Consider the following premises. forall z: W(z) -> T_1(z). forall z: W(z). exists z: S(z). forall z: T_1(z) -> T_2(z). forall z: T_2(z) -> P_3(z). Can we infer exists z: P_3(z) and S(z) from them?
 From forall z: W(z) -> T_1(z), forall z: T_1(z) -> T_2(z) we can infer forall z: W(z) -> T_2(z). From forall z: W(z) -> T_2(z), forall z: W(z) we can infer forall z: T_2(z). From forall z: T_2(z) -> P_3(z), forall z: T_2(z) we can infer forall z: P_3(z). Finally, from forall z: P_3(z), exists z: S(z) we can infer exists z: P_3(z) and S(z). Therefore, the answer is yes.