Consider the following premises. exists x: U_2(x) <-> T(x). forall x: P(x). forall x: U_2(x) -> ~P(x). Can we infer exists x: ~T(x) from them?
 From forall x: U_2(x) -> ~P(x), forall x: P(x) we can infer forall x: ~U_2(x). Finally, from exists x: U_2(x) <-> T(x), forall x: ~U_2(x) we can infer exists x: ~T(x). Therefore, the answer is yes.