Contradiction (noun)

1. A statement or situation that contradicts or denies another statement or situation.
2. A logical inconsistency or opposition between two statements or propositions.
3. A situation in which two things are incompatible.

Origin:

From the latin contradictio, meaning "opposition, resistance", from contradicere, meaning "to speak against".

Examples:

1. The statement was a contradiction of what he said earlier.
2. The claim that all animals are equal but some animals are more equal than others is a contradiction.
3. The argument contained several contradictions.
4. The story had a contradiction, which made it hard to believe.
5. The data contained a contradiction which made the analysis difficult.