----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 00:52:28 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_seconds,7).
include("4To8booleanLaws.txt").
------- start included file 4To8booleanLaws.txt-------

formula_list(usable).
all x y i(n(x,y),y).
all x y z i(n(x,u(y,z)),u(y,n(x,z))).
all x y (x=u(n(x,y),n(x,c(y)))).
all x y z (i(x,y)->i(u(z,x),u(z,y))).
all x y z (i(x,y)->i(n(z,x),n(z,y))).
end_of_list.

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

list(usable).
0 [] i(n(x,y),y).
0 [] i(n(x,u(y,z)),u(y,n(x,z))).
0 [] x=u(n(x,y),n(x,c(y))).
0 [] -i(x,y)|i(u(z,x),u(z,y)).
0 [] -i(x,y)|i(n(z,x),n(z,y)).
end_of_list.
------- end included file 4To8booleanLaws.txt-------
include("9_10booleanLaws.txt").
------- start included file 9_10booleanLaws.txt-------

formula_list(usable).
all x (u(x,Z)=x).
all x y z (i(x,y)&i(y,z)->i(x,z)).
end_of_list.

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

list(usable).
0 [] u(x,Z)=x.
0 [] -i(x,y)| -i(y,z)|i(x,z).
end_of_list.
------- end included file 9_10booleanLaws.txt-------
include("monotLaws.txt").
------- start included file monotLaws.txt-------
include("1To3monotLaws.txt").
------- start included file 1To3monotLaws.txt-------

formula_list(usable).
all x y z (u(x,y)=y->u(k(z,x),k(z,y))=k(z,y)).
all x y z (u(x,y)=y->u(c(u(z,y)),c(x))=c(x)).
all x y z (u(x,y)=y->u(k(x,z),k(y,z))=k(y,z)).
end_of_list.

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

list(usable).
0 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y).
0 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x).
0 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z).
end_of_list.
------- end included file 1To3monotLaws.txt-------
include("4_5monotLaws.txt").
------- start included file 4_5monotLaws.txt-------

formula_list(usable).
all x y w v i(k(n(x,w),n(y,v)),k(x,y)).
all x y w v i(k(n(x,w),n(y,v)),k(w,v)).
end_of_list.

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

list(usable).
0 [] i(k(n(x,w),n(y,v)),k(x,y)).
0 [] i(k(n(x,w),n(y,v)),k(w,v)).
end_of_list.
------- end included file 4_5monotLaws.txt-------
------- end included file monotLaws.txt-------
include("cycleLawsB.txt").
------- start included file cycleLawsB.txt-------

formula_list(usable).
all x y z (n(y,k(x,n(z,c(k(r(x),y)))))=Z).
all x y z v (n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y)).
all x y z (n(y,k(n(x,c(k(y,r(z)))),z))=Z).
end_of_list.

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

list(usable).
0 [] n(y,k(x,n(z,c(k(r(x),y)))))=Z.
0 [] n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y).
0 [] n(y,k(n(x,c(k(y,r(z)))),z))=Z.
end_of_list.
------- end included file cycleLawsB.txt-------
include("cycleLawC.txt").
------- start included file cycleLawC.txt-------

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

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

list(usable).
0 [] n(y,k(n(x,k(y,r(z))),z))=n(k(x,z),y).
end_of_list.
------- end included file cycleLawC.txt-------
include("xv_a_ghost.txt").
------- start included file xv_a_ghost.txt-------

formula_list(usable).
-(all y z v i(k(n(y,z),v),k(y,v))).
end_of_list.

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

list(usable).
0 [] -i(k(n($c3,$c2),$c1),k($c3,$c1)).
end_of_list.
------- end included file xv_a_ghost.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=10): 1 [] -i(x,y)|i(u(z,x),u(z,y)).
** KEPT (pick-wt=10): 2 [] -i(x,y)|i(n(z,x),n(z,y)).
** KEPT (pick-wt=9): 3 [] -i(x,y)| -i(y,z)|i(x,z).
** KEPT (pick-wt=16): 4 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y).
** KEPT (pick-wt=15): 5 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x).
** KEPT (pick-wt=16): 6 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z).
** KEPT (pick-wt=9): 7 [] -i(k(n($c3,$c2),$c1),k($c3,$c1)).

