Fun idea (I see what you meant by our games are similar xD).
Unfortunately, especially on the first levels I think, the solution to who is lying is not unique. And then you might cut the wrong wire (just tested this, at least in the first levels I got this situation). Maybe it would be better if the puzzles were handcrafted instead of randomly generated to make sure they work (or you would need to check that there is only one solution to the generated ones).
Also, the game really needs some audio and crashed on the 6th level for me.