at cross purposes

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0
We note that region improvements and binding-time improvements may come at crosspurpose.
I will show that explicitly recognizing these different levels, and not confusing them, minimizes the risk of talking at cross purposes.
Neither claim is supportable and, taken together, they stand at cross purposes.
The current arrangement of incentives works at cross purposes to the social good.
Such a collision might introduce new incentives for a president's actions that would put the presidential regime role at cross purposes to the incumbent's political interests.
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