Consider the following premises. exists y_4: S(y_4) <-> R(y_4). forall y_4: S(y_4) <-> U(y_4). Can we infer forall y_4: ~(U(y_4) -> R(y_4)) from them?
 From exists y_4: S(y_4) <-> R(y_4) we can infer exists y_4: S(y_4) -> R(y_4). Finally, from forall y_4: S(y_4) <-> U(y_4) we can infer forall y_4: U(y_4) -> S(y_4), which contradicts forall y_4: ~(U(y_4) -> R(y_4)). Therefore, the answer is no.