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