With all the name changes in the Cattleya alliance, and with several hybrids in the alliance called Cornelia, and with the tags on plants even from reputable nurseries not always reflecting to most up to date nomenclature, I just want to make sure I know which one you are referring to. Cattleya Cornelia is a primary hybrid of labiata x pumila (at the time it was registered, pumila was considered Laelia, so it would have been originally registered as Laeliocattleya) and its direct descendants can be viewed here:
OrchidRoots
There is also Cattleya Cornelia registered in 1954 which involves three species and its lineage and direct descendants can be viewed here:
OrchidRoots
There is also a 1976 hybrid which in the current nomenclature is Rhyncholaeliocattleya Cornelia which is a complex hybrid, and its information can be viewed here:
OrchidRoots
Which one of these are you referring to, or is there yet another Cornelia that I have missed?