Consider the following premises. forall x_8: ~P_8(x_8). forall x_8: P_8(x_8) <-> Q_8(x_8). Q_8(a_3) or w_4. Can we infer ~w_4 from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) <-> Q_8(x_8), forall x_8: ~P_8(x_8) we can infer forall x_8: ~Q_8(x_8) via universal biconditional elimination. From forall x_8: ~Q_8(x_8) we can infer ~Q_8(a_3) via universal instantiation. Finally, from Q_8(a_3) or w_4, ~Q_8(a_3) we can infer w_4 via disjunctive syllogism, which contradicts ~w_4. Therefore, the answer is no.