Consider the following premises. For all x_18, x_18 is a lawyer. For all x_18, if x_18 makes tea, then x_18 is a bartender. There is at least one x_18 for which x_18 will not make tea. For all x_18, x_18 is a bartender or x_18 is a sailor. For all x_18, if x_18 were a bartender, then x_18 is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_18, either x_18 is a sailor or x_18 is a lawyer are not true.
 From the fact that for all x_18, if x_18 makes tea, then x_18 is a bartender, and that for all x_18, if x_18 were a bartender, then x_18 is making tea we can infer that for all x_18, x_18 will make tea if and only if x_18 is a bartender via universal biconditional introduction. From the fact that for all x_18, x_18 will make tea if and only if x_18 is a bartender, and that there is at least one x_18 for which x_18 will not make tea we can infer that there is at least one x_18 for which x_18 is not a bartender via existential biconditional elimination. From the fact that for all x_18, x_18 is a bartender or x_18 is a sailor, and that there is at least one x_18 for which x_18 is not a bartender we can infer that there is at least one x_18 for which x_18 is a sailor via existential disjunctive syllogism. Finally, from the fact that there is at least one x_18 for which x_18 is a sailor, and that for all x_18, x_18 is a lawyer we can infer that some sailors are lawyers via existential conjunction, which contradicts that For all x_18, either x_18 is a sailor or x_18 is a lawyer are not true. Therefore, the answer is no.