Consider the following premises. forall z: R_2(z) <-> W_3(z). forall z: W_3(z) -> U(z). forall z: U(z) -> W_3(z). forall z: ~U(z). Can we infer forall z: ~R_2(z) from them?
 From forall z: W_3(z) -> U(z), forall z: U(z) -> W_3(z) we can infer forall z: W_3(z) <-> U(z). From forall z: W_3(z) <-> U(z), forall z: ~U(z) we can infer forall z: ~W_3(z). From forall z: R_2(z) <-> W_3(z) we can infer forall z: R_2(z) -> W_3(z). Finally, from forall z: R_2(z) -> W_3(z), forall z: ~W_3(z) we can infer forall z: ~R_2(z). Therefore, the answer is yes.