Consider the following premises. exists y: S_2(y) <-> W_1(y). forall y: W(y) <-> W_1(y). Can we infer forall y: ~(S_2(y) -> W(y)) from them? If possible, name the inference rules being used at each step.
 From exists y: S_2(y) <-> W_1(y) we can infer exists y: S_2(y) -> W_1(y) via existential biconditional elimination. Finally, from forall y: W(y) <-> W_1(y) we can infer forall y: W_1(y) -> W(y) via universal biconditional elimination, which contradicts forall y: ~(S_2(y) -> W(y)). Therefore, the answer is no.