cross-purpose
noun
                                                                                                                            
                                                            cross-pur·pose
                    
                                                                                                              
                                                                                                                                  ˈkrȯs-ˈpər-pəs  
                                                      
                                                          
            
                                
              
          
                                                      : a purpose usually unintentionally contrary to another purpose of oneself or of someone or something else                                      
                
                  —usually used in plural
the two were always working at cross-purposes
    
                
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  Merriam-Webster unabridged




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