----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 01:43:41 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("dDef.txt").
------- start included file dDef.txt-------

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

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

list(usable).
0 [] d(x,y)=c(k(c(x),c(y))).
end_of_list.
------- end included file dDef.txt-------
include("xviii_ghost.txt").
------- start included file xviii_ghost.txt-------

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

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

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

formula_list(usable).
-(all x y z i(k(x,d(y,z)),d(k(x,y),z))).
end_of_list.

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

list(usable).
0 [] -i(k($c3,d($c2,$c1)),d(k($c3,$c2),$c1)).
end_of_list.
------- end included file xviii.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=13): 1 [] -i(k(r(x),y),z)|i(k(x,c(z)),c(y)).
** KEPT (pick-wt=11): 2 [] -i(k($c3,d($c2,$c1)),d(k($c3,$c2),$c1)).

------------> process sos:
** KEPT (pick-wt=10): 4 [copy,3,flip.1] c(k(c(x),c(y)))=d(x,y).
---> New Demodulator: 5 [new_demod,4] c(k(c(x),c(y)))=d(x,y).
** KEPT (pick-wt=11): 7 [copy,6,demod,5,5] i(k(x,d(y,z)),d(k(x,y),z)).

----> UNIT CONFLICT at   0.01 sec ----> 8 [binary,7.1,2.1] $F.

Length of proof is 2.  Level of proof is 2.

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

2 [] -i(k($c3,d($c2,$c1)),d(k($c3,$c2),$c1)).
3 [] d(x,y)=c(k(c(x),c(y))).
5,4 [copy,3,flip.1] c(k(c(x),c(y)))=d(x,y).
6 [] i(k(x,c(k(c(y),c(z)))),c(k(c(k(x,y)),c(z)))).
7 [copy,6,demod,5,5] i(k(x,d(y,z)),d(k(x,y),z)).
8 [binary,7.1,2.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                  0
clauses generated              0
clauses kept                   4
clauses forward subsumed       0
clauses back subsumed          0
Kbytes malloced               95

----------- 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 01:43:41 2003