----- Otter 3.2, August 2001 -----
The process was started by ??? on ???,
Sun Nov 30 22:26:21 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(y,c(x)))!=Z|u(x,y)=y.
end_of_list.
------- end included file 15_16booleanLaws.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)).
end_of_list.
-------> usable clausifies to:
list(usable).
0 [] u(x,x)=x.
0 [] u($c3,$c2)=$c2.
0 [] u($c2,$c1)=$c1.
0 [] u($c3,$c1)!=$c1.
end_of_list.
------- end included file 17To19booleanLaws.txt-------
------- end included file booleanLaws.txt-------
SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
This is a Horn set with equality. The strategy will be
Knuth-Bendix and hyper_res, with positive clauses in
sos and nonpositive clauses in usable.
dependent: set(knuth_bendix).
dependent: set(para_from).
dependent: set(para_into).
dependent: clear(para_from_right).
dependent: clear(para_into_right).
dependent: set(para_from_vars).
dependent: set(eq_units_both_ways).
dependent: set(dynamic_demod_all).
dependent: set(dynamic_demod).
dependent: set(order_eq).
dependent: set(back_demod).
dependent: set(lrpo).
dependent: set(hyper_res).
dependent: clear(order_hyper).
------------> process usable:
** KEPT (pick-wt=8): 1 [] -i(x,y)|u(x,y)=y.
** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y.
** KEPT (pick-wt=11): 3 [] -i(x,u(y,z))|i(n(x,c(z)),y).
** KEPT (pick-wt=10): 4 [] -i(x,y)|i(u(z,x),u(z,y)).
Following clause subsumed by 4 during input processing: 0 [] -i(x,y)|i(u(z,x),u(z,y)).
** KEPT (pick-wt=10): 5 [] -i(x,y)|i(n(z,x),n(z,y)).
** KEPT (pick-wt=9): 6 [] -i(x,y)| -i(y,z)|i(x,z).
** KEPT (pick-wt=11): 7 [] -i(x,y)| -i(z,y)|i(u(x,z),y).
** KEPT (pick-wt=9): 8 [] -i(x,y)| -i(y,x)|x=y.
** KEPT (pick-wt=12): 9 [] u(x,y)!=y|c(u(y,c(x)))=Z.
** KEPT (pick-wt=12): 10 [] c(u(x,c(y)))!=Z|u(y,x)=x.
** KEPT (pick-wt=5): 11 [] u($c3,$c1)!=$c1.
------------> process sos:
** KEPT (pick-wt=7): 12 [] u(x,y)=u(y,x).
** KEPT (pick-wt=11): 14 [copy,13,flip.1] u(u(x,y),z)=u(x,u(y,z)).
---> New Demodulator: 15 [new_demod,14] u(u(x,y),z)=u(x,u(y,z)).
** KEPT (pick-wt=14): 16 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
---> New Demodulator: 17 [new_demod,16] u(c(u(c(x),y)),c(u(c(x),c(y))))=x.
** KEPT (pick-wt=10): 19 [copy,18,flip.1] c(u(c(x),c(y)))=n(x,y).
---> New Demodulator: 20 [new_demod,19] c(u(c(x),c(y)))=n(x,y).
** KEPT (pick-wt=4): 22 [copy,21,flip.1] c(I)=D.
---> New Demodulator: 23 [new_demod,22] c(I)=D.
** KEPT (pick-wt=5): 25 [copy,24,flip.1] u(I,D)=U.
---> New Demodulator: 26 [new_demod,25] u(I,D)=U.
** KEPT (pick-wt=4): 28 [copy,27,flip.1] c(U)=Z.
---> New Demodulator: 29 [new_demod,28] c(U)=Z.
** KEPT (pick-wt=10): 31 [copy,30,flip.1] u(n(x,c(y)),n(x,y))=x.
---> New Demodulator: 32 [new_demod,31] u(n(x,c(y)),n(x,y))=x.
** KEPT (pick-wt=5): 33 [] i(n(x,y),y).
Following clause subsumed by 33 during input processing: 0 [] i(n(x,y),y).
