Consider the following premises. ~R(i). p <-> P_3(i). forall x_1: P_3(x_1) <-> R(x_1). Can we infer ~p from them?
 From forall x_1: P_3(x_1) <-> R(x_1) we can infer P_3(i) <-> R(i). From P_3(i) <-> R(i), ~R(i) we can infer ~P_3(i). Finally, from p <-> P_3(i), ~P_3(i) we can infer ~p. Therefore, the answer is yes.