In this talk, we will investigate the lengths of proofs in the usual Gentzen calculus for the substructural logic FL_e. We will present a sequence of tautologies of the system and show any short proof for them implies a short proof for Hrubes' formulas for intuitionistic logic, hence the exponential lower bound follows. We will then conclude that this lower bound also applies to any proof system for a logic between FL_e and IPC.