Consider the following premises. forall x_8: Q_8(x_8) or Q_6(x_8). forall x_8: Q_6(x_8) -> Q_4(x_8). forall x_8: Q_4(x_8) or ~Q_8(x_8). exists x_8: Q_2(x_8). Can we infer forall x_8: ~Q_4(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: Q_4(x_8) or ~Q_8(x_8) we can infer forall x_8: Q_8(x_8) -> Q_4(x_8) via universal rewriting. Finally, from forall x_8: Q_8(x_8) -> Q_4(x_8), forall x_8: Q_6(x_8) -> Q_4(x_8), forall x_8: Q_8(x_8) or Q_6(x_8) we can infer forall x_8: Q_4(x_8) via universal disjunction elimination, which contradicts forall x_8: ~Q_4(x_8). Therefore, the answer is no.