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