"Breaking" Epimenide's Loop

Traditionally:

However by adding a separate level of depth we resolve the antinomy to a summation of nonzero value:

Which continues with an alternating true false pattern, Note that as G(F) is false we may say it is false:

As it is false, the statement that it is false is in and of itself false:

This is thus true, and now the alternating takes place:

Thus this series evaluates to an overall False statement which breaks Epimenide’s loop when this second level of using a falsification cascade is used. Naturally one could go further and only use false statements, by negating True statements: