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