This program fails to compile:

interface Sup<X> {
    boolean m(X x);
}

interface Sub<X> extends Sup<String> {
    boolean m(String s);
}

class Test {
    void test() {
        Sub s = new Sub() {
            @Override
            public boolean m(String o) { return true; }
        };
    }

Compiler says:

Main.java:15: error: <anonymous Test$1> is not abstract and does not override abstract method m(Object) in Sup
        Sub s2 = new Sub() {
                           ^
1 error

This seems to be inconsistent with the notion that 'overridden methods should not be inherited'. 

Note: this also affect the functional interface check as of JDK 8.