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