Another way to do it would be to read the data in paragraph mode so that each readline gets a record rather than a line. You could then extract all the numeric data from the record using a global regex, join the numbers with another character (to avoid false positives with 9 and 87 versus 98 and 7) then use the string as a hash key to eliminate duplicates.

use strict;
use warnings;

my %seen = ();
{
    local $/ = q{};     # Paragraph mode
    while ( <DATA> )
    {
        my $key = join q{:}, m{(\d+)}g;
        print unless $seen{ $key } ++;
    }
}

__DATA__
A  83    GLU       A  90    GLU^?     
A 163    ARG       A  83    ARG^?     
A 222    ARG       A   5    ARG^?

A 229    ALA       A 115    ALA~?     
A 257    ALA       A 118    ALA~?     
A 328    ASP       A  95    ASP~?

A  83    GLU       A  90    GLU^?     
A 163    ARG       A  83    ARG^?     
A 222    ARG       A   5    ARG^?

A  83    GLU       B  90    GLU^?     
A 163    ARG       B  83    ARG^?     
A 222    ARG       B  5     ARG^?
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The output.

A  83    GLU       A  90    GLU^?     
A 163    ARG       A  83    ARG^?     
A 222    ARG       A   5    ARG^?

A 229    ALA       A 115    ALA~?     
A 257    ALA       A 118    ALA~?     
A 328    ASP       A  95    ASP~?
[download]

I hope this is helpful.