First of all some errors I wanted to point out in your program. The first is shouldn't 'a' be appended before 't' to obtain 'cat'. And you can use only one sequence and append 'cat' to it.
Secondly I'm assuming the .current() function returns the current character and so the '==' boolean operator has two operands which are character data type. So the one you defined is not called.
Thirdly your '+=' operator is being called first at line 8 and then line 9. But your '+=' operator function is doing nothing and so the sequence s3 is empty till the end of the program. And that is why your boolean statements return false.
The code you've shown for operators ==, !=, + and += don't do anything. When overloading an operator you have to write the code that does whatever the overloaded operators mean.