Consider the following premises. exists x_11: P_11(x_11) -> R_6(x_11). forall x_11: P_11(x_11) or ~Q_11(x_11). forall x_11: Q_11(x_11) and Q_3(x_11). Can we infer forall x_11: ~R_6(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) or ~Q_11(x_11) we can infer forall x_11: Q_11(x_11) -> P_11(x_11) via universal rewriting. From forall x_11: Q_11(x_11) -> P_11(x_11), exists x_11: P_11(x_11) -> R_6(x_11) we can infer exists x_11: Q_11(x_11) -> R_6(x_11) via existential transitivity. From forall x_11: Q_11(x_11) and Q_3(x_11) we can infer forall x_11: Q_11(x_11) via universal simplification. Finally, from exists x_11: Q_11(x_11) -> R_6(x_11), forall x_11: Q_11(x_11) we can infer exists x_11: R_6(x_11) via existential modus ponens, which contradicts forall x_11: ~R_6(x_11). Therefore, the answer is no.