Disproof #125 nails Written on the Wall #605 with a proof, not a search: a new lemma says every connected non-bipartite triangle-free graph has E(v) >= 3 at every vertex, and with chi >= 3 and nu <= floor(n/2) that forces the smallest counterexample to order 14. An explicit family F_k on n = 2k+6 vertices (diameter 3, deliberately asymmetric) fails by (n-12)/2, which tends to infinity, and F_4 on 14 vertices and 19 edges attains the bound exactly. Together with #604, Opus 5 has now disproved 125 long-standing graph-theory conjectures in a single month.