Refute study by unknown (4)
I believe the answer is:
deny
'refute' is the definition.
(I've seen this before)
'study by unknown' is the wordplay.
'study' becomes 'den' (term for a study or office).
'by' says to put letters next to each other.
'unknown' becomes 'y' (algebra).
'den'+'y'='DENY'
(Other definitions for deny that I've seen before include "Refuse; repudiate" , "Refuse access to" , "Refuse to grant" , "Refuse to acknowledge" , "Disclaim" .)