A not-insignificant amount of time was spent trying to figure out the significance of allowing output conditionals. At first, I was trying to find an efficient way to cycle through all 24 permutations of 4 atoms, but this was way too slow and cannot be the intended idea. Then, I thought about only distilling out the fire and permuting the rest, but I have no idea how to execute that. Ultimately just treated the puzzle as using standard computation rules.