that the casting occurs is right if the actuarialness occurs.
sent1: if the dynamic and the actuarialness occurs that the repossessing does not occur is not incorrect. sent2: that the homesteading does not occur and the vacating does not occur triggers that the casting occurs. sent3: if the fact that the homesteading does not occur and the vacating does not occur is not right then the dynamic occurs. sent4: the headshake or the grouping or both occurs. sent5: if not the homestead but the vacating happens then the casting occurs. sent6: if the headshake happens then the repossessing occurs. sent7: the repossessing occurs if the grouping happens. sent8: the fact that the dynamic occurs is not wrong if that the vacating happens is not false.
void -> assump2: Let's assume that that the homesteading does not occur and the vacating does not occur is not true.; sent3 & assump2 -> int1: the dynamic occurs.; void -> assump1: Let's assume that the actuarialness occurs.; int1 & assump1 -> int2: the dynamicness occurs and the actuarialness happens.; int2 & sent1 -> int3: the repossessing does not occur.; sent4 & sent6 & sent7 -> int4: the fact that the repossessing occurs hold.; int3 & int4 -> int5: this is contradiction.; [assump2] & int5 -> int6: the homestead does not occur and the vacating does not occur.; int6 & sent2 -> int7: the casting occurs.; [assump1] & int7 -> hypothesis;
$hypothesis$ = that the casting occurs is right if the actuarialness occurs. ; $context$ = sent1: if the dynamic and the actuarialness occurs that the repossessing does not occur is not incorrect. sent2: that the homesteading does not occur and the vacating does not occur triggers that the casting occurs. sent3: if the fact that the homesteading does not occur and the vacating does not occur is not right then the dynamic occurs. sent4: the headshake or the grouping or both occurs. sent5: if not the homestead but the vacating happens then the casting occurs. sent6: if the headshake happens then the repossessing occurs. sent7: the repossessing occurs if the grouping happens. sent8: the fact that the dynamic occurs is not wrong if that the vacating happens is not false. ; $proof$ = 
void -> assump2: Let's assume that that the homesteading does not occur and the vacating does not occur is not true.; sent3 & assump2 -> int1: the dynamic occurs.; void -> assump1: Let's assume that the actuarialness occurs.; int1 & assump1 -> int2: the dynamicness occurs and the actuarialness happens.; int2 & sent1 -> int3: the repossessing does not occur.; sent4 & sent6 & sent7 -> int4: the fact that the repossessing occurs hold.; int3 & int4 -> int5: this is contradiction.; [assump2] & int5 -> int6: the homestead does not occur and the vacating does not occur.; int6 & sent2 -> int7: the casting occurs.; [assump1] & int7 -> hypothesis; __PROVED__