Consider the following premises. t <-> P_13(j). ~t. forall x_13: P_13(x_13) -> Q_13(x_13). R_13(j) -> P_13(j). forall x_13: Q_13(x_13) -> R_13(x_13). Can we infer R_13(j) 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), forall x_13: Q_13(x_13) -> R_13(x_13) we can infer forall x_13: P_13(x_13) -> R_13(x_13) via universal transitivity. From forall x_13: P_13(x_13) -> R_13(x_13) we can infer P_13(j) -> R_13(j) via universal instantiation. From R_13(j) -> P_13(j), P_13(j) -> R_13(j) we can infer R_13(j) <-> P_13(j) via biconditional introduction. From t <-> P_13(j), ~t we can infer ~P_13(j) via biconditional elimination. Finally, from R_13(j) <-> P_13(j), ~P_13(j) we can infer ~R_13(j) via biconditional elimination, which contradicts R_13(j). Therefore, the answer is no.