Consider the following premises. forall x_6: T(x_6) -> ~Q_2(x_6). forall x_6: P_6(x_6) -> ~Q_6(x_6). forall x_6: P_6(x_6) or Q_2(x_6). forall x_6: Q_6(x_6). Can we infer exists x_6: T(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) -> ~Q_6(x_6), forall x_6: Q_6(x_6) we can infer forall x_6: ~P_6(x_6) via universal modus tollens. From forall x_6: P_6(x_6) or Q_2(x_6), forall x_6: ~P_6(x_6) we can infer forall x_6: Q_2(x_6) via universal disjunctive syllogism. Finally, from forall x_6: T(x_6) -> ~Q_2(x_6), forall x_6: Q_2(x_6) we can infer forall x_6: ~T(x_6) via universal modus tollens, which contradicts exists x_6: T(x_6). Therefore, the answer is no.