Skip to main content
SpringerLink
Log in

Thousands of Geometric Problems for Geometric Theorem Provers (TGTP)

  • Conference paper
Automated Deduction in Geometry (ADG 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6877))

Included in the following conference series:

Abstract

Thousands of Geometric problems for geometric Theorem Provers (TGTP) is a Web-based library of problems in geometry.

The principal motivation in building TGTP is to create an appropriate context for testing and evaluating geometric automated theorem proving systems (GATP). For that purpose TGTP provides a centralised common library of geometric problems with an already significant size but aiming to became large enough to ensure meaningful system evaluations and comparisons. TGTP provides also a workbench were it is possible to test any given geometric conjecture.

TGTP is independent of any given GATP. For each problem the code for each GATP (whenever available) is kept in the library. A common format for geometric conjectures, extending the i2g format, is being developed. This common format, plus a list of converters, one for each GATP, will allow to test all the GATPs with all the problems in the library.

TGTP is well structured, documented and with a powerful querying mechanism, allowing an easy access to the information. All information in the library, and also the supporting formats and tools are freely available.

TGTP aims, in a similar spirit of TPTP and other libraries, to provide the automated reasoning in geometry community with a comprehensive and easily accessible library of GATP test problems. The development of TGTP problem library is an ongoing project.

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB Standard: Version 2.0. In: Gupta, A., Kroening, D. (eds.) Proceedings of the 8th International Workshop on Satisfiability Modulo Theories, Edinburgh, England (2010)

    Google Scholar 

  2. Bertot, Y., Guilhot, F., Pottier, L.: Visualizing geometrical statements with GeoView. Electronic Notes in Theoretical Computer Science 103, 49–65 (2004)

    Article  Google Scholar 

  3. Botana, F., Valcarce, J.L.: A dynamic-symbolic interface for geometric theorem discovery. Computers and Education 38, 21–35 (2002)

    Article  Google Scholar 

  4. Buchberger, B., Craciun, A., Jebelean, T., Kovacs, L., Kutsia, T., Nakagawa, K., Piroi, F., Popov, N., Robu, J., Rosenkranz, M., Windsteiger, W.: Theorema: Towards computer-aided mathematical theory exploration. Journal of Applied Logic 4(4), 470–504 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Davenport, J.H.: On writing OpenMath content dictionaries. SIGSAM Bulletin 34(2), 12–15 (2000)

    Article  Google Scholar 

  6. DIMACS: Satisfiability suggested format (May 1993), ftp://dimacs.rutgers.edu/pub/challenge/satisfiability/doc/

  7. Egido, S., Hendriks, M., Kreis, Y., Kortenkamp, U., Marquès, D.: i2g Common File Format Final Version. Tech. Rep. D3.10, The Intergeo Consortium (2010)

    Google Scholar 

  8. Fuchs, K., Hohenwarter, M.: Combination of dynamic geometry, algebra and calculus in the software system geogebra. In: Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching Conference 2004, pp. 128–133. Pécs, Hungary (2004)

    Google Scholar 

  9. Gao, X.-S., Lin, Q.: MMP/Geometer - a Software Package for Automated Geometric Reasoning. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 44–66. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Hoos, H., Stützle, T.: SATLIB: An online resource for research on SAT. In: Gent, I.P., Maaren, H.V., Walsh, T. (eds.) SAT 2000, pp. 283–292. IOS Press, Amsterdam (2000)

    Google Scholar 

  11. Janičić, P., Narboux, J., Quaresma, P.: The Area Method: a recapitulation. Journal of Automated Reasoning 7 (to appear, 2011), doi:10.1007/s10817-010-9209-7

    Google Scholar 

  12. Janičić, P.: GCLC — A Tool for Constructive Euclidean Geometry and More Than That. In: Iglesias, A., Takayama, N. (eds.) ICMS 2006. LNCS, vol. 4151, pp. 58–73. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Janičić, P., Quaresma, P.: System Description: GCLCprover + Geothms. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 145–150. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Kapur, D.: Using Gröbner bases to reason about geometry problems. Journal of Symbolic Computation 2(4), 399–408 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kortenkamp, U., Richter-Gebert, J.: Using automatic theorem proving to improve the usability of geometry software. In: Procedings of the Mathematical User-Interfaces Workshop 2004 (2004)

    Google Scholar 

  16. Narboux, J.: A graphical user interface for formal proofs in geometry. Journal of Automated Reasoning 39, 161–180 (2007)

    Article  MATH  Google Scholar 

  17. Oracle: MySQL 5.5 Reference Manual, 5.5 edn. (January 2011), revision: 24956

    Google Scholar 

  18. Quaresma, P., Janičić, P., Tomašević, J., Vujošević-Janičić, M., Tošić, D.: XML-Bases Format for Descriptions of Geometric Constructions and Proofs. In: Communicating Mathematics in The Digital Era, pp. 183–197. A. K. Peters, Ltd. (2008)

    Google Scholar 

  19. Quaresma, P., Janičić, P.: Geothms – a Web System for Euclidean Constructive Geometry. Electronic Notes in Theoretical Computer Science 174(2), 35–48 (2007)

    Article  MATH  Google Scholar 

  20. Richter-Gebert, J., Kortenkamp, U.: The Interactive Geometry Software Cinderella. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  21. Sutcliffe, G.: The TPTP problem library and associated infrastructure. Jounal of Automated Reasoning 43(4), 337–362 (2009)

    Article  MATH  Google Scholar 

  22. Wang, D.: GEOTHER 1.1: Handling and Proving Geometric Theorems Automatically. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 194–215. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  23. Wilson, S., Fleuriot, J.: Combining dynamic geometry, automated geometry theorem proving and diagrammatic proofs. In: Proceedings of the European Joint Conferences on Theory and Practice of Software (ETAPS) Satellite Workshop on User Interfaces for Theorem Provers (UITP). Springer, Heidelberg (2005)

    Google Scholar 

  24. Wu, W.T.: The characteristic set method and its application. In: Gao, X.S., Wang, D. (eds.) Mathematics Mechanization and Applications, pp. 3–41. Academic Press, San Diego (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CISUC, Department of Mathematics, University of Coimbra, 3001-454, Coimbra, Portugal

    Pedro Quaresma

Authors
  1. Pedro Quaresma
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LSIIT, Pôle API, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cédex, France

    Pascal Schreck  & Julien Narboux  & 

  2. Technische Universität München, Zentrum Mathematik (M10), Lehrstuhl für Geometrie und Visualisierung, Boltzmannstraße 3, 85748, Garching, Germany

    Jürgen Richter-Gebert

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Quaresma, P. (2011). Thousands of Geometric Problems for Geometric Theorem Provers (TGTP). In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds) Automated Deduction in Geometry. ADG 2010. Lecture Notes in Computer Science(), vol 6877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25070-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25070-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25069-9

  • Online ISBN: 978-3-642-25070-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation