G4 Prover
    
Result of the test for sequent ~(p\/q) <--> ~p/\ ~q 



G4 Prover: a Prolog Prover for Roy Dyckhoff's Sequent Calculus G4
This prover is a fork made by Joseph Vidal-Rosset (joseph.vidal-rosset@gmail.com),
from seqprover.pl, the sequent prover for CL-X, written by Naoyuki Tamura (tamura@kobe-u.ac.jp).
Type "help." if you need some help.
fol(g4i)> fol(g4i).
yes
fol(g4i)> output(pretty).
yes
fol(g4i)> ~ (p\/q)<--> ~p/\ ~q.
Trying to prove with threshold = 0
Succeed in proving ~ (p\/q) --> ~p/\ ~q (2 msec.)
pretty:1 =
-------------------- Ax        -------------------- Ax
bot,p,q->bot --> bot           bot,p->bot,q --> bot
----------------------- L0->1  ----------------------- L0->1
p,p->bot,q->bot --> bot        q,p->bot,q->bot --> bot
----------------------- R~     ----------------------- R~
 p->bot,q->bot --> ~p           p->bot,q->bot --> ~q
 --------------------------------------------------- R/\
              p->bot,q->bot --> ~p/\ ~q
              ------------------------- L\/->(3)
               (p\/q)->bot --> ~p/\ ~q
               ----------------------- L~def
                ~ (p\/q) --> ~p/\ ~q
Trying to prove with threshold = 0
Succeed in proving ~p/\ ~q --> ~ (p\/q) (2 msec.)
pretty:2 =
-------------------- Ax        -------------------- Ax
bot,p,q->bot --> bot           bot,p->bot,q --> bot
----------------------- L0->1  ----------------------- L0->1
p,p->bot,q->bot --> bot        q,p->bot,q->bot --> bot
------------------------------------------------------ L\/
              p\/q,p->bot,q->bot --> bot
              -------------------------- R~
              p->bot,q->bot --> ~ (p\/q)
              -------------------------- L~def
                p->bot,~q --> ~ (p\/q)
                ---------------------- L~def
                  ~p,~q --> ~ (p\/q)
                  -------------------- L/\
                  ~p/\ ~q --> ~ (p\/q)
yes
fol(g4i)> quit.
yes
Exit from Sequent Calculus Prover...
Total CPU time = 11 msec.
true 


  

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Maintained by  Joseph Vidal-Rosset