Consider the following premises. Q_10(e_1) <-> q_3. R_10(e_1) -> q_3. forall x_10: ~P_10(x_10) or R_10(x_10). forall x_10: P_10(x_10) or Q_10(x_10). Can we infer q_3 from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) or Q_10(x_10), forall x_10: ~P_10(x_10) or R_10(x_10) we can infer forall x_10: Q_10(x_10) or R_10(x_10) via universal resolution. From forall x_10: Q_10(x_10) or R_10(x_10) we can infer Q_10(e_1) or R_10(e_1) via universal instantiation. From Q_10(e_1) <-> q_3 we can infer Q_10(e_1) -> q_3 via biconditional elimination. Finally, from Q_10(e_1) -> q_3, R_10(e_1) -> q_3, Q_10(e_1) or R_10(e_1) we can infer q_3 via disjunction elimination. Therefore, the answer is yes.