Consider the following premises. forall y_1: P_2(y_1) -> U(y_1). exists y_1: U(y_1) -> P_2(y_1). Can we infer forall y_1: ~(U(y_1) <-> P_2(y_1)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.