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