Consider the following premises. forall x_12: Q_12(x_12) -> P_12(x_12). ~P_12(g). ~Q_12(g) -> s_4. forall x_12: P_12(x_12) -> Q_12(x_12). Can we infer s_4 from them? If possible, name the inference rules being used at each step.
 From forall x_12: P_12(x_12) -> Q_12(x_12), forall x_12: Q_12(x_12) -> P_12(x_12) we can infer forall x_12: P_12(x_12) <-> Q_12(x_12) via universal biconditional introduction. From forall x_12: P_12(x_12) <-> Q_12(x_12) we can infer P_12(g) <-> Q_12(g) via universal instantiation. From P_12(g) <-> Q_12(g), ~P_12(g) we can infer ~Q_12(g) via biconditional elimination. Finally, from ~Q_12(g) -> s_4, ~Q_12(g) we can infer s_4 via modus ponens. Therefore, the answer is yes.