Puzzle #13: Selling Grandma

Family finances have been rather tight lately, and to save the old homestead, Grandma and the grandchildren are discussing possibly selling Grandma. Widowed a few years ago, Grandma is still a looker. Bob, as eldest grandchild, is the supposed owner. In the discussion, each of them made two statements:

B1: “I would not sell Grandma for $1,000,000.”
B2: “Grandma is a cougar.”
T1: “Grandma‚Äôs apple pie is terrible.”
T2: “Bob always does what Grandma wants.”
W1: “Bob never lies.”
W2: “Tom always lies.”
G1: “If you do sell me, I want it to be to a young stud who can keep me warm and happy at night.”
G2: “I make great apple pie.”

One of them always tells the truth, one always lies, and the other two are fencesitters (alternating between telling the truth and lying).

Is it reasonable to assume that Grandma will be getting lucky in the near future? Why or why not?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, September 4, 2013 at noon Pacific Time. I will post the answer shortly after.