Consider the following premises. forall z: W(z) -> U_2(z). forall z: T_2(z) <-> U_2(z). forall z: T_2(z) -> R(z). exists z: R(z) -> W(z). Can we infer exists z: W(z) -> T_2(z) from them?
 From forall z: T_2(z) <-> U_2(z) we can infer forall z: U_2(z) -> T_2(z). From forall z: T_2(z) -> R(z), exists z: R(z) -> W(z) we can infer exists z: T_2(z) -> W(z). From forall z: W(z) -> U_2(z), forall z: U_2(z) -> T_2(z) we can infer forall z: W(z) -> T_2(z). From forall z: W(z) -> T_2(z), exists z: T_2(z) -> W(z) we can infer exists z: W(z) <-> T_2(z). Finally, from exists z: W(z) <-> T_2(z) we can infer exists z: W(z) -> T_2(z). Therefore, the answer is yes.