----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 22:23:44 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,20).
assign(max_distinct_vars,3).
assign(max_literals,1).
include("booleanAx.txt").
------- start included file booleanAx.txt-------
include("1_2booleanAx.txt").
------- start included file 1_2booleanAx.txt-------

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

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

list(usable).
0 [] u(x,y)=u(y,x).
0 [] u(x,u(y,z))=u(u(x,y),z).
end_of_list.
------- end included file 1_2booleanAx.txt-------
include("3booleanAx.txt").
------- start included file 3booleanAx.txt-------

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

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

list(usable).
0 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
end_of_list.
------- end included file 3booleanAx.txt-------
------- end included file booleanAx.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("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("uzDef.txt").
------- start included file uzDef.txt-------

formula_list(usable).
D=c(I).
U=u(I,D).
Z=c(U).
end_of_list.

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

list(usable).
0 [] D=c(I).
0 [] U=u(I,D).
0 [] Z=c(U).
end_of_list.
------- end included file uzDef.txt-------
include("booleanLaws.txt").
------- start included file booleanLaws.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("4To8booleanLaws.txt").
------- start included file 4To8booleanLaws.txt-------

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

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

list(usable).
0 [] i(n(x,y),y).
0 [] i(n(x,u(y,z)),u(y,n(x,z))).
0 [] x=u(n(x,y),n(x,c(y))).
0 [] -i(x,y)|i(u(z,x),u(z,y)).
0 [] -i(x,y)|i(n(z,x),n(z,y)).
end_of_list.
------- end included file 4To8booleanLaws.txt-------
include("9_10booleanLaws.txt").
------- start included file 9_10booleanLaws.txt-------

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

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

list(usable).
0 [] u(x,Z)=x.
0 [] -i(x,y)| -i(y,z)|i(x,z).
end_of_list.
------- end included file 9_10booleanLaws.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("12booleanLaws.txt").
------- start included file 12booleanLaws.txt-------

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

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

list(usable).
0 [] -i(x,z)| -i(y,z)|i(u(x,y),z).
end_of_list.
------- end included file 12booleanLaws.txt-------
include("13booleanLaws.txt").
------- start included file 13booleanLaws.txt-------

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

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

list(usable).
0 [] -i(x,y)| -i(y,x)|x=y.
end_of_list.
------- end included file 13booleanLaws.txt-------
include("14booleanLaws.txt").
------- start included file 14booleanLaws.txt-------

formula_list(usable).
c(D)=I.
c(Z)=U.
end_of_list.

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

list(usable).
0 [] c(D)=I.
0 [] c(Z)=U.
end_of_list.
------- end included file 14booleanLaws.txt-------
include("15_16booleanLaws.txt").
------- start included file 15_16booleanLaws.txt-------

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

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

list(usable).
0 [] c(c(x))=x.
0 [] u(x,y)!=y|c(u(y,c(x)))=Z.
0 [] c(u($c1,c($c2)))=Z.
0 [] u($c2,$c1)!=$c1.
end_of_list.
------- end included file 15_16booleanLaws.txt-------
------- end included file booleanLaws.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=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)).
  Following clause subsumed by 4 during input processing: 0 [] -i(x,y)|i(u(z,x),u(z,y)).
** KEPT (pick-wt=10): 5 [] -i(x,y)|i(n(z,x),n(z,y)).
** KEPT (pick-wt=9): 6 [] -i(x,y)| -i(y,z)|i(x,z).
** KEPT (pick-wt=11): 7 [] -i(x,y)| -i(z,y)|i(u(x,z),y).
** KEPT (pick-wt=9): 8 [] -i(x,y)| -i(y,x)|x=y.
** KEPT (pick-wt=12): 9 [] u(x,y)!=y|c(u(y,c(x)))=Z.
** KEPT (pick-wt=5): 10 [] u($c2,$c1)!=$c1.

