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