Consider the following premises. forall x_9: ~Q_9(x_9). P_9(b) or r_2. forall x_9: P_9(x_9) <-> Q_9(x_9). Can we infer r_2 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), forall x_9: ~Q_9(x_9) we can infer forall x_9: ~P_9(x_9) via universal biconditional elimination. From forall x_9: ~P_9(x_9) we can infer ~P_9(b) via universal instantiation. Finally, from P_9(b) or r_2, ~P_9(b) we can infer r_2 via disjunctive syllogism. Therefore, the answer is yes.