Consider the following premises. exists z_2: S(z_2) or ~Q(z_2). forall z_2: S(z_2) -> S_3(z_2). forall z_2: S_3(z_2) -> Q(z_2). Can we infer forall z_2: ~(S(z_2) <-> Q(z_2)) from them? If possible, name the inference rules being used at each step.
 From exists z_2: S(z_2) or ~Q(z_2) we can infer exists z_2: Q(z_2) -> S(z_2) via existential rewriting. From forall z_2: S(z_2) -> S_3(z_2), forall z_2: S_3(z_2) -> Q(z_2) we can infer forall z_2: S(z_2) -> Q(z_2) via universal transitivity. Finally, from forall z_2: S(z_2) -> Q(z_2), exists z_2: Q(z_2) -> S(z_2) we can infer exists z_2: S(z_2) <-> Q(z_2) via existential biconditional introduction, which contradicts forall z_2: ~(S(z_2) <-> Q(z_2)). Therefore, the answer is no.