Consider the following premises. forall z: T_2(z) -> S_4(z). forall z: T_2(z) -> T(z). forall z: S_4(z) -> T_2(z). exists z: P_4(z) -> S_4(z). Can we infer exists z: P_4(z) -> T(z) from them?
 From forall z: T_2(z) -> S_4(z), forall z: S_4(z) -> T_2(z) we can infer forall z: T_2(z) <-> S_4(z). From forall z: T_2(z) <-> S_4(z) we can infer forall z: S_4(z) -> T_2(z). From forall z: S_4(z) -> T_2(z), forall z: T_2(z) -> T(z) we can infer forall z: S_4(z) -> T(z). Finally, from exists z: P_4(z) -> S_4(z), forall z: S_4(z) -> T(z) we can infer exists z: P_4(z) -> T(z). Therefore, the answer is yes.