Piece of wood’s rotten? Stop surfing (3,3)

I believe the answer is:

log off

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'piece of wood's rotten? stop surfing' is the definition.
I can't tell whether this defines the answer.

'piece of wood's rotten?' is the wordplay.
'piece of wood' becomes 'log'.
'rotten?' becomes 'off' (rotten food is 'off').
'log'+'off'='LOG OFF'

Can you help me to learn more?

(Other definitions for log off that I've seen before include "Exit a computer" , "Leave a computer system" , "make an exit on screen" , "Terminate (computer session)" , "finish" .)

I've seen this clue in The Guardian.

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