If your separation agreement states that cohabitation terminates alimony and you are certain that the cohabitation going on with your ex-spouse fits the cohabitation definition, then you can stop paying alimony unless your separation agreement states otherwise.
Your ex-spouse could file a breach of contract lawsuit against you for failing to perform under the contract as obligated to do so. However, your defense would be the cohabitation, and you would need to have the evidence ready to support your claim of cohabitation meeting the definition in your separation agreement. If you could not satisfactorily prove cohabitation, then you could be required to pay your ex-spouse’s attorney’s fees for the breach of contract lawsuit as the “losing” party.
Rather than simply stopping payment, perhaps you can send your ex-spouse a letter stating that she has terminated the alimony pursuant to the separation agreement and therefore, you will no longer be paying it, also pursuant to the separation agreement (assuming you are confident that the current circumstances meet the definition of cohabitation in your separation agreement).
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