Consider the following premises. Q_3(g) <-> q_3. forall x_15: P_15(x_15) or ~Q_15(x_15). forall x_15: Q_15(x_15) <-> Q_3(x_15). forall x_15: ~P_15(x_15). Can we infer ~q_3 from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) or ~Q_15(x_15) we can infer forall x_15: Q_15(x_15) -> P_15(x_15) via universal rewriting. From forall x_15: Q_15(x_15) -> P_15(x_15), forall x_15: ~P_15(x_15) we can infer forall x_15: ~Q_15(x_15) via universal modus tollens. From forall x_15: Q_15(x_15) <-> Q_3(x_15), forall x_15: ~Q_15(x_15) we can infer forall x_15: ~Q_3(x_15) via universal biconditional elimination. From forall x_15: ~Q_3(x_15) we can infer ~Q_3(g) via universal instantiation. Finally, from Q_3(g) <-> q_3, ~Q_3(g) we can infer ~q_3 via biconditional elimination. Therefore, the answer is yes.