Consider the following premises. forall x_8: Q_8(x_8) -> W_2(x_8). forall x_8: W_2(x_8) -> Q_8(x_8). W_2(a_7). Can we infer ~Q_8(a_7) from them? If possible, name the inference rules being used at each step.
 From forall x_8: W_2(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> W_2(x_8) we can infer forall x_8: W_2(x_8) <-> Q_8(x_8) via universal biconditional introduction. From forall x_8: W_2(x_8) <-> Q_8(x_8) we can infer W_2(a_7) <-> Q_8(a_7) via universal instantiation. From W_2(a_7) <-> Q_8(a_7) we can infer W_2(a_7) -> Q_8(a_7) via biconditional elimination. Finally, from W_2(a_7) -> Q_8(a_7), W_2(a_7) we can infer Q_8(a_7) via modus ponens, which contradicts ~Q_8(a_7). Therefore, the answer is no.