Consider the following premises. forall x_3: W_2(x_3) -> Q_3(x_3). exists x_3: U_3(x_3) -> R_3(x_3). forall x_3: W_2(x_3). forall x_3: Q_3(x_3) -> R_3(x_3). Can we infer forall x_3: ~R_3(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: W_2(x_3) -> Q_3(x_3), forall x_3: Q_3(x_3) -> R_3(x_3) we can infer forall x_3: W_2(x_3) -> R_3(x_3) via universal transitivity. From forall x_3: W_2(x_3) we can infer forall x_3: W_2(x_3) or U_3(x_3) via universal addition. Finally, from forall x_3: W_2(x_3) -> R_3(x_3), exists x_3: U_3(x_3) -> R_3(x_3), forall x_3: W_2(x_3) or U_3(x_3) we can infer exists x_3: R_3(x_3) via existential disjunction elimination, which contradicts forall x_3: ~R_3(x_3). Therefore, the answer is no.