----- Otter 3.3-beta-1, May 2003 -----
The process was started by mccune on theorem.mcs.anl.gov,
Tue Jul  1 16:24:12 2003
The command was "../../source/otter".  The process ID is 10624.

op(400,xfx,+).
clear(print_kept).
clear(print_new_demod).
clear(print_back_demod).
assign(pick_given_ratio,4).
assign(max_mem,20000).
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(process_input).
   dependent: set(lrpo).
set(build_proof_object_2).
   dependent: set(order_history).
set(dynamic_demod_lex_dep).
assign(max_weight,30).

lex([A,B,E,c,d,e,f,g(x),n(x),x+x]).

list(usable).
0 [] x=x.
0 [] x+y=y+x.
0 [] (x+y)+z=x+ (y+z).
0 [] x+ (y+z)=y+ (x+z).
end_of_list.

list(sos).
0 [] n(n(x+y)+n(x+n(y)))=x.
0 [] c+d=c.
0 [] n(A+n(B))+n(n(A)+n(B))!=B.
end_of_list.
assign(bsub_hint_wt,-20).

list(hints).
1 [] n(n(x+ (y+z))+n(y+n(x+z)))=y   # label(step_1).
2 [] n(n(x+y)+n(y+n(x)))=y   # label(step_2).
3 [] n(n(x+y)+n(x+ (n(y+z)+n(y+n(z)))))=x   # label(step_3).
4 [] n(n(x+y)+n(n(y)+x))=x   # label(step_4).
5 [] c+ (d+x)=c+x   # label(step_5).
6 [] n(n(x+c)+n(c+n(x+d)))=c   # label(step_6).
7 [] n(n(x+ (y+z))+n(z+n(x+y)))=z   # label(step_7).
8 [] n(n(x+ (y+z))+n(y+n(z+x)))=y   # label(step_8).
9 [] n(n(c)+n(d+n(c)))=d   # label(step_9).
10 [] n(n(x+y)+n(n(x)+y))=y   # label(step_10).
11 [] n(n(x+n(y))+n(y+x))=x   # label(step_11).
12 [] n(n(x+ (n(y+z)+n(z+n(y))))+n(z+x))=x   # label(step_12).
13 [] n(n(x+c)+n(c+n(d+x)))=c   # label(step_13).
14 [] n(n(x+ (c+y))+n(d+ (y+n(x+c))))=d+y   # label(step_14).
15 [] n(n(x+ (y+z))+n(z+n(y+x)))=z   # label(step_15).
16 [] n(n(x+ (y+z))+n(n(z+x)+y))=y   # label(step_16).
17 [] n(d+n(c+n(d+n(c))))=n(d+n(c))   # label(step_17).
18 [] n(d+n(n(c)+ (n(n(d+n(c))+x)+n(n(d+n(c))+n(x)))))=n(c)   # label(step_18).
19 [] n(x+n(y+ (x+n(n(y)+x))))=n(n(y)+x)   # label(step_19).
20 [] n(n(x+ (y+n(z)))+n(x+ (z+y)))=x+y   # label(step_20).
21 [] n(n(x+n(y+n(z)))+n(x+ (y+n(z+ (y+n(y+n(z)))))))=x   # label(step_21).
22 [] n(n(c)+n(d+ (n(x+c)+n(c+n(x)))))=d   # label(step_22).
23 [] n(n(d+n(c))+n(c+n(d+n(c))))=d   # label(step_23).
24 [] n(n(c+n(d+n(c)))+n(c+n(c+n(d+n(c)))))=c   # label(step_24).
25 [] n(d+n(d+ (n(c)+n(c+n(d+n(c))))))=n(c)   # label(step_25).
26 [] n(c+n(d+n(c)))=n(c)   # label(step_26).
27 [] n(n(c)+n(c+n(c)))=c   # label(step_27).
28 [] n(c+n(c+ (n(c)+n(c+ (c+n(c+n(c)))))))=n(c)   # label(step_28).
29 [] n(n(c+n(c))+n(c+ (c+n(c+n(c)))))=c   # label(step_29).
30 [] n(c+ (c+n(c+n(c))))=n(c)   # label(step_30).
31 [] d+n(c+n(c))=d   # label(step_31).
32 [] n(n(x+d)+n(x+ (n(d)+n(c+n(c)))))=x+n(c+n(c))   # label(step_32).
33 [] x+n(c+n(c))=x   # label(step_33).
end_of_list.

