Here is my current impression of Byron Katie's inquiry process...
Is it true?
Creates a crack in and some space around the belief, a chink in the armor. I open up for the possibility that it is not absolutely true, which makes it easier to inquire into it further and allow it to drop (me).
Who/what am I with/without the thought?
First, examining the many forms of suffering which arises when I believe in the thought - on all levels and areas of my life. Then, realizing who I am without the thought. Coming to the nature of mind. And also visualize - make come alive - how I would live my life without it. I live it in myself which makes it available for me to live it in the world.
I recognize and integrate projections. The advice that arises in me (in the form of "you should") is always an advice for me. It is what brings me to myself.