Consider the following premises. forall z: W_1(z). forall z: W_1(z) <-> R_2(z). exists z: W_2(z) -> ~R_2(z). Can we infer exists z: ~W_2(z) from them? If possible, name the inference rules being used at each step.
 From forall z: W_1(z) <-> R_2(z) we can infer forall z: W_1(z) -> R_2(z) via universal biconditional elimination. From forall z: W_1(z) -> R_2(z), forall z: W_1(z) we can infer forall z: R_2(z) via universal modus ponens. Finally, from exists z: W_2(z) -> ~R_2(z), forall z: R_2(z) we can infer exists z: ~W_2(z) via existential modus tollens. Therefore, the answer is yes.