Consider the following premises. forall x_6: ~P_6(x_6) or W_4(x_6). forall x_6: R_3(x_6) or ~R(x_6). exists x_6: W_4(x_6) -> R_3(x_6). forall x_6: P_6(x_6) or R(x_6). Can we infer exists x_6: R_3(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) or R(x_6), forall x_6: ~P_6(x_6) or W_4(x_6) we can infer forall x_6: R(x_6) or W_4(x_6) via universal resolution. From forall x_6: R_3(x_6) or ~R(x_6) we can infer forall x_6: R(x_6) -> R_3(x_6) via universal rewriting. Finally, from forall x_6: R(x_6) -> R_3(x_6), exists x_6: W_4(x_6) -> R_3(x_6), forall x_6: R(x_6) or W_4(x_6) we can infer exists x_6: R_3(x_6) via existential disjunction elimination. Therefore, the answer is yes.