We prove that for a natural distribution over random satisfiable 3--CNF formulas with $\Theta(n)$ clauses, every $\mathsf{AC}^0$ circuit family of constant depth $d$ and polynomial size $n^k$ fails to decide satisfiability with probability at least $2/3$ under the standard random restriction method with parameter $p = n^{-1/(2d)}$. The proof follows ... more >>>