Consider the following premises. forall z_3: T_3(z_3) -> S(z_3). forall z_3: S(z_3) -> T_3(z_3). forall z_3: S(z_3) or ~T_3(z_3). Can we infer forall z_3: S(z_3) -> T_3(z_3) from them?
That is one of the premises. Therefore, the answer is yes.