Consider the following premises. For all x_17, x_17 will sleep. There is at least one x_17 for which if x_17 climbs a mountain, then x_17 is an artist. For all x_17, if x_17 were a sailor, then x_17 is climbing a mountain. For all x_17, if x_17 were an artist, then x_17 is a sailor. For all x_17, if x_17 were a sailor, then x_17 is not sleeping. For all x_17, if x_17 makes tea, then x_17 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, x_17 will make tea.
 From the fact that for all x_17, if x_17 were a sailor, then x_17 is not sleeping, and that for all x_17, x_17 will sleep we can infer that for all x_17, x_17 is not a sailor via universal modus tollens. From the fact that there is at least one x_17 for which if x_17 climbs a mountain, then x_17 is an artist, and that for all x_17, if x_17 were an artist, then x_17 is a sailor we can infer that there is at least one x_17 for which if x_17 climbs a mountain, then x_17 is a sailor via existential transitivity. From the fact that there is at least one x_17 for which if x_17 climbs a mountain, then x_17 is a sailor, and that for all x_17, if x_17 were a sailor, then x_17 is climbing a mountain we can infer that there is at least one x_17 for which x_17 will climb a mountain if and only if x_17 is a sailor via existential biconditional introduction. From the fact that there is at least one x_17 for which x_17 will climb a mountain if and only if x_17 is a sailor, and that for all x_17, x_17 is not a sailor we can infer that there is at least one x_17 for which x_17 will not climb a mountain via existential biconditional elimination. Finally, from the fact that for all x_17, if x_17 makes tea, then x_17 is climbing a mountain, and that there is at least one x_17 for which x_17 will not climb a mountain we can infer that there is at least one x_17 for which x_17 will not make tea via existential modus tollens, which contradicts that For all x_17, x_17 will make tea. Therefore, the answer is no.