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