Consider the following premises. forall x: R_2(x) or T(x). forall x: T(x) <-> U(x). forall x: P(x) -> U(x). exists x: ~R_2(x) or P(x). Can we infer exists x: U(x) from them?
 From forall x: R_2(x) or T(x), exists x: ~R_2(x) or P(x) we can infer exists x: T(x) or P(x). From forall x: T(x) <-> U(x) we can infer forall x: T(x) -> U(x). Finally, from forall x: T(x) -> U(x), forall x: P(x) -> U(x), exists x: T(x) or P(x) we can infer exists x: U(x). Therefore, the answer is yes.