----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 00:44:39 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("25booleanLaws.txt").
------- start included file 25booleanLaws.txt-------

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

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

list(usable).
0 [] n(z,y)!=Z|n(u(x,y),z)=n(z,x).
end_of_list.
------- end included file 25booleanLaws.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($c2,k(n($c3,k($c2,r($c1))),$c1))!=n(k($c3,$c1),$c2).
end_of_list.
------- end included file cycleLawC.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=14): 1 [] n(x,y)!=Z|n(u(z,y),x)=n(x,z).
** KEPT (pick-wt=16): 2 [] n($c2,k(n($c3,k($c2,r($c1))),$c1))!=n(k($c3,$c1),$c2).

------------> process sos:
** KEPT (pick-wt=13): 3 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z.
---> New Demodulator: 4 [new_demod,3] n(x,k(y,n(z,c(k(r(y),x)))))=Z.
** KEPT (pick-wt=20): 6 [copy,5,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u).
---> New Demodulator: 7 [new_demod,6] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u).
** KEPT (pick-wt=13): 8 [] n(x,k(n(y,c(k(x,r(z)))),z))=Z.
---> New Demodulator: 9 [new_demod,8] n(x,k(n(y,c(k(x,r(z)))),z))=Z.
>>>> Starting back demodulation with 4.
>>>> Starting back demodulation with 7.
>>>> Starting back demodulation with 9.

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

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

----> UNIT CONFLICT at   0.02 sec ----> 146 [binary,145.1,2.1] $F.

Length of proof is 4.  Level of proof is 3.

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

1 [] n(x,y)!=Z|n(u(z,y),x)=n(x,z).
2 [] n($c2,k(n($c3,k($c2,r($c1))),$c1))!=n(k($c3,$c1),$c2).
5 [] n(k(x,y),z)=n(u(k(n(x,u),y),k(n(x,c(u)),y)),z).
6 [copy,5,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u).
8 [] n(x,k(n(y,c(k(x,r(z)))),z))=Z.
17 [hyper,8,1] n(u(x,k(n(y,c(k(z,r(u)))),u)),z)=n(z,x).
144 [para_into,17.1.1,6.1.1] n(k(x,y),z)=n(z,k(n(x,k(z,r(y))),y)).
145 [copy,144,flip.1] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x).
146 [binary,145.1,2.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                 16
clauses generated            249
clauses kept                  97
clauses forward subsumed     164
clauses back subsumed          1
Kbytes malloced              319

----------- times (seconds) -----------
user CPU time          0.22          (0 hr, 0 min, 0 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 00:44:40 2003