OK so let me confirm to see if I get it and sorry for my insistence: So if I had:
CFJ 1: A is True. CFJ 2: A is False. I can reductio ad absurdum (although a really short one) CFJ 1 by just presenting CFJ 2, and CFJ 2 by presenting CFJ 1. With that, I would be barred from deducing anything from those ad absurdum (i.e. attempt to summon Principle of Explosion?)