Consider the following premises. exists z: W(z). forall z: P(z) <-> S_1(z). forall z: S_1(z). Can we infer exists z: P(z) and W(z) from them?
 From forall z: P(z) <-> S_1(z) we can infer forall z: S_1(z) -> P(z). From forall z: S_1(z) -> P(z), forall z: S_1(z) we can infer forall z: P(z). Finally, from forall z: P(z), exists z: W(z) we can infer exists z: P(z) and W(z). Therefore, the answer is yes.