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