Consider the following premises. exists x_11: R_3(x_11) or ~Q(x_11). forall x_11: P_6(x_11) -> R_3(x_11). forall x_11: P_6(x_11) or ~W_2(x_11). forall x_11: W_2(x_11) or Q(x_11). Can we infer forall x_11: ~R_3(x_11) from them? If possible, name the inference rules being used at each step.
 From exists x_11: R_3(x_11) or ~Q(x_11) we can infer exists x_11: Q(x_11) -> R_3(x_11) via existential rewriting. From forall x_11: P_6(x_11) or ~W_2(x_11) we can infer forall x_11: W_2(x_11) -> P_6(x_11) via universal rewriting. From forall x_11: W_2(x_11) -> P_6(x_11), forall x_11: P_6(x_11) -> R_3(x_11) we can infer forall x_11: W_2(x_11) -> R_3(x_11) via universal transitivity. Finally, from forall x_11: W_2(x_11) -> R_3(x_11), exists x_11: Q(x_11) -> R_3(x_11), forall x_11: W_2(x_11) or Q(x_11) we can infer exists x_11: R_3(x_11) via existential disjunction elimination, which contradicts forall x_11: ~R_3(x_11). Therefore, the answer is no.