When I’m not sure which adaptors were used for the construction of a sequencing library, but I know they were Illumina, I take the top ~100k reads and run trimmomatic using more-or-less default settings against the 2 different Illumina truseq adaptors that ‘ship’ with that software. Then compare how the two trim-logs look — the one that trimmed off more crap is the one to proceed with. Something like this (these are set for small RNA libraries where the inserts are very short!):
java -jar trimmomatic-0.36.jar SE -threads 5 -trimlog trimlog_test test.fastq out.test.fastq ILLUMINACLIP:TruSeq2-SE.fa:2:30:10 LEADING:3 TRAILING:3 SLIDINGWINDOW:4:15 MINLEN:1
awk ‘$6>0 {print}’ trimlog_test | wc