Not public accommodation for soldiers? (7,6)

I believe the answer is:

private houses

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'not public accommodation for soldiers?' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'not public accommodation for soldiers?' is the wordplay.
'not public' becomes 'private' ('private' is the opposite to 'public').
'accommodation' becomes 'house'.
'for soldiers?' becomes 's' (I am not sure about this - if you are sure you should believe this answer much more).
'private'+'house'+'s'='PRIVATE HOUSES'

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I've seen this clue in The Globe and Mail.

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