Looking on the internet deeply has found these results:

seems not to is the most popular phrase on the web.

did not seem 10 results on the web	seems not to 1449,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Dec 2, 2013 ... She seems not to know. She doesn't seem to know. Is there a name to this type of construction? negation auxiliary support�... Apr 30, 2012 ... Try not to be alarmed if a rule doesn't seem to work for a specific sentence. Try not to be alarmed if a rule seems not to work for a specific�... verbs do May 3, 2014 ... He seems not to want to help us. and. He seems want to help us. Is it correct if I use "seem" in a negative sentence? Which role does "seem"�... Nov 26, 2005 ... The construction, "it seems not to be", is perfectly correct, and it is perfectly current too (i.e., not old fashioned). Nevertheless, when used outside�...

did not seem

10 results on the web

seems not to

1449,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Dec 2, 2013 ... She seems not to know. She doesn't seem to know. Is there a name to this type of construction? negation auxiliary
support�...
Apr 30, 2012 ... Try not to be alarmed if a rule doesn't seem to work for a specific sentence. Try not to be alarmed if a rule seems not to work for a specific�...
verbs do
May 3, 2014 ... He seems not to want to help us. and. He seems want to help us. Is it correct if I use "seem" in a negative sentence? Which role does "seem"�...
Nov 26, 2005 ... The construction, "it seems not to be", is perfectly correct, and it is perfectly current too (i.e., not old fashioned). Nevertheless, when used outside�...