Exercise logic.propositional.consequence
Description
Prove that formula is a logical consequence of a set of formulas
All applications
Rule | absorpand-subset |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ~p) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | absorpand-subset |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ~p)
ready: no
Rule | command.sort |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || (~p /\ (~p || ~q))) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | command.sort |
Location | [1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((p /\ q) || ((~p || ~q) /\ ~p))
ready: no
Rule | command.sort |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || (~p /\ (~p || ~q)))
ready: no
Rule | commor.sort |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ (((~p || ~q) /\ ~p) || (q /\ p))
ready: no
Rule | introfalseleft |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
F || q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => F || ((p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p)))
ready: no
Rule | introfalseleft |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (F || p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (F || p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || F || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((F || ~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((F || ~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~(F || p) || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || F || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~(F || q)) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ (F || ~p))) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~(F || p))) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ (F || (q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ (F || (q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ (((F || q) /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ (F || p)) || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || F || ((~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((F || ~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((F || ~p || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~(F || p) || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || F || ~q) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~(F || q)) /\ ~p))
ready: no
Rule | introfalseleft |
Location | [1,1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ (F || ~p)))
ready: no
Rule | introfalseleft |
Location | [1,1,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~(F || p)))
ready: no
Rule | logic.propositional.absorpand |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ~p) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | logic.propositional.absorpand |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ~p)
ready: no
Rule | logic.propositional.andoveror |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => ((p || ((~p || ~q) /\ ~p)) /\ q /\ p) || ((p || ((~p || ~q) /\ ~p)) /\ (~p || ~q) /\ ~p)
ready: no
Rule | logic.propositional.andoveror |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p /\ ((q /\ p) || ((~p || ~q) /\ ~p))) || ((~p || ~q) /\ ~p /\ ((q /\ p) || ((~p || ~q) /\ ~p)))
ready: no
Rule | logic.propositional.andoveror |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || (~p /\ ~p) || (~q /\ ~p)) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | logic.propositional.andoveror |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || (~p /\ ~p) || (~q /\ ~p))
ready: no
Rule | logic.propositional.oroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ~p || ~q) /\ (p || ~p) /\ ((q /\ p) || ((~p || ~q) /\ ~p))
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ ((q /\ p) || ~p || ~q) /\ ((q /\ p) || ~p)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
q => (p || ((~p || ~q) /\ ~p)) /\ (q || ((~p || ~q) /\ ~p)) /\ (p || ((~p || ~q) /\ ~p))
ready: no