Consider the following premises. ~T_1(b_4). forall x_11: Q_11(x_11) -> T_1(x_11). forall x_11: T_1(x_11) <-> Q_11(x_11). Can we infer ~Q_11(b_4) from them? If possible, name the inference rules being used at each step.
 From forall x_11: T_1(x_11) <-> Q_11(x_11) we can infer forall x_11: T_1(x_11) -> Q_11(x_11) via universal biconditional elimination. From forall x_11: T_1(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> T_1(x_11) we can infer forall x_11: T_1(x_11) <-> Q_11(x_11) via universal biconditional introduction. From forall x_11: T_1(x_11) <-> Q_11(x_11) we can infer T_1(b_4) <-> Q_11(b_4) via universal instantiation. From T_1(b_4) <-> Q_11(b_4) we can infer Q_11(b_4) -> T_1(b_4) via biconditional elimination. Finally, from Q_11(b_4) -> T_1(b_4), ~T_1(b_4) we can infer ~Q_11(b_4) via modus tollens. Therefore, the answer is yes.