Consider the following premises. For all x_14, x_14 is a mechanic if and only if x_14 is poor. There is at least one x_14 for which x_14 will cook or x_14 is a mechanic. For all x_14, x_14 will work or x_14 is not poor. For all x_14, x_14 will cook if and only if x_14 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 will not work.
 From the fact that for all x_14, x_14 will work or x_14 is not poor we can infer that for all x_14, if x_14 were poor, then x_14 is working via universal rewriting. From the fact that for all x_14, x_14 is a mechanic if and only if x_14 is poor we can infer that for all x_14, if x_14 were a mechanic, then x_14 is poor via universal biconditional elimination. From the fact that for all x_14, x_14 will cook if and only if x_14 will work we can infer that for all x_14, if x_14 cooks, then x_14 is working via universal biconditional elimination. From the fact that for all x_14, if x_14 were a mechanic, then x_14 is poor, and that for all x_14, if x_14 were poor, then x_14 is working we can infer that for all x_14, if x_14 were a mechanic, then x_14 is working via universal transitivity. Finally, from the fact that for all x_14, if x_14 cooks, then x_14 is working, that for all x_14, if x_14 were a mechanic, then x_14 is working, and that there is at least one x_14 for which x_14 will cook or x_14 is a mechanic we can infer that there is at least one x_14 for which x_14 will work via existential disjunction elimination, which contradicts that For all x_14, x_14 will not work. Therefore, the answer is no.