Which Farmer Owned the Horse? (Who Stole What from Whom? Part VI)

The horse was recovered and was to be given back to the rightful owner, who was either Farmer White, Farmer Brown, or Farmer Black. The three farmers each made two statements:

Farmer White:

1. The horse does not belong to Farmer Brown.
2. It belongs to me.

Farmer Brown:

1. The horse does not belong to Farmer Black.
2. It belongs to Farmer White.

Farmer Black:

1. The horse does not belong to Farmer White.
2. It belongs to me.

As it happened, one of the three made two true statements; one made just one true statement; and one made statements that were both false.
Who owns the horse?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Assume that Farmer White is making two true statements. Accordingly, Farmer Brown is also making two true statements, which is a contradiction. Conversely, the assumption that Farmer Brown is making two true statements is rendered a contradiction by the statements of Farmer White, who would also be required to make two true statements under this assumption. Therefore, only Farmer Black can be making two true statements.

It has now already been established that Farmer Black is the owner of the horse but to complete the puzzle, it should be pointed out that Farmer Brown is making two false statements and Farmer White is making one true and one false statement.