Complex sentence: They convinced one member of the cabinet (Lyonne) and nineteen bishops of their position, these bishops argued, in a letter to Clement IX, that the infallibility of the Church applied only to matters of revelation, and not to matters of fact.
Split into simpler sentences: They convinced one member of the cabinet (Lyonne) and nineteen bishops of their position. As a result, these bishops wrote to Clement IX, arguing that the infallibility of the Church applied only to matters of revelation, and not to matters of fact.