Consider the following premises. ~w. forall x: P(x). w <-> u_4. Can we infer ~u_4 and P(e) from them?
 From forall x: P(x) we can infer P(e). From w <-> u_4, ~w we can infer ~u_4. Finally, from ~u_4, P(e) we can infer ~u_4 and P(e). Therefore, the answer is yes.