Consider the following premises. S(e) -> ~u. u. forall x_8: Q_8(x_8) -> S(x_8). forall x_8: S(x_8) -> Q_8(x_8). Can we infer ~Q_8(e) from them? If possible, name the inference rules being used at each step.
 From forall x_8: S(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> S(x_8) we can infer forall x_8: S(x_8) <-> Q_8(x_8) via universal biconditional introduction. From forall x_8: S(x_8) <-> Q_8(x_8) we can infer S(e) <-> Q_8(e) via universal instantiation. From S(e) -> ~u, u we can infer ~S(e) via modus tollens. Finally, from S(e) <-> Q_8(e), ~S(e) we can infer ~Q_8(e) via biconditional elimination. Therefore, the answer is yes.