It is highly likely that Lily is gray. It is likely that John discarded the apple. There is a better than even chance that Daniel got the football. There is almost no chance that if 'Daniel got the football and John discarded the apple' then Mary grabbed the milk. It is highly unlikely that if 'Daniel got the football and Lily is gray' then Bernhard is a rhino. It is probable that if either 'Lily is gray' or 'Daniel got the football' but not both then Julius is a lion.
It is probably not the case that either 'John discarded the apple' or 'Lily is gray' but not both.
It is probably not the case that either 'John discarded the apple' or 'Lily is gray' but not both.
It is probable that either 'John discarded the apple' or 'Lily is gray' but not both.

  and(A,B) :- A,B.
  or(A,B) :- A;B.
  nand(A,B) :- not(and(A,B)).
  nor(A,B) :- not(or(A,B)).
  xor(A,B) :- or(A,B), nand(A,B).

  %hop0
  0.9::factA.
  0.7::factB.
  0.6::factC.
  %hop1
  0.02::factX:-and(factC,factB).
  0.05::factY:-and(factC,factA).
  0.7::factZ:-xor(factA,factC).

  %hop2
  conclusion:-xor(factB,factA).

  query(conclusion).
  
Either 'John discarded the apple' or 'Lily is gray' but not both.