Sentence 1: On the other hand, if buyers at online auctions are persistently disappointed, it's possible that after a while they'll stop bidding.

Sentence 2: Buyers are more likely to continue bidding after being disappointed consistently.
Is this second sentence entailed by the first?

Answer: no

Sentence 1: or indirectly in Congress.

Sentence 2: The rage is indirectly festering in Congress.
Is this second sentence entailed by the first?

Answer: it is not possible to tell

Sentence 1: The position of Bishop of Rome as primate of the Western Church (pope derived from papa, the Latin word for father), first claimed in the second century, was later asserted by Pope Leo I (440 461), who traced the succession back to St. Peter.

Sentence 2: St. Peter was the first to be the primate.
Is this second sentence entailed by the first?

Answer:
yes