Consider the following premises. forall x: P(x) <-> R(x). exists x: Q_4(x) or ~P(x). forall x: ~Q_4(x). Can we infer forall x: R(x) from them?
 From exists x: Q_4(x) or ~P(x) we can infer exists x: P(x) -> Q_4(x). From exists x: P(x) -> Q_4(x), forall x: ~Q_4(x) we can infer exists x: ~P(x). Finally, from forall x: P(x) <-> R(x), exists x: ~P(x) we can infer exists x: ~R(x), which contradicts forall x: R(x). Therefore, the answer is no.