Consider the following premises. exists y_2: R(y_2) -> P(y_2). forall y_2: R(y_2) -> P(y_2). forall y_2: R(y_2) or ~P(y_2). Can we infer forall y_2: ~(P(y_2) -> R(y_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.