----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sat Nov 29 22:55:08 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("26_27booleanLaws.txt").
------- start included file 26_27booleanLaws.txt-------

formula_list(usable).
all x y z (i(x,y)&i(x,z)->i(x,n(y,z))).
all x y (i(n(x,y),x)&i(n(x,y),y)).
end_of_list.

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

list(usable).
0 [] -i(x,y)| -i(x,z)|i(x,n(y,z)).
0 [] i(n(x,y),x).
0 [] i(n(x,y),y).
end_of_list.
------- end included file 26_27booleanLaws.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("viii.txt").
------- start included file viii.txt-------

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

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

list(usable).
0 [] -i(k(n($c4,$c2),n($c3,$c1)),n(k($c4,$c3),k($c2,$c1))).
end_of_list.
------- end included file viii.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=11): 1 [] -i(x,y)| -i(x,z)|i(x,n(y,z)).
** KEPT (pick-wt=16): 2 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y).
** KEPT (pick-wt=15): 3 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x).
** KEPT (pick-wt=16): 4 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z).
** KEPT (pick-wt=15): 5 [] -i(k(n($c4,$c2),n($c3,$c1)),n(k($c4,$c3),k($c2,$c1))).

------------> process sos:
** KEPT (pick-wt=5): 6 [] i(n(x,y),x).
** KEPT (pick-wt=5): 7 [] i(n(x,y),y).
** KEPT (pick-wt=11): 8 [] i(k(n(x,y),n(z,u)),k(x,z)).
** KEPT (pick-wt=11): 9 [] i(k(n(x,y),n(z,u)),k(y,u)).

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

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

----> UNIT CONFLICT at   0.01 sec ----> 94 [binary,93.1,5.1] $F.

Length of proof is 1.  Level of proof is 1.

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

1 [] -i(x,y)| -i(x,z)|i(x,n(y,z)).
5 [] -i(k(n($c4,$c2),n($c3,$c1)),n(k($c4,$c3),k($c2,$c1))).
8 [] i(k(n(x,y),n(z,u)),k(x,z)).
9 [] i(k(n(x,y),n(z,u)),k(y,u)).
93 [hyper,9,1,8] i(k(n(x,y),n(z,u)),n(k(x,z),k(y,u))).
94 [binary,93.1,5.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                 11
clauses generated             94
clauses kept                  93
clauses forward subsumed      10
clauses back subsumed          0
Kbytes malloced              127

----------- 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 Sat Nov 29 22:55:08 2003