"Alien" distinguisher
You're on the right track.  Good job using the try-with-resources block for the BufferedReader.  You could use a Scanner instead for convenience.  (You could even use Scanner.nextInt(), but it would work slightly differently: the newline in the input would be optional.)

The variables antenna and eye can be local to main(), and therefore should not be static members of the class.

In Java, a common naming convention for methods that return a boolean is isSomething() or hasSomething().  In this case, though, maybeSomething() seems more appropriate.

It is rarely necessary to write return true; or return false; explicitly.  Usually, you would be better off returning a boolean expression.

import java.util.Scanner;

public class Alien {
    public static void main(String args[]) {
        try (Scanner in = new Scanner(System.in)) {
            System.out.println("How many antennas?");
            int antenna = Integer.parseInt(in.nextLine());

            System.out.println("How many eyes?");
            int eye = Integer.parseInt(in.nextLine());

            if (maybeTroy(antenna, eye)) {
                System.out.println("TroyMartian");
            }

            if (maybeVlad(antenna, eye)) {
                System.out.println("VladSaturnian");
            }

            if (maybeGraeme(antenna, eye)) {
                System.out.println("GraemeMercurian");
            }
        }
    }

    public static boolean maybeTroy(int antenna, int eye) {
        return ((antenna &gt;= 3) &amp;&amp; (eye &lt;= 4));
    }

    public static boolean maybeVlad(int antenna, int eye) {
        return ((antenna &lt;= 6) &amp;&amp; (eye &gt;= 2));
    }

    public static boolean maybeGraeme(int antenna, int eye) {
        return ((antenna &lt;= 2) &amp;&amp; (eye &lt;= 3));
    }
}