Berg and Ulfberg and Amano and Maruoka have used CNFDNFapproximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev’s function. We show that these approximators can be used to prove the same lower bound for their nonmonotone network complexity. This implies P not equal NP.
Source: [1708.03486] A Solution of the P versus NP Problem
More background at: The PversusNP page
This page collects links around papers that try to settle the “P versus NP” question (in either way). Here are some links that explain/discuss this question:

A clear formulation of the “P versus NP” question by Stephen Cook.
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