22. 22.
    Sutcliffe, G.: The 8th IJCAR automated theorem proving system competition - CASC-J8. AI Commun. 29(5), 607–619 (2016)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Urban, J.: BliStr: The Blind Strategymaker. In: Gottlob et al. [6], pp. 312–319Google Scholar
  24. 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 CrossRefGoogle Scholar
  25. 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 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Czech Technical University in PraguePragueCzech Republic

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