Using liverpole's hash idea, I've come up with this (updated with comments):

use strict;
use warnings;

my (%pos, @order);

# collect the position information
{
  local $/ = "";
  while (<DATA>) {
    chomp;
    my $i = 0;

    # $pos{TERM}{SET #} = POSITION
    $pos{$_}{$. - 1} = $i++ for split /\n/;
  }
}

# extract order from the positions
for my $i (1 .. keys %pos) {

  # get all terms who appear ONLY in position 0
  # across all the sets they're in
  my ($first, @extra) = grep {
    my $t = $_;
    my %p = map { $_ => 1 } values %{ $pos{$t} };
    $p{0} and keys(%p) == 1
  } keys %pos;

  # if there was more than one term found, cause a fuss
  warn "iteration #$i: multiple candidates [$first @extra]\n" if @extr
+a;

  # uncomment for debugging to see how %pos changes
  # use Data::Dumper; print Dumper(\%pos);

  # get the sets this term appeared in and alter
  # the positions of terms found in those sets
  for my $set (keys %{ delete $pos{$first} }) {
    $pos{$_}{$set} and $pos{$_}{$set}-- for keys %pos;
  }

  # store this term in the ordered list
  push @order, $first;
}

print "<@order>\n";

__DATA__
alpha
beta

epsilon
zeta

beta
gamma
zeta

alpha
gamma
delta
epsilon
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