It is likely that Jessica is a wolf. It is certain that John left the football. Chances are about even that Gertrude is a sheep. There is little chance that if Gertrude is a sheep, or John left the football, then Lily is gray. We doubt that if John left the football, and Jessica is a wolf, then Brian is a frog. We doubt that if John left the football, or Jessica is a wolf, then Sandra took the apple.
We believe that sandra took the apple, or Lily is gray.
It is probably not the case that sandra took the apple, or Lily is gray.
We believe that sandra took the apple, or Lily is gray.
Sandra took the apple, or Lily is gray.