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