there is something such that if it is monometallic either it is not a bugbear or it is a cardigan or both.
sent1: the fact that the falls does not casket ETA and/or it is a kind of the bugbear if the falls is unsusceptible is correct. sent2: there exists something such that if it does ask Castile it either is not fictile or is lobate or both. sent3: that either the high is not monometallic or it is facultative or both is not false if it is not non-suctorial. sent4: something that is a kind of a Dinornithidae does leach Vespertilionidae and/or does agonize. sent5: if the high is monometallic it is a bugbear or it is a cardigan or both. sent6: if something is monometallic then either it is not a bugbear or it is a cardigan or both.
sent6 -> int1: the high is not a bugbear and/or is a kind of a cardigan if that it is not monometallic does not hold.; int1 -> hypothesis;
$hypothesis$ = there is something such that if it is monometallic either it is not a bugbear or it is a cardigan or both. ; $context$ = sent1: the fact that the falls does not casket ETA and/or it is a kind of the bugbear if the falls is unsusceptible is correct. sent2: there exists something such that if it does ask Castile it either is not fictile or is lobate or both. sent3: that either the high is not monometallic or it is facultative or both is not false if it is not non-suctorial. sent4: something that is a kind of a Dinornithidae does leach Vespertilionidae and/or does agonize. sent5: if the high is monometallic it is a bugbear or it is a cardigan or both. sent6: if something is monometallic then either it is not a bugbear or it is a cardigan or both. ; $proof$ = 
sent6 -> int1: the high is not a bugbear and/or is a kind of a cardigan if that it is not monometallic does not hold.; int1 -> hypothesis; __PROVED__