Include taxonomy slug in url?

This can be a bit challenging for WordPress, because it wouldn’t know whether you are referring to post, page or taxonomy. Nevertheless, rename your taxonomy to something like product_category and try changing the slug in your post type arguments to system/%product_category%, and slug in your taxonomy arguments to just system. WordPress should now handle /system/your-product-category/post-name/

Out of the box WordPress doesn’t recognize the permalink structure tag %product_category%, so we need to declare it:

function filter_post_type_permalink($link, $post)
{
    if ($post->post_type != 'system')
        return $link;

    if ($cats = get_the_terms($post->ID, 'product_category'))
        $link = str_replace('%product_category%', array_pop($cats)->slug, $link);
    return $link;
}
add_filter('post_type_link', 'filter_post_type_permalink', 10, 2);

NOTES:

1. This will just grab the first product category for the post ordered
   by name.
2. There still may be some 404 errors, if pages, posts etc., have same names.