I'm not sure if this is possible as a single line awk. At least not easy. Is awk required? Since there is one shell shell solution, if awk is only part of the solution.
For example, this is a single-layer shell (only a long line):
awk '{ print $2 }' < {infile} | while read line; do grep -i "false $line" {infile} > /dev/null || echo $line; done | uniq
It is inefficient, but it does the job.
For comparison, the shortest awk solution I have is about 25 lines (which I can here, if you want, leave a comment and I will update this accordingly). But that would mean that you could save this to a file and run awk -f alltrue.awk < {infile} . I'm not sure if these are strictly classes like perl one-liner though :-)
A better understanding of what you end up trying to achieve or what it is may be helpful.
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