------------> process usable:
** KEPT (pick-wt=3): 34 [] x=x.
** KEPT (pick-wt=7): 35 [] x+y=y+x.
---> New Demodulator: (lex-dependent) 36 [new_demod,35] x+y=y+x.
** KEPT (pick-wt=11): 37 [] (x+y)+z=x+ (y+z).
---> New Demodulator: 38 [new_demod,37] (x+y)+z=x+ (y+z).
** KEPT (pick-wt=11): 39 [] x+ (y+z)=y+ (x+z).
---> New Demodulator: (lex-dependent) 40 [new_demod,39] x+ (y+z)=y+ (x+z).
  Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] x=x.
  Following clause subsumed by 35 during input processing: 0 [copy,35,flip.1] x+y=y+x.
>>>> Starting back demodulation with 36.
>>>> Starting back demodulation with 38.
  Following clause subsumed by 39 during input processing: 0 [copy,39,flip.1] x+ (y+z)=y+ (x+z).
>>>> Starting back demodulation with 40.

------------> process sos:
** KEPT (pick-wt=13): 41 [] n(n(x+y)+n(x+n(y)))=x.
---> New Demodulator: 42 [new_demod,41] n(n(x+y)+n(x+n(y)))=x.
** KEPT (pick-wt=5): 43 [] c+d=c.
---> New Demodulator: 44 [new_demod,43] c+d=c.
** KEPT (pick-wt=14): 45 [] n(A+n(B))+n(n(A)+n(B))!=B.
>>>> Starting back demodulation with 42.
>>>> Starting back demodulation with 44.

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

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

given clause #1: (wt=13) 41 [] n(n(x+y)+n(x+n(y)))=x.

given clause #2: (wt=-20) 46 [para_into,41.1.1.1.1.1,39.1.1] n(n(x+ (y+z))+n(y+n(x+z)))=y   # label(step_1).

given clause #3: (wt=-20) 50 [para_into,41.1.1.1.1.1,35.1.1] n(n(x+y)+n(y+n(x)))=y   # label(step_2).

given clause #4: (wt=-20) 54 [para_into,41.1.1.1.2.1.2,41.1.1,demod,36] n(n(x+y)+n(x+ (n(y+z)+n(y+n(z)))))=x   # label(step_3).

given clause #5: (wt=-20) 56 [para_into,41.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(y)+x))=x   # label(step_4).

given clause #6: (wt=5) 43 [] c+d=c.

given clause #7: (wt=-20) 64 [para_into,46.1.1.1.1.1.2,35.1.1] n(n(x+ (y+z))+n(z+n(x+y)))=z   # label(step_7).

given clause #8: (wt=-20) 70 [para_into,46.1.1.1.2.1.2.1,35.1.1] n(n(x+ (y+z))+n(y+n(z+x)))=y   # label(step_8).

given clause #9: (wt=-20) 102 [para_into,50.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(x)+y))=y   # label(step_10).

given clause #10: (wt=-20) 106 [para_into,50.1.1.1,35.1.1] n(n(x+n(y))+n(y+x))=x   # label(step_11).

given clause #11: (wt=14) 45 [] n(A+n(B))+n(n(A)+n(B))!=B.

given clause #12: (wt=-20) 158 [para_into,56.1.1.1.2.1.1,50.1.1] n(n(x+ (n(y+z)+n(z+n(y))))+n(z+x))=x   # label(step_12).

given clause #13: (wt=-20) 196 [para_from,43.1.1,46.1.1.1.1.1.2] n(n(x+c)+n(c+n(x+d)))=c   # label(step_6).

given clause #14: (wt=-20) 204 [para_from,43.1.1,50.1.1.1.1.1] n(n(c)+n(d+n(c)))=d   # label(step_9).

