Consider the following premises. For all x_15, x_15 is not an office clerk. For all x_15, if x_15 were a taxi driver, then x_15 is an office clerk. There is at least one x_15 for which x_15 is a taxi driver or x_15 is sad. For all x_15, x_15 is sad if and only if x_15 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will not sleep.
 From the fact that for all x_15, x_15 is sad if and only if x_15 is an office clerk we can infer that for all x_15, if x_15 were sad, then x_15 is an office clerk via universal biconditional elimination. From the fact that for all x_15, if x_15 were a taxi driver, then x_15 is an office clerk, that for all x_15, if x_15 were sad, then x_15 is an office clerk, and that there is at least one x_15 for which x_15 is a taxi driver or x_15 is sad we can infer that there is at least one x_15 for which x_15 is an office clerk via existential disjunction elimination. From the fact that there is at least one x_15 for which x_15 is an office clerk we can infer that there is at least one x_15 for which x_15 is an office clerk or x_15 will sleep via existential addition. Finally, from the fact that there is at least one x_15 for which x_15 is an office clerk or x_15 will sleep, and that for all x_15, x_15 is not an office clerk we can infer that there is at least one x_15 for which x_15 will sleep via existential disjunctive syllogism, which contradicts that For all x_15, x_15 will not sleep. Therefore, the answer is no.