Interface conflicts with PHP Pimple

I have a custom class that extends Pimple\Container. The idea was to wrap the, to my eyes, ugly methods for accessing defined services (see below):

offsetGet($key)       -> get($key)
offsetSet($key, $val) -> set($key, $val)
offsetExists($key)    -> has($key)

This idea worked fine for what i wanted to be able to do. i then went on to create an Application class that I chose INHERITANCE over AGGREGATION not for any particular reason than seeming to be logic.

The issue now is when I have a ServiceProvider that accepts an application instance instead of the Pimple\Container since I created my very own ServiceProviderInterface that defines this contract.

i realize now that assuming that Application was and still is a type of Container and have it use a different type of contract from the parent class wasn't a great idea. However, conceptually in my mind an application instance is some kind of a container because in it I have some key => value pair data stored.

I was thinking that Interface Segration principle would save my day but I am not sure.

1. Could I have violated the Liskorv Substitution Principle here with my assumption with regards to the Application extends Pimple\Container relationship?

2. Is there any way I can use my own Interface to register my service providers with stumbling on the error that whatever service I pass doesn't conform to the pimple\ServiceProvider contract?

In simply terms is it possible to extend Pimple's container and ignore the library's service provider and use your which defines the same contract but with different parameter?