We consider the minimal number of AND and OR gates in monotone
circuits for quadratic boolean functions, i.e. disjunctions of
length-$2$ monomials. The single level conjecture claims that
monotone single level circuits, i.e. circuits which have only one
level of AND gates, for quadratic functions are not much larger
than arbitrary monotone circuits.
In this paper we disprove the conjecture: there are quadratic
functions in $n$ variables whose monotone circuits have linear
size whereas their monotone single level circuits require
size $\Omega(n^{2-\epsilon})$.
