As the OP said A and B are never null, C may be null, use this:

if(A.equals(B) || B.equals(C) || A.equals(C))
   // not unique

and, as others have already suggested, you can put it in a method for reuse. Or a generic method if you need more reuse ;-)

Note that in Java, a feature of equals is that if its argument is null it should not throw, but return false.

Since I never start a Java project without using Apache commons-lang, try ObjectUtils.equals (it s null safe):

if (ObjectUtils.equals(a, b) || ObjectUtils.equals(b, c) || ObjectUtils.equals(a, c)) {
  // error condition
}

Put that logic in a generic method, and you ll do even better.

While the business logic allows C to be null, in scenarios like this, it s often better to code defensively and assume that either A or B could be null as well.

You can abstract that method in a utilities method like:

public boolean allUnique(Object... objs) {
  Set<Object> set = new HashSet<Object>();
  for (Object o : objs)
    set.add(o);
  return set.size() == objs.length
}

The method may not perform well for small numbers (due to the overhead of creating the Set and the varargs array). However, it grows linearly O(n), and for large values it s better than the quadratic growth of a nested if statements.

boolean areDistinct(Object a, Object b, Object c) {
    return (!a.equals(b) &&
            (c == null || (!c.equals(a) && !c.equals(b))));
}

As long as your objects implement equals, you can use the Stream API to get a distinct set of values, and if that distinct count is 1, they are all the same.

boolean allEqual = Stream.of(obj1, obj2, obj3).distinct().count() == 1

As the apache s common.lang3.ObjectUtils.equals() is @Deprecated. Use Objects.equals(aObj,bObj). Comparison should be made with && if you want that all 3 objects are the same. Use || if you want that just one combination of a&b, a&c or b&c is the same.

/**
 * Compare 3 objects of the same {@link TYPE}, if they are all equal using {@link Objects#equals(Object, Object)}.
 * 
 * @param aObj the 1st object
 * @param bObj the 2nd object
 * @param cObj the 3th object
 * @param <TYPE> the type of the objects
 * @return true if the are all the same
 */
public static <TYPE> boolean equals(TYPE aObj, TYPE bObj, TYPE cObj) {
    return Objects.equals(aObj, bObj) && Objects.equals(bObj, cObj) && Objects.equals(cObj, aObj);
}

package com.test;

public class Equality {

    public static void main(String[] args) {

        Boolean flag;

        int[] arr={1,1,1,12};
        flag=check_equal(arr);
        System.out.println(flag);
    }

    public static Boolean check_equal(int[] arr){
        Boolean flag=true;

        outerloop:
        for(int i=1; i< arr.length; i++)
            {
                for(int j=1; j< arr.length; j++){
                    if(arr[i]==arr[j]){
                        flag=true;
                    }   
                    else{
                        flag=false;
                        break outerloop;
                    }

                }

            }
        return flag;
    }
}