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