Consider the following premises. forall x_5: ~P_5(x_5) or R_5(x_5). forall x_5: P_5(x_5) or P(x_5). R_5(d) -> q. P(d) -> q. Can we infer q from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_5(x_5) or P(x_5), forall x_5: ~P_5(x_5) or R_5(x_5) we can infer forall x_5: P(x_5) or R_5(x_5) via universal resolution. From forall x_5: P(x_5) or R_5(x_5) we can infer P(d) or R_5(d) via universal instantiation. Finally, from P(d) -> q, R_5(d) -> q, P(d) or R_5(d) we can infer q via disjunction elimination. Therefore, the answer is yes.