Consider the following premises. forall x_20: ~P_11(x_20). forall x_20: P_20(x_20) or ~Q_20(x_20). exists x_20: P_20(x_20) -> T_1(x_20). forall x_20: P_11(x_20) or Q_20(x_20). Can we infer exists x_20: T_1(x_20) or T(x_20) from them? If possible, name the inference rules being used at each step.
 From forall x_20: P_20(x_20) or ~Q_20(x_20) we can infer forall x_20: Q_20(x_20) -> P_20(x_20) via universal rewriting. From forall x_20: Q_20(x_20) -> P_20(x_20), exists x_20: P_20(x_20) -> T_1(x_20) we can infer exists x_20: Q_20(x_20) -> T_1(x_20) via existential transitivity. From forall x_20: P_11(x_20) or Q_20(x_20), forall x_20: ~P_11(x_20) we can infer forall x_20: Q_20(x_20) via universal disjunctive syllogism. From exists x_20: Q_20(x_20) -> T_1(x_20), forall x_20: Q_20(x_20) we can infer exists x_20: T_1(x_20) via existential modus ponens. Finally, from exists x_20: T_1(x_20) we can infer exists x_20: T_1(x_20) or T(x_20) via existential addition. Therefore, the answer is yes.