Consider the following premises. Q_8(j_4) -> ~p. forall x_8: P_8(x_8) -> Q_8(x_8). p. forall x_8: Q_8(x_8) -> P_8(x_8). Can we infer P_8(j_4) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> P_8(x_8) we can infer forall x_8: P_8(x_8) <-> Q_8(x_8) via universal biconditional introduction. From forall x_8: P_8(x_8) <-> Q_8(x_8) we can infer P_8(j_4) <-> Q_8(j_4) via universal instantiation. From Q_8(j_4) -> ~p, p we can infer ~Q_8(j_4) via modus tollens. Finally, from P_8(j_4) <-> Q_8(j_4), ~Q_8(j_4) we can infer ~P_8(j_4) via biconditional elimination, which contradicts P_8(j_4). Therefore, the answer is no.