  In 2001, J.-M. Le Bars disproved the zero-one law (that says that every
sentence from a certain logic is either true asymptotically almost surely
(a.a.s.), or false a.a.s.) for existential monadic second order sentences
(EMSO) about undirected graphs. He proved that there exists an EMSO sentence
$\phi$ such that ${\sf P}(G_n \models\phi)$ does not converge as $n\to\infty$
(here, the probability distribution is uniform over the set of all graphs on
the labeled set of vertices $\{1, \dots, n\}$). In the same paper, he
conjectured that, for EMSO sentences with 2 first order variables, the zero-one
law holds. In this paper, we disprove this conjecture.
