Rewrite Rule for default post type

When you register your custom post type using register_post_type function, you have to be very careful with rewrite param.

You should pass an array with following keys:

  • slug => string Customize the permalink structure slug. Defaults to
    the $post_type value. Should be translatable.
  • with_front => bool
    Should the permalink structure be prepended with the front base.
    (example: if your permalink structure is /blog/, then your links will
    be: false->/news/, true->/blog/news/). Defaults to true
  • feeds =>
    bool Should a feed permalink structure be built for this post type.
    Defaults to has_archive value.
  • pages => bool Should the permalink
    structure provide for pagination. Defaults to true
  • ep_mask => const
    As of 3.4 Assign an endpoint mask for this post type. For more info
    see Rewrite API/add_rewrite_endpoint, and Make WordPress Plugins
    summary of endpoints. If not specified, then it inherits from
    permalink_epmask(if permalink_epmask is set), otherwise defaults to
    EP_PERMALINK.

In your case, setting with_front to false for your CPT should solve your problem.