Consider the following premises. forall x_5: T(x_5) -> ~T_3(x_5). exists x_5: ~P_5(x_5). forall x_5: P_5(x_5) or T_3(x_5). Can we infer forall x_5: T(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_5(x_5) or T_3(x_5), exists x_5: ~P_5(x_5) we can infer exists x_5: T_3(x_5) via existential disjunctive syllogism. Finally, from forall x_5: T(x_5) -> ~T_3(x_5), exists x_5: T_3(x_5) we can infer exists x_5: ~T(x_5) via existential modus tollens, which contradicts forall x_5: T(x_5). Therefore, the answer is no.