The following three statements cannot be simultaneously true: (a) formula_34 has a short proof in a some proof system; (b) such proof system has feasible interpolation; (c) the interpolant circuit solves a computationally hard problem. It is clear that (a) and (b) imply that there is a small interpolant circuit, which is in contradiction with (c). Such relation allows to turn proof length upper bounds into lower bounds on computations, and dually to turn efficient interpolation algorithms into lower bounds on proof length.