"Known not to ..." or "Known to not ..."

Which one of the following word orders is correct:

This program is known not to work correctly.

or

This program is known to not work correctly.

They are both acceptable.

There is a common notion that it is incorrect to "split an infinitive", but this appears to have been invented by authors of Grammar Handbooks. Following this rule, known not to work would be preferred. But English speakers will understand eiher version without difficulty.

Yes, this is perhaps counter-intuitive. With

The man was advised to not wear red.

the order seems logical, and the sentence sounds reasonable, if the last three words are given moderate stress. However,

The man was advised not to wear red.

is by far the more idiomatic (usually used) variant.

I've given a different pair of examples; I think that, in some cases, the more logical version is bordering on unacceptable because it would sound so strange.

He was believed to not be the former Nazi leader.