Symbolic Logic, Proof with Conditional

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Step 6 in the proof cannot be concluded as FrontOf(d, e) from step 4, indicating a need for further clarification. Another quantifier elimination may be necessary to establish that Cube(e) and Dodec(d) imply FrontOf(d, e). There is also a suggestion that the order of variables e and y in step 4 may have been mixed up, which could affect the validity of the argument. Ensuring the correct order and addressing the quantifier elimination are crucial for the proof's integrity. The discussion emphasizes the importance of precise logical structure in symbolic logic proofs.
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Any advice on how to make step 6 check out?
 
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The problem is you can't conclude
FrontOf(d, e)​
from step 4, isn't it?
Then isn't another quantifier elimination all you need (i.e. prove that Cube(e) and Dodec(d) implies FrontOf(d, e)) ?

Also I'm wondering if you mixed up the order of e and y in step 4.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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