Almost every 2-SAT function is unate

Bollobás, Brightwell and Leader [2] showed that there are at most \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$2^{\left( \begin{subarray}{l} n \\ 2 \end{subarray} \right) + o(n^2 )} $$ \end{document} 2-SAT functions on n variables, and conjectured that in fact the number of 2-SAT functions on n variables is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$2^{\left( \begin{subarray}{l} n \\ 2 \end{subarray} \right) + n} (1 + o(1))$$ \end{document}. We prove their conjecture.