The phrase "appear to be not" is correct and usable in written English.
It can be used when expressing a perception or observation that something does not seem to be the case.
Example: "They appear to be not interested in the proposal, despite the initial enthusiasm."
Alternatives: "seem to not be" or "seem not to be".
The performers appear to be not on but inside the set, and eventually inside your head.
Because Connecticut's boards of education are established by state statute, they appear to be not subject to local control.
From this meeting, at least, the Company of Friends would appear to be not all that far from the Kiwanis or Elks Club.
Mr. Thomas has lost a lot of money in an investment in a cousin's Georgia dealership, but many of his problems appear to be not of his making.
The second factor is that out-of-state visitors appear to be not only afraid of flying, but also afraid of coming to New York in particular.
Insidiously, the photographs also make the text appear to be not fictional but real, despite the widespread knowledge that even in the predigital age, photographs could be manipulated.
In Iran, whose relations with Saudi Arabia are tense, the relatives appear to be not exactly prisoners, but not quite guests.
Notwithstanding Miller's resignation, which the President himself announced on Tuesday evening, the answers appear to be: not nearly as much as recent headlines suggest; and, nobody in the Obama Administration.
What Mr. van Hooydonk calls its exoskeleton is a series of ribbon- or shell-like pieces that appear to be not so much attached as floating together in formation.
We're not yet at the stage of thinking the same thing of a boy turning 13, although in some parts of urban Britain we appear to be not far off it.
She can appear to be not one person but several, high-achieving and high-strung, tumbled together in a gunny sack and made to wrestle their ways out into the public gaze.