given clause #15: (wt=-20) 206 [para_from,43.1.1,37.1.1.1,flip.1] c+ (d+x)=c+x   # label(step_5).

given clause #16: (wt=19) 48 [para_into,41.1.1.1.1.1,37.1.1,demod,38] n(n(x+ (y+z))+n(x+ (y+n(z))))=x+y.

given clause #17: (wt=-20) 214 [para_into,64.1.1.1.1.1,39.1.1] n(n(x+ (y+z))+n(z+n(y+x)))=z   # label(step_15).

given clause #18: (wt=-20) 244 [para_into,70.1.1.1.1.1.2,43.1.1] n(n(x+c)+n(c+n(d+x)))=c   # label(step_13).

given clause #19: (wt=-20) 272 [para_into,70.1.1.1.2.1,35.1.1] n(n(x+ (y+z))+n(n(z+x)+y))=y   # label(step_16).

given clause #20: (wt=-20) 338 [para_into,102.1.1.1.2,102.1.1,demod,38,36] n(x+n(y+ (x+n(n(y)+x))))=n(n(y)+x)   # label(step_19).

given clause #21: (wt=20) 52 [para_into,41.1.1.1.1,41.1.1] n(x+n(n(x+y)+n(n(x+n(y)))))=n(x+y).
896 back subsumes 860.
896 back subsumes 824.

given clause #22: (wt=-20) 376 [para_into,106.1.1.1.2.1,39.1.1,demod,38] n(n(x+ (y+n(z)))+n(x+ (z+y)))=x+y   # label(step_20).

given clause #23: (wt=-20) 378 [para_from,106.1.1,54.1.1.1.2.1.2.2,demod,40,36,36] n(n(x+n(y+n(z)))+n(x+ (y+n(z+ (y+n(y+n(z)))))))=x   # label(step_21).

given clause #24: (wt=-20) 432 [para_into,158.1.1.1.2.1,43.1.1,demod,36] n(n(c)+n(d+ (n(x+c)+n(c+n(x)))))=d   # label(step_22).

given clause #25: (wt=-20) 496 [para_from,204.1.1,102.1.1.1.2,demod,36] n(d+n(c+n(d+n(c))))=n(d+n(c))   # label(step_17).

given clause #26: (wt=18) 58 [para_into,41.1.1.1.2,41.1.1,demod,40,36,36] n(x+n(x+ (n(y)+n(x+y))))=n(x+y).

given clause #27: (wt=-20) 528 [para_from,204.1.1,54.1.1.1.1] n(d+n(n(c)+ (n(n(d+n(c))+x)+n(n(d+n(c))+n(x)))))=n(c)   # label(step_18).

given clause #28: (wt=-20) 548 [para_from,206.1.1,64.1.1.1.1.1.2,demod,38] n(n(x+ (c+y))+n(d+ (y+n(x+c))))=d+y   # label(step_14).

given clause #29: (wt=-20) 832 [para_into,338.1.1.1.2.1.2.2,204.1.1,demod,36,207,205] n(n(d+n(c))+n(c+n(d+n(c))))=d   # label(step_23).

given clause #30: (wt=-20) 1278 [para_from,832.1.1,272.1.1.1.2,demod,36,40,36,1043,flip.1] n(c+n(d+n(c)))=n(c)   # label(step_26).

given clause #31: (wt=21) 60 [para_into,46.1.1.1.1.1.2,39.1.1] n(n(x+ (y+ (z+u)))+n(z+n(x+ (y+u))))=z.

given clause #32: (wt=-20) 1298 [back_demod,1112,demod,1279,1279] n(n(c)+n(c+n(c)))=c   # label(step_27).

given clause #33: (wt=-20) 1404 [para_from,1298.1.1,378.1.1.1.1,demod,40] n(c+n(c+ (n(c)+n(c+ (c+n(c+n(c)))))))=n(c)   # label(step_28).

given clause #34: (wt=-20) 1420 [para_from,1298.1.1,338.1.1.1.2.1.2.2,demod,36,1299] n(n(c+n(c))+n(c+ (c+n(c+n(c)))))=c   # label(step_29).

