if the lug occurs then the alternation does not occur but the punch happens.
sent1: the certification happens but the plagiarism does not occur. sent2: the directing loan occurs. sent3: the overshooting does not occur. sent4: the reprisal does not occur but the splash occurs. sent5: that the lugging does not occur is caused by that the certification occurs and the alternation occurs. sent6: if the splashing happens but the overshooting does not occur the punching happens.
sent1 -> int1: the certification happens.; void -> assump2: Let's assume that the alternation happens.; int1 & assump2 -> int2: the fact that both the certification and the alternation happens is correct.; int2 & sent5 -> int3: the lugging does not occur.; void -> assump1: Let's assume that the lugging occurs.; int3 & assump1 -> int4: this is contradiction.; [assump2] & int4 -> int5: the alternation does not occur.; sent4 -> int6: the splashing happens.; int6 & sent3 -> int7: the splashing occurs but the overshoot does not occur.; sent6 & int7 -> int8: the punching happens.; int5 & int8 -> int9: the fact that the alternation does not occur but the punching occurs is not incorrect.; [assump1] & int9 -> hypothesis;
$hypothesis$ = if the lug occurs then the alternation does not occur but the punch happens. ; $context$ = sent1: the certification happens but the plagiarism does not occur. sent2: the directing loan occurs. sent3: the overshooting does not occur. sent4: the reprisal does not occur but the splash occurs. sent5: that the lugging does not occur is caused by that the certification occurs and the alternation occurs. sent6: if the splashing happens but the overshooting does not occur the punching happens. ; $proof$ = 
sent1 -> int1: the certification happens.; void -> assump2: Let's assume that the alternation happens.; int1 & assump2 -> int2: the fact that both the certification and the alternation happens is correct.; int2 & sent5 -> int3: the lugging does not occur.; void -> assump1: Let's assume that the lugging occurs.; int3 & assump1 -> int4: this is contradiction.; [assump2] & int4 -> int5: the alternation does not occur.; sent4 -> int6: the splashing happens.; int6 & sent3 -> int7: the splashing occurs but the overshoot does not occur.; sent6 & int7 -> int8: the punching happens.; int5 & int8 -> int9: the fact that the alternation does not occur but the punching occurs is not incorrect.; [assump1] & int9 -> hypothesis; __PROVED__