Consider the following premises. For all x, if x were a sailor, then x is playing squash. For all x, if x plays squash, then x is sleeping. For all x, x is a sailor or x will not sleep. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which the fact that x sleeps does not imply that x is a sailor.
 From the fact that for all x, if x were a sailor, then x is playing squash, and that for all x, if x plays squash, then x is sleeping we can infer that for all x, if x were a sailor, then x is sleeping via universal transitivity. From the fact that for all x, x is a sailor or x will not sleep we can infer that for all x, if x sleeps, then x is a sailor via universal rewriting. From the fact that for all x, if x were a sailor, then x is sleeping, and that for all x, if x sleeps, then x is a sailor we can infer that for all x, x is a sailor if and only if x will sleep via universal biconditional introduction. Finally, from the fact that for all x, x is a sailor if and only if x will sleep we can infer that for all x, if x sleeps, then x is a sailor via universal biconditional elimination, which contradicts that There is at least one x for which the fact that x sleeps does not imply that x is a sailor. Therefore, the answer is no.