Consider the following premises. For all x_15, x_15 will sleep or x_15 will not climb a mountain. There is at least one x_15 for which x_15 is a sailor if and only if x_15 will climb a mountain. For all x_15, if x_15 drinks water, then x_15 is a sailor. For all x_15, if x_15 sleeps, then x_15 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, if is not true that x_15 will climb a mountain if and only if x_15 is a sailor.
 From the fact that for all x_15, x_15 will sleep or x_15 will not climb a mountain we can infer that for all x_15, if x_15 climbs a mountain, then x_15 is sleeping via universal rewriting. From the fact that for all x_15, if x_15 climbs a mountain, then x_15 is sleeping, and that for all x_15, if x_15 sleeps, then x_15 is drinking water we can infer that for all x_15, if x_15 climbs a mountain, then x_15 is drinking water via universal transitivity. From the fact that there is at least one x_15 for which x_15 is a sailor if and only if x_15 will climb a mountain we can infer that there is at least one x_15 for which if x_15 were a sailor, then x_15 is climbing a mountain via existential biconditional elimination. From the fact that for all x_15, if x_15 climbs a mountain, then x_15 is drinking water, and that for all x_15, if x_15 drinks water, then x_15 is a sailor we can infer that for all x_15, if x_15 climbs a mountain, then x_15 is a sailor via universal transitivity. Finally, from the fact that for all x_15, if x_15 climbs a mountain, then x_15 is a sailor, and that there is at least one x_15 for which if x_15 were a sailor, then x_15 is climbing a mountain we can infer that there is at least one x_15 for which x_15 will climb a mountain if and only if x_15 is a sailor via existential biconditional introduction, which contradicts that For all x_15, if is not true that x_15 will climb a mountain if and only if x_15 is a sailor. Therefore, the answer is no.