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The Collaborative International Dictionary
Sciomachy

Sciomachy \Sci*om"a*chy\, n. [Gr. ?, ?; ? a shadow + ? battle: cf. F. sciomachie, sciamachie.] A fighting with a shadow; a mock contest; an imaginary or futile combat. [Written also scimachy.]
--Cowley.

Wiktionary
sciomachy

n. battling an imaginary enemy