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In separate batches, finely chop cucumbers, cabbage and apples in food processor, using pulsing action. Do not overprocess. Mix chopped vegetables. Set aside.
Mix remaining ingredients in 6-quart saucepot. Bring to boil. Add vegetables; return to boil. Reduce heat to low; simmer, uncovered, 15 minutes.
Ladle into 5 hot sterilized pint or 10 half-pint canning jars, leaving 1/4-inch headspace. Run thin, non-metallic utensil down inside of jars to remove air bubbles. Wipe rim of jars clean with damp cloth. Cover jars with metal lids and screw on bands.
Process in boiling water canner 10 minutes. After processing jars, remove from water bath canner. Cool at room temperature on towel or rack for 12 to 24 hours. Check for seal.