Consider the following premises. forall x_19: P_15(x_19) or Q_15(x_19). forall x_19: R(x_19) -> Q_2(x_19). forall x_19: P_19(x_19) or R(x_19). exists x_19: P_15(x_19) -> T(x_19). forall x_19: ~P_19(x_19) or R_19(x_19). forall x_19: Q_15(x_19) -> T(x_19). forall x_19: R_19(x_19) <-> Q_2(x_19). Can we infer forall x_19: ~(Q_2(x_19) and T(x_19)) from them? If possible, name the inference rules being used at each step.
 From forall x_19: P_19(x_19) or R(x_19), forall x_19: ~P_19(x_19) or R_19(x_19) we can infer forall x_19: R(x_19) or R_19(x_19) via universal resolution. From exists x_19: P_15(x_19) -> T(x_19), forall x_19: Q_15(x_19) -> T(x_19), forall x_19: P_15(x_19) or Q_15(x_19) we can infer exists x_19: T(x_19) via existential disjunction elimination. From forall x_19: R_19(x_19) <-> Q_2(x_19) we can infer forall x_19: R_19(x_19) -> Q_2(x_19) via universal biconditional elimination. From forall x_19: R(x_19) -> Q_2(x_19), forall x_19: R_19(x_19) -> Q_2(x_19), forall x_19: R(x_19) or R_19(x_19) we can infer forall x_19: Q_2(x_19) via universal disjunction elimination. Finally, from forall x_19: Q_2(x_19), exists x_19: T(x_19) we can infer exists x_19: Q_2(x_19) and T(x_19) via existential conjunction, which contradicts forall x_19: ~(Q_2(x_19) and T(x_19)). Therefore, the answer is no.