Consider the following premises. exists x: R(x) <-> W_3(x). forall x: R(x) -> ~R_1(x). forall x: R_1(x). Can we infer forall x: W_3(x) from them?
 From forall x: R(x) -> ~R_1(x), forall x: R_1(x) we can infer forall x: ~R(x). Finally, from exists x: R(x) <-> W_3(x), forall x: ~R(x) we can infer exists x: ~W_3(x), which contradicts forall x: W_3(x). Therefore, the answer is no.