Which step number is the following output?
rise not moon gem does big aim 15 with 92 85 63 56 47 31 25

After careful analysis of the given input and various steps of rearrangement it is evident that in each step one word and one number are rearranged. The word are rearranged from left in alphabetical order and the numbers are rearranged from the right in descending order but in the final step the word get rearranged in alphabetical order in reserves manner and number appear in descending order.

Input : 31 rise gem 15 92 47 aim big 25 does 56 not 85 63 with moon
Step I : aim 31 rise gem 15 47 big 25 does 56 not 85 63 with moon 92
Step II : big aim 31 rise gem 15 47 25 does 56 not 63 with moon 92 85
Step III : does big aim 31 rise gem 15 47 25 56 not with moon 92 85 63
Step IV : gem does big aim 31 rise 15 47 25 not with moon 92 85 63 56
Step V : moon gem does big aim 31 rise 15 25 not with 92 85 63 56 47
Step VI : not moon gem does big aim rise 15 25 with 92 85 63 56 47 31
Step VII : rise not moon gem does big aim 15 with 92 85 63 56 47 31 25
Step VIII : with rise not moon gem does big aim 92 85 63 56 47 31 25 15

Step VII is the answer.