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 s/(^| )$i( |s|$)/"$1$def{$i}$2"/gie;

s/^\s+//; #trim leading whitespace

s/\s+$//; #trim trailing whitespace
...
s/(\S+)\s{2,}/"$1 "/gie; #replace more then one space with one space

s/\s{2,}(\S+)/" $1"/gie; #replace more then one space with one space

T:
Problem #3
...
( m segment AB / m segment DE ) = ( m segment CX / m segment FH ) = ( 
+m segment AC / m segment DF ) => similar reasoning #-2
( m segment AC / m segment DF ) = ( m segment AZ / m segment DJ ) => s
+imilar reasoning #-4
( m segment AB / m segment DE ) = ( m segment BC / m segment EF ) = ( 
+m segment AZ / m segment DJ ) => similar reasoning #-4

#!/usr/bin/perl -w
use strict;
...
    print OUTPUT $i+1 . "." . " " x (length($#stmts+1) - length($i+1)+
+1) . $stmts[$i] . " " x ($len_stmts - length($stmts[$i])) . "  |  " .
+ $reasons[$i] . "\n"; #print the statements and resons
}
close (OUTPUT);