A feasible interpolation for random resolution

Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen clauses (modulo a technical condition). We show how to apply the general feasible interpolation theorem for semantic derivations of Krajicek (JSL, 1997) to random resolution. As a consequence we get a lower bound for random resolution refutations of the clique-coloring formulas.