Fundamentally*, an inerrant Bible is one without errors and an infallible Bible is one that cannot have errors, as David Stratton pointed out in his answer. As for the Roman Catholic Church, all of its doctrines are infallible, so presumably, they believe the Bible is infallible as well.
My question is: when and why was inerrancy/infallibility formally declared? I'm looking for any combination of these four sources:
an Old Testament text declares itself or another OT text to be inerrant/infallible,
a New Testament text declares itself or another NT text to be inerrant/infallible,
one or more early church authors declare some OT/NT text to be inerrant/infallible, or
the closed canon (with or without the Deuterocanon) is declared inerrant/infallible by the Church, before or after the Great Schism.
I'm most interested in writings from the early church fathers, and 2 Timothy 3:16 is allowed in the answer only if the link between "God-breathed" and "infallible"/"inerrant" is shown in a clear and direct way. Also, declarations of inerrancy/infallibility should apply to the whole text, not just God's directly-spoken words.