----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 00:33:05 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).
assign(max_distinct_vars,3).
assign(max_literals,1).
include("booleanAx.txt").
------- start included file booleanAx.txt-------
include("1_2booleanAx.txt").
------- start included file 1_2booleanAx.txt-------

formula_list(usable).
all x y (u(x,y)=u(y,x)).
all x y z (u(x,u(y,z))=u(u(x,y),z)).
end_of_list.

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

list(usable).
0 [] u(x,y)=u(y,x).
0 [] u(x,u(y,z))=u(u(x,y),z).
end_of_list.
------- end included file 1_2booleanAx.txt-------
include("3booleanAx.txt").
------- start included file 3booleanAx.txt-------

formula_list(usable).
all x y (u(c(u(c(x),y)),c(u(c(x),c(y))))=x).
end_of_list.

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

list(usable).
0 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
end_of_list.
------- end included file 3booleanAx.txt-------
------- end included file booleanAx.txt-------
include("peirceanAx2.txt").
------- start included file peirceanAx2.txt-------

formula_list(usable).
all x (k(x,I)=x).
all x y (u(k(r(x),c(k(x,y))),c(y))=c(y)).
end_of_list.

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

list(usable).
0 [] k(x,I)=x.
0 [] u(k(r(x),c(k(x,y))),c(y))=c(y).
end_of_list.
------- end included file peirceanAx2.txt-------
include("iDef.txt").
------- start included file iDef.txt-------

formula_list(usable).
all x y (i(x,y)<->u(x,y)=y).
end_of_list.

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

list(usable).
0 [] -i(x,y)|u(x,y)=y.
0 [] i(x,y)|u(x,y)!=y.
end_of_list.
------- end included file iDef.txt-------
include("nDef.txt").
------- start included file nDef.txt-------

formula_list(usable).
all x y (n(x,y)=c(u(c(x),c(y)))).
end_of_list.

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

list(usable).
0 [] n(x,y)=c(u(c(x),c(y))).
end_of_list.
------- end included file nDef.txt-------
include("xii.txt").
------- start included file xii.txt-------

formula_list(usable).
all x y z (i(k(x,y),c(z))<->i(k(r(x),z),c(y))).
all x y z (i(k(x,y),c(z))<->i(k(z,r(y)),c(x))).
end_of_list.

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

list(usable).
0 [] -i(k(x,y),c(z))|i(k(r(x),z),c(y)).
0 [] i(k(x,y),c(z))| -i(k(r(x),z),c(y)).
0 [] -i(k(x,y),c(z))|i(k(z,r(y)),c(x)).
0 [] i(k(x,y),c(z))| -i(k(z,r(y)),c(x)).
end_of_list.
------- end included file xii.txt-------
include("20To24booleanLaws.txt").
------- start included file 20To24booleanLaws.txt-------

formula_list(usable).
all x y (n(x,y)=n(y,x)).
all x y (n(x,c(y))=Z->u(x,y)=y).
all x y (u(x,y)=y->n(x,c(y))=Z).
all x y (n(x,y)=Z&u(x,y)=U->c(x)=y).
all x y (c(x)=y->n(x,y)=Z).
all x y (c(x)=y->u(x,y)=U).
end_of_list.

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

list(usable).
0 [] n(x,y)=n(y,x).
0 [] n(x,c(y))!=Z|u(x,y)=y.
0 [] u(x,y)!=y|n(x,c(y))=Z.
0 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y.
0 [] c(x)!=y|n(x,y)=Z.
0 [] c(x)!=y|u(x,y)=U.
end_of_list.
------- end included file 20To24booleanLaws.txt-------
include("cycleLawA.txt").
------- start included file cycleLawA.txt-------

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

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

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

SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.

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=8): 1 [] -i(x,y)|u(x,y)=y.
** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y.
** KEPT (pick-wt=13): 3 [] -i(k(x,y),c(z))|i(k(r(x),z),c(y)).
** KEPT (pick-wt=13): 4 [] i(k(x,y),c(z))| -i(k(r(x),z),c(y)).
** KEPT (pick-wt=13): 5 [] -i(k(x,y),c(z))|i(k(z,r(y)),c(x)).
** KEPT (pick-wt=13): 6 [] i(k(x,y),c(z))| -i(k(z,r(y)),c(x)).
** KEPT (pick-wt=11): 7 [] n(x,c(y))!=Z|u(x,y)=y.
** KEPT (pick-wt=11): 8 [] u(x,y)!=y|n(x,c(y))=Z.
** KEPT (pick-wt=14): 9 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y.
** KEPT (pick-wt=9): 10 [] c(x)!=y|n(x,y)=Z.
** KEPT (pick-wt=9): 11 [] c(x)!=y|u(x,y)=U.
** KEPT (pick-wt=7): 12 [] n($c1,k($c3,$c2))!=Z.

