Consider the following premises. forall x_18: P_14(x_18) -> R_14(x_18). forall x_18: R(x_18) <-> R_3(x_18). exists x_18: Q_14(x_18) -> R_14(x_18). forall x_18: Q_1(x_18) -> R_3(x_18). forall x_18: ~R_14(x_18) or Q_1(x_18). forall x_18: P_14(x_18) or Q_14(x_18). Can we infer exists x_18: R_3(x_18) from them? If possible, name the inference rules being used at each step.
 From forall x_18: R(x_18) <-> R_3(x_18) we can infer forall x_18: R(x_18) -> R_3(x_18) via universal biconditional elimination. From forall x_18: P_14(x_18) -> R_14(x_18), exists x_18: Q_14(x_18) -> R_14(x_18), forall x_18: P_14(x_18) or Q_14(x_18) we can infer exists x_18: R_14(x_18) via existential disjunction elimination. From exists x_18: R_14(x_18) we can infer exists x_18: R_14(x_18) or R(x_18) via existential addition. From exists x_18: R_14(x_18) or R(x_18), forall x_18: ~R_14(x_18) or Q_1(x_18) we can infer exists x_18: R(x_18) or Q_1(x_18) via existential resolution. Finally, from forall x_18: R(x_18) -> R_3(x_18), forall x_18: Q_1(x_18) -> R_3(x_18), exists x_18: R(x_18) or Q_1(x_18) we can infer exists x_18: R_3(x_18) via existential disjunction elimination. Therefore, the answer is yes.