contradiction in terms vs cross-purpose

contradiction in terms

noun
  • A phrase or expression in which the component words contradict one another, often unintentionally, or are claimed to do so when seen from a particular point of view. 

cross-purpose

noun
  • A contrary or conflicting purpose or understanding, especially an unintentional or misconceived one. 

How often have the words contradiction in terms and cross-purpose occurred in a corpus of books? (source: Google Ngram Viewer )