Automated Theorem Proving in Incidence Geometry – A Bracket Algebra Based Elimination Method

Abstract. In this paper we propose a bracket algebra based elimination method for automated generation of readable proofs for theorems in incidence geometry. This method is based on two techniques, the first being some heuristic elimination rules which improve the performance of the area method of Chou et al. (1994) without introduc-ing signed length ratios, the second being a simplification technique called contraction, which reduces the size of bracket polynomials. More than twenty theorems in incidence geometry have been proved, for which short proofs are produced swiftly. An interesting phenomenon is that a proof composed of polynomials of at most two terms can always be found for any of these theorems, similar to that by the final biquadratic polynomial method of Richter-Gebert (1995). 1