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

Abstract

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 computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving some complex proofs.