First, what defines an infallible teaching of the church?
The Catechism of the Catholic church?
Or the pope speaking ex cathedra?
Is it pronouncements from the Council of Trent or Vatican II?
Could you give us some examples of infallible teachings?
two come to mind at once...The Immaculate Conception" which states that Mary was concieved without original sin, and the "assumption" which states that Mary was bodily assumed into Heaven by the power of God. (didn't ascend on her own)