----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sat Nov 29 22:49:06 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).

formula_list(usable).
all x (x=x).
end_of_list.

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

list(usable).
0 [] x=x.
end_of_list.
include("peirceanAx0.txt").
------- start included file peirceanAx0.txt-------

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

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

list(usable).
0 [] k(x,k(y,z))=k(k(x,y),z).
0 [] r(r(x))=x.
0 [] r(u(x,y))=u(r(x),r(y)).
0 [] r(k(x,y))=k(r(y),r(x)).
end_of_list.
------- end included file peirceanAx0.txt-------
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("nDef.txt").
------- start included file nDef.txt-------

formula_list(usable).
all x y (n(x,y)=c(u(c(x),c(y)))).
end_of_list.

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

list(usable).
0 [] n(x,y)=c(u(c(x),c(y))).
end_of_list.
------- end included file nDef.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("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("11booleanLaws.txt").
------- start included file 11booleanLaws.txt-------

formula_list(usable).
all x y (c(n(x,y))=u(c(x),c(y))).
all x y (c(u(x,y))=n(c(x),c(y))).
end_of_list.

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

list(usable).
0 [] c(n(x,y))=u(c(x),c(y)).
0 [] c(u(x,y))=n(c(x),c(y)).
end_of_list.
------- end included file 11booleanLaws.txt-------
include("17To19booleanLaws.txt").
------- start included file 17To19booleanLaws.txt-------

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

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

list(usable).
0 [] u(x,x)=x.
0 [] u(x,y)!=y|u(y,z)!=z|u(x,z)=z.
0 [] u(x,y)!=y|u(c(y),c(x))=c(x).
end_of_list.
------- end included file 17To19booleanLaws.txt-------
include("vi.txt").
------- start included file vi.txt-------

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

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

list(usable).
0 [] d(x,n(y,z))=n(d(x,y),d(x,z)).
0 [] d(n(x,y),z)=n(d(x,z),d(y,z)).
end_of_list.
------- end included file vi.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)))).
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($c3,$c2).
0 [] -i(d($c3,$c1),d($c2,$c1)).
end_of_list.
------- end included file vii.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=8): 1 [] -i(x,y)|u(x,y)=y.
** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y.
** KEPT (pick-wt=15): 3 [] u(x,y)!=y|u(y,z)!=z|u(x,z)=z.
** KEPT (pick-wt=13): 4 [] u(x,y)!=y|u(c(y),c(x))=c(x).
** 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=7): 7 [] -i(d($c3,$c1),d($c2,$c1)).

------------> process sos:
** KEPT (pick-wt=3): 8 [] x=x.
** KEPT (pick-wt=11): 10 [copy,9,flip.1] k(k(x,y),z)=k(x,k(y,z)).
---> New Demodulator: 11 [new_demod,10] k(k(x,y),z)=k(x,k(y,z)).
** KEPT (pick-wt=5): 12 [] r(r(x))=x.
---> New Demodulator: 13 [new_demod,12] r(r(x))=x.
** KEPT (pick-wt=10): 14 [] r(u(x,y))=u(r(x),r(y)).
---> New Demodulator: 15 [new_demod,14] r(u(x,y))=u(r(x),r(y)).
** KEPT (pick-wt=10): 16 [] r(k(x,y))=k(r(y),r(x)).
---> New Demodulator: 17 [new_demod,16] r(k(x,y))=k(r(y),r(x)).
** KEPT (pick-wt=13): 19 [copy,18,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y).
---> New Demodulator: 20 [new_demod,19] u(k(x,y),k(z,y))=k(u(x,z),y).
** KEPT (pick-wt=10): 22 [copy,21,flip.1] c(u(c(x),c(y)))=n(x,y).
---> New Demodulator: 23 [new_demod,22] c(u(c(x),c(y)))=n(x,y).
** KEPT (pick-wt=10): 25 [copy,24,flip.1] c(k(c(x),c(y)))=d(x,y).
---> New Demodulator: 26 [new_demod,25] c(k(c(x),c(y)))=d(x,y).
** KEPT (pick-wt=10): 27 [] c(n(x,y))=u(c(x),c(y)).
---> New Demodulator: 28 [new_demod,27] c(n(x,y))=u(c(x),c(y)).
** KEPT (pick-wt=10): 29 [] c(u(x,y))=n(c(x),c(y)).
---> New Demodulator: 30 [new_demod,29] c(u(x,y))=n(c(x),c(y)).
** KEPT (pick-wt=5): 31 [] u(x,x)=x.
---> New Demodulator: 32 [new_demod,31] u(x,x)=x.
** KEPT (pick-wt=13): 34 [copy,33,flip.1] n(d(x,y),d(x,z))=d(x,n(y,z)).
---> New Demodulator: 35 [new_demod,34] n(d(x,y),d(x,z))=d(x,n(y,z)).
** KEPT (pick-wt=13): 37 [copy,36,flip.1] n(d(x,y),d(z,y))=d(n(x,z),y).
---> New Demodulator: 38 [new_demod,37] n(d(x,y),d(z,y))=d(n(x,z),y).
** KEPT (pick-wt=3): 39 [] i($c3,$c2).
  Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] x=x.
>>>> Starting back demodulation with 11.
>>>> Starting back demodulation with 13.
>>>> Starting back demodulation with 15.
>>>> Starting back demodulation with 17.
>>>> Starting back demodulation with 20.
>>>> Starting back demodulation with 23.
>>>> Starting back demodulation with 26.
>>>> Starting back demodulation with 28.
>>>> Starting back demodulation with 30.
    >> back demodulating 22 with 30.
>>>> Starting back demodulation with 32.
>>>> Starting back demodulation with 35.
>>>> Starting back demodulation with 38.
>>>> Starting back demodulation with 41.