given clause #35: (wt=-20) 1482 [para_from,1420.1.1,272.1.1.1.2,demod,36,40,36,1405,flip.1] n(c+ (c+n(c+n(c))))=n(c)   # label(step_30).

given clause #36: (wt=23) 62 [para_into,46.1.1.1.1.1.2,37.1.1,demod,38] n(n(x+ (y+ (z+u)))+n(y+ (z+n(x+u))))=y+z.

given clause #37: (wt=-20) 1520 [para_from,1482.1.1,548.1.1.1.1,demod,36,433,flip.1] d+n(c+n(c))=d   # label(step_31).

given clause #38: (wt=-20) 1642 [para_from,1520.1.1,54.1.1.1.2.1.2.2.1,demod,40,207,36,1629] x+n(c+n(c))=x   # label(step_31).

given clause #39: (wt=5) 1646 [para_from,1520.1.1,46.1.1.1.2.1,demod,207,36,1643] n(n(d))=d.

given clause #40: (wt=5) 1682 [back_demod,1522,demod,1643,1643,1643] n(n(c))=c.

given clause #41: (wt=17) 66 [para_into,46.1.1.1.1.1,35.1.1,demod,38] n(n(x+ (y+z))+n(x+n(z+y)))=x.

given clause #42: (wt=7) 1684 [back_demod,1482,demod,1643] n(c+c)=n(c).

given clause #43: (wt=9) 198 [para_from,43.1.1,39.1.1.2,flip.1] c+ (x+d)=x+c.

given clause #44: (wt=9) 896 [para_into,52.1.1.1.2.1.1.1,35.1.1,demod,113] n(x+y)=n(y+x).

given clause #45: (wt=9) 1698 [para_into,1642.1.1,35.1.1] n(c+n(c))+x=x.

given clause #46: (wt=21) 68 [para_into,46.1.1.1.2.1.2.1,39.1.1] n(n(x+ (y+ (z+u)))+n(y+n(z+ (x+u))))=y.

given clause #47: (wt=7) 1961 [para_from,1698.1.1,52.1.1.1,demod,1699,1699,1753,1699] n(n(n(x)))=n(x).

given clause #48: (wt=5) 2031 [para_into,1961.1.1.1.1,378.1.1,demod,379] n(n(x))=x.

----> UNIT CONFLICT at   0.99 sec ----> 2174 [binary,2173.1,34.1] $F.

Length of proof is 37.  Level of proof is 17.

