at odds vs self-contradictory

at odds and self-contradictory both are adjectives.

Word	Noun	Adjective	Verb	Adverb
at odds	No	Yes	No	No
self-contradictory	No	Yes	No	No

As adjectives, at odds and self-contradictory are synonyms defined as:

Other synonyms of at odds include conflicting, contradictory.

at odds (adjective)	self-contradictory (adjective)
in disagreement	in disagreement
	seemingly contradictory but nonetheless possibly true