Thanx for the solution... we determined independently that 12 qtw
seemed to be minimal, but couldn't be absolutely sure.

Since you say with a couple of days of CPU time you could deal with 18
qtw processes, doesn't this mean that \any/ cube process can be
checked for minimality? I can't recall whether the maximum number of
moves from solved is 17 or 19... if the former, 18 qtw may be
unnecessary. If the latter, then almost every cube process can be
checked directly, save the absolute longest ones (which are then
provably 19 anyway, since that's all they can be). Is my reasoning
faulty here? In any case, exactly how much more work in involved for
each qtw in solving the cube? In other words, how fast does it grow
(what's the power on the exponent, if describable this way)?

Thanx much folks.

<LNF>