Consider the following premises. For all x, x is bored if and only if x is an office clerk. For all x, x is an office clerk or x is not bored. Can we infer the following from them? There is at least one x for which the fact that x were bored does not imply that x is an office clerk.
 From the fact that for all x, x is an office clerk or x is not bored we can infer that for all x, if x were bored, then x is an office clerk. From the fact that for all x, x is bored if and only if x is an office clerk we can infer that for all x, if x were an office clerk, then x is bored. From the fact that for all x, if x were an office clerk, then x is bored, and that for all x, if x were bored, then x is an office clerk we can infer that for all x, x is an office clerk if and only if x is bored. Finally, from the fact that for all x, x is an office clerk if and only if x is bored we can infer that for all x, if x were bored, then x is an office clerk, which contradicts that There is at least one x for which the fact that x were bored does not imply that x is an office clerk. Therefore, the answer is no.