Consider the following premises. For all x_4, if x_4 cooks, then x_4 is a poet. For all x_4, x_4 will cook or x_4 is not a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which the fact that x_4 were a sailor does not imply that x_4 is a poet.
 From the fact that for all x_4, x_4 will cook or x_4 is not a sailor we can infer that for all x_4, if x_4 were a sailor, then x_4 is cooking via universal rewriting. Finally, from the fact that for all x_4, if x_4 were a sailor, then x_4 is cooking, and that for all x_4, if x_4 cooks, then x_4 is a poet we can infer that for all x_4, if x_4 were a sailor, then x_4 is a poet via universal transitivity, which contradicts that There is at least one x_4 for which the fact that x_4 were a sailor does not imply that x_4 is a poet. Therefore, the answer is no.