Consider the following premises. For all x_13, if x_13 were rich, then x_13 is a janitor. For all x_13, x_13 is not a poet. For all x_13, if x_13 were a janitor, then x_13 is a poet. There is at least one x_13 for which x_13 is a scientist if and only if x_13 is a bartender. For all x_13, if x_13 were a poet, then x_13 is a janitor. For all x_13, x_13 is a bartender if and only if x_13 is rich. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 is a scientist.
 From the fact that for all x_13, if x_13 were a poet, then x_13 is a janitor, and that for all x_13, if x_13 were a janitor, then x_13 is a poet we can infer that for all x_13, x_13 is a poet if and only if x_13 is a janitor via universal biconditional introduction. From the fact that for all x_13, x_13 is a poet if and only if x_13 is a janitor, and that for all x_13, x_13 is not a poet we can infer that for all x_13, x_13 is not a janitor via universal biconditional elimination. From the fact that for all x_13, if x_13 were rich, then x_13 is a janitor, and that for all x_13, x_13 is not a janitor we can infer that for all x_13, x_13 is not rich via universal modus tollens. From the fact that for all x_13, x_13 is a bartender if and only if x_13 is rich, and that for all x_13, x_13 is not rich we can infer that for all x_13, x_13 is not a bartender via universal biconditional elimination. Finally, from the fact that there is at least one x_13 for which x_13 is a scientist if and only if x_13 is a bartender, and that for all x_13, x_13 is not a bartender we can infer that there is at least one x_13 for which x_13 is not a scientist via existential biconditional elimination, which contradicts that For all x_13, x_13 is a scientist. Therefore, the answer is no.