Consider the following premises. P_2(c_3) -> q. u -> ~q. forall z: P_2(z). Can we infer ~u from them?
 From forall z: P_2(z) we can infer P_2(c_3). From P_2(c_3) -> q, P_2(c_3) we can infer q. Finally, from u -> ~q, q we can infer ~u. Therefore, the answer is yes.