Consider the following premises. exists x: S(x) <-> U_1(x). forall x: ~S(x). forall x: U_1(x) or ~T_1(x). Can we infer exists x: ~T_1(x) from them?
 From exists x: S(x) <-> U_1(x), forall x: ~S(x) we can infer exists x: ~U_1(x). From forall x: U_1(x) or ~T_1(x) we can infer forall x: T_1(x) -> U_1(x). Finally, from forall x: T_1(x) -> U_1(x), exists x: ~U_1(x) we can infer exists x: ~T_1(x). Therefore, the answer is yes.