Consider the following premises. exists y: U(y) or ~S_1(y). forall y: U(y) <-> S_1(y). Can we infer forall y: ~(U(y) -> S_1(y)) from them? If possible, name the inference rules being used at each step.
 From exists y: U(y) or ~S_1(y) we can infer exists y: S_1(y) -> U(y) via existential rewriting. Finally, from forall y: U(y) <-> S_1(y) we can infer forall y: U(y) -> S_1(y) via universal biconditional elimination, which contradicts forall y: ~(U(y) -> S_1(y)). Therefore, the answer is no.