Wiktionary
cross purposes
n. (cross purpose English)
Wikipedia
Cross Purposes
Cross Purposes is the seventeenth studio album by English rock band Black Sabbath, released in January 1994.
Usage examples of "cross purposes".
Can you imagine the General here having two men working for him on the same project in, say, Warsaw, men who were not only unknown to each other but completely at cross purposes and potentially at each other's throats.
Both systems are haphazard and inefficient, and often operate at cross purposes.