QUESTION $1[15]$

Create your own translation manual $($using as few predicates as possible$),$ and translate the following complex English sentences into First$-$Order Logic $($FOL$).$ Define your own predicates, constants, and functions to reflect the complexity of these sentences. Ensure consistency in your symbols across translations.

John consistently excels as a student in Symbolic Logic whenever the topic is advanced.

If Claire is the best student of Class $2100,$ then every other student in the class is not as skilled in Symbolic Logic as Claire.

Max's best friend has a girlfriend, and Claire is taller than her. However, if Max's best friend were single, Claire would be taller than Max.

Claire prefers herself over any partner that John might have had in the past or may have in the future.

The height difference between John and Claire's youngest son and their oldest daughter is greater than the height difference between their middle child and the neighbor's tallest child.

For every integer, if the sum of $2$ and the integer is less than or equal to $10,$ then the successor of that integer is always greater than or equal to the next prime number after $11.$