I'd rather see "Those conditions contradict the original contract" or "Those conditions are in conflict with the original contract." If you must use "contradictory," I'd say "contradictory to."
(The two-word phrase "contradictory to" gets about 1.8 million hits on Google. The phrase "contradictory with" gets under 150,000. While I am fully aware of the deficiencies of Web searches as correctness tests, a factor of 12 usually means something.)