----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 17:39:36 2003
The command was "otter".

set(auto).
   dependent: set(auto1).
   dependent: set(process_input).
   dependent: clear(print_kept).
   dependent: clear(print_new_demod).
   dependent: clear(print_back_demod).
   dependent: clear(print_back_sub).
   dependent: set(control_memory).
   dependent: assign(max_mem, 12000).
   dependent: assign(pick_given_ratio, 4).
   dependent: assign(stats_level, 1).
   dependent: assign(max_seconds, 10800).
clear(print_given).
include("xxvii_a.txt").
------- start included file xxvii_a.txt-------

formula_list(usable).
all x y z (i(k(r(x),x),I)->i(n(k(x,y),k(x,z)),k(x,n(y,z)))).
all x y z (i(k(r(x),x),I)->k(x,n(y,z))=n(k(x,y),k(x,z))).
end_of_list.

-------> usable clausifies to:

list(usable).
0 [] -i(k(r(x),x),I)|i(n(k(x,y),k(x,z)),k(x,n(y,z))).
0 [] -i(k(r(x),x),I)|k(x,n(y,z))=n(k(x,y),k(x,z)).
end_of_list.
------- end included file xxvii_a.txt-------
include("xxvii_b_ghost.txt").
------- start included file xxvii_b_ghost.txt-------

formula_list(usable).
all x y z (i(k(r(x),x),I)->k(x,r(n(y,z)))=n(k(x,r(y)),k(x,r(z)))).
all x y z (r(k(x,r(n(y,z))))=k(n(y,z),r(x))).
all x y z (r(n(k(x,r(y)),k(x,r(z))))=n(k(y,r(x)),k(z,r(x)))).
end_of_list.

-------> usable clausifies to:

list(usable).
0 [] -i(k(r(x),x),I)|k(x,r(n(y,z)))=n(k(x,r(y)),k(x,r(z))).
0 [] r(k(x,r(n(y,z))))=k(n(y,z),r(x)).
0 [] r(n(k(x,r(y)),k(x,r(z))))=n(k(y,r(x)),k(z,r(x))).
end_of_list.
------- end included file xxvii_b_ghost.txt-------
include("xxvii.txt").
------- start included file xxvii.txt-------

formula_list(usable).
-(all x y z (i(k(r(x),x),I)->k(n(y,z),r(x))=n(k(y,r(x)),k(z,r(x))))).
end_of_list.

-------> usable clausifies to:

list(usable).
0 [] i(k(r($c3),$c3),I).
0 [] k(n($c2,$c1),r($c3))!=n(k($c2,r($c3)),k($c1,r($c3))).
end_of_list.
------- end included file xxvii.txt-------

SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.

This is a Horn set with equality.  The strategy will be
Knuth-Bendix and hyper_res, with positive clauses in
sos and nonpositive clauses in usable.

   dependent: set(knuth_bendix).
   dependent: set(para_from).
   dependent: set(para_into).
   dependent: clear(para_from_right).
   dependent: clear(para_into_right).
   dependent: set(para_from_vars).
   dependent: set(eq_units_both_ways).
   dependent: set(dynamic_demod_all).
   dependent: set(dynamic_demod).
   dependent: set(order_eq).
   dependent: set(back_demod).
   dependent: set(lrpo).
   dependent: set(hyper_res).
   dependent: clear(order_hyper).

------------> process usable:
** KEPT (pick-wt=19): 1 [] -i(k(r(x),x),I)|i(n(k(x,y),k(x,z)),k(x,n(y,z))).
** KEPT (pick-wt=19): 3 [copy,2,flip.2] -i(k(r(x),x),I)|n(k(x,y),k(x,z))=k(x,n(y,z)).
** KEPT (pick-wt=22): 4 [] -i(k(r(x),x),I)|k(x,r(n(y,z)))=n(k(x,r(y)),k(x,r(z))).
** KEPT (pick-wt=16): 6 [copy,5,flip.1] n(k($c2,r($c3)),k($c1,r($c3)))!=k(n($c2,$c1),r($c3)).

------------> process sos:
** KEPT (pick-wt=14): 7 [] r(k(x,r(n(y,z))))=k(n(y,z),r(x)).
---> New Demodulator: 8 [new_demod,7] r(k(x,r(n(y,z))))=k(n(y,z),r(x)).
** KEPT (pick-wt=20): 9 [] r(n(k(x,r(y)),k(x,r(z))))=n(k(y,r(x)),k(z,r(x))).
---> New Demodulator: 10 [new_demod,9] r(n(k(x,r(y)),k(x,r(z))))=n(k(y,r(x)),k(z,r(x))).
** KEPT (pick-wt=6): 11 [] i(k(r($c3),$c3),I).
>>>> Starting back demodulation with 8.
>>>> Starting back demodulation with 10.

======= end of input processing =======

=========== start of search ===========

----> UNIT CONFLICT at   0.01 sec ----> 66 [binary,64.1,6.1] $F.

Length of proof is 7.  Level of proof is 4.

---------------- PROOF ----------------

2 [] -i(k(r(x),x),I)|k(x,n(y,z))=n(k(x,y),k(x,z)).
3 [copy,2,flip.2] -i(k(r(x),x),I)|n(k(x,y),k(x,z))=k(x,n(y,z)).
4 [] -i(k(r(x),x),I)|k(x,r(n(y,z)))=n(k(x,r(y)),k(x,r(z))).
5 [] k(n($c2,$c1),r($c3))!=n(k($c2,r($c3)),k($c1,r($c3))).
6 [copy,5,flip.1] n(k($c2,r($c3)),k($c1,r($c3)))!=k(n($c2,$c1),r($c3)).
7 [] r(k(x,r(n(y,z))))=k(n(y,z),r(x)).
9 [] r(n(k(x,r(y)),k(x,r(z))))=n(k(y,r(x)),k(z,r(x))).
11 [] i(k(r($c3),$c3),I).
18 [hyper,11,4] k($c3,r(n(x,y)))=n(k($c3,r(x)),k($c3,r(y))).
21,20 [hyper,11,3] n(k($c3,x),k($c3,y))=k($c3,n(x,y)).
23 [back_demod,18,demod,21] k($c3,r(n(x,y)))=k($c3,n(r(x),r(y))).
46,45 [para_into,9.1.1.1,20.1.1] r(k($c3,n(r(x),r(y))))=n(k(x,r($c3)),k(y,r($c3))).
64 [para_from,23.1.1,7.1.1.1,demod,46] n(k(x,r($c3)),k(y,r($c3)))=k(n(x,y),r($c3)).
66 [binary,64.1,6.1] $F.

------------ end of proof -------------


Search stopped by max_proofs option.

============ end of search ============

-------------- statistics -------------
clauses given                  8
clauses generated             50
clauses kept                  46
clauses forward subsumed      15
clauses back subsumed          0
Kbytes malloced              191

----------- times (seconds) -----------
user CPU time          0.21          (0 hr, 0 min, 0 sec)
system CPU time        0.00          (0 hr, 0 min, 0 sec)
wall-clock time        0             (0 hr, 0 min, 0 sec)
hyper_res time         0.00
para_into time         0.00
para_from time         0.00
for_sub time           0.00
back_sub time          0.00
conflict time          0.00
demod time             0.00

That finishes the proof of the theorem.

Process 0 finished Sun Nov 30 17:39:36 2003