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      lex: "Measured: 100 six-Nand three-variable single axioms {X = a} (of 288684) whose models on domains of size 2, 3 and 4 are exactly those of Boolean Nand (n = 327042, exact enumeration). Interpretation: Finite-model screening is a necessary condition for axiomatising Boolean algebra (every Boolean algebra is a model, and no 3-element algebra is), not a sufficient one; the sufficiency of the six-Nand axiom rests on the equational proof the book presents on pp. 810-811 (found with automated theorem provers) which standard tooling here cannot re-run. The test therefore checks everything about the claim that is checkable by enumeration: that the published axiom is consistent with being an axiom for logic on all domains up to 4 elements, that six Nands is the minimum passing even the weakest screens, and that a screen-passing system appears within the first few thousand systems of the book\'s own enumeration. \'Simplest few thousand\' is read against the book\'s own ordering (by total number of Nands, systems {X = a} and {X = a, a.b = b.a})."
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      lex: "Criterion (c) fails only on the count bound, and only because the pre-registered enumeration order places every single axiom with fewer Nands before the two-axiom family: the first family-II system that works up to 4 values is number 1248 of the 3402 family-II systems with 6 Nands (number 1716 counting family-II systems of all sizes), but up to 36204 when all 34956 shorter single axioms are counted first. Whether that is \'the first few thousand\' depends on the order chosen; the book\'s own text counts only the family it searches."
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