There is an out-by-one error in the logic somewhere that I cannot find right now, but otherwise, I think this complies with the rules of the challenge.

#! perl -slw
use strict;
local $, = ' ';

my( $A, $C, @B ) = ( undef, 0 );
open SPARSE, '+> :raw', \$A;

sub readA{  
    seek SPARSE, 4 * $_[ 0 ], 0; 
    sysread  SPARSE, my $n, 4; 
    unpack 'N', $n; 
}

sub writeA{ 
    seek SPARSE, 4 * $_[ 0 ], 0; 
    syswrite SPARSE, pack( 'N', $_[ 1 ] ), 4; 
} 

sub query{
    my $i = shift;
    my $a = readA( $i ) || -1;
    return 0 unless 0 <= $a and $a < $C;
    my $b = $B[ $a ];
    return $b == $i ? 1 : 0;
}

sub insert{
    my $i = shift;
    if( !query( $i ) ) {
        $B[ $C ] = $i;
        writeA( $i, $C );
        $C++
    }
}

sub del{
    my $i = shift;
    if( query( $i ) ) {
        my $a = readA( $i );
        my $b = $B[ --$C ];
        $B[ $a ] = $b;
        writeA( $b, $a );
    }
}

sub clear{
    $C = 0;
}

my @numbers = map{ int rand( 2**16 ) } 1 .. 10;
   
print 'Query before insert';
printf "%5d : %s\n", $_, query( $_ ) for @numbers;

insert $_ for @numbers;

print "\nQuery after insert";
printf "%5d : %s\n", $_, query( $_ ) for @numbers;

del $_ for @numbers[ 0..4 ]; ## Delete half

print "\nQuery after deleting half";
printf "%5d : %s\n", $_, query( $_ ) for @numbers;

del $_ for @numbers; ## Delete them all regardless if they still exist
+s

print "\nQuery after deleting the rest";
printf "%5d : %s\n", $_, query( $_ ) for @numbers;
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