Consider the following premises. For all x_14, if x_14 sleeps, then x_14 is not driving a car. For all x_14, x_14 will drive a car. For all x_14, if x_14 writes a letter, then x_14 is sleeping. There is at least one x_14 for which x_14 will write a letter or x_14 is rich. For all x_14, if x_14 were rich, then x_14 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will climb a mountain.
 From the fact that for all x_14, if x_14 sleeps, then x_14 is not driving a car, and that for all x_14, x_14 will drive a car we can infer that for all x_14, x_14 will not sleep via universal modus tollens. From the fact that for all x_14, if x_14 writes a letter, then x_14 is sleeping, that for all x_14, if x_14 were rich, then x_14 is sleeping, and that there is at least one x_14 for which x_14 will write a letter or x_14 is rich we can infer that there is at least one x_14 for which x_14 will sleep via existential disjunction elimination. From the fact that there is at least one x_14 for which x_14 will sleep we can infer that there is at least one x_14 for which x_14 will sleep or x_14 will climb a mountain via existential addition. Finally, from the fact that there is at least one x_14 for which x_14 will sleep or x_14 will climb a mountain, and that for all x_14, x_14 will not sleep we can infer that there is at least one x_14 for which x_14 will climb a mountain via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.