Serving American in pub one litre at first is not reasonable (9)

I believe the answer is:

illogical

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'serving american in pub one litre at first is not reasonable' is the definition.
I can't judge whether this defines the answer.

'litre at first is not reasonable' is the wordplay.
'litre' becomes 'L' (abbreviation).
'at' means one lot of letters go next to another (I've seen this in other clues).
'first is' becomes 'i' (lst letter of 'is').
'not reasonable' becomes 'logical' (similar in meaning. I am not sure about the 'not' bit.).
'l' put after 'i' is 'il'.
'il'+'logical'='ILLOGICAL'

Can you help me to learn more?

(Other definitions for illogical that I've seen before include "Irrational" , "Unreasonable" , "making little sense" , "Lacking sound reasoning" , "Without reason" .)

I've seen this clue in The Times.

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