  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 $n \times n$ 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
complex proofs.
