Consider the following premises. forall x: T_2(x) -> S(x). forall x: Q(x) <-> S(x). exists x: ~Q(x). Can we infer forall x: T_2(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q(x) <-> S(x), exists x: ~Q(x) we can infer exists x: ~S(x) via existential biconditional elimination. Finally, from forall x: T_2(x) -> S(x), exists x: ~S(x) we can infer exists x: ~T_2(x) via existential modus tollens, which contradicts forall x: T_2(x). Therefore, the answer is no.