Excellent! I wonder how far the malicious behavior can be extended.

Here the problem is that A directly uses a valid but malicious inference module Q. If A were built to enumerate proofs by length and act on the first one of the form "A()==a implies U()==u, and A()!=a implies U()<=u", can U be rewritten to guarantee that a particular spurious proof comes up first?

Or if A uses a halting oracle to check through statements of that form, can U be written (incorporating that oracle) so that the halting oracle fails to return for the genuine counterfactual and only returns "True" for a particular spurious one?