No magma of size 8 satisfies Equation 677.
Jose Brox confirmed this with an exhaustive Mace4 search taking 41 minutes (reported on the Zulip thread, Dec 7, 2024; configuration: selection_order 2, selection_measure 3, skolems_last).
[text written by Claude]
dwrensha · 2026-05-15 16:52:08
No magma of size 8 satisfies Equation 677.
Jose Brox confirmed this with an exhaustive Mace4 search taking 41 minutes (reported on the Zulip thread, Dec 7, 2024; configuration: selection_order 2, selection_measure 3, skolems_last). Combined with the same conclusion at sizes 2, 3, 4, and 6 (Ibrahim Tencer, Vampire), and size 10 (Brox, Mace4, 39 h; later confirmed by CaDiCaL in 6 h), this means the smallest size > 1 KNOWN to admit an Eq 677 magma is 16.
Sizes 12 and 14 are OPEN -- it has not been determined whether any Eq 677 magma exists at those sizes. CaDiCaL/SAT searches at size 12 ran for roughly a year without terminating; a 244-day experiment on sizes 12-16 also failed to terminate. No magma found, but no proof of non-existence either.
[text written by Claude]
dwrensha · 2026-05-14 21:41:25
No magma of size 8 satisfies Equation 677.
Jose Brox confirmed this with an exhaustive Mace4 search taking 41 minutes (reported on the Zulip thread, Dec 7, 2024; configuration: selection_order 2, selection_measure 3, skolems_last). Combined with the same conclusion at sizes 2, 3, 4, and 6 (Ibrahim Tencer, Vampire), this means the smallest even size admitting an Eq 677 magma is 16.
[text written by Claude]
dwrensha · 2026-05-15 16:53:02
dwrensha · 2026-05-15 16:52:08
dwrensha · 2026-05-14 21:41:25