Ubuntu 14.04 apache mod_rewrite won't work with codeigniter htaccess

Hi, It looks like I have a huge problem. After all trying to fix it, nothing has changed. I have a problem with mod_rewrite engine - it is not working on my project.

I’ve created new fresh ubuntu 14.04 droplet with LAMP. Then, I’ve logged in with my CMD and entered following lines…:

sudo a2enmod rewrite
sudo nano /etc/apache2/sites-available/default

and than I rewrited default file with this info:

<Directory /var/www/>
                Options Indexes FollowSymLinks MultiViews
                AllowOverride All
                Order allow,deny
                allow from all
 </Directory>

and after all I’ve restarted my apache. Then I have uploaded my project to /var/www/html/project/ directory. My project is using codeigniter framework and this is the .htaccess of my project:

RewriteEngine On
RewriteBase /html/project/

RewriteCond %{THE_REQUEST} \s/+(.*?)/{2,}([^\s]*)
RewriteRule ^ %1/%2 [R=302,L,NE]

RewriteCond %{THE_REQUEST} ^[A-Z]{3,}\s/+(.+?)/{2,}[?\s] [NC]
RewriteRule ^ /%1/ [L,R=301]

RewriteCond %{HTTP_HOST} !^www\. [NC]
RewriteRule ^ http://www.%{HTTP_HOST}%{REQUEST_URI}  [R=301,L]

RewriteCond %{REQUEST_URI} system|application
RewriteRule ^(.*)$ index.php?/$1 [L]

RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?/$1 [L]

but the problem is, that mod_rewrite is not working… I can access pages via http://…/project/index.php/article instead of http://…/project/article

any ideas about it?