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