Consider the following premises. forall x_11: P_11(x_11) or Q_11(x_11). exists x_11: P_2(x_11) -> T_2(x_11). forall x_11: ~P_11(x_11). forall x_11: P_2(x_11). Can we infer forall x_11: ~(T_2(x_11) and Q_11(x_11)) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) or Q_11(x_11), forall x_11: ~P_11(x_11) we can infer forall x_11: Q_11(x_11) via universal disjunctive syllogism. From exists x_11: P_2(x_11) -> T_2(x_11), forall x_11: P_2(x_11) we can infer exists x_11: T_2(x_11) via existential modus ponens. Finally, from exists x_11: T_2(x_11), forall x_11: Q_11(x_11) we can infer exists x_11: T_2(x_11) and Q_11(x_11) via existential conjunction, which contradicts forall x_11: ~(T_2(x_11) and Q_11(x_11)). Therefore, the answer is no.