Consider the following premises. forall x_24: P_24(x_24) or Q_24(x_24). forall x_24: P_24(x_24) -> R_24(x_24). t. forall x_24: Q_24(x_24) -> R_24(x_24). Can we infer t or w from them? If possible, name the inference rules being used at each step.
 From forall x_24: P_24(x_24) -> R_24(x_24), forall x_24: Q_24(x_24) -> R_24(x_24), forall x_24: P_24(x_24) or Q_24(x_24) we can infer forall x_24: R_24(x_24) via universal disjunction elimination. From forall x_24: R_24(x_24) we can infer R_24(d) via universal instantiation. From t, R_24(d) we can infer t and R_24(d) via conjunction. From t and R_24(d) we can infer t via simplification. Finally, from t we can infer t or w via addition. Therefore, the answer is yes.