Catalysis of the reaction: (1S,3R,4S)-3,4-dihydroxycyclohexane-1-carboxylate + NAD+ = (1S,4S)-4-hydroxy-3-oxocyclohexane-1-carboxylate + H+ + NADH.
(-)t-3,t-4-dihydroxycyclohexane-c-1-carboxylate-NAD oxidoreductase activity