Anchor: I am well aware of my deplorable lack of humility, generally considered a crucial component of any sincere apologia.
Entailed: I am aware that I'm lacking humility.
Contradiction: I am not aware of my lack of humility.
Contradiction: May our paths never cross again.
Contradiction: In 1997, following a renovation project which spanned 14 years, the Borghese Gallery was reopened. 
Contradiction: Two people are watching tv.
Contradiction: The Office of Management and Budget has the authority to review information collections.