----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sat Nov 29 22:49:32 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))).
-(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($c2,$c1).
0 [] -i(r($c2),r($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=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=5): 9 [] -i(r($c2),r($c1)).

------------> process sos:
** KEPT (pick-wt=3): 10 [] x=x.
** KEPT (pick-wt=11): 12 [copy,11,flip.1] k(k(x,y),z)=k(x,k(y,z)).
---> New Demodulator: 13 [new_demod,12] k(k(x,y),z)=k(x,k(y,z)).
** KEPT (pick-wt=5): 14 [] r(r(x))=x.
---> New Demodulator: 15 [new_demod,14] r(r(x))=x.
** KEPT (pick-wt=10): 16 [] r(u(x,y))=u(r(x),r(y)).
---> New Demodulator: 17 [new_demod,16] r(u(x,y))=u(r(x),r(y)).
** KEPT (pick-wt=10): 18 [] r(k(x,y))=k(r(y),r(x)).
---> New Demodulator: 19 [new_demod,18] r(k(x,y))=k(r(y),r(x)).
** KEPT (pick-wt=13): 21 [copy,20,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y).
---> New Demodulator: 22 [new_demod,21] u(k(x,y),k(z,y))=k(u(x,z),y).
** KEPT (pick-wt=10): 24 [copy,23,flip.1] c(u(c(x),c(y)))=n(x,y).
---> New Demodulator: 25 [new_demod,24] c(u(c(x),c(y)))=n(x,y).
** KEPT (pick-wt=10): 27 [copy,26,flip.1] c(k(c(x),c(y)))=d(x,y).
---> New Demodulator: 28 [new_demod,27] c(k(c(x),c(y)))=d(x,y).
** KEPT (pick-wt=10): 29 [] c(n(x,y))=u(c(x),c(y)).
---> New Demodulator: 30 [new_demod,29] c(n(x,y))=u(c(x),c(y)).
** KEPT (pick-wt=10): 31 [] c(u(x,y))=n(c(x),c(y)).
---> New Demodulator: 32 [new_demod,31] c(u(x,y))=n(c(x),c(y)).
** KEPT (pick-wt=5): 33 [] u(x,x)=x.
---> New Demodulator: 34 [new_demod,33] u(x,x)=x.
** KEPT (pick-wt=13): 36 [copy,35,flip.1] n(d(x,y),d(x,z))=d(x,n(y,z)).
---> New Demodulator: 37 [new_demod,36] n(d(x,y),d(x,z))=d(x,n(y,z)).
** KEPT (pick-wt=13): 39 [copy,38,flip.1] n(d(x,y),d(z,y))=d(n(x,z),y).
---> New Demodulator: 40 [new_demod,39] n(d(x,y),d(z,y))=d(n(x,z),y).
** KEPT (pick-wt=3): 41 [] i($c2,$c1).
  Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] x=x.
>>>> Starting back demodulation with 13.
>>>> Starting back demodulation with 15.
>>>> Starting back demodulation with 17.
>>>> Starting back demodulation with 19.
>>>> Starting back demodulation with 22.
>>>> Starting back demodulation with 25.
>>>> Starting back demodulation with 28.
>>>> Starting back demodulation with 30.
>>>> Starting back demodulation with 32.
    >> back demodulating 24 with 32.
>>>> Starting back demodulation with 34.
>>>> Starting back demodulation with 37.
>>>> Starting back demodulation with 40.
>>>> Starting back demodulation with 43.

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

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

----> UNIT CONFLICT at   0.03 sec ----> 97 [binary,96.1,9.1] $F.

Length of proof is 3.  Level of proof is 3.

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

1 [] -i(x,y)|u(x,y)=y.
2 [] i(x,y)|u(x,y)!=y.
9 [] -i(r($c2),r($c1)).
16 [] r(u(x,y))=u(r(x),r(y)).
41 [] i($c2,$c1).
48 [hyper,41,1] u($c2,$c1)=$c1.
76 [para_into,16.1.1.1,48.1.1,flip.1] u(r($c2),r($c1))=r($c1).
96 [hyper,76,2] i(r($c2),r($c1)).
97 [binary,96.1,9.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                 15
clauses generated            108
clauses kept                  68
clauses forward subsumed      63
clauses back subsumed          0
Kbytes malloced              159

----------- times (seconds) -----------
user CPU time          0.23          (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 22:49:33 2003