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)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~r || ~s) /\ ((p /\ q /\ r /\ s) || ~(p /\ q))
ready: no
Rule | commor.sort |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (~(p /\ q) || (p /\ q /\ r /\ s)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
![](http://ideas.cs.uu.nl/images/external.png)
(p <-> r) /\ (q <-> s) => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
F || (p <-> r), q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(F || p) <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> (F || r), q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, F || (q <-> s) => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, (F || q) <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> (F || s) => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => F || (((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s))
ready: no
Rule | introfalseleft |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (F || (p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (F || (p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (((F || p) /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ (F || (q /\ r /\ s))) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ (F || q) /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ (F || (r /\ s))) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,0,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ (F || r) /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,0,1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ (F || s)) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || F || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(F || (p /\ q))) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~((F || p) /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,0,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ (F || q))) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (F || (p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (F || (p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (((F || p) /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ (F || (q /\ r /\ s))) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ (F || q) /\ r /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ (F || (r /\ s))) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,0,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ (F || r) /\ s) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,0,1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ (F || s)) || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || F || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || F || ~r || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~(F || r) || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || F || ~s)
ready: no
Rule | introfalseleft |
Location | [1,1,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~(F || s))
ready: no
Rule | logic.propositional.andoveror |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (((p /\ q /\ r /\ s) || ~(p /\ q)) /\ p /\ q /\ r /\ s) || (((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (~r || ~s))
ready: no
Rule | logic.propositional.andoveror |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r)) || (((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ~s)
ready: no
Rule | logic.propositional.andoveror |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (p /\ q /\ r /\ s /\ ((p /\ q /\ r /\ s) || ~r || ~s)) || (~(p /\ q) /\ ((p /\ q /\ r /\ s) || ~r || ~s))
ready: no
Rule | logic.propositional.defequiv |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(p /\ r) || (~p /\ ~r), q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.defequiv |
Location | [0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, (q /\ s) || (~q /\ ~s) => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.demorganand |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~p || ~q) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (p || ~(p /\ q)) /\ (q || ~(p /\ q)) /\ (r || ~(p /\ q)) /\ (s || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (p || ~(p /\ q)) /\ (q || ~(p /\ q)) /\ ((r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (p || ~(p /\ q)) /\ ((q /\ r) || ~(p /\ q)) /\ (s || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q) || ~(p /\ q)) /\ (r || ~(p /\ q)) /\ (s || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (p || ~r || ~s) /\ (q || ~r || ~s) /\ (r || ~r || ~s) /\ (s || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (p || ~r || ~s) /\ (q || ~r || ~s) /\ ((r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (p || ~r || ~s) /\ ((q /\ r) || ~r || ~s) /\ (s || ~r || ~s)
ready: no
Rule | logic.propositional.genoroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q) || ~r || ~s) /\ (r || ~r || ~s) /\ (s || ~r || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => (p || ~(p /\ q)) /\ ((q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q) || ~(p /\ q)) /\ ((r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r) || ~(p /\ q)) /\ (s || ~(p /\ q)) /\ ((p /\ q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (p || ~r || ~s) /\ ((q /\ r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q) || ~r || ~s) /\ ((r /\ s) || ~r || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((p /\ q /\ r) || ~r || ~s) /\ (s || ~r || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ (((p || ~r) /\ ((q /\ r /\ s) || ~r)) || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((((p /\ q) || ~r) /\ ((r /\ s) || ~r)) || ~s)
ready: no
Rule | logic.propositional.oroverand |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
p <-> r, q <-> s => ((p /\ q /\ r /\ s) || ~(p /\ q)) /\ ((((p /\ q /\ r) || ~r) /\ (s || ~r)) || ~s)
ready: no