The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. The principle is important as the basis for ecological theory. On a relatively simple model we show a mechanism of indefinite coexistence of complete competitors which violates the known formulations of the competitive exclusion principle. This mechanism is based on timely recovery of limiting resources and their spatio-temporal allocation between competitors. Because of limitations of the black-box modeling there was a problem to formulate the exclusion principle correctly. Our white-box multiscale model of two-species competition is based on logical deterministic individual-based cellular automata. This approach provides an automatic deductive inference on the basis of a system of axioms, and gives a direct insight into mechanisms of the studied system. It is one of the most promising methods of artificial intelligence. We reformulate and generalize the competitive exclusion principle and explain why this formulation provides a solution of the biodiversity paradox. In addition, we propose a principle of competitive coexistence.