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