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Consider the following logic puzzle, which is one of many created by Lewis Carroll, the author of Alice in Wonderland.

No birds, except ostriches, are 9 feet high. There are no birds in this aviary that belong to anyone but me. No ostrich lives on mince pies. I have no birds less than 9 feet high. 

Prove that these premises imply the following conclusion:

Any bird in this aviary does not live on mince pies. 

Use the following symbols to represent statements:

H:  Height of the bird is not less than nine feet. O:  The bird is an ostrich. M:  The bird lives on mince pies. I:  I own the bird. A:  The bird is in this aviary. 
  1. Show the premises as logical formulas represented using these symbols. $$O \rightarrow H$$ $$A \rightarrow I$$ $$O \rightarrow \neg M$$ $$I \rightarrow H$$
  2. Show the conclusion as a logical formula represented using these symbols. $$A \rightarrow \neg M$$
  3. Show the negation of the conclusion using these symbols. $$\neg (A \rightarrow \neg M)$$
  4. Show all premises and the negation of the conclusion as a set of clauses. $$A \wedge M, \neg O \vee H, \neg A \vee I, \neg O \vee \neg M, \neg I \vee H$$
  5. Use the resolution method for your proof, and show for each resolution step which formulas are involved as parents and what the resolvent is. ???
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    So where are you stuck? What have you done so far?? Or are you just asking someone else to do all your homework???2012-11-05
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    Sorry, Peter. I added some of the things I had tried to do so far on the problem. I am very not sure if they are right.2012-11-05

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