I'm trying to find a combinator that can derive all other
combinators, so there is an expression in terms of this combinator
(I'll call it U, for universal), for any (computable) combinator. I
also want a proper combinator, which means that Uabc..., will be
entirely in terms of a,b,c, etc. With such a combinator, I can make
a new minimalist version of the Xi function. I've worked out a few
properties such a combinator must posess:

1) The Cancellation Effect, which means when Uabc... is
betareduced, one of the variables will disappear. As an example,
the combinator K is defined as: Kxy=x, so y disaapears. No
combinator with the cancellative property can be derived solely
from combinators without said property.