Consider the following premises. If it is late, then Joseph is climbing a mountain. If Sarah were a soldier, then Joseph is climbing a mountain. If Joseph climbs a mountain, then it is late. It is not late. If Joseph climbs a mountain, then Sarah is a soldier. Can we infer the following from them? If we can, name the inference rule being used: Sarah is a soldier.
 From the fact that if Joseph climbs a mountain, then it is late, and that if it is late, then Joseph is climbing a mountain we can infer that Joseph is climbing a mountain if and only if it is late via biconditional introduction. From the fact that if Sarah were a soldier, then Joseph is climbing a mountain, and that if Joseph climbs a mountain, then Sarah is a soldier we can infer that Sarah is a soldier if and only if Joseph is climbing a mountain via biconditional introduction. From the fact that Joseph is climbing a mountain if and only if it is late, and that it is not late we can infer that Joseph is not climbing a mountain via biconditional elimination. Finally, from the fact that Sarah is a soldier if and only if Joseph is climbing a mountain, and that Joseph is not climbing a mountain we can infer that Sarah is not a soldier via biconditional elimination, which contradicts that Sarah is a soldier. Therefore, the answer is no.