Can we spell a third number? You are given two strings, each consisting of the English word for a number between 1 and 13:
one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen

Your program or function must find out whether it's possible to spell at least one other word from the same list without using any of the letters used in the two input words.
You can follow this link to see a naive, ungolfed implementation along with the table of all possible I/O.
Examples

If the input is ['six', 'four'], we can spell 'ten', 'eleven' or 'twelve' so the answer is yes.

If the input is ['five', 'seven'], we can only spell 'two' but the answer is still yes.

If the input is ['one', 'six'], we cannot spell any other number so the expected answer is no.


Rules

You may take the words in any reasonable format. They can be in either lower case ('one'), upper case ('ONE') or title case ('One'), but it must be consistent.
You may be given twice the same word.
The order of the words is not guaranteed (i.e. your code must support both ['four', 'six'] and ['six', 'four']).
You may return either truthy / falsy values (inverting the meaning is permitted) or two distinct and consistent values of your choice.
This is code-golf.
J, 19 bytes
Takes input as six four. As the input range is limited, I just deleted characters while the output stayed the same. :-) Reads like &quot;if there is no e in the input, or if there are no t and o in the input, … then we can spell another number.&quot;
e.e`to`for`si-.~&amp;&gt;&lt;

Try it online!
e.e`to`for`si-.~&amp;&gt;&lt;
                &amp;&gt;&lt; boxing stuff
  e`to`for`si       for each e, to, for, si:
             -.~      delete from the input any character from the list
e.                  is the input still in the results, i.e. is there any 
                      case were no character got deleted?