Consider the following premises. forall x_13: P_13(x_13) -> Q_9(x_13). forall x_13: P_13(x_13). forall x_13: Q_13(x_13). forall x_13: Q_9(x_13) -> T_2(x_13). Can we infer exists x_13: ~(T_2(x_13) or P(x_13)) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13), forall x_13: Q_13(x_13) we can infer forall x_13: P_13(x_13) and Q_13(x_13) via universal conjunction. From forall x_13: P_13(x_13) -> Q_9(x_13), forall x_13: Q_9(x_13) -> T_2(x_13) we can infer forall x_13: P_13(x_13) -> T_2(x_13) via universal transitivity. From forall x_13: P_13(x_13) and Q_13(x_13) we can infer forall x_13: P_13(x_13) via universal simplification. From forall x_13: P_13(x_13) -> T_2(x_13), forall x_13: P_13(x_13) we can infer forall x_13: T_2(x_13) via universal modus ponens. Finally, from forall x_13: T_2(x_13) we can infer forall x_13: T_2(x_13) or P(x_13) via universal addition, which contradicts exists x_13: ~(T_2(x_13) or P(x_13)). Therefore, the answer is no.