the luger is corrected.
sent1: that there is something such that it does not batch traveler is not false. sent2: if the escalator does not batch traveler the luger corrects and does not batch traveler. sent3: there exists something such that it is a kind of a sedge that is not philological. sent4: the escalator does not batch traveler if there is something such that it is a kind of a sedge and it is not philological.
sent3 & sent4 -> int1: the escalator does not batch traveler.; sent2 & int1 -> int2: the luger is not uncorrected but it does not batch traveler.; int2 -> hypothesis;
$hypothesis$ = the luger is corrected. ; $context$ = sent1: that there is something such that it does not batch traveler is not false. sent2: if the escalator does not batch traveler the luger corrects and does not batch traveler. sent3: there exists something such that it is a kind of a sedge that is not philological. sent4: the escalator does not batch traveler if there is something such that it is a kind of a sedge and it is not philological. ; $proof$ = 
sent3 & sent4 -> int1: the escalator does not batch traveler.; sent2 & int1 -> int2: the luger is not uncorrected but it does not batch traveler.; int2 -> hypothesis; __PROVED__