I did some research on this and I don't think there is a studio recording of the song "Perfect Enemy", but..
Quote:
The song "Passive" that appeared on the 2004 album eMOTIVe is actually adapted from the defunct band Tapeworm (also known as The Tapeworm Project). Tapeworm was essentially a project involving Maynard James Keenan and Trent Reznor (of Nine Inch Nails) as well as Danny Lohner. The project never fully developed due to apparent contractual conflicts that could not be negotiated. During several shows on their tour in early 2001, A Perfect Circle played a cover of an unreleased Tapeworm song, then apparently titled "Vacant" (also referred to as "Perfect Enemy"). The song was never released by any artist until it appeared on eMOTIVe as the song "Passive".
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http://en.wikipedia.org/wiki/A_Perfect_Circle