Consider the following premises. forall y_2: ~P(y_2). u -> P(a_3). u or w_3. Can we infer ~w_3 from them?
 From forall y_2: ~P(y_2) we can infer ~P(a_3). From u -> P(a_3), ~P(a_3) we can infer ~u. Finally, from u or w_3, ~u we can infer w_3, which contradicts ~w_3. Therefore, the answer is no.