Consider the following premises. S(a_4) -> w_1. ~w_1. forall z_3: S(z_3) <-> R(z_3). Can we infer ~R(a_4) from them?
 From forall z_3: S(z_3) <-> R(z_3) we can infer S(a_4) <-> R(a_4). From S(a_4) -> w_1, ~w_1 we can infer ~S(a_4). Finally, from S(a_4) <-> R(a_4), ~S(a_4) we can infer ~R(a_4). Therefore, the answer is yes.