** KEPT (pick-wt=11): 34 [] i(n(x,u(y,z)),u(y,n(x,z))).
** KEPT (pick-wt=10): 36 [copy,35,flip.1] u(n(x,y),n(x,c(y)))=x.
---> New Demodulator: 37 [new_demod,36] u(n(x,y),n(x,c(y)))=x.
** KEPT (pick-wt=5): 38 [] u(x,Z)=x.
---> New Demodulator: 39 [new_demod,38] u(x,Z)=x.
** KEPT (pick-wt=10): 40 [] c(n(x,y))=u(c(x),c(y)).
---> New Demodulator: 41 [new_demod,40] c(n(x,y))=u(c(x),c(y)).
** KEPT (pick-wt=10): 42 [] c(u(x,y))=n(c(x),c(y)).
---> New Demodulator: 43 [new_demod,42] c(u(x,y))=n(c(x),c(y)).
** KEPT (pick-wt=4): 44 [] c(D)=I.
---> New Demodulator: 45 [new_demod,44] c(D)=I.
** KEPT (pick-wt=4): 46 [] c(Z)=U.
---> New Demodulator: 47 [new_demod,46] c(Z)=U.
** KEPT (pick-wt=5): 48 [] c(c(x))=x.
---> New Demodulator: 49 [new_demod,48] c(c(x))=x.
** KEPT (pick-wt=5): 50 [] u(x,x)=x.
---> New Demodulator: 51 [new_demod,50] u(x,x)=x.
** KEPT (pick-wt=5): 52 [] u($c3,$c2)=$c2.
---> New Demodulator: 53 [new_demod,52] u($c3,$c2)=$c2.
** KEPT (pick-wt=5): 54 [] u($c2,$c1)=$c1.
---> New Demodulator: 55 [new_demod,54] u($c2,$c1)=$c1.
Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] u(x,y)=u(y,x).
>>>> Starting back demodulation with 15.
>>>> Starting back demodulation with 17.
>>>> Starting back demodulation with 20.
>> back demodulating 16 with 20.
>>>> Starting back demodulation with 23.
>>>> Starting back demodulation with 26.
>>>> Starting back demodulation with 29.
>>>> Starting back demodulation with 32.
>>>> Starting back demodulation with 37.
>>>> Starting back demodulation with 39.
>>>> Starting back demodulation with 41.
>>>> Starting back demodulation with 43.
>> back demodulating 19 with 43.
>> back demodulating 10 with 43.
>> back demodulating 9 with 43.
>>>> Starting back demodulation with 45.
>>>> Starting back demodulation with 47.
>>>> Starting back demodulation with 49.
>>>> Starting back demodulation with 51.
>>>> Starting back demodulation with 53.
>>>> Starting back demodulation with 55.
Following clause subsumed by 56 during input processing: 0 [copy,56,flip.1] x=x.
======= end of input processing =======
=========== start of search ===========
----> UNIT CONFLICT at 0.05 sec ----> 141 [binary,139.1,11.1] $F.
Length of proof is 4. Level of proof is 3.
---------------- PROOF ----------------
1 [] -i(x,y)|u(x,y)=y.
2 [] i(x,y)|u(x,y)!=y.
6 [] -i(x,y)| -i(y,z)|i(x,z).
11 [] u($c3,$c1)!=$c1.
52 [] u($c3,$c2)=$c2.
54 [] u($c2,$c1)=$c1.
105 [hyper,52,2] i($c3,$c2).
116 [hyper,54,2] i($c2,$c1).
124 [hyper,116,6,105] i($c3,$c1).
139 [hyper,124,1] u($c3,$c1)=$c1.
141 [binary,139.1,11.1] $F.
------------ end of proof -------------
Search stopped by max_proofs option.
============ end of search ============
-------------- statistics -------------
clauses given 22
clauses generated 294
clauses kept 98
clauses forward subsumed 115
clauses back subsumed 2
Kbytes malloced 191
----------- times (seconds) -----------
user CPU time 0.25 (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 22:26:21 2003