Consider the following premises. forall z_4: R(z_4) -> W_1(z_4). R(a_7) -> ~r. forall z_4: W_1(z_4) -> R(z_4). r. Can we infer W_1(a_7) from them? If possible, name the inference rules being used at each step.
 From forall z_4: R(z_4) -> W_1(z_4), forall z_4: W_1(z_4) -> R(z_4) we can infer forall z_4: R(z_4) <-> W_1(z_4) via universal biconditional introduction. From forall z_4: R(z_4) <-> W_1(z_4) we can infer R(a_7) <-> W_1(a_7) via universal instantiation. From R(a_7) -> ~r, r we can infer ~R(a_7) via modus tollens. Finally, from R(a_7) <-> W_1(a_7), ~R(a_7) we can infer ~W_1(a_7) via biconditional elimination, which contradicts W_1(a_7). Therefore, the answer is no.