TYPE= should not be certain about (not (satisfies pred))

example 1: suppose P returns NIL, so that all objects satisfy (NOT P).
Then (NOT P) is a specifier for *Universal-Type* "in disguise" (as the comments refer to such constructs).
But:
(type= (specifier-type '(not (satisfies P))) (specifier-type 't)) => NIL and T

example 2: suppose P returns T so that no object satisfies (NOT P).
Then (NOT P) is *EMPTY-TYPE* in disguise. But:
(type= (specifier-type '(not (satisfies p))) (specifier-type 'nil)) => NIL and T

example 3: (an appropriate P is left to your imagination)
(type= (specifier-type '(not (satisfies p))) (specifier-type '(double-float 0d0 0d0))) = NIL and T
And this example is not commutative.

example 4: change 'double-float' to REAL. Same issue.
This one is related to https://bugs.launchpad.net/sbcl/+bug/308938, possibly the same.