If astronauts spend long periods in zero gravity only if calcium is resorbed in their bodies, then astronauts on a Mars voyage will arrive with brittle bones. If astronauts attempt a voyage to Mars only if they spend long periods in zero gravity, then astronauts on a Mars voyage will arrive with brittle bones. Therefore, astronauts on a Mars voyage will arrive with brittle bones. (Z, C, B, V )

Translate the following arguments into symbolic form, using the letters in the order in which they are listed. Then use indirect proof and the eighteen rules of inference to derive the conclusion of each. Having done so, attempt to derive the conclusion without using indirect proof.