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

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\/r<-->(p/\q)\/p/\r.
Trying to prove with threshold = 0 1
Succeed in proving p/\q\/r --> (p/\q)\/p/\r (8 msec.)
pretty:1 =
--------- Ax  --------- Ax   --------- Ax  --------- Ax
p,q --> p     p,q --> q      p,r --> p     p,r --> r
----------------------- R/\  ----------------------- R/\
p,q --> p/\q                 p,r --> p/\r
-------------------- R\/     -------------------- R\/
p,q --> (p/\q)\/p/\r         p,r --> (p/\q)\/p/\r
------------------------------------------------- L\/
p,q\/r --> (p/\q)\/p/\r
------------------------ L/\
p/\q\/r --> (p/\q)\/p/\r
Trying to prove with threshold = 0
Succeed in proving (p/\q)\/p/\r --> p/\q\/r (4 msec.)
pretty:2 =
--------- Ax                    --------- Ax
p,q --> q                       p,r --> r
--------- Ax  ------------ R\/  --------- Ax  ------------ R\/
p,q --> p     p,q --> q\/r      p,r --> p     p,r --> q\/r
-------------------------- R/\  -------------------------- R/\
p,q --> p/\q\/r                 p,r --> p/\q\/r
---------------- L/\            ---------------- L/\
p/\q --> p/\q\/r                p/\r --> p/\q\/r
------------------------------------------------ L\/
(p/\q)\/p/\r --> p/\q\/r
yes
fol(g4i)> quit.
yes
Exit from Sequent Calculus Prover...
Total CPU time = 17 msec.
true

Back to g4-prover
Maintained by  Joseph Vidal-Rosset
```