System Description: E.T. 0.1

  • Cezary Kaliszyk
  • Stephan Schulz
  • Josef UrbanEmail author
  • Jiří Vyskočil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9195)


E.T. 0.1 is a meta-system specialized for theorem proving over large first-order theories containing thousands of axioms. Its design is motivated by the recent theorem proving experiments over the Mizar, Flyspeck and Isabelle data-sets. Unlike other approaches, E.T. does not learn from related proofs, but assumes a situation where previous proofs are not available or hard to get. Instead, E.T. uses several layers of complementary methods and tools with different speed and precision that ultimately select small sets of the most promising axioms for a given conjecture. Such filtered problems are then passed to E, running a large number of suitable automatically invented theorem-proving strategies. On the large-theory Mizar problems, E.T. considerably outperforms E, Vampire, and any other prover that does not learn from related proofs. As a general ATP, E.T. improved over the performance of unmodified E in the combined FOF division of CASC 2014 by 6 %.


Large Problem Related Clause Recursive Call Automate Theorem Prove Training Problem 
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.
    Alama, J., Heskes, T., Kühlwein, D., Tsivtsivadze, E., Urban, J.: Premise selection for mathematics by corpus analysis and kernel methods. J. Autom. Reasoning 52(2), 191–213 (2014)CrossRefGoogle Scholar
  2. 2.
    Beeson, M., Wos, L.: OTTER proofs in Tarskian geometry. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 495–510. Springer, Heidelberg (2014) Google Scholar
  3. 3.
    Blanchette, J.C., Kaliszyk, C., Paulson, L.C., Urban, J.: Hammering towards QED (2015).
  4. 4.
    Cambazoglu, B.B., Zaragoza, H., Chapelle, O., Chen, J., Liao, C., Zheng, Z., Degenhardt, J.: Early exit optimizations for additive machine learned ranking systems. In: Davison, B.D., Suel, T., Craswell, N., Liu, B. (eds.) WSDM, pp. 411–420. ACM, New York (2010)Google Scholar
  5. 5.
    Chaudhri, V.K., Elenius, D., Goldenkranz, A., Gong, A., Martone, M.E., Webb, W., Yorke-Smith, N.: Comparative analysis of knowledge representation and reasoning requirements across a range of life sciences textbooks. J. Biomed. Semant. 5, 51 (2014)CrossRefzbMATHGoogle Scholar
  6. 6.
    Furbach, U., Glöckner, I., Pelzer, B.: An application of automated reasoning in natural language question answering. AI Commun. 23(2–3), 241–265 (2010)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Hoder, K., Voronkov, A.: Sine Qua Non for large theory reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 299–314. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Kaliszyk, C., Urban, J.: MizAR 40 for Mizar 40. CoRR, abs/1310.2805 (2013)Google Scholar
  10. 10.
    Kaliszyk, C., Urban, J.: Stronger automation for Flyspeck by feature weighting and strategy evolution. In: Blanchette, J.C., Urban, J. (eds.) PxTP 2013, EPiC Series, vol. 14, pp. 87–95. EasyChair (2013)Google Scholar
  11. 11.
    Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. J. Autom. Reasoning 53(2), 173–213 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kaliszyk, C., Urban, J.: HOL(y)Hammer: online ATP service for HOL Light. Math. Comput. Sci. 9(1), 5–22 (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, PAAR 2014 (2014, to appear)Google Scholar
  14. 14.
    Kaliszyk, C., Urban, J., Vyskočil,J.: Efficient semantic features for automated reasoning over large theories. In: IJCAI (2015, to appear)Google Scholar
  15. 15.
    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
  16. 16.
    Kühlwein, D., Blanchette, J.C., Kaliszyk, C., Urban, J.: MaSh: machine learning for Sledgehammer. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 35–50. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  17. 17.
    Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Appl. Logic 7(1), 41–57 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Pease, A., Schulz, S.: Knowledge engineering for large ontologies with sigma KEE 3.0. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 519–525. Springer, Heidelberg (2014) Google Scholar
  19. 19.
    Quaife, A.: Automated Development of Fundamental Mathematical Theories. Kluwer Academic Publishers, Dordrecht (1992)Google Scholar
  20. 20.
    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
  21. 21.
    Sutcliffe, G.: Proceedings of the 7th IJCAR ATP system competition.
  22. 22.
    Sutcliffe, G.: The TPTP problem library and associated infrastructure: the FOF and CNF parts, v3.5.0. J. Autom. Reasoning 43(4), 337–362 (2009)CrossRefzbMATHGoogle Scholar
  23. 23.
    Sutcliffe, G.: The 6th IJCAR automated theorem proving system competition - CASC-J6. AI Commun. 26(2), 211–223 (2013)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Sutcliffe, G., Puzis, Y.: SRASS - a semantic relevance axiom selection system. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 295–310. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  25. 25.
    Sutcliffe, G., Suda, M., Teyssandier, A., Dellis, N., de Melo, G.: Progress towards effective automated reasoning with world knowledge. In: Guesgen, H.W., Murray, R.C. (eds.) FLAIRS. AAAI Press, Menlo Park (2010)Google Scholar
  26. 26.
    Urban, J.: MPTP - motivation, implementation, first experiments. J. Autom. Reasoning 33(3–4), 319–339 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Urban, J.: MPTP 0.2: design, implementation, and initial experiments. J. Autom. Reasoning 37(1–2), 21–43 (2006)zbMATHGoogle Scholar
  28. 28.
    Urban, J.: BliStr: The Blind Strategymaker. CoRR, abs/1301.2683 (2013)Google Scholar
  29. 29.
    Urban, J., Hoder, K., Voronkov, A.: Evaluation of automated theorem proving on the Mizar mathematical library. In: Fukuda, K., Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 155–166. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  30. 30.
    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

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Cezary Kaliszyk
    • 1
  • Stephan Schulz
    • 2
  • Josef Urban
    • 3
    Email author
  • Jiří Vyskočil
    • 4
  1. 1.University of InnsbruckInnsbruckAustria
  2. 2.DHBW StuttgartStuttgartGermany
  3. 3.Radboud University NijmegenNijmegenThe Netherlands
  4. 4.Czech Technical University in PraguePragueCzech Republic

Personalised recommendations