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

34 [] x=x.
36,35 [] x+y=y+x.
38,37 [] (x+y)+z=x+ (y+z).
40,39 [] x+ (y+z)=y+ (x+z).
41 [] n(n(x+y)+n(x+n(y)))=x.
43 [] c+d=c.
45 [] n(A+n(B))+n(n(A)+n(B))!=B.
46 [para_into,41.1.1.1.1.1,39.1.1] n(n(x+ (y+z))+n(y+n(x+z)))=y   # label(step_1).
50 [para_into,41.1.1.1.1.1,35.1.1] n(n(x+y)+n(y+n(x)))=y   # label(step_2).
52 [para_into,41.1.1.1.1,41.1.1] n(x+n(n(x+y)+n(n(x+n(y)))))=n(x+y).
54 [para_into,41.1.1.1.2.1.2,41.1.1,demod,36] n(n(x+y)+n(x+ (n(y+z)+n(y+n(z)))))=x   # label(step_3).
56 [para_into,41.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(y)+x))=x   # label(step_4).
64 [para_into,46.1.1.1.1.1.2,35.1.1] n(n(x+ (y+z))+n(z+n(x+y)))=z   # label(step_7).
70 [para_into,46.1.1.1.2.1.2.1,35.1.1] n(n(x+ (y+z))+n(y+n(z+x)))=y   # label(step_8).
102 [para_into,50.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(x)+y))=y   # label(step_10).
106 [para_into,50.1.1.1,35.1.1] n(n(x+n(y))+n(y+x))=x   # label(step_11).
158 [para_into,56.1.1.1.2.1.1,50.1.1] n(n(x+ (n(y+z)+n(z+n(y))))+n(z+x))=x   # label(step_12).
205,204 [para_from,43.1.1,50.1.1.1.1.1] n(n(c)+n(d+n(c)))=d   # label(step_9).
207,206 [para_from,43.1.1,37.1.1.1,flip.1] c+ (d+x)=c+x   # label(step_5).
244 [para_into,70.1.1.1.1.1.2,43.1.1] n(n(x+c)+n(c+n(d+x)))=c   # label(step_13).
272 [para_into,70.1.1.1.2.1,35.1.1] n(n(x+ (y+z))+n(n(z+x)+y))=y   # label(step_16).
338 [para_into,102.1.1.1.2,102.1.1,demod,38,36] n(x+n(y+ (x+n(n(y)+x))))=n(n(y)+x)   # label(step_19).
376 [para_into,106.1.1.1.2.1,39.1.1,demod,38] n(n(x+ (y+n(z)))+n(x+ (z+y)))=x+y   # label(step_20).
379,378 [para_from,106.1.1,54.1.1.1.2.1.2.2,demod,40,36,36] n(n(x+n(y+n(z)))+n(x+ (y+n(z+ (y+n(y+n(z)))))))=x   # label(step_21).
433,432 [para_into,158.1.1.1.2.1,43.1.1,demod,36] n(n(c)+n(d+ (n(x+c)+n(c+n(x)))))=d   # label(step_22).
496 [para_from,204.1.1,102.1.1.1.2,demod,36] n(d+n(c+n(d+n(c))))=n(d+n(c))   # label(step_17).
548 [para_from,206.1.1,64.1.1.1.1.1.2,demod,38] n(n(x+ (c+y))+n(d+ (y+n(x+c))))=d+y   # label(step_14).
832 [para_into,338.1.1.1.2.1.2.2,204.1.1,demod,36,207,205] n(n(d+n(c))+n(c+n(d+n(c))))=d   # label(step_23).
1043,1042 [para_into,378.1.1.1.1,204.1.1,demod,207,40] n(d+n(d+ (n(c)+n(c+n(d+n(c))))))=n(c)   # label(step_25).
1112 [para_from,496.1.1,244.1.1.1.2.1.2,demod,36,36] n(n(c+n(d+n(c)))+n(c+n(c+n(d+n(c)))))=c   # label(step_24).
1279,1278 [para_from,832.1.1,272.1.1.1.2,demod,36,40,36,1043,flip.1] n(c+n(d+n(c)))=n(c)   # label(step_26).
1299,1298 [back_demod,1112,demod,1279,1279] n(n(c)+n(c+n(c)))=c   # label(step_27).
1405,1404 [para_from,1298.1.1,378.1.1.1.1,demod,40] n(c+n(c+ (n(c)+n(c+ (c+n(c+n(c)))))))=n(c)   # label(step_28).
1420 [para_from,1298.1.1,338.1.1.1.2.1.2.2,demod,36,1299] n(n(c+n(c))+n(c+ (c+n(c+n(c)))))=c   # label(step_29).
1482 [para_from,1420.1.1,272.1.1.1.2,demod,36,40,36,1405,flip.1] n(c+ (c+n(c+n(c))))=n(c)   # label(step_30).
1520 [para_from,1482.1.1,548.1.1.1.1,demod,36,433,flip.1] d+n(c+n(c))=d   # label(step_31).
1629,1628 [para_from,1520.1.1,376.1.1.1.2.1.2,demod,36,36] n(n(x+d)+n(x+ (n(d)+n(c+n(c)))))=x+n(c+n(c))   # label(step_32).
1643,1642 [para_from,1520.1.1,54.1.1.1.2.1.2.2.1,demod,40,207,36,1629] x+n(c+n(c))=x   # label(step_31).
1699,1698 [para_into,1642.1.1,35.1.1] n(c+n(c))+x=x.
1753,1752 [para_from,1642.1.1,338.1.1.1.2.1.2.2.1,demod,1699,1699,1643] n(n(x+n(n(x))))=n(n(x)).
1961 [para_from,1698.1.1,52.1.1.1,demod,1699,1699,1753,1699] n(n(n(x)))=n(x).
2032,2031 [para_into,1961.1.1.1.1,378.1.1,demod,379] n(n(x))=x.
2144,2143 [para_into,2031.1.1.1,102.1.1,flip.1] n(x+y)+n(n(x)+y)=n(y).
2173 [back_demod,45,demod,2144,2032] B!=B.
2174 [binary,2173.1,34.1] $F.

