Will the HP LaserJet Pro 4001-4004 work with third-party or non-HP toner cartridges?

This printer is intended to work only with cartridges that have a new or reused HP chip, and it uses dynamic security measures to block cartridges using a non-HP chip. Periodic firmware updates will maintain the effectiveness of these measures and block cartridges that previously worked. A reused HP chip does enable the use of reused, remanufactured, and refilled cartridges. More information is available at http://www.hp.com/learn/ds. (Page 1)