Consider the following premises. forall x: U_1(x) -> T(x). forall x: ~P_1(x). forall x: T(x) -> U_1(x). exists x: T(x) <-> P_1(x). Can we infer exists x: ~U_1(x) from them?
 From forall x: U_1(x) -> T(x), forall x: T(x) -> U_1(x) we can infer forall x: U_1(x) <-> T(x). From exists x: T(x) <-> P_1(x), forall x: ~P_1(x) we can infer exists x: ~T(x). Finally, from forall x: U_1(x) <-> T(x), exists x: ~T(x) we can infer exists x: ~U_1(x). Therefore, the answer is yes.