Pattern - Logic & Equations

DSU is great for checking consistency in logic. If someone tells you: "$A$ equals $B$" and "$B$ equals $C$" and "$A$ does not equal $C$," there is a contradiction.

Model "equals" as union. Process all equality constraints first, unioning elements. Then check inequality constraints: if two elements that must be unequal are in the same group, it is unsatisfiable.

This pattern solves satisfiability problems with equality and inequality constraints.