Consider the following premises. For all x_5, if x_5 works, then x_5 is a mechanic. For all x_5, if x_5 were rich, then x_5 is a poet. For all x_5, if x_5 were a poet, then x_5 is a sailor. For all x_5, if x_5 were a mechanic, then x_5 is rich. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which the fact that x_5 works does not imply that x_5 is a sailor.
 From the fact that for all x_5, if x_5 works, then x_5 is a mechanic, and that for all x_5, if x_5 were a mechanic, then x_5 is rich we can infer that for all x_5, if x_5 works, then x_5 is rich via universal transitivity. From the fact that for all x_5, if x_5 were rich, then x_5 is a poet, and that for all x_5, if x_5 were a poet, then x_5 is a sailor we can infer that for all x_5, if x_5 were rich, then x_5 is a sailor via universal transitivity. Finally, from the fact that for all x_5, if x_5 works, then x_5 is rich, and that for all x_5, if x_5 were rich, then x_5 is a sailor we can infer that for all x_5, if x_5 works, then x_5 is a sailor via universal transitivity, which contradicts that There is at least one x_5 for which the fact that x_5 works does not imply that x_5 is a sailor. Therefore, the answer is no.