Consider the following premises. forall z_3: S(z_3) <-> T(z_3). exists z_3: Q(z_3) -> T(z_3). forall z_3: Q(z_3) or ~T_4(z_3). forall z_3: S(z_3) -> T_4(z_3). Can we infer exists z_3: T(z_3) <-> T_4(z_3) from them?
 From forall z_3: Q(z_3) or ~T_4(z_3) we can infer forall z_3: T_4(z_3) -> Q(z_3). From forall z_3: S(z_3) <-> T(z_3) we can infer forall z_3: T(z_3) -> S(z_3). From forall z_3: T(z_3) -> S(z_3), forall z_3: S(z_3) -> T_4(z_3) we can infer forall z_3: T(z_3) -> T_4(z_3). From forall z_3: T_4(z_3) -> Q(z_3), exists z_3: Q(z_3) -> T(z_3) we can infer exists z_3: T_4(z_3) -> T(z_3). Finally, from forall z_3: T(z_3) -> T_4(z_3), exists z_3: T_4(z_3) -> T(z_3) we can infer exists z_3: T(z_3) <-> T_4(z_3). Therefore, the answer is yes.