Consider the following premises. U(b) -> P_2(b). ~u. forall z: P_2(z) -> U(z). P_2(b) -> u. Can we infer ~U(b) from them? If possible, name the inference rules being used at each step.
 From forall z: P_2(z) -> U(z) we can infer P_2(b) -> U(b) via universal instantiation. From U(b) -> P_2(b), P_2(b) -> U(b) we can infer U(b) <-> P_2(b) via biconditional introduction. From P_2(b) -> u, ~u we can infer ~P_2(b) via modus tollens. From U(b) <-> P_2(b) we can infer U(b) -> P_2(b) via biconditional elimination. Finally, from U(b) -> P_2(b), ~P_2(b) we can infer ~U(b) via modus tollens. Therefore, the answer is yes.