Consider the following premises. p_1 <-> w. p_1 -> P_1(a_10). forall x_3: ~P_1(x_3). Can we infer ~w from them?
 From forall x_3: ~P_1(x_3) we can infer ~P_1(a_10). From p_1 -> P_1(a_10), ~P_1(a_10) we can infer ~p_1. Finally, from p_1 <-> w, ~p_1 we can infer ~w. Therefore, the answer is yes.