Does the husband's saying to his wife, "I have annulled the contract between us," intending the agreement to live together and not the marriage contract, constitute an annulment of the marriage?

This phrase is a metaphorical expression for divorce (kinayah), so divorce does not occur by it unless the husband intends it. The reference for his intention is his own statement, as he knows it best. So, if the husband says that he did not intend divorce, it does not occur.