Very interesting game. Had quite some fun with it. It's simple and efficient, like a puzzle game should. Great job at making every pieces fit together nicely !
The difficulty is perfect for an"all public" audience I think. Which is hard to achieve I guess.
Another layer of difficulty could be implemented easily if you plan on making a sequel : have multiple "machines / people / whatever" give the player the assertions, and gradually increase the challenge by making them possible lyers (always lying first, and then possibly lying).
This way, you can increase difficulty at will without relying on multiplicating assertions that much. And without sentences with actual double negatives.