Consider the following premises. forall x_7: Q_1(x_7) <-> S_7(x_7). S_7(a_7) -> Q_1(a_7). Can we infer ~(Q_1(a_7) <-> S_7(a_7)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.