Two ways to outface with a contradiction (6)

I believe the answer is:

denial

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'contradiction' is the definition.
(thesaurus)

I cannot understand how the rest of the clue works.

(Other definitions for denial that I've seen before include "Refusal to accept an unpalatable truth" , "Rejection of a request" , "Repudiation" , "Daniel (anag.)" , "Refusal to believe an unacceptable truth" .)

I've seen this clue in the Evening Standard.

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