In Gödel's 3-valued logic $G_3$, truth values are $V = \{0, \frac{1}{2}, 1\}$, with $1$ being the designated value (representing "True"). The conjunction is $v(A \land B) = \min(v(A), v(B))$, disjunction is $v(A \lor B) = \max(v(A), v(B))$, and implication is $v(A \implies B) = 1$ if $v(A) \le v(B)$, and $v(B)$ otherwise. Negation is defined as $\neg A = A \implies 0$. Which of the following formulas is NOT a tautology (i.e., does not always evaluate to $1$ under all valuations) in $G_3$?