Maybe you can adapt something like this...

use warnings;
use strict;

my %log;

while (my $line = <DATA>){ 
    chomp  $line;
    next unless length $line;
    my ($event, $time) = split / at /, $line;
    push @{$log{$event}}, $time;
}

for my $key (keys %log){
    print $key, ${$log{$key}}[0] ? " at ${$log{$key}}[0]" : ''; 
    print "\nThe above event occurred ", $#{$log{$key}}, " additional 
+times.\n";
}


__DATA__
User logged in successfully at 10:35:33

User logged in successfully at 10:35:34

User logged in successfully at 10:35:35

Error: Login failure!

User logged in successfully at 10:35:37

Error: Login failure!

Error: System failure at 01:23:22

Error: System failure at 01:23:40

User logged in successfully at 10:35:39

Error: System failure at 01:23:41
[download]

Yields: (on my system, output order may vary.)

Error: Login failure!
The above event occurred 1 additional times.
Error: System failure at 01:23:22
The above event occurred 2 additional times.
User logged in successfully at 10:35:33
The above event occurred 4 additional times.