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


;; BEGINNING OF PROOF OBJECT
(
(1 (input) (= v0 v0) (34))
(2 (input) (= (+ v0 v1) (+ v1 v0)) (35))
(3 (input) (= (+ (+ v0 v1) v2) (+ v0 (+ v1 v2))) (37))
(4 (input) (= (+ v0 (+ v1 v2)) (+ v1 (+ v0 v2))) (39))
(5 (input) (= (n (+ (n (+ v0 v1)) (n (+ v0 (n v1))))) v0) (41))
(6 (input) (= (+ (c) (d)) (c)) (43))
(7 (input) (not (= (+ (n (+ (A) (n (B)))) (n (+ (n (A)) (n (B))))) (B))) (45))
(8 (instantiate 4 ((v0 . v64))) (= (+ v64 (+ v1 v2)) (+ v1 (+ v64 v2))) NIL)
(9 (instantiate 5 ((v0 . v64)(v1 . (+ v1 v2)))) (= (n (+ (n (+ v64 (+ v1 v2))) (n (+ v64 (n (+ v1 v2)))))) v64) NIL)
(10 (paramod 8 (1) 9 (1 1 1 1)) (= (n (+ (n (+ v1 (+ v64 v2))) (n (+ v64 (n (+ v1 v2)))))) v64) NIL)
(11 (instantiate 10 ((v1 . v0)(v64 . v1))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ v1 (n (+ v0 v2)))))) v1) (46))
(12 (instantiate 2 ((v0 . v64)(v1 . v65))) (= (+ v64 v65) (+ v65 v64)) NIL)
(13 (instantiate 5 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v64 (n v65))))) v64) NIL)
(14 (paramod 12 (1) 13 (1 1 1 1)) (= (n (+ (n (+ v65 v64)) (n (+ v64 (n v65))))) v64) NIL)
(15 (instantiate 14 ((v64 . v1)(v65 . v0))) (= (n (+ (n (+ v0 v1)) (n (+ v1 (n v0))))) v1) (50))
(16 (instantiate 5 ((v0 . (n (+ v0 v1)))(v1 . (n (+ v0 (n v1)))))) (= (n (+ (n (+ (n (+ v0 v1)) (n (+ v0 (n v1))))) (n (+ (n (+ v0 v1)) (n (n (+ v0 (n v1)))))))) (n (+ v0 v1))) NIL)
(17 (paramod 5 (1) 16 (1 1 1)) (= (n (+ v0 (n (+ (n (+ v0 v1)) (n (n (+ v0 (n v1)))))))) (n (+ v0 v1))) (52))
(18 (instantiate 5 ((v0 . v64)(v1 . (+ (n (+ v0 v1)) (n (+ v0 (n v1))))))) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))) (n (+ v64 (n (+ (n (+ v0 v1)) (n (+ v0 (n v1))))))))) v64) NIL)
(19 (paramod 5 (1) 18 (1 1 2 1 2)) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))) (n (+ v64 v0)))) v64) NIL)
(20 (instantiate 2 ((v0 . (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))))(v1 . (n (+ v64 v0))))) (= (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))) (n (+ v64 v0))) (+ (n (+ v64 v0)) (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))))) NIL)
(21 (paramod 20 (1) 19 (1 1)) (= (n (+ (n (+ v64 v0)) (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))))) v64) NIL)
(22 (instantiate 21 ((v0 . v1)(v1 . v2)(v64 . v0))) (= (n (+ (n (+ v0 v1)) (n (+ v0 (+ (n (+ v1 v2)) (n (+ v1 (n v2)))))))) v0) (54))
(23 (instantiate 2 ((v0 . v64)(v1 . (n v65)))) (= (+ v64 (n v65)) (+ (n v65) v64)) NIL)
(24 (instantiate 5 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v64 (n v65))))) v64) NIL)
