To engage in a desperate and almost equal contest.

1

1839.  They are enemies, and let them lock horns. Of what age is that wondrous man you speak of?—‘History of Virgil A. Stewart,’ p. 23 (N.Y.).

2

1888.  The struggle in the convention came to be really a duel between Mr. Cleveland and the Boss of Tammany, with whom Mr. Cleveland had at an earlier period in his career “locked horns.”—Bryce, ‘American Commonwealth,’ ii. 562 note. (N.E.D.)

3