Consider the following premises. forall x_6: Q_4(x_6) -> P(x_6). forall x_6: Q_6(x_6) or Q_4(x_6). forall x_6: P(x_6) or ~Q_6(x_6). exists x_6: P(x_6) -> R_2(x_6). Can we infer forall x_6: ~R_2(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P(x_6) or ~Q_6(x_6) we can infer forall x_6: Q_6(x_6) -> P(x_6) via universal rewriting. From forall x_6: Q_6(x_6) -> P(x_6), forall x_6: Q_4(x_6) -> P(x_6), forall x_6: Q_6(x_6) or Q_4(x_6) we can infer forall x_6: P(x_6) via universal disjunction elimination. Finally, from exists x_6: P(x_6) -> R_2(x_6), forall x_6: P(x_6) we can infer exists x_6: R_2(x_6) via existential modus ponens, which contradicts forall x_6: ~R_2(x_6). Therefore, the answer is no.