Consider the following premises. exists x: U_3(x) or ~T(x). forall x: U(x) or T(x). forall x: U(x) <-> U_3(x). Can we infer exists x: U_3(x) from them?
 From exists x: U_3(x) or ~T(x) we can infer exists x: T(x) -> U_3(x). From forall x: U(x) <-> U_3(x) we can infer forall x: U(x) -> U_3(x). Finally, from forall x: U(x) -> U_3(x), exists x: T(x) -> U_3(x), forall x: U(x) or T(x) we can infer exists x: U_3(x). Therefore, the answer is yes.