The Dome Petroleum company listed in your link, Teribus, cannot possibly be the one in Iraq. It is listed under the heading, "Status of Oil Development Deals with Foreign Companies". Not Iraqi companies. So the Dome mentioned in your link must be the one owned by BP Amoco. BP stands for British Petroleum. Amoco stands for American Oil Company. So that's a major British and US oil company.

If you had clicked on the link I provided for Shell, you would have seen that Shell describes itself as a major US oil company.

You said there were no major US oil companies listed in your linked page.

Based on your ridiculous claim about Dome, and your ignorance of Shell as a major US oil company, I think we can dismiss the whole rest of your post with the contempt it so richly deserves.