Consider the following premises. forall x_2: T(x_2) -> Q(x_2). exists x_2: P_2(x_2) -> T(x_2). forall x_2: P_2(x_2). Can we infer forall x_2: ~Q(x_2) from them? If possible, name the inference rules being used at each step.
 From exists x_2: P_2(x_2) -> T(x_2), forall x_2: P_2(x_2) we can infer exists x_2: T(x_2) via existential modus ponens. Finally, from forall x_2: T(x_2) -> Q(x_2), exists x_2: T(x_2) we can infer exists x_2: Q(x_2) via existential modus ponens, which contradicts forall x_2: ~Q(x_2). Therefore, the answer is no.