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