Skip to main content
SpringerLink
Log in
Book cover

International Conference on Automated Deduction

CADE 2015: Automated Deduction - CADE-25 pp 389–398Cite as

System Description: E.T. 0.1

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

Abstract

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 %.

C. Kaliszyk—Supported by the Austrian Science Fund FWF grant P26201.

J. Urban—Supported by NWO grant nr. 612.001.208.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Notes

  1. 1.

    We will use AITP as an abbreviation for the ATP/ITP cooperation, hinting also at the AI aspects of that topic.

  2. 2.

    Although never publicly described, similar methods used are one of the main dark sources of Vampire’s success.

  3. 3.

    The current limit for formula/clause size is 5kb. This filters out only a few of formulas from the large corpora of interest, and in practice does not influence completeness.

  4. 4.

    E.T. runs its strategies sequentially by default. It is also possible to run the strategies, premise selectors, and feature extractors in parallel when more cores are available.

  5. 5.

    Parameters are used in the order given above. Missing parameters use E’s built-in default values.

References

  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)

    Article  Google Scholar 

  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. Blanchette, J.C., Kaliszyk, C., Paulson, L.C., Urban, J.: Hammering towards QED (2015). http://www4.in.tum.de/~blanchet/h4qed.pdf

  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. 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)

    Article  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  9. Kaliszyk, C., Urban, J.: MizAR 40 for Mizar 40. CoRR, abs/1310.2805 (2013)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Kaliszyk, C., Urban, J.: HOL(y)Hammer: online ATP service for HOL Light. Math. Comput. Sci. 9(1), 5–22 (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, PAAR 2014 (2014, to appear)

    Google Scholar 

  14. Kaliszyk, C., Urban, J., Vyskočil,J.: Efficient semantic features for automated reasoning over large theories. In: IJCAI (2015, to appear)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  17. Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Appl. Logic 7(1), 41–57 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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. Quaife, A.: Automated Development of Fundamental Mathematical Theories. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  21. Sutcliffe, G.: Proceedings of the 7th IJCAR ATP system competition.http://www.cs.miami.edu/~tptp/CASC/J7/Proceedings.pdf

  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)

    Article  MATH  Google Scholar 

  23. Sutcliffe, G.: The 6th IJCAR automated theorem proving system competition - CASC-J6. AI Commun. 26(2), 211–223 (2013)

    MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Urban, J.: MPTP - motivation, implementation, first experiments. J. Autom. Reasoning 33(3–4), 319–339 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  27. Urban, J.: MPTP 0.2: design, implementation, and initial experiments. J. Autom. Reasoning 37(1–2), 21–43 (2006)

    MATH  Google Scholar 

  28. Urban, J.: BliStr: The Blind Strategymaker. CoRR, abs/1301.2683 (2013)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  2. DHBW Stuttgart, Stuttgart, Germany

    Stephan Schulz

  3. Radboud University Nijmegen, Nijmegen, The Netherlands

    Josef Urban

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

    Jiří Vyskočil

Authors
  1. Cezary Kaliszyk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephan Schulz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Josef Urban
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiří Vyskočil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Josef Urban .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kaliszyk, C., Schulz, S., Urban, J., Vyskočil, J. (2015). System Description: E.T. 0.1. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21401-6_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation