I'm guessing the Cyrix chip is a Cx486DRx2 upgrade CPU. Those were strange hybrid chips that fit a 386 socket and lacked an onboard math coprocessor but had a small 1k onboard cache and understood the 486 instruction set. (Making them neither fish nor fowl, really.) The 8580-111 ran at 16 Mhz so that CPU probably clock doubles it to 32Mhz.

Sadly that's probably rare enough to count as a collector's item, assuming you could find the right crazy chip collector to sell it to.