Consider the following premises. Q_10(a_1) -> W(a_1). forall x_10: W(x_10) -> Q_10(x_10). forall x_10: Q_10(x_10) -> W(x_10). Can we infer ~(W(a_1) <-> Q_10(a_1)) from them?
That contradicts the premises. Therefore the answer is no.