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

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

Resetting weight limit to 16.

sos_size=3417

----> UNIT CONFLICT at   5.91 sec ----> 5295 [binary,5294.1,7.1] $F.

Length of proof is 16.  Level of proof is 9.

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

1 [] -i(x,y)|u(x,y)=y.
2 [] i(x,y)|u(x,y)!=y.
4 [] u(x,y)!=y|u(c(y),c(x))=c(x).
5 [] -i(x,y)|i(k(x,z),k(y,z)).
7 [] -i(d($c3,$c1),d($c2,$c1)).
8 [] x=x.
21 [] n(x,y)=c(u(c(x),c(y))).
22 [copy,21,flip.1] c(u(c(x),c(y)))=n(x,y).
24 [] d(x,y)=c(k(c(x),c(y))).
26,25 [copy,24,flip.1] c(k(c(x),c(y)))=d(x,y).
28,27 [] c(n(x,y))=u(c(x),c(y)).
30,29 [] c(u(x,y))=n(c(x),c(y)).
32,31 [] u(x,x)=x.
39 [] i($c3,$c2).
41,40 [back_demod,22,demod,30] n(c(c(x)),c(c(y)))=n(x,y).
44 [hyper,39,1] u($c3,$c2)=$c2.
50 [hyper,44,4] u(c($c2),c($c3))=c($c3).
60 [hyper,50,2] i(c($c2),c($c3)).
71 [hyper,60,5] i(k(c($c2),x),k(c($c3),x)).
117 [para_into,29.1.1.1,31.1.1,flip.1] n(c(x),c(x))=c(x).
121 [para_into,29.1.1.1,4.2.1,demod,41] c(c(x))=n(y,x)|u(x,y)!=y.
173,172 [para_into,40.1.1,117.1.1] c(c(x))=n(x,x).
194 [back_demod,121,demod,173] n(x,x)=n(y,x)|u(x,y)!=y.
586 [para_into,194.2.1,1.2.1] n(x,x)=n(y,x)|y!=y| -i(x,y).
1251 [para_from,586.1.1,27.1.1.1,demod,28,32] u(c(x),c(y))=c(y)|x!=x| -i(y,x).
4533 [para_from,1251.1.1,2.2.1] i(c(x),c(y))|c(y)!=c(y)|x!=x| -i(y,x).
5244 [hyper,4533,8,8,71] i(c(k(c($c3),x)),c(k(c($c2),x))).
5294 [para_into,5244.1.1,25.1.1,demod,26] i(d($c3,x),d($c2,x)).
5295 [binary,5294.1,7.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                815
clauses generated         147711
clauses kept                4799
clauses forward subsumed   36965
clauses back subsumed        193
Kbytes malloced             4726

----------- times (seconds) -----------
user CPU time          6.11          (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 Sat Nov 29 22:49:12 2003