Consider the following premises. For all x, x will sleep if and only if x will work. Linda is sleeping. For all x, if x works, then x is sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not work.
 From the fact that for all x, x will sleep if and only if x will work we can infer that for all x, if x sleeps, then x is working via universal biconditional elimination. From the fact that for all x, if x sleeps, then x is working, and that for all x, if x works, then x is sleeping we can infer that for all x, x will sleep if and only if x will work via universal biconditional introduction. From the fact that Linda is sleeping we can infer that there is at least one x for which x will sleep via existential generalization. From the fact that for all x, x will sleep if and only if x will work we can infer that for all x, if x sleeps, then x is working via universal biconditional elimination. Finally, from the fact that for all x, if x sleeps, then x is working, and that there is at least one x for which x will sleep we can infer that there is at least one x for which x will work via existential modus ponens, which contradicts that For all x, x will not work. Therefore, the answer is no.