------------> process sos:
** KEPT (pick-wt=7): 13 [] u(x,y)=u(y,x).
** KEPT (pick-wt=11): 15 [copy,14,flip.1] u(u(x,y),z)=u(x,u(y,z)).
---> New Demodulator: 16 [new_demod,15] u(u(x,y),z)=u(x,u(y,z)).
** KEPT (pick-wt=14): 17 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
---> New Demodulator: 18 [new_demod,17] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
** KEPT (pick-wt=5): 19 [] k(x,I)=x.
---> New Demodulator: 20 [new_demod,19] k(x,I)=x.
** KEPT (pick-wt=13): 21 [] u(k(r(x),c(k(x,y))),c(y))=c(y).
---> New Demodulator: 22 [new_demod,21] u(k(r(x),c(k(x,y))),c(y))=c(y).
** KEPT (pick-wt=10): 24 [copy,23,flip.1] c(u(c(x),c(y)))=n(x,y).
---> New Demodulator: 25 [new_demod,24] c(u(c(x),c(y)))=n(x,y).
** KEPT (pick-wt=7): 26 [] n(x,y)=n(y,x).
** KEPT (pick-wt=8): 27 [] n($c3,k($c1,r($c2)))=Z.
---> New Demodulator: 28 [new_demod,27] n($c3,k($c1,r($c2)))=Z.
  Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] u(x,y)=u(y,x).
>>>> Starting back demodulation with 16.
>>>> Starting back demodulation with 18.
>>>> Starting back demodulation with 20.
>>>> Starting back demodulation with 22.
>>>> Starting back demodulation with 25.
    >> back demodulating 17 with 25.
  Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] n(x,y)=n(y,x).
>>>> Starting back demodulation with 28.
>>>> Starting back demodulation with 30.

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

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

----> UNIT CONFLICT at   0.95 sec ----> 6022 [binary,6020.1,69.1] $F.

Length of proof is 35.  Level of proof is 17.

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

1 [] -i(x,y)|u(x,y)=y.
2 [] i(x,y)|u(x,y)!=y.
6 [] i(k(x,y),c(z))| -i(k(z,r(y)),c(x)).
7 [] n(x,c(y))!=Z|u(x,y)=y.
8 [] u(x,y)!=y|n(x,c(y))=Z.
9 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y.
10 [] c(x)!=y|n(x,y)=Z.
11 [] c(x)!=y|u(x,y)=U.
12 [] n($c1,k($c3,$c2))!=Z.
13 [] u(x,y)=u(y,x).
14 [] u(x,u(y,z))=u(u(x,y),z).
15 [copy,14,flip.1] u(u(x,y),z)=u(x,u(y,z)).
17 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
19 [] k(x,I)=x.
23 [] n(x,y)=c(u(c(x),c(y))).
25,24 [copy,23,flip.1] c(u(c(x),c(y)))=n(x,y).
26 [] n(x,y)=n(y,x).
27 [] n($c3,k($c1,r($c2)))=Z.
29 [back_demod,17,demod,25] u(c(u(c(x),y)),n(x,y))=x.
32 [para_into,19.1.1,19.1.1] x=x.
34,33 [hyper,32,11] u(x,c(x))=U.
35 [hyper,32,10] n(x,c(x))=Z.
37 [para_into,33.1.1,13.1.1] u(c(x),x)=U.
39 [hyper,35,7] u(x,x)=x.
41 [para_into,15.1.1.1,33.1.1,flip.1] u(x,u(c(x),y))=u(U,y).
68,67 [para_into,26.1.1,35.1.1,flip.1] n(c(x),x)=Z.
69 [para_from,26.1.1,12.1.1] n(k($c3,$c2),$c1)!=Z.
71,70 [hyper,67,9,37] c(c(x))=x.
81,80 [para_into,24.1.1.1.1,70.1.1] c(u(x,c(y)))=n(c(x),y).
82 [para_into,24.1.1.1.1,24.1.1,demod,81] n(c(n(x,y)),z)=n(u(c(x),c(y)),z).
85,84 [para_into,24.1.1.1.2,70.1.1] c(u(c(x),y))=n(x,c(y)).
91,90 [para_into,24.1.1.1,37.1.1,demod,68] c(U)=Z.
92 [back_demod,29,demod,85] u(n(x,c(y)),n(x,y))=x.
102,101 [para_from,90.1.1,70.1.1.1] c(Z)=U.
115 [para_into,41.1.1.2,39.1.1,demod,34,flip.1] u(U,c(x))=U.
123 [para_into,115.1.1.2,70.1.1] u(U,x)=U.
137 [para_into,123.1.1,13.1.1] u(x,U)=U.
139 [hyper,137,8,demod,91] n(x,Z)=Z.
149 [para_into,139.1.1,26.1.1] n(Z,x)=Z.
151 [hyper,149,7] u(Z,x)=x.
155,154 [para_into,151.1.1,13.1.1] u(x,Z)=x.
522 [para_into,80.1.1.1,151.1.1,demod,71,102,flip.1] n(U,x)=x.
591,590 [para_into,522.1.1,26.1.1] n(x,U)=x.
597 [para_into,82.1.1,590.1.1,demod,591] c(n(x,y))=u(c(x),c(y)).
619 [para_into,92.1.1.2,27.1.1,demod,155] n($c3,c(k($c1,r($c2))))=$c3.
1295 [para_into,619.1.1,26.1.1] n(c(k($c1,r($c2))),$c3)=$c3.
3478 [para_into,597.1.1.1,1295.1.1,demod,71,flip.1] u(k($c1,r($c2)),c($c3))=c($c3).
5941 [hyper,3478,2] i(k($c1,r($c2)),c($c3)).
5975 [hyper,5941,6] i(k($c3,$c2),c($c1)).
5982 [hyper,5975,1] u(k($c3,$c2),c($c1))=c($c1).
6020 [hyper,5982,8,demod,71] n(k($c3,$c2),$c1)=Z.
6022 [binary,6020.1,69.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                545
clauses generated          42542
clauses kept                4050
clauses forward subsumed   34805
clauses back subsumed         31
Kbytes malloced             3384

----------- times (seconds) -----------
user CPU time          1.16          (0 hr, 0 min, 1 sec)
system CPU time        0.00          (0 hr, 0 min, 0 sec)
wall-clock time        1             (0 hr, 0 min, 1 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 00:33:06 2003