the missionary is a foxhound or it is not extraordinary or both if the LCD is not a shoot-down.
sent1: if that the missionary is a foxhound and/or is not extraordinary is false the fact that it is subatomic hold. sent2: something that is a bore is not a shoot-down and is subatomic. sent3: if the fact that the missionary is subatomic is not false the LCD is a shoot-down. sent4: the missionary is a foxhound and/or it is extraordinary if the LCD is not a shoot-down.
void -> assump1: Let's assume that that the missionary is a kind of a foxhound and/or is not extraordinary is not right.; sent1 & assump1 -> int1: the missionary is subatomic.; sent3 & int1 -> int2: that the LCD is a kind of a shoot-down is not false.; void -> assump2: Let's assume that the LCD is not a shoot-down.; int2 & assump2 -> int3: this is contradiction.; [assump1] & int3 -> int4: the missionary is a foxhound and/or it is not extraordinary.; [assump2] & int4 -> hypothesis;
the LCD is subatomic.
sent2 -> int5: the LCD is not a shoot-down but it is subatomic if it is a bore.;
$hypothesis$ = the missionary is a foxhound or it is not extraordinary or both if the LCD is not a shoot-down. ; $context$ = sent1: if that the missionary is a foxhound and/or is not extraordinary is false the fact that it is subatomic hold. sent2: something that is a bore is not a shoot-down and is subatomic. sent3: if the fact that the missionary is subatomic is not false the LCD is a shoot-down. sent4: the missionary is a foxhound and/or it is extraordinary if the LCD is not a shoot-down. ; $proof$ = 
void -> assump1: Let's assume that that the missionary is a kind of a foxhound and/or is not extraordinary is not right.; sent1 & assump1 -> int1: the missionary is subatomic.; sent3 & int1 -> int2: that the LCD is a kind of a shoot-down is not false.; void -> assump2: Let's assume that the LCD is not a shoot-down.; int2 & assump2 -> int3: this is contradiction.; [assump1] & int3 -> int4: the missionary is a foxhound and/or it is not extraordinary.; [assump2] & int4 -> hypothesis; __PROVED__