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