Puzzle: Zermelo-Fraenkel set theory is inconsistent

In this note, we present a puzzle. We prove that Zermelo-Fraenkel set theory is inconsistent by proving, using Zermelo-Fraenkel set theory, the false statement that any algorithm that determines whether any $n \times n$ matrix over $\mathbb F_2$, the finite field of order 2, is nonsingular must run in exponential time in the worst-case scenario. The object of the puzzle is to find the error in the proof.