Consider the following premises. P_9(a_8) -> q_3. forall x_9: P_9(x_9). Q_9(a_8) <-> q_3. Can we infer ~q_3 from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) we can infer forall x_9: P_9(x_9) or Q_9(x_9) via universal addition. From forall x_9: P_9(x_9) or Q_9(x_9) we can infer P_9(a_8) or Q_9(a_8) via universal instantiation. From Q_9(a_8) <-> q_3 we can infer Q_9(a_8) -> q_3 via biconditional elimination. Finally, from P_9(a_8) -> q_3, Q_9(a_8) -> q_3, P_9(a_8) or Q_9(a_8) we can infer q_3 via disjunction elimination, which contradicts ~q_3. Therefore, the answer is no.