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