Consider the following premises. s -> P_13(b). s. forall x_13: P_13(x_13) <-> Q_13(x_13). Can we infer ~Q_13(b) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) <-> Q_13(x_13) we can infer forall x_13: P_13(x_13) -> Q_13(x_13) via universal biconditional elimination. From forall x_13: P_13(x_13) -> Q_13(x_13) we can infer P_13(b) -> Q_13(b) via universal instantiation. From s -> P_13(b), P_13(b) -> Q_13(b) we can infer s -> Q_13(b) via transitivity. Finally, from s -> Q_13(b), s we can infer Q_13(b) via modus ponens, which contradicts ~Q_13(b). Therefore, the answer is no.