Consider the following premises. forall x_10: Q_6(x_10) -> T(x_10). forall x_10: P_10(x_10) or Q_6(x_10). forall x_10: P_10(x_10) -> ~Q_10(x_10). forall x_10: Q_10(x_10). forall x_10: Q(x_10). Can we infer forall x_10: T(x_10) and Q(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> ~Q_10(x_10), forall x_10: Q_10(x_10) we can infer forall x_10: ~P_10(x_10) via universal modus tollens. From forall x_10: P_10(x_10) or Q_6(x_10), forall x_10: ~P_10(x_10) we can infer forall x_10: Q_6(x_10) via universal disjunctive syllogism. From forall x_10: Q_6(x_10) -> T(x_10), forall x_10: Q_6(x_10) we can infer forall x_10: T(x_10) via universal modus ponens. Finally, from forall x_10: T(x_10), forall x_10: Q(x_10) we can infer forall x_10: T(x_10) and Q(x_10) via universal conjunction. Therefore, the answer is yes.