Consider the following premises. forall x: R_3(x) -> U(x). forall x: R_3(x) or ~U(x). exists x: R_3(x). Can we infer forall x: ~U(x) from them?
 From forall x: R_3(x) or ~U(x) we can infer forall x: U(x) -> R_3(x). From forall x: R_3(x) -> U(x), forall x: U(x) -> R_3(x) we can infer forall x: R_3(x) <-> U(x). From forall x: R_3(x) <-> U(x) we can infer forall x: R_3(x) -> U(x). Finally, from forall x: R_3(x) -> U(x), exists x: R_3(x) we can infer exists x: U(x), which contradicts forall x: ~U(x). Therefore, the answer is no.