Consider the following premises. ~p_7. p_7 or ~Q_2(b_4). forall y: Q_2(y) <-> R_1(y). Can we infer ~R_1(b_4) from them? If possible, name the inference rules being used at each step.
 From forall y: Q_2(y) <-> R_1(y) we can infer Q_2(b_4) <-> R_1(b_4) via universal instantiation. From p_7 or ~Q_2(b_4) we can infer Q_2(b_4) -> p_7 via rewriting. From Q_2(b_4) -> p_7, ~p_7 we can infer ~Q_2(b_4) via modus tollens. Finally, from Q_2(b_4) <-> R_1(b_4), ~Q_2(b_4) we can infer ~R_1(b_4) via biconditional elimination. Therefore, the answer is yes.