By "Prove you should press the switch", the first 'question'.
If you select the 3rd option "IF I do NOT want the lights to come on, THEN I should NOT press the switch.", you implicate that "IF I press the switch, THEN the lights come on."
Since you want the light to come on, you should press the switch in this case, so you proofed you should press the switch.
The first option "IF I would like the lights to come on, THEN I should press the switch", does not imply that pressing the switch makes the light come on. So you do not prove that you should press the switch, you rather proof that without pressing the switch, light is impossible, but it might as well be needed to run 15 rounds in the dark room.
So like stinky472 already said, you do not respect the rules of propositional logic, I sincerely hope you will do so in your sequel :).
@gibaa, You can only use three skills at the same time, so you have to change some skills. To do that, press spacebar, and then click on one of the spells, and then you can select a skill from al your skills.