Consider the following premises. forall x_6: ~P_2(x_6) or R_2(x_6). exists x_6: Q_6(x_6). forall x_6: P_2(x_6) or W_2(x_6). forall x_6: W_2(x_6) -> ~Q_6(x_6). Can we infer exists x_6: R_2(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: W_2(x_6) -> ~Q_6(x_6), exists x_6: Q_6(x_6) we can infer exists x_6: ~W_2(x_6) via existential modus tollens. From forall x_6: P_2(x_6) or W_2(x_6), forall x_6: ~P_2(x_6) or R_2(x_6) we can infer forall x_6: W_2(x_6) or R_2(x_6) via universal resolution. Finally, from forall x_6: W_2(x_6) or R_2(x_6), exists x_6: ~W_2(x_6) we can infer exists x_6: R_2(x_6) via existential disjunctive syllogism. Therefore, the answer is yes.