How do I print line if a pair of columns matches neither of 2 strings

Question

I've got it working as expected when looking at 1 column:

cat /tmp/inputfile | awk -F : '$12 !~ /100/ { print $6,$12,$13}'
cat /tmp/inputfile | awk -F : '$12 ~ /100/ { print $6,$12,$13}'
4726753 100 137

But when I try to make the next step in the process (look at 2 columns and print if the pair is not "100 137" it prints under BOTH conditions. Since it simultaneously meets both conditions (does match and does not match), it must be ignoring my conditional right?

cat /tmp/inputfile | awk -F : '$12,$13 ~ /100 137/ { print $6,$12,$13}'
4726753 100 137
cat /tmp/inputfile | awk -F : '$12,$13 !~ /100 137/ { print $6,$12,$13}'
4726753 100 137

Fixing/understanding this is step 1. The finished result should check for "100 137" and "0 0" and only print if $12,$13 are neither of those pairs.

Answer 1

If I read your question correctly, you are looking to print fields 6, 12, and 13 if and only if fields 12 and 13 are not either (100, 137) or (0, 0). So:

awk -F: '! ( ( $12 == 0 && $13 == 0 ) || ( $12 == 100 && $13 == 137 ) ) { print $6, $12, $13 }' inputfile