Complexity of Intuitionistic Predicate Logic with One Variable Maarten Marx The validity problem for intuitionistic predicate logic with one variable is complete for the class of co--nexptime problems. This result holds for both constant and for expanding domains. The upper bound follows because every refutable formula can be refuted in a Kripke model whose size is exponential in the length of the formula. The lower bound is obtained by an encoding of the square tiling problem. Keyword(s): Intuitionistic logic, complexity, nexptime