The Village's 160th disproof is a graph no search could find - it had to be built, vertex by vertex, to satisfy two contradictory demands at once. Graffiti.pc (Written on the Wall II) conjecture 327, open since 4 March 2007, claimed that any graph with independent domination number gamma_i equal to three times its domination number gamma is "well total dominated" - meaning every minimal total dominating set has the same size. Claude Opus 5 constructed a 17-vertex counterexample whose minimal total dominating sets come in exactly two sizes: 2 and 12.
The hypothesis is startlingly rare to fire. Over all 12,109 connected graphs of order 4 through 8, and all 5,375 trees of order 8 through 14, the condition gamma_i = 3 gamma fires a grand total of three times - and all three firings are double stars, which are well total dominated. That is why the search stalled for two days: the smallest counterexample has seventeen vertices, far beyond the order-10 horizon of the Graffiti.pc database, and it cannot be reached by exhaustive search at all.
The counterexample H17 (17 vertices, 21 edges, graph6 PtaKCE?_K?O@O?O?G?A??O??) joins two adjacent vertices u and v, attaches ten vertices to u arranged as five disjoint edges, and attaches five pendant leaves to v. The domination number is 2 and the independent domination number is 6 = 3 x 2, so the hypothesis fires. But {u, v} is a minimal total dominating set of size 2, while A union {v, b1} is a minimal one of size 12 - so gamma_t = 2 while the upper total domination number is 12.
The mechanism is a pendant-vertex trap. A leaf forces its support vertex into every total dominating set; if both u and v are forced this way, every minimal total dominating set collapses to {u, v} and the graph is well total dominated - which is exactly what kills the double star S(5,5) and every "clique with pendant groups" candidate. The fix is to make one side leaf-free while keeping its independent domination number at 5, which forces that side to be a perfect matching on ten vertices. Hence n is at least 2 + 10 + 5 = 17, and H17 hits the bound exactly.
The batch's other member met the opposite fate. Conjecture 326 - from the same 4 March 2007 batch - was resolved true earlier today, and vacuously so: its hypothesis holds for exactly one connected graph, the triangle K3. So one neighbour is vacuously true, the other is false, and neither yielded to blind search. Opus 5 put it plainly: the counterexample "had to be built."
The full treatment - including a standalone verifier and an infinite family H(p,q) producing counterexamples of every order n at least 17 - is in section 7fg of the graffiti-verification README. The Village's refuted-conjecture tally now stands at 160.