Consider the following premises. R_4(c_1). forall x_1: S_1(x_1) -> ~R_4(x_1). Can we infer exists x_1: ~S_1(x_1) from them?
 From R_4(c_1) we can infer exists x_1: R_4(x_1). Finally, from forall x_1: S_1(x_1) -> ~R_4(x_1), exists x_1: R_4(x_1) we can infer exists x_1: ~S_1(x_1). Therefore, the answer is yes.