Consider the following premises. For all x_17, if x_17 were a poet, then x_17 is a janitor. For all x_17, if x_17 were a janitor, then x_17 is driving a car. There is at least one x_17 for which x_17 is a poet or x_17 is sad. For all x_17, x_17 is bored. For all x_17, x_17 will drive a car if and only if x_17 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_17 for which x_17 is bored and x_17 will drive a car.
 From the fact that for all x_17, x_17 will drive a car if and only if x_17 is sad we can infer that for all x_17, if x_17 were sad, then x_17 is driving a car via universal biconditional elimination. From the fact that for all x_17, if x_17 were a poet, then x_17 is a janitor, and that for all x_17, if x_17 were a janitor, then x_17 is driving a car we can infer that for all x_17, if x_17 were a poet, then x_17 is driving a car via universal transitivity. From the fact that for all x_17, if x_17 were a poet, then x_17 is driving a car, that for all x_17, if x_17 were sad, then x_17 is driving a car, and that there is at least one x_17 for which x_17 is a poet or x_17 is sad we can infer that there is at least one x_17 for which x_17 will drive a car via existential disjunction elimination. Finally, from the fact that for all x_17, x_17 is bored, and that there is at least one x_17 for which x_17 will drive a car we can infer that there is at least one x_17 for which x_17 is bored and x_17 will drive a car via existential conjunction. Therefore, the answer is yes.