The more common problem is that to modify CT alimony is a 3 step process , 1 to prove cohabitation, 2 to prove an economic change , 3 to apply some formula to the new economic picture. You are seemingly very lucky in that you need only show #1
Don't blow it.
Cohabitation per se does not require sex or shared economics or always under same roof but it sure seems like the more links the easier it is to demonstrate .
Start with this idea and search forward for clues, basically cohabitation is the romantic dwelling of a man and woman together in the same place.
“Cohabitation is a dwelling together of man and woman in the same place
in the manner of husband and wife.” Wolk v. Wolk, 191 Conn. 328, 332,
464 A.2d 780 (1983). (Note this was pre the days of sex neutral everything! )
Personally I think you are light/short of a convincing foundation that they are cohabitating --at least as you post it. I think this is one place where quantity of separate comments about living together will be key to sustaining your point of view --and I'd sure try for a few more nails to build this one and then act swiftly .
Read literally as a layman I don't think the order as to that section prevents you from unilaterally taking the view that she is cohabitating and applying that wording already in the order to your payments --for sure it will be a big invitation to debate but it may be a point that can be successfully defended.