Consider the following premises. ~R(j) -> p. forall x_4: R(x_4) -> W(x_4). forall x_4: W(x_4) -> R(x_4). ~W(j). Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From forall x_4: W(x_4) -> R(x_4), forall x_4: R(x_4) -> W(x_4) we can infer forall x_4: W(x_4) <-> R(x_4) via universal biconditional introduction. From forall x_4: W(x_4) <-> R(x_4) we can infer W(j) <-> R(j) via universal instantiation. From W(j) <-> R(j), ~W(j) we can infer ~R(j) via biconditional elimination. Finally, from ~R(j) -> p, ~R(j) we can infer p via modus ponens, which contradicts ~p. Therefore, the answer is no.