Challenging Theorem Provers with Mathematical Olympiad Problems in Solid Geometry

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 Grobner 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.