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