Invented a cover having no effect (7)

I believe the answer is:

invalid

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'having no effect' is the definition.
(I've seen this before)

'invented a cover' is the wordplay.
'invented' becomes 'inv' (I can't explain this - if you can you should give a lot more credence to this answer).
'cover' becomes 'lid' (lid is a kind of cover).
'inv'+'a'+'lid'='INVALID'

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(Other definitions for invalid that I've seen before include "patient [found]" , "Null and void" , "One disabled by illness" , "Not legally binding" , "Disable" .)

I've seen this clue in The Times.

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