Consider the following premises. forall y: T_4(y) -> Q_4(y). forall y: Q_4(y) -> T_4(y). exists y: T_4(y) <-> P_2(y). Can we infer forall y: ~(P_2(y) -> Q_4(y)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.