there exists something such that if the fact that it is a kind of a sprocket is right then it is non-empty and it is photochemical.
sent1: if something is not leaden it is non-empty thing that is photochemical. sent2: that the absinthe is quiet is not incorrect. sent3: the fact that something is not leaden is right if it is both a sprocket and quiet.
void -> assump1: Let's assume that the absinthe is a kind of a sprocket.; assump1 & sent2 -> int1: the absinthe is a sprocket and is not unquiet.; sent3 -> int2: if the absinthe is a kind of a sprocket and it is quiet then it is not leaden.; int1 & int2 -> int3: the absinthe is not leaden.; sent1 -> int4: if the absinthe is not leaden then it is non-empty thing that is photochemical.; int3 & int4 -> int5: the absinthe is both not an empty and photochemical.; [assump1] & int5 -> int6: the absinthe is non-empty thing that is photochemical if it is a sprocket.; int6 -> hypothesis;
$hypothesis$ = there exists something such that if the fact that it is a kind of a sprocket is right then it is non-empty and it is photochemical. ; $context$ = sent1: if something is not leaden it is non-empty thing that is photochemical. sent2: that the absinthe is quiet is not incorrect. sent3: the fact that something is not leaden is right if it is both a sprocket and quiet. ; $proof$ = 
void -> assump1: Let's assume that the absinthe is a kind of a sprocket.; assump1 & sent2 -> int1: the absinthe is a sprocket and is not unquiet.; sent3 -> int2: if the absinthe is a kind of a sprocket and it is quiet then it is not leaden.; int1 & int2 -> int3: the absinthe is not leaden.; sent1 -> int4: if the absinthe is not leaden then it is non-empty thing that is photochemical.; int3 & int4 -> int5: the absinthe is both not an empty and photochemical.; [assump1] & int5 -> int6: the absinthe is non-empty thing that is photochemical if it is a sprocket.; int6 -> hypothesis; __PROVED__