How do I protect myself from termination for not signing something that specifically says "no signature required"?

The Dipute Resolution Program at work specifically says "The submission of an application, acceptance of employment or the continuation of employment by an individual shall be deemed to be acceptance of the Dispute Resolution Program. No signature shall be required for the policy to be applicable. I didn't sign it. Now the company and specifically the HR rep are threatening to fire me stating that my signature is required for further employment. What steps can I take to protect my job? I've been with the store for 11 years but this new franchise just bought us out in February.