Exercise logic.propositional.consequence
Description
Prove that formula is a logical consequence of a set of formulas
All applications
Rule | absorpand-subset |
Location | [1,0] |
q <-> s => (p /\ q /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | command.sort |
Location | [1,0] |
q <-> s => (p /\ p /\ q /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | command.sort |
Location | [1,0,1] |
q <-> s => (p /\ p /\ q /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | compland.sort |
Location | [1,0] |
q <-> s => (p /\ p /\ q /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [0,0] |
F || (q <-> s) => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [0,0,0] |
(F || q) <-> s => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [0,0,1] |
q <-> (F || s) => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1] |
q <-> s => F || (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0] |
q <-> s => F || (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,0] |
q <-> s => ((F || p) /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1] |
q <-> s => (p /\ (F || (q /\ p /\ s))) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0] |
q <-> s => (p /\ (F || q) /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1] |
q <-> s => (p /\ q /\ (F || (p /\ s))) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1,0] |
q <-> s => (p /\ q /\ (F || p) /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1,1] |
q <-> s => (p /\ q /\ p /\ (F || s)) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1] |
q <-> s => (p /\ q /\ p /\ s) || F || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0] |
q <-> s => (p /\ q /\ p /\ s) || ((F || ~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0] |
q <-> s => (p /\ q /\ p /\ s) || ((F || ~p || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0,0] |
q <-> s => (p /\ q /\ p /\ s) || ((~(F || p) || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0,1] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || F || ~q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0,1,0] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || ~(F || q)) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,1] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || ~q) /\ (F || ~(p /\ s)))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(F || (p /\ s)))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,0] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~((F || p) /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,1] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ (F || s)))
ready: no
Rule | logic.propositional.andoveror |
Location | [1,1] |
q <-> s => (p /\ q /\ p /\ s) || (~p /\ ~(p /\ s)) || (~q /\ ~(p /\ s))
ready: no
Rule | logic.propositional.defequiv |
Location | [0,0] |
(q /\ s) || (~q /\ ~s) => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | logic.propositional.demorganand |
Location | [1,1,1] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || ~q) /\ (~p || ~s))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => (p || ((~p || ~q) /\ ~(p /\ s))) /\ (q || ((~p || ~q) /\ ~(p /\ s))) /\ (p || ((~p || ~q) /\ ~(p /\ s))) /\ (s || ((~p || ~q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => (p || ((~p || ~q) /\ ~(p /\ s))) /\ (q || ((~p || ~q) /\ ~(p /\ s))) /\ ((p /\ s) || ((~p || ~q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => (p || ((~p || ~q) /\ ~(p /\ s))) /\ ((q /\ p) || ((~p || ~q) /\ ~(p /\ s))) /\ (s || ((~p || ~q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => ((p /\ q) || ((~p || ~q) /\ ~(p /\ s))) /\ (p || ((~p || ~q) /\ ~(p /\ s))) /\ (s || ((~p || ~q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => ((p /\ q /\ p /\ s) || ~p || ~q) /\ ((p /\ q /\ p /\ s) || ~(p /\ s))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => (p || ((~p || ~q) /\ ~(p /\ s))) /\ ((q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => ((p /\ q) || ((~p || ~q) /\ ~(p /\ s))) /\ ((p /\ s) || ((~p || ~q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => ((p /\ q /\ p) || ((~p || ~q) /\ ~(p /\ s))) /\ (s || ((~p || ~q) /\ ~(p /\ s)))
ready: no