Nowadays, the modern economy critically requires reliable yet cheap protection solutions against product counterfeiting for the mass market. Copy detection patterns (CDP) are considered as such solution in several applications. It is assumed that being printed at the maximum achievable limit of a printing resolution of an industrial printer with the smallest symbol size 1x1 elements, the CDP cannot be copied with sufficient accuracy and thus are unclonable. In this paper, we challenge this hypothesis and consider a copy attack against the CDP based on machine learning. The experimental based on samples produced on two industrial printers demonstrate that simple detection metrics used in the CDP authentication cannot reliably distinguish the original CDP from their fakes. Thus, the paper calls for a need of careful reconsideration of CDP cloneability and search for new authentication techniques and CDP optimization because of the current attack.