----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sat Nov 29 22:49:20 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))).
-(all x y z (i(x,y)->i(d(z,x),d(z,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($c3,$c2).
0 [] -i(d($c1,$c3),d($c1,$c2)).
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=10): 7 [] -i(x,y)|i(d(x,z),d(y,z)).
** KEPT (pick-wt=7): 8 [] -i(d($c1,$c3),d($c1,$c2)).

------------> process sos:
** KEPT (pick-wt=3): 9 [] x=x.
** KEPT (pick-wt=11): 11 [copy,10,flip.1] k(k(x,y),z)=k(x,k(y,z)).
---> New Demodulator: 12 [new_demod,11] k(k(x,y),z)=k(x,k(y,z)).
** KEPT (pick-wt=5): 13 [] r(r(x))=x.
---> New Demodulator: 14 [new_demod,13] r(r(x))=x.
** KEPT (pick-wt=10): 15 [] r(u(x,y))=u(r(x),r(y)).
---> New Demodulator: 16 [new_demod,15] r(u(x,y))=u(r(x),r(y)).
** KEPT (pick-wt=10): 17 [] r(k(x,y))=k(r(y),r(x)).
---> New Demodulator: 18 [new_demod,17] r(k(x,y))=k(r(y),r(x)).
** KEPT (pick-wt=13): 20 [copy,19,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y).
---> New Demodulator: 21 [new_demod,20] u(k(x,y),k(z,y))=k(u(x,z),y).
** KEPT (pick-wt=10): 23 [copy,22,flip.1] c(u(c(x),c(y)))=n(x,y).
---> New Demodulator: 24 [new_demod,23] c(u(c(x),c(y)))=n(x,y).
** KEPT (pick-wt=10): 26 [copy,25,flip.1] c(k(c(x),c(y)))=d(x,y).
---> New Demodulator: 27 [new_demod,26] c(k(c(x),c(y)))=d(x,y).
** KEPT (pick-wt=10): 28 [] c(n(x,y))=u(c(x),c(y)).
---> New Demodulator: 29 [new_demod,28] c(n(x,y))=u(c(x),c(y)).
** KEPT (pick-wt=10): 30 [] c(u(x,y))=n(c(x),c(y)).
---> New Demodulator: 31 [new_demod,30] c(u(x,y))=n(c(x),c(y)).
** KEPT (pick-wt=5): 32 [] u(x,x)=x.
---> New Demodulator: 33 [new_demod,32] u(x,x)=x.
** KEPT (pick-wt=13): 35 [copy,34,flip.1] n(d(x,y),d(x,z))=d(x,n(y,z)).
---> New Demodulator: 36 [new_demod,35] n(d(x,y),d(x,z))=d(x,n(y,z)).
** KEPT (pick-wt=13): 38 [copy,37,flip.1] n(d(x,y),d(z,y))=d(n(x,z),y).
---> New Demodulator: 39 [new_demod,38] n(d(x,y),d(z,y))=d(n(x,z),y).
** KEPT (pick-wt=3): 40 [] i($c3,$c2).
  Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] x=x.
>>>> Starting back demodulation with 12.
>>>> Starting back demodulation with 14.
>>>> Starting back demodulation with 16.
>>>> Starting back demodulation with 18.
>>>> Starting back demodulation with 21.
>>>> Starting back demodulation with 24.
>>>> Starting back demodulation with 27.
>>>> Starting back demodulation with 29.
>>>> Starting back demodulation with 31.
    >> back demodulating 23 with 31.
>>>> Starting back demodulation with 33.
>>>> Starting back demodulation with 36.
>>>> Starting back demodulation with 39.
>>>> Starting back demodulation with 42.

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

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

----> UNIT CONFLICT at   0.34 sec ----> 2246 [binary,2245.1,8.1] $F.

Length of proof is 9.  Level of proof is 7.

---------------- 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).
6 [] -i(x,y)|i(k(z,x),k(z,y)).
8 [] -i(d($c1,$c3),d($c1,$c2)).
25 [] d(x,y)=c(k(c(x),c(y))).
27,26 [copy,25,flip.1] c(k(c(x),c(y)))=d(x,y).
40 [] i($c3,$c2).
46 [hyper,40,1] u($c3,$c2)=$c2.
52 [hyper,46,4] u(c($c2),c($c3))=c($c3).
74 [hyper,52,2] i(c($c2),c($c3)).
80 [hyper,74,6] i(k(x,c($c2)),k(x,c($c3))).
98 [hyper,80,1] u(k(x,c($c2)),k(x,c($c3)))=k(x,c($c3)).
128 [para_from,26.1.1,4.2.1.2,demod,27] u(k(c(x),c(y)),z)!=z|u(c(z),d(x,y))=d(x,y).
2190 [hyper,128,98,demod,27] u(d(x,$c3),d(x,$c2))=d(x,$c2).
2245 [hyper,2190,2] i(d(x,$c3),d(x,$c2)).
2246 [binary,2245.1,8.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                187
clauses generated           4985
clauses kept                1906
clauses forward subsumed    3113
clauses back subsumed         60
Kbytes malloced             2075

----------- times (seconds) -----------
user CPU time          0.54          (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 22:49:21 2003