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