------------> process sos:
** KEPT (pick-wt=7): 11 [] u(x,y)=u(y,x).
** KEPT (pick-wt=11): 13 [copy,12,flip.1] u(u(x,y),z)=u(x,u(y,z)).
---> New Demodulator: 14 [new_demod,13] u(u(x,y),z)=u(x,u(y,z)).
** KEPT (pick-wt=14): 15 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
---> New Demodulator: 16 [new_demod,15] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
** KEPT (pick-wt=10): 18 [copy,17,flip.1] c(u(c(x),c(y)))=n(x,y).
---> New Demodulator: 19 [new_demod,18] c(u(c(x),c(y)))=n(x,y).
** KEPT (pick-wt=4): 21 [copy,20,flip.1] c(I)=D.
---> New Demodulator: 22 [new_demod,21] c(I)=D.
** KEPT (pick-wt=5): 24 [copy,23,flip.1] u(I,D)=U.
---> New Demodulator: 25 [new_demod,24] u(I,D)=U.
** KEPT (pick-wt=4): 27 [copy,26,flip.1] c(U)=Z.
---> New Demodulator: 28 [new_demod,27] c(U)=Z.
** KEPT (pick-wt=10): 30 [copy,29,flip.1] u(n(x,c(y)),n(x,y))=x.
---> New Demodulator: 31 [new_demod,30] u(n(x,c(y)),n(x,y))=x.
** KEPT (pick-wt=5): 32 [] i(n(x,y),y).
  Following clause subsumed by 32 during input processing: 0 [] i(n(x,y),y).
** KEPT (pick-wt=11): 33 [] i(n(x,u(y,z)),u(y,n(x,z))).
** KEPT (pick-wt=10): 35 [copy,34,flip.1] u(n(x,y),n(x,c(y)))=x.
---> New Demodulator: 36 [new_demod,35] u(n(x,y),n(x,c(y)))=x.
** KEPT (pick-wt=5): 37 [] u(x,Z)=x.
---> New Demodulator: 38 [new_demod,37] u(x,Z)=x.
** KEPT (pick-wt=10): 39 [] c(n(x,y))=u(c(x),c(y)).
---> New Demodulator: 40 [new_demod,39] c(n(x,y))=u(c(x),c(y)).
** KEPT (pick-wt=10): 41 [] c(u(x,y))=n(c(x),c(y)).
---> New Demodulator: 42 [new_demod,41] c(u(x,y))=n(c(x),c(y)).
** KEPT (pick-wt=4): 43 [] c(D)=I.
---> New Demodulator: 44 [new_demod,43] c(D)=I.
** KEPT (pick-wt=4): 45 [] c(Z)=U.
---> New Demodulator: 46 [new_demod,45] c(Z)=U.
** KEPT (pick-wt=5): 47 [] c(c(x))=x.
---> New Demodulator: 48 [new_demod,47] c(c(x))=x.
** KEPT (pick-wt=6): 50 [copy,49,demod,42,48] n(c($c1),$c2)=Z.
---> New Demodulator: 51 [new_demod,50] n(c($c1),$c2)=Z.
  Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] u(x,y)=u(y,x).
>>>> Starting back demodulation with 14.
>>>> Starting back demodulation with 16.
>>>> Starting back demodulation with 19.
    >> back demodulating 15 with 19.
>>>> Starting back demodulation with 22.
>>>> Starting back demodulation with 25.
>>>> Starting back demodulation with 28.
>>>> Starting back demodulation with 31.
>>>> Starting back demodulation with 36.
>>>> Starting back demodulation with 38.
>>>> Starting back demodulation with 40.
>>>> Starting back demodulation with 42.
    >> back demodulating 18 with 42.
    >> back demodulating 9 with 42.
>>>> Starting back demodulation with 44.
>>>> Starting back demodulation with 46.
>>>> Starting back demodulation with 48.
>>>> Starting back demodulation with 51.
  Following clause subsumed by 52 during input processing: 0 [copy,52,flip.1] x=x.

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

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

----> UNIT CONFLICT at   0.06 sec ----> 317 [binary,315.1,10.1] $F.

Length of proof is 10.  Level of proof is 7.

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

1 [] -i(x,y)|u(x,y)=y.
10 [] u($c2,$c1)!=$c1.
11 [] u(x,y)=u(y,x).
26 [] Z=c(U).
28,27 [copy,26,flip.1] c(U)=Z.
32 [] i(n(x,y),y).
34 [] x=u(n(x,y),n(x,c(y))).
35 [copy,34,flip.1] u(n(x,y),n(x,c(y)))=x.
37 [] u(x,Z)=x.
39 [] c(n(x,y))=u(c(x),c(y)).
42,41 [] c(u(x,y))=n(c(x),c(y)).
46,45 [] c(Z)=U.
48,47 [] c(c(x))=x.
49 [] c(u($c1,c($c2)))=Z.
50 [copy,49,demod,42,48] n(c($c1),$c2)=Z.
70,69 [para_into,37.1.1,11.1.1] u(Z,x)=x.
219 [para_from,50.1.1,39.1.1.1,demod,46,48,flip.1] u($c1,c($c2))=U.
241 [para_into,219.1.1,11.1.1] u(c($c2),$c1)=U.
263 [para_from,241.1.1,41.1.1.1,demod,28,48,flip.1] n($c2,c($c1))=Z.
293 [para_from,263.1.1,35.1.1.1,demod,48,70] n($c2,$c1)=$c2.
297 [para_from,293.1.1,32.1.1] i($c2,$c1).
315 [hyper,297,1] u($c2,$c1)=$c1.
317 [binary,315.1,10.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                 52
clauses generated           1031
clauses kept                 221
clauses forward subsumed     564
clauses back subsumed         18
Kbytes malloced              255

----------- times (seconds) -----------
user CPU time          0.26          (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 Sun Nov 30 22:23:44 2003