Use "irreconcilably" in a sentence

1. The marriage ended in April 1920, with Chaplin explaining in his autobiography that they were "irreconcilably mismated".

2. Suppose, then, that the expressions defining the authority of the convention were irreconcilably at variance with each other; that a NATIONAL and Adequate GOVERNMENT could not possibly, in the judgment of the convention, be affected by ALTERATIONS and PROVISIONS in the ARTICLES OF CONFEDERATION; which part of the definition ought to have been embraced, and which rejected?