[Underground Secrets] Unsolvable Light Puzzle

[LepusCavum]

Top left button controls lights 1, 2, and 4.
Top right button controls lights 2 and 4.
Bottom left button controls light 3.
Bottom right button controls lights 1, 2, 3, and 4.

Currently Lights 1 and 2 are on, and Lights 3 and 4 are off.

As far as I and some recruited friends (and ChatGPT) can figure out... this puzzle is impossible to solve.