Consider the following premises. For all x_10, if x_10 were a sailor, then x_10 is cooking. There is at least one x_10 for which x_10 is not a sailor. For all x_10, if x_10 takes a plane, then x_10 is a sailor. For all x_10, if x_10 cooks, then x_10 is sad. For all x_10, if x_10 were sad, then x_10 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will cook.
 From the fact that for all x_10, if x_10 were sad, then x_10 is taking a plane, and that for all x_10, if x_10 takes a plane, then x_10 is a sailor we can infer that for all x_10, if x_10 were sad, then x_10 is a sailor via universal transitivity. From the fact that for all x_10, if x_10 cooks, then x_10 is sad, and that for all x_10, if x_10 were sad, then x_10 is a sailor we can infer that for all x_10, if x_10 cooks, then x_10 is a sailor via universal transitivity. From the fact that for all x_10, if x_10 cooks, then x_10 is a sailor, and that for all x_10, if x_10 were a sailor, then x_10 is cooking we can infer that for all x_10, x_10 will cook if and only if x_10 is a sailor via universal biconditional introduction. From the fact that for all x_10, x_10 will cook if and only if x_10 is a sailor we can infer that for all x_10, if x_10 cooks, then x_10 is a sailor via universal biconditional elimination. Finally, from the fact that for all x_10, if x_10 cooks, then x_10 is a sailor, and that there is at least one x_10 for which x_10 is not a sailor we can infer that there is at least one x_10 for which x_10 will not cook via existential modus tollens, which contradicts that For all x_10, x_10 will cook. Therefore, the answer is no.