Consider the following premises. w -> ~Q_4(a_3). forall x_3: Q_4(x_3) and S(x_3). Can we infer ~w from them?
 From forall x_3: Q_4(x_3) and S(x_3) we can infer Q_4(a_3) and S(a_3). From Q_4(a_3) and S(a_3) we can infer Q_4(a_3). Finally, from w -> ~Q_4(a_3), Q_4(a_3) we can infer ~w. Therefore, the answer is yes.