Variables

• Filled: for all i in Rows, j in Columns, f(i,j) if position i,j contains a ship.
• Part: for all i in Rows, j in Columns, pa(i,j), pb(i,j), and pc(i,j) encode the type of ship part in the given grid cell. i,j contains a ship.
• Battleship: bi(i), bj(j), bd encodes the position and direction of the battleship.
• Cruisers: ci(k,i), cj(k,j), cd(k) encodes the position and direction of each cruiser, $k\in\{1,2\}$.
• Destroyers: di(k,i), dj(k,j), dd(k) encodes the position and direction of each destroyer, $k\in\{1,2,3\}$.
• Submarines: si(k,i), sj(k,j) encodes the position of each submarine, $k\in\{1,2,3,4\}$.

Total variables: $10\times 10+ 3(10\times 10)+ (10 + 10 + 1)+ 2(10+10+1) + 3(10+10+1) + 4 (10+10) = 606$.