Consider the following premises. forall x_8: Q_1(x_8) -> P(x_8). forall x_8: R(x_8) -> Q_1(x_8). exists x_8: P(x_8) <-> R(x_8). Can we infer forall x_8: ~(P(x_8) <-> R(x_8)) from them? If possible, name the inference rules being used at each step.
 From exists x_8: P(x_8) <-> R(x_8) we can infer exists x_8: P(x_8) -> R(x_8) via existential biconditional elimination. From forall x_8: R(x_8) -> Q_1(x_8), forall x_8: Q_1(x_8) -> P(x_8) we can infer forall x_8: R(x_8) -> P(x_8) via universal transitivity. Finally, from exists x_8: P(x_8) -> R(x_8), forall x_8: R(x_8) -> P(x_8) we can infer exists x_8: P(x_8) <-> R(x_8) via existential biconditional introduction, which contradicts forall x_8: ~(P(x_8) <-> R(x_8)). Therefore, the answer is no.