Consider the following premises. forall z: S_4(z) <-> S(z). forall z: ~S_4(z). exists z: S(z) or R_4(z). Can we infer exists z: R_4(z) from them?
 From forall z: S_4(z) <-> S(z), forall z: ~S_4(z) we can infer forall z: ~S(z). Finally, from exists z: S(z) or R_4(z), forall z: ~S(z) we can infer exists z: R_4(z). Therefore, the answer is yes.