----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 22:19:42 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($c2,$c1).
0 [] i($c1,$c2).
0 [] $c2!=$c1.
end_of_list.
------- end included file 13booleanLaws.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=3): 8 [] $c2!=$c1.

------------> process sos:
** KEPT (pick-wt=7): 9 [] u(x,y)=u(y,x).
** KEPT (pick-wt=11): 11 [copy,10,flip.1] u(u(x,y),z)=u(x,u(y,z)).
---> New Demodulator: 12 [new_demod,11] u(u(x,y),z)=u(x,u(y,z)).
** KEPT (pick-wt=14): 13 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
---> New Demodulator: 14 [new_demod,13] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
** KEPT (pick-wt=10): 16 [copy,15,flip.1] c(u(c(x),c(y)))=n(x,y).
---> New Demodulator: 17 [new_demod,16] c(u(c(x),c(y)))=n(x,y).
** KEPT (pick-wt=4): 19 [copy,18,flip.1] c(I)=D.
---> New Demodulator: 20 [new_demod,19] c(I)=D.
** KEPT (pick-wt=5): 22 [copy,21,flip.1] u(I,D)=U.
---> New Demodulator: 23 [new_demod,22] u(I,D)=U.
** KEPT (pick-wt=4): 25 [copy,24,flip.1] c(U)=Z.
---> New Demodulator: 26 [new_demod,25] c(U)=Z.
** KEPT (pick-wt=10): 28 [copy,27,flip.1] u(n(x,c(y)),n(x,y))=x.
---> New Demodulator: 29 [new_demod,28] u(n(x,c(y)),n(x,y))=x.
** KEPT (pick-wt=5): 30 [] i(n(x,y),y).
  Following clause subsumed by 30 during input processing: 0 [] i(n(x,y),y).
** KEPT (pick-wt=11): 31 [] i(n(x,u(y,z)),u(y,n(x,z))).
** KEPT (pick-wt=10): 33 [copy,32,flip.1] u(n(x,y),n(x,c(y)))=x.
---> New Demodulator: 34 [new_demod,33] u(n(x,y),n(x,c(y)))=x.
** KEPT (pick-wt=5): 35 [] u(x,Z)=x.
---> New Demodulator: 36 [new_demod,35] u(x,Z)=x.
** KEPT (pick-wt=10): 37 [] c(n(x,y))=u(c(x),c(y)).
---> New Demodulator: 38 [new_demod,37] c(n(x,y))=u(c(x),c(y)).
** KEPT (pick-wt=10): 39 [] c(u(x,y))=n(c(x),c(y)).
---> New Demodulator: 40 [new_demod,39] c(u(x,y))=n(c(x),c(y)).
** KEPT (pick-wt=3): 41 [] i($c2,$c1).
** KEPT (pick-wt=3): 42 [] i($c1,$c2).
  Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] u(x,y)=u(y,x).
>>>> Starting back demodulation with 12.
>>>> Starting back demodulation with 14.
>>>> Starting back demodulation with 17.
    >> back demodulating 13 with 17.
>>>> Starting back demodulation with 20.
>>>> Starting back demodulation with 23.
>>>> Starting back demodulation with 26.
>>>> Starting back demodulation with 29.
>>>> Starting back demodulation with 34.
>>>> Starting back demodulation with 36.
>>>> Starting back demodulation with 38.
>>>> Starting back demodulation with 40.
    >> back demodulating 16 with 40.
>>>> Starting back demodulation with 44.
  Following clause subsumed by 45 during input processing: 0 [copy,45,flip.1] n(x,y)=n(x,y).

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

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

----> UNIT CONFLICT at   0.04 sec ----> 134 [binary,132.1,8.1] $F.

Length of proof is 3.  Level of proof is 2.

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

1 [] -i(x,y)|u(x,y)=y.
8 [] $c2!=$c1.
9 [] u(x,y)=u(y,x).
41 [] i($c2,$c1).
42 [] i($c1,$c2).
50 [hyper,41,1] u($c2,$c1)=$c1.
58,57 [hyper,42,1] u($c1,$c2)=$c2.
132 [para_into,50.1.1,9.1.1,demod,58] $c2=$c1.
134 [binary,132.1,8.1] $F.

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                 23
clauses generated            199
clauses kept                  96
clauses forward subsumed      99
clauses back subsumed         15
Kbytes malloced              159

----------- times (seconds) -----------
user CPU time          0.24          (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 Sun Nov 30 22:19:43 2003