Consider the following premises. forall x: ~T_3(x). forall x: T(x) <-> U_1(x). forall x: U_1(x) <-> T_3(x). Can we infer exists x: T(x) from them?
 From forall x: U_1(x) <-> T_3(x), forall x: ~T_3(x) we can infer forall x: ~U_1(x). Finally, from forall x: T(x) <-> U_1(x), forall x: ~U_1(x) we can infer forall x: ~T(x), which contradicts exists x: T(x). Therefore, the answer is no.