Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture – correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to n× n board (for natural n greater than 3). We demonstrate that different approaches for computerbased theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs.