How does one search the internet without using Google, Yahoo, Bing or a "3rd party" search engine that actually just uses Google, Yahoo or Bing?

It is disconcerting the notion that I am unable to run a search without the use of one of the “Big Three” I find that even so called 3rd party search engines after a little digging or sometimes with no digging at all are infact just using queries from one of the Big Three’s engines. I am forming this image of an encapsulated system of inter-connectedness which I am unable to escape from. Couple this with Google’s recent changes to their search engine in their own words of “relevant results” it seems to me If there is something that falls outside the capsule It will be non-accessible.