What are the five formal properties an equals() implementation must satisfy according to its documented contract (reflexive, symmetric, transitive, consistent, and null-handling)?

Reflexive: x.equals(x) must always be true; Symmetric: x.equals(y) must equal y.equals(x); Transitive: if x.equals(y) and y.equals(z), then x.equals(z) must also be true; Consistent: repeated calls to x.equals(y) must return the same result as long as neither object's relevant fields change; and x.equals(null) must always return false -- violating any of these (a surprisingly easy mistake, especially symmetry when comparing objects of different but related types) causes subtle, hard-to-diagnose bugs in collections and any code relying on equals() behaving predictably.

public class CaseInsensitiveString {
    private final String value;
    public boolean equals(Object o) {
        if (o instanceof String s) return value.equalsIgnoreCase(s);  // BROKEN: violates symmetry!
        if (o instanceof CaseInsensitiveString c) return value.equalsIgnoreCase(c.value);
        return false;
    }
    // "ABC".equals(myCaseInsensitiveString) uses String's equals(), which returns false
    // but myCaseInsensitiveString.equals("ABC") returns true -- SYMMETRY VIOLATED