Consider the following premises. exists y: S_4(y) or ~R(y). forall y: R(y) <-> S_4(y). Can we infer forall y: ~(R(y) -> S_4(y)) from them? If possible, name the inference rules being used at each step.
 From exists y: S_4(y) or ~R(y) we can infer exists y: R(y) -> S_4(y) via existential rewriting. Finally, from forall y: R(y) <-> S_4(y) we can infer forall y: S_4(y) -> R(y) via universal biconditional elimination, which contradicts forall y: ~(R(y) -> S_4(y)). Therefore, the answer is no.