Puzzle #229: Follow the Logic

Start with the number 7. Then follow these steps in order.

Step 1: If it is true that arutta, then add 5; if not, add 7.
Step 2: If it is true that budrist, then multiply by 2; if not, multiply by 3.
Step 3: Subtract twice the number you added two steps ago.
Step 4: Divide by two.

Your answer is a two-digit prime. Is arutta true, and is budrist true?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, October 25, 2017 at noon Pacific Time. I will post the answer shortly after.