Consider the following premises. forall x_14: W_1(x_14) -> Q_14(x_14). forall x_14: P_10(x_14) -> S(x_14). exists x_14: W_1(x_14) or T(x_14). forall x_14: ~Q_14(x_14). forall x_14: P_10(x_14). Can we infer exists x_14: T(x_14) and S(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: W_1(x_14) -> Q_14(x_14), forall x_14: ~Q_14(x_14) we can infer forall x_14: ~W_1(x_14) via universal modus tollens. From forall x_14: P_10(x_14) -> S(x_14), forall x_14: P_10(x_14) we can infer forall x_14: S(x_14) via universal modus ponens. From exists x_14: W_1(x_14) or T(x_14), forall x_14: ~W_1(x_14) we can infer exists x_14: T(x_14) via existential disjunctive syllogism. Finally, from exists x_14: T(x_14), forall x_14: S(x_14) we can infer exists x_14: T(x_14) and S(x_14) via existential conjunction. Therefore, the answer is yes.