edit: don't read the question right... -.-
this theme is using bootstrap, the width of the search boxes depends on the width of the columns. if you want to increase the width for only the inputfield, i think you have to remove one or more of the other fields. else the other fields will move down.
if you want to do it anymore... remove one of the other boxes (theyre still needed for the search i think) and change the number of columns in header.php
<?php $showCountry = (osc_get_preference('show_search_country', 'osclasswizards_theme') == '1') ? true : false; ?>
<div class="col-md-<?php echo ($showCountry)? '3' : '4'; ?>">
bootstrap uses generally 12 columns, you can define the width for your search box, by increase or decrease the amount of used columns.
if you want to use a width for 50%, you have to use e.g. col-md-6
if you want to use a width for 25%, you have to use e.g. col-md-3
but remember, all boxes in the searchbar use together 12 columns, if you increase one of this, decrease the others
you can read more about it here:
http://v4-alpha.getbootstrap.com/layout/grid/