Exercise logic.propositional.dnf
Description
Proposition to DNF
Derivation
Final term is not finished(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q))) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.notnot(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q))) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.truezeroand(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.notnot(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.notnot(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(~(q /\ ~q) /\ ~(p /\ ~q)) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.compland(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(~F /\ ~(p /\ ~q)) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.notfalse(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(T /\ ~(p /\ ~q)) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.truezeroand(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~~(p /\ ~q) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.demorganand(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(~p || ~~q) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)
⇒ logic.propositional.notnot(q || ~r) /\ ~(~~T /\ ~~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)))) /\ ~(~p || q) /\ ~(~~T /\ ~~(~(q /\ ~~~q) /\ ~(p /\ ~q)) /\ T)