Consider the following premises. forall x_9: P_6(x_9) or Q_6(x_9). forall x_9: Q_9(x_9) -> R_9(x_9). forall x_9: ~P_6(x_9). exists x_9: T_4(x_9) -> Q_9(x_9). forall x_9: Q_6(x_9) -> T_4(x_9). Can we infer forall x_9: ~R_9(x_9) from them? If possible, name the inference rules being used at each step.
 From exists x_9: T_4(x_9) -> Q_9(x_9), forall x_9: Q_9(x_9) -> R_9(x_9) we can infer exists x_9: T_4(x_9) -> R_9(x_9) via existential transitivity. From forall x_9: P_6(x_9) or Q_6(x_9), forall x_9: ~P_6(x_9) we can infer forall x_9: Q_6(x_9) via universal disjunctive syllogism. From forall x_9: Q_6(x_9) -> T_4(x_9), forall x_9: Q_6(x_9) we can infer forall x_9: T_4(x_9) via universal modus ponens. Finally, from exists x_9: T_4(x_9) -> R_9(x_9), forall x_9: T_4(x_9) we can infer exists x_9: R_9(x_9) via existential modus ponens, which contradicts forall x_9: ~R_9(x_9). Therefore, the answer is no.