Consider the following premises. forall y: S_1(y) -> W_4(y). exists y: S_1(y) or ~W_4(y). Can we infer forall y: ~(S_1(y) <-> W_4(y)) from them? If possible, name the inference rules being used at each step.
 From exists y: S_1(y) or ~W_4(y) we can infer exists y: W_4(y) -> S_1(y) via existential rewriting. Finally, from forall y: S_1(y) -> W_4(y), exists y: W_4(y) -> S_1(y) we can infer exists y: S_1(y) <-> W_4(y) via existential biconditional introduction, which contradicts forall y: ~(S_1(y) <-> W_4(y)). Therefore, the answer is no.