Proving Correctness of a KRK Chess Endgame Strategy by SAT-based Constraint Solving

Chess endgame strategies in a concise and intuitive way describe the rules the player should follow to ensure win (or draw). Endgame strategies are useful for both computer and human players. Their correctness can be proved in several ways, and in this paper we present one of them: computer assisted proof based on reduction to propositional logic, more precisely to SAT. We focus on a strategy for the KRK endgame and reduction to SAT is performed by using a constraint solving system URSA. The relevant lemmas produced SAT instances with hundreds of thousands variables and clauses, but URSA still successfully handled them. As we are aware of, this is the first computer-assisted high-level proof of a correctness of a strategy for some chess endgame. The presented methodology can be applied to other endgames and other games as well. Therefore, the point of this paper is not only presenting a proof of correctness of an endgame strategy, but also presenting a new methodology for computer-assisted reasoning about chess problems.