Consider the following premises. forall x_6: ~R_6(x_6). forall x_6: P_6(x_6) or Q_6(x_6). forall x_6: ~Q_6(x_6) or R_2(x_6). exists x_6: ~P_6(x_6) or R_6(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_6(x_6) or Q_6(x_6), exists x_6: ~P_6(x_6) or R_6(x_6) we can infer exists x_6: Q_6(x_6) or R_6(x_6) via existential resolution. From exists x_6: Q_6(x_6) or R_6(x_6), forall x_6: ~Q_6(x_6) or R_2(x_6) we can infer exists x_6: R_6(x_6) or R_2(x_6) via existential resolution. Finally, from exists x_6: R_6(x_6) or R_2(x_6), forall x_6: ~R_6(x_6) we can infer exists x_6: R_2(x_6) via existential disjunctive syllogism, which contradicts forall x_6: ~R_2(x_6). Therefore, the answer is no.