[FEATURE] Short Truth Table Free Variable Direct Rule

[charlestian23]

Describe the current behavior of what you're trying to improve. If your enhancement request related to a problem, please also describe the problem.

Suppose we had the following statements in LEGUP:

A ^ B (^ is true)
C

Currently in LEGUP, in order to solve this puzzle, you can prove A and B are true using And Elimination. However, if you leave the puzzle as is, it counts as not solved. In order to solve the puzzle, you have to use the True or False Case Rule on C. Only then will the puzzle be marked as solved.

Describe the improvement you'd like

We should create a new Direct Rule called "Free Variable Direct Rule". This rule would check if the variable in question is a free variable. If it is, it would denote that it is a free variable using a new color (say yellow). So in our example above, the entire first statement would be green (since A, ^, and B are true) and C would be yellow. This would also mean students can avoid having to create multiple branches using case rules if there are multiple free variables involved in a puzzle file.

Describe alternatives you've considered

We could leave the current functionality as is, but I thought this feature might be useful, especially now that we have allowed people to create their own puzzle files and users may intentionally want to include multiple free variables. Our provided Short Truth Table puzzle files, to my knowledge, don't have any free variables.

Additional Context

No response