  In the paper "On P versus NP," Lev Gordeev attempts to extend the method of
approximation, which successfully proved exponential lower bounds for monotone
circuits, to the case of De Morgan Normal (DMN) circuits. As in Razborov's
proof of exponential lower bounds for monotone circuits, Gordeev's work is
focused on the NP-complete problem CLIQUE. If successful in proving exponential
DMN circuit lower bounds for CLIQUE, Gordeev would prove that P $\neq$ NP.
However, we show that Gordeev makes a crucial mistake in Lemma 12. This mistake
comes from only approximating operations over positive circuit inputs.
Furthermore, we argue that efforts to extend the method of approximation to DMN
circuits will need to approximate negated inputs as well.
