I wonder whether such constructions with infinitives other than TO BE are correct
I believe him to work there
The church believed Bill to sin often
The active construction 'believe smb. to V' in the contemporary language is generally limited to cases where V is either a stative verb (esp. 'be')
I believe him to be honest.
or an auxiliary
I believe him to have committed a terrible crime.
Other types of verb will tend to be unacceptable:
*I believe him to work as a doorman at the Ritz.
(--> I believe that he works...)
Interestingly, however, the corresponding passive construction tends to accept any type of verb, e.g.
He is believed to work as a doorman at the Ritz.