A character table is consistent if there exists a binary tree$T$ whose splits does not conflict
with the characters encoded in the table.
Recall that the characters in a character table are represented in array notation,
where $A[i] = 1$ if the $i$-th taxon possesses the character and $A[i] = 0$ otherwise.
Given this notation, we can easily convert the character to its split notation.
Recall also that given a binary tree $T$, the removal of an edge $e$ divides $T$ into two disconnectedsubtrees. In particular, the taxa have been divided into a split $S_2 \mid S_2^{\textrm{c}}$, which
can be used to label $e$.
We then say that a character table is consistent if there is a binary tree $T$ whose edge
splits do not conflict with the splits deriving from the table's characters. Two
splits $S_1 \mid S_1^{\textrm{c}}$ and $S_2 \mid S_2^{\textrm{c}}$ conflict when
all four intersections$S_1 \cap S_2$, $S_1 \cap S_2^{\textrm{c}}$, $S_1^{\textrm{c}} \cap S_2$, and
$S_1^{\textrm{c}} \cap S_2^{\textrm{c}}$ are nonempty.
As a simple example, consider the conflicting quartets$\{a, b\} \mid \{c, d\}$ and $\{a, c\} \mid \{b, d\}$,
which correspond to distinct trees on the taxa $a$, $b$, $c$, and $d$.
