Consider the following premises. forall x: Q_2(x) <-> W(x). exists x: ~W(x). forall x: R_4(x) -> Q_2(x). forall x: Q_2(x) -> R_4(x). Can we infer forall x: R_4(x) from them?
 From forall x: Q_2(x) <-> W(x), exists x: ~W(x) we can infer exists x: ~Q_2(x). From forall x: Q_2(x) -> R_4(x), forall x: R_4(x) -> Q_2(x) we can infer forall x: Q_2(x) <-> R_4(x). Finally, from forall x: Q_2(x) <-> R_4(x), exists x: ~Q_2(x) we can infer exists x: ~R_4(x), which contradicts forall x: R_4(x). Therefore, the answer is no.