Consider the following premises. forall x: W(x) -> P_2(x). forall x: ~P_2(x). exists x: R(x) -> W(x). forall x: P_2(x) -> R(x). Can we infer forall x: W(x) from them?
 From forall x: P_2(x) -> R(x), exists x: R(x) -> W(x) we can infer exists x: P_2(x) -> W(x). From exists x: P_2(x) -> W(x), forall x: W(x) -> P_2(x) we can infer exists x: P_2(x) <-> W(x). Finally, from exists x: P_2(x) <-> W(x), forall x: ~P_2(x) we can infer exists x: ~W(x), which contradicts forall x: W(x). Therefore, the answer is no.