Consider the following premises. forall x_8: Q_8(x_8) -> R_8(x_8). forall x_8: P_4(x_8) -> Q_8(x_8). forall x_8: P_4(x_8) or ~R_8(x_8). Can we infer P_4(j) -> R_8(j) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_4(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> R_8(x_8) we can infer forall x_8: P_4(x_8) -> R_8(x_8) via universal transitivity. From forall x_8: P_4(x_8) or ~R_8(x_8) we can infer forall x_8: R_8(x_8) -> P_4(x_8) via universal rewriting. From forall x_8: P_4(x_8) -> R_8(x_8), forall x_8: R_8(x_8) -> P_4(x_8) we can infer forall x_8: P_4(x_8) <-> R_8(x_8) via universal biconditional introduction. From forall x_8: P_4(x_8) <-> R_8(x_8) we can infer P_4(j) <-> R_8(j) via universal instantiation. Finally, from P_4(j) <-> R_8(j) we can infer P_4(j) -> R_8(j) via biconditional elimination. Therefore, the answer is yes.