Python 2, 56 bytes

lambda s:all(set(x)&set(s)for x in"e to for si".split())

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Take inputs like two four, outputs negated. Checks whether the string has an e, and intersects the non-e numbers of two, four, and six.

Python 2, 56 bytes

lambda s:all(set(x)&set(s)for x in"e to for si".split())

Try it online!

Take inputs like two four, outputs negated. Checks whether the string has an e, and intersects the non-e numbers of two, four, and six.

52 bytes in Python 3 using {*x} for set(x).