----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sat Nov 29 23:01:49 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,1).
include("peirceanAx1.txt").
------- start included file peirceanAx1.txt-------

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

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

list(usable).
0 [] k(u(x,y),z)=u(k(x,z),k(y,z)).
end_of_list.
------- end included file peirceanAx1.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("1To4booleanLaws.txt").
------- start included file 1To4booleanLaws.txt-------

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

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

list(usable).
0 [] -i(x,u(y,z))|i(n(x,c(z)),y).
0 [] -i(x,y)|i(u(z,x),u(z,y)).
0 [] x=u(n(x,c(y)),n(x,y)).
0 [] i(n(x,y),y).
end_of_list.
------- end included file 1To4booleanLaws.txt-------
include("vii.txt").
------- start included file vii.txt-------

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

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

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

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

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

list(usable).
0 [] -i(n(k($c3,$c1),c(k($c2,$c1))),k(n($c3,c($c2)),$c1)).
end_of_list.
------- end included file x_a.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=8): 1 [] -i(x,y)|u(x,y)=y.
** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y.
** KEPT (pick-wt=11): 3 [] -i(x,u(y,z))|i(n(x,c(z)),y).
** KEPT (pick-wt=10): 4 [] -i(x,y)|i(u(z,x),u(z,y)).
** KEPT (pick-wt=10): 5 [] -i(x,y)|i(k(x,z),k(y,z)).
** KEPT (pick-wt=10): 6 [] -i(x,y)|i(k(z,x),k(z,y)).
** KEPT (pick-wt=10): 7 [] -i(x,y)|i(d(x,z),d(y,z)).
** KEPT (pick-wt=10): 8 [] -i(x,y)|i(d(z,x),d(z,y)).
** KEPT (pick-wt=8): 9 [] -i(x,y)|i(r(x),r(y)).
** KEPT (pick-wt=15): 10 [] -i(n(k($c3,$c1),c(k($c2,$c1))),k(n($c3,c($c2)),$c1)).

------------> process sos:
** KEPT (pick-wt=13): 12 [copy,11,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y).
---> New Demodulator: 13 [new_demod,12] u(k(x,y),k(z,y))=k(u(x,z),y).
** KEPT (pick-wt=10): 15 [copy,14,flip.1] u(n(x,c(y)),n(x,y))=x.
---> New Demodulator: 16 [new_demod,15] u(n(x,c(y)),n(x,y))=x.
** KEPT (pick-wt=5): 17 [] i(n(x,y),y).
>>>> Starting back demodulation with 13.
>>>> Starting back demodulation with 16.

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

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

----> UNIT CONFLICT at   0.66 sec ----> 4567 [binary,4566.1,10.1] $F.

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

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

3 [] -i(x,u(y,z))|i(n(x,c(z)),y).
4 [] -i(x,y)|i(u(z,x),u(z,y)).
5 [] -i(x,y)|i(k(x,z),k(y,z)).
10 [] -i(n(k($c3,$c1),c(k($c2,$c1))),k(n($c3,c($c2)),$c1)).
11 [] k(u(x,y),z)=u(k(x,z),k(y,z)).
12 [copy,11,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y).
14 [] x=u(n(x,c(y)),n(x,y)).
15 [copy,14,flip.1] u(n(x,c(y)),n(x,y))=x.
17 [] i(n(x,y),y).
22 [para_from,12.1.1,3.1.2] -i(x,k(u(y,z),u))|i(n(x,c(k(z,u))),k(y,u)).
29 [hyper,17,4] i(u(x,n(y,z)),u(x,z)).
103 [para_into,29.1.1,15.1.1] i(x,u(n(x,c(y)),y)).
113 [hyper,103,5] i(k(x,y),k(u(n(x,c(z)),z),y)).
4566 [hyper,113,22] i(n(k(x,y),c(k(z,y))),k(n(x,c(z)),y)).
4567 [binary,4566.1,10.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                203
clauses generated           6033
clauses kept                4296
clauses forward subsumed    2001
clauses back subsumed        133
Kbytes malloced             3544

----------- times (seconds) -----------
user CPU time          0.86          (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 Sat Nov 29 23:01:50 2003