Consider the following premises. forall x_12: P_6(x_12) or ~Q_6(x_12). forall x_12: S(x_12) <-> R_2(x_12). forall x_12: S(x_12) -> Q_6(x_12). Can we infer forall x_12: R_2(x_12) -> P_6(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: S(x_12) <-> R_2(x_12) we can infer forall x_12: R_2(x_12) -> S(x_12) via universal biconditional elimination. From forall x_12: P_6(x_12) or ~Q_6(x_12) we can infer forall x_12: Q_6(x_12) -> P_6(x_12) via universal rewriting. From forall x_12: S(x_12) -> Q_6(x_12), forall x_12: Q_6(x_12) -> P_6(x_12) we can infer forall x_12: S(x_12) -> P_6(x_12) via universal transitivity. Finally, from forall x_12: R_2(x_12) -> S(x_12), forall x_12: S(x_12) -> P_6(x_12) we can infer forall x_12: R_2(x_12) -> P_6(x_12) via universal transitivity. Therefore, the answer is yes.