Which outputs are paradoxical?

shell.txt

$ cat paradoxical
sub paradox($p) {

    # Either they refer to themselves...
    return True if $p.substr(0, 1) eq 'n';
    return True if $p.substr(1, 1) eq 'p';
    return True if $p.substr(2, 1) eq 'r';

    # ...or to each other in a 3-loop...
    return True if $p eq 'prn';
    return True if $p eq 'rnp';

    # ...or it's not a paradox.
    return False;
}

my @outputs = <n p r> X~ <n p r> X~ <n p r>;

for @outputs {
    say "$_: ", (paradox($_) ?? '' !! 'not '), "paradoxical";
}

$ nom paradoxical
nnn: paradoxical
nnp: paradoxical
nnr: paradoxical
npn: paradoxical
npp: paradoxical
npr: paradoxical
nrn: paradoxical
nrp: paradoxical
nrr: paradoxical
pnn: not paradoxical
pnp: not paradoxical
pnr: paradoxical
ppn: paradoxical
ppp: paradoxical
ppr: paradoxical
prn: not paradoxical
prp: not paradoxical
prr: paradoxical
rnn: not paradoxical
rnp: not paradoxical
rnr: paradoxical
rpn: paradoxical
rpp: paradoxical
rpr: paradoxical
rrn: not paradoxical
rrp: not paradoxical
rrr: paradoxical