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CHICAGO, May 12 (Reuters) - Chicago soybean futures fell on Friday, led by deferred contracts representing the 2023 harvest after the U.S. Department of Agriculture (USDA) projected record-large U.S. production that should raise inventories.

But wheat futures rose after the USDA forecast a smaller-than-expected winter wheat crop in the drought-hit U.S. Plains.

By 12:56 p.m. CDT (1756 GMT), Chicago Board of Trade July soybeans were down 15 cents at $13.90-1/2 per bushel and new-crop November soybeans were down 25 cents at $12.23. July corn was up 3/4 cent at $5.83 a bushel while new-crop December corn was down 6-1/2 cents at $5.07-1/4.

The USDA projected that U.S. farmers would produce a record 15.265 billion bushels of corn, raising stocks by the end of the 2023/24 marketing year to 2.222 billion bushels, up from 1.417 billion by the end of 2022/23.

For soybeans, the government forecast a 4.510 billion-bushel crop and pegged 2023/24 soy ending stocks 335 million bushels, up from 215 million expected at the end of 2022/23.

"The numbers on corn and beans were irredeemably bearish," Marex Capital analyst Charlie Sernatinger said in a note to clients.

The USDA projected that average farm prices for 2023/24 corn would fall to $4.80 per bushel, from the 2022/23 average of $6.60, while new-crop soybean prices were seen at $12.10 a bushel, down from $14.20 in 2022/23.

The corn and soy production forecasts will be highly dependent on favourable Midwest weather over the next several months, which will be a key market concern as farmers finish planting and crops start to develop.

For wheat, overall U.S. supplies are expected to tighten in 2023/24. The USDA forecast the smallest crop of hard red winter wheat, used for bread, since 1957. Hard red winter wheat, grown in Plains states including Kansas, is normally the biggest U.S. wheat class. The USDA's estimate of hard red winter wheat production, at 514 million bushels, fell below most analysts' expectations.

However, overall U.S. winter wheat output was seen rising 2% from a year ago due to increased production of soft red winter wheat, grown in the Midwest and used for snack foods.

CBOT July soft red winter wheat was up 8-3/4 cents at $6.36 a bushel late in Friday's session and K.C. July hard red winter wheat was up 34-1/4 cents at $8.75-3/4 after reaching $8.99-1/2, the contract's highest since Nov. 25. (Additional reporting by Naveen Thukral in Singaporeand Sybille de La Hamaide in Paris; editing by Rashmi Aich, Kirsten Donovan)