Can you decide equivalence for monotone Boolean expressions that do not contain negation in PTIME?
Corollary 3.5 of [BHR84] shows that the problem is coNP-complete.

[BHR84] P. A. Bloniarz, H. B. Hunt, III, and D. J. Rosenkrantz.  Algebraic structures with hard equivalence and minimization problems.  Journal of the ACM, 31(4):879–904, Oct. 1984.  http://dx.doi.org/10.1145/1634.1639