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Challenging Theorem Provers with Mathematical Olympiad Problems in Solid Geometry

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Abstract

Mathematical Olympiad problems can be used to evaluate the performance of theorem provers. In the encyclopedia (Wu et al. in The Dictionary of International Mathematical Olympiads, Volume of Geometry. Hebei Children Press, Shijiazhuang, 2012) there are 207 Mathematical Olympiad contest problems in solid geometry collected around the world and ranging over one century, among which 97 problems can be used to test algebraic provers of equality type. Three general-purpose theorem proving methods are used in the test: the characteristic set method, the Gröbner basis method, and the vector algebra method. 91 out of the 97 problems are proved by the provers, and some contest problems are found to need additional specification to be correct. The proving efficiency and geometric interpretability of the additional non-degeneracy conditions for the 91 problems by the three provers are compared.

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Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Zhong Guan Cun East Road 55 South Building, Haidian, Beijing, 100190, China

    Changpeng Shao, Hongbo Li & Lei Huang

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  1. Changpeng Shao
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  2. Hongbo Li
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  3. Lei Huang
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Correspondence to Hongbo Li.

Additional information

Partially supported by NSFC project 2011CB302404.

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Shao, C., Li, H. & Huang, L. Challenging Theorem Provers with Mathematical Olympiad Problems in Solid Geometry. Math.Comput.Sci. 10, 75–96 (2016). https://doi.org/10.1007/s11786-016-0256-2

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  • DOI: https://doi.org/10.1007/s11786-016-0256-2

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