How to run trimmomatic in HPC
Depending on the cluster management tool, you might have received e-mails when the "job" begins and ends. If so, you can check the "Exit status" of the job. For example, in the case of our HPC the relevant lines from the "job completion e-mail" would be:

Execution terminated
Exit_status=0


BTW, at first I was confused with the phrase "Execution terminated", however, in the scheduler used in our system, it means "the run has been successfully or unsuccessfully completed". Exit_status=0 int the next line means a successful run and for the unsuccessful runs there is a list with the error codes.

Secondly, if your run was successful, you would see new fastq files containing "_trimmed" in the filename (reading this from your code). These fastqs should be more or less similar in size to the original depending on how aggressive the trimming settings are.

If you can provide more information, i.e. the type of cluster management tool used, the log file, ..., you can get more help and precise answers from the community.