Consider the following premises. forall x_9: P_9(x_9). P_9(a_8) -> t. Q_9(a_8) -> w. w -> t. Can we infer ~t 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) -> w, w -> t we can infer Q_9(a_8) -> t via transitivity. Finally, from P_9(a_8) -> t, Q_9(a_8) -> t, P_9(a_8) or Q_9(a_8) we can infer t via disjunction elimination, which contradicts ~t. Therefore, the answer is no.