Consider the following premises. exists y: Q_2(y) -> Q_1(y). forall y: Q_1(y) -> Q_2(y). forall y: Q_1(y) <-> Q_2(y). Can we infer forall y: ~(Q_1(y) -> Q_2(y)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.