Consider the following premises. forall y: R(y) <-> P(y). exists y: P(y) <-> R(y). Can we infer forall y: ~(P(y) -> R(y)) from them?
 From exists y: P(y) <-> R(y) we can infer exists y: R(y) -> P(y). Finally, from forall y: R(y) <-> P(y) we can infer forall y: P(y) -> R(y), which contradicts forall y: ~(P(y) -> R(y)). Therefore, the answer is no.