  In this paper, we disprove EMSO(FO$^2$) convergence law for the binomial
random graph $G(n,p)$ for any constant probability $p$. More specifically, we
prove that there exists an existential monadic second order sentence with 2
first order variables such that, for every $p\in(0,1)$, the probability that it
is true on $G(n,p)$ does not converge.
