Thanks, you're right that this isn't self refuting. But with that P1, the argument seems invalid:

P1: For most predicates X: Not (For all minds m: X(m))

P2: UCMAs are X

C: Not UMCA

is like

P1: For most prime numbers n: (odd)n

P2: 2 is prime

C: 2 is odd

Edit: you might think that the conclusion is not that not 'not UMCA' but 'UMCA is unlikely', but this doesn't follow either. I don't know quite how 'most' quantifiers work, but I don't think we can read a probabilistic conclusion off of them. I don't think it follows from the above, for example, that 2 is likely to be odd.