Find out first two did leave redesigned mattress in Kyoto, for example (5)

I believe the answer is:
futon
'example' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'find out first two did leave redesigned mattress in kyoto' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'out' is 'uto' which is within the answer.
This may be the basis of the clue (or it may be nonsense).
'for' is the link.
Can you help me to learn more?
(Other definitions for futon that I've seen before include "Kind of Japanese chair-bed" , "A Japanese bed-mattress" , "Jap. quilt bed" , "Kind of mattress" , "Sleep on it" .)