------------> process sos:
** KEPT (pick-wt=5): 8 [] i(n(x,y),y).
** KEPT (pick-wt=11): 9 [] i(n(x,u(y,z)),u(y,n(x,z))).
** KEPT (pick-wt=10): 11 [copy,10,flip.1] u(n(x,y),n(x,c(y)))=x.
---> New Demodulator: 12 [new_demod,11] u(n(x,y),n(x,c(y)))=x.
** KEPT (pick-wt=5): 13 [] u(x,Z)=x.
---> New Demodulator: 14 [new_demod,13] u(x,Z)=x.
** KEPT (pick-wt=11): 15 [] i(k(n(x,y),n(z,u)),k(x,z)).
** KEPT (pick-wt=11): 16 [] i(k(n(x,y),n(z,u)),k(y,u)).
** KEPT (pick-wt=13): 17 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z.
---> New Demodulator: 18 [new_demod,17] n(x,k(y,n(z,c(k(r(y),x)))))=Z.
** KEPT (pick-wt=20): 20 [copy,19,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u).
---> New Demodulator: 21 [new_demod,20] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u).
** KEPT (pick-wt=13): 22 [] n(x,k(n(y,c(k(x,r(z)))),z))=Z.
---> New Demodulator: 23 [new_demod,22] n(x,k(n(y,c(k(x,r(z)))),z))=Z.
** KEPT (pick-wt=16): 24 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x).
>>>> Starting back demodulation with 12.
>>>> Starting back demodulation with 14.
>>>> Starting back demodulation with 18.
>>>> Starting back demodulation with 21.
>>>> Starting back demodulation with 23.
** KEPT (pick-wt=16): 25 [copy,24,flip.1] n(k(x,y),z)=n(z,k(n(x,k(z,r(y))),y)).
  Following clause subsumed by 24 during input processing: 0 [copy,25,flip.1] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x).

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

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

Resetting weight limit to 13.

sos_size=5954

Resetting weight limit to 11.

sos_size=3306

----> UNIT CONFLICT at   6.14 sec ----> 8553 [binary,8552.1,7.1] $F.

Length of proof is 17.  Level of proof is 9.

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

1 [] -i(x,y)|i(u(z,x),u(z,y)).
2 [] -i(x,y)|i(n(z,x),n(z,y)).
3 [] -i(x,y)| -i(y,z)|i(x,z).
7 [] -i(k(n($c3,$c2),$c1),k($c3,$c1)).
9 [] i(n(x,u(y,z)),u(y,n(x,z))).
10 [] x=u(n(x,y),n(x,c(y))).
12,11 [copy,10,flip.1] u(n(x,y),n(x,c(y)))=x.
13 [] u(x,Z)=x.
15 [] i(k(n(x,y),n(z,u)),k(x,z)).
17 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z.
19 [] n(k(x,y),z)=n(u(k(n(x,u),y),k(n(x,c(u)),y)),z).
21,20 [copy,19,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u).
22 [] n(x,k(n(y,c(k(x,r(z)))),z))=Z.
24 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x).
39 [para_from,13.1.1,1.2.2] -i(x,Z)|i(u(y,x),y).
40 [para_from,13.1.1,1.2.1] -i(Z,x)|i(y,u(y,x)).
137 [hyper,15,2] i(n(x,k(n(y,z),n(u,v))),n(x,k(y,u))).
272 [para_from,17.1.1,15.1.1.2] i(k(n(x,y),Z),k(x,z)).
302 [para_into,272.1.1.1,17.1.1] i(k(Z,Z),k(x,y)).
316 [hyper,302,2] i(n(x,k(Z,Z)),n(x,k(y,z))).
359 [para_from,20.1.1,11.1.1.2,demod,21,12,flip.1] u(k(n(x,y),z),k(n(x,c(y)),z))=k(x,z).
6025 [para_into,316.1.2,22.1.1] i(n(x,k(Z,Z)),Z).
6026 [hyper,6025,39] i(u(x,n(y,k(Z,Z))),x).
6111 [hyper,6026,3,9] i(n(x,u(y,k(Z,Z))),y).
6657 [para_into,137.1.1,22.1.1] i(Z,n(x,k(y,z))).
6701 [para_into,6657.1.2,24.1.1] i(Z,n(k(x,y),z)).
6776 [hyper,6701,3,6111] i(Z,x).
6787 [hyper,6776,40] i(x,u(x,y)).
8552 [para_from,359.1.1,6787.1.2] i(k(n(x,y),z),k(x,z)).
8553 [binary,8552.1,7.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                891
clauses generated         256991
clauses kept                8507
clauses forward subsumed   65612
clauses back subsumed       4717
Kbytes malloced             4598

----------- times (seconds) -----------
user CPU time          6.34          (0 hr, 0 min, 6 sec)
system CPU time        0.00          (0 hr, 0 min, 0 sec)
wall-clock time        6             (0 hr, 0 min, 6 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 00:52:34 2003