Actually I am 100% correct.
According to USPTO Records, Patent 5,842,437 is a Continuation in part of 5,799,609 (application 08/643,985 filed on 05-07-1996) (all maintenance fees have been paid)
Patent 6,055,934 is a continuation of 5,799,609 (application 08/643,985 05-07-1996). I would need to review this patent to see what type of “continuation” it happens to be. (all maintenance fees have been paid)
Now it is true that one can call a patent application a "CIP" when it is not and the records at the USPTO are based on what the person filing the application calls the application (CIP, Divisional, continuation, etc.).
Thus one would need to verify a patent called a "CIP" is a true "CIP". More specifically, the important issues is what is claimed in the "CIP" and if the claims are directed to the new material.
In the future, since you clearly value your patents, as you paid those expensive 12 year maintenance fees, I would direct my patent questions to a local patent attorney. Patent validity is a mine field and one wrong step and boom . .. you have made an expensive mistake listening to wrong answers regarding same and there are plenty of wrong answers out there.