A. D. Alexandrov's problem for CAT(0)-spaces

We solve the well-known problem by A. D. Alexandrov for nonpositively curved spaces. Let $X$ be a geodesically complete locally compact space nonpositively curved in the sense of Alexandrov and connected at infinity. The main theorem reads as follows: Each bijection $f\colon X\to X$ such that f and the inverse $f^{-1}$ of f preserve distance 1 is an isometry of $X$.