Your problem is to use first-order logic to represent the following example of reasoning, and use the Prover9 theorem prover to prove that the reasoning is valid.
You should use the following template file to create your
Prover9 encoding of the problem:
parts_and_overlaps.p9
Marks: There are two marks for each sentence, making a total of 10 marks.
Outline:
A2: Definition of Parthood: A region, A, is part of a region, B, if and only if whenever a region, C, is in contact with A then it is in contact with B.
A3: Definition of Proper Parthood: A region A is a proper part of a region B if and only if A is part of B but B is not part of A.
A4: Definition of Overlap: A region A overlaps a region B if and only if there is a region which is part of both region A and B.
Goal: If any region A is a proper part of any region B then A overlaps B and A is in contact with B.