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