if the dunning opened does not occur both the spacing catwalk and the barter happens.
sent1: that the dunning opened occurs is caused by that the main happens and the bubalineness does not occur. sent2: the main occurs. sent3: both the mainness and the non-bubalineness happens if the spacing catwalk does not occur. sent4: that the pneumonectomy but not the petting occurs causes that the bartering happens. sent5: the pneumonectomy occurs but the pet does not occur.
void -> assump1: Let's assume that the spacing catwalk does not occur.; sent3 & assump1 -> int1: both the main and the non-bubalineness occurs.; int1 & sent1 -> int2: the dunning opened happens.; void -> assump2: Let's assume that the dunning opened does not occur.; int2 & assump2 -> int3: this is contradiction.; [assump1] & int3 -> int4: the spacing catwalk happens.; sent4 & sent5 -> int5: the bartering happens.; int4 & int5 -> int6: the spacing catwalk happens and the bartering occurs.; [assump2] & int6 -> hypothesis;
$hypothesis$ = if the dunning opened does not occur both the spacing catwalk and the barter happens. ; $context$ = sent1: that the dunning opened occurs is caused by that the main happens and the bubalineness does not occur. sent2: the main occurs. sent3: both the mainness and the non-bubalineness happens if the spacing catwalk does not occur. sent4: that the pneumonectomy but not the petting occurs causes that the bartering happens. sent5: the pneumonectomy occurs but the pet does not occur. ; $proof$ = 
void -> assump1: Let's assume that the spacing catwalk does not occur.; sent3 & assump1 -> int1: both the main and the non-bubalineness occurs.; int1 & sent1 -> int2: the dunning opened happens.; void -> assump2: Let's assume that the dunning opened does not occur.; int2 & assump2 -> int3: this is contradiction.; [assump1] & int3 -> int4: the spacing catwalk happens.; sent4 & sent5 -> int5: the bartering happens.; int4 & int5 -> int6: the spacing catwalk happens and the bartering occurs.; [assump2] & int6 -> hypothesis; __PROVED__