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] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | command.sort |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ p /\ q /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | command.sort |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ p /\ q /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | compland.sort |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ p /\ q /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
F || ((~p || q) /\ (~p || r)) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(F || ~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(F || ~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~(F || p) || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || F || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (F || ~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (F || ~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~(F || p) || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [0,0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || F || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => F || (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => F || (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => ((F || p) /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ (F || (q /\ p /\ r))) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ (F || q) /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ (F || (p /\ r))) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ (F || p) /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ (F || r)) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || F || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || ((F || ~(p /\ q)) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(F || (p /\ q)) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~((F || p) /\ q) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ (F || q)) /\ ~(p /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ (F || ~(p /\ r)))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(F || (p /\ r)))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~((F || p) /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ (F || r)))
ready: no
Rule | logic.propositional.andoveror |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | logic.propositional.andoveror |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p /\ (~p || r)) || (q /\ (~p || r)) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r))
ready: no
Rule | logic.propositional.demorganand |
Location | [1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || ((~p || ~q) /\ ~(p /\ r))
ready: no
Rule | logic.propositional.demorganand |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p /\ q /\ p /\ r) || (~(p /\ q) /\ (~p || ~r))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p || (~(p /\ q) /\ ~(p /\ r))) /\ (q || (~(p /\ q) /\ ~(p /\ r))) /\ (p || (~(p /\ q) /\ ~(p /\ r))) /\ (r || (~(p /\ q) /\ ~(p /\ r)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p || (~(p /\ q) /\ ~(p /\ r))) /\ (q || (~(p /\ q) /\ ~(p /\ r))) /\ ((p /\ r) || (~(p /\ q) /\ ~(p /\ r)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p || (~(p /\ q) /\ ~(p /\ r))) /\ ((q /\ p) || (~(p /\ q) /\ ~(p /\ r))) /\ (r || (~(p /\ q) /\ ~(p /\ r)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => ((p /\ q) || (~(p /\ q) /\ ~(p /\ r))) /\ (p || (~(p /\ q) /\ ~(p /\ r))) /\ (r || (~(p /\ q) /\ ~(p /\ r)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => ((p /\ q /\ p /\ r) || ~(p /\ q)) /\ ((p /\ q /\ p /\ r) || ~(p /\ r))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => (p || (~(p /\ q) /\ ~(p /\ r))) /\ ((q /\ p /\ r) || (~(p /\ q) /\ ~(p /\ r)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => ((p /\ q) || (~(p /\ q) /\ ~(p /\ r))) /\ ((p /\ r) || (~(p /\ q) /\ ~(p /\ r)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p || q) /\ (~p || r) => ((p /\ q /\ p) || (~(p /\ q) /\ ~(p /\ r))) /\ (r || (~(p /\ q) /\ ~(p /\ r)))
ready: no