Consider the following premises. forall x_16: T(x_16). forall x_16: ~Q_16(x_16). forall x_16: P_9(x_16) -> Q_9(x_16). forall x_16: P_9(x_16) or W(x_16). forall x_16: Q_9(x_16) -> P_16(x_16). forall x_16: P_16(x_16) <-> Q_16(x_16). Can we infer forall x_16: T(x_16) and W(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) <-> Q_16(x_16), forall x_16: ~Q_16(x_16) we can infer forall x_16: ~P_16(x_16) via universal biconditional elimination. From forall x_16: P_9(x_16) -> Q_9(x_16), forall x_16: Q_9(x_16) -> P_16(x_16) we can infer forall x_16: P_9(x_16) -> P_16(x_16) via universal transitivity. From forall x_16: P_9(x_16) -> P_16(x_16), forall x_16: ~P_16(x_16) we can infer forall x_16: ~P_9(x_16) via universal modus tollens. From forall x_16: P_9(x_16) or W(x_16), forall x_16: ~P_9(x_16) we can infer forall x_16: W(x_16) via universal disjunctive syllogism. Finally, from forall x_16: T(x_16), forall x_16: W(x_16) we can infer forall x_16: T(x_16) and W(x_16) via universal conjunction. Therefore, the answer is yes.