(25 (paramod 23 (1) 24 (1 1 2 1)) (= (n (+ (n (+ v64 v65)) (n (+ (n v65) v64)))) v64) NIL)
(26 (instantiate 25 ((v64 . v0)(v65 . v1))) (= (n (+ (n (+ v0 v1)) (n (+ (n v1) v0)))) v0) (56))
(27 (instantiate 2 ((v0 . v65)(v1 . v66))) (= (+ v65 v66) (+ v66 v65)) NIL)
(28 (instantiate 11 ((v0 . v64)(v1 . v65)(v2 . v66))) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v64 v66)))))) v65) NIL)
(29 (paramod 27 (1) 28 (1 1 1 1 2)) (= (n (+ (n (+ v64 (+ v66 v65))) (n (+ v65 (n (+ v64 v66)))))) v65) NIL)
(30 (instantiate 29 ((v64 . v0)(v65 . v2)(v66 . v1))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ v2 (n (+ v0 v1)))))) v2) (64))
(31 (instantiate 2 ((v0 . v64)(v1 . v66))) (= (+ v64 v66) (+ v66 v64)) NIL)
(32 (instantiate 11 ((v0 . v64)(v1 . v65)(v2 . v66))) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v64 v66)))))) v65) NIL)
(33 (paramod 31 (1) 32 (1 1 2 1 2 1)) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v66 v64)))))) v65) NIL)
(34 (instantiate 33 ((v64 . v0)(v65 . v1)(v66 . v2))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ v1 (n (+ v2 v0)))))) v1) (70))
(35 (instantiate 2 ((v0 . v65)(v1 . (n v64)))) (= (+ v65 (n v64)) (+ (n v64) v65)) NIL)
(36 (instantiate 15 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v65 (n v64))))) v65) NIL)
(37 (paramod 35 (1) 36 (1 1 2 1)) (= (n (+ (n (+ v64 v65)) (n (+ (n v64) v65)))) v65) NIL)
(38 (instantiate 37 ((v64 . v0)(v65 . v1))) (= (n (+ (n (+ v0 v1)) (n (+ (n v0) v1)))) v1) (102))
(39 (instantiate 2 ((v0 . (n (+ v64 v65)))(v1 . (n (+ v65 (n v64)))))) (= (+ (n (+ v64 v65)) (n (+ v65 (n v64)))) (+ (n (+ v65 (n v64))) (n (+ v64 v65)))) NIL)
(40 (instantiate 15 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v65 (n v64))))) v65) NIL)
(41 (paramod 39 (1) 40 (1 1)) (= (n (+ (n (+ v65 (n v64))) (n (+ v64 v65)))) v65) NIL)
(42 (instantiate 41 ((v64 . v1)(v65 . v0))) (= (n (+ (n (+ v0 (n v1))) (n (+ v1 v0)))) v0) (106))
(43 (instantiate 26 ((v0 . v64)(v1 . (+ (n (+ v0 v1)) (n (+ v1 (n v0))))))) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v1 (n v0)))))) (n (+ (n (+ (n (+ v0 v1)) (n (+ v1 (n v0))))) v64)))) v64) NIL)
(44 (paramod 15 (1) 43 (1 1 2 1 1)) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v1 (n v0)))))) (n (+ v1 v64)))) v64) NIL)
(45 (instantiate 44 ((v0 . v1)(v1 . v2)(v64 . v0))) (= (n (+ (n (+ v0 (+ (n (+ v1 v2)) (n (+ v2 (n v1)))))) (n (+ v2 v0)))) v0) (158))
(46 (instantiate 15 ((v0 . (c))(v1 . (d)))) (= (n (+ (n (+ (c) (d))) (n (+ (d) (n (c)))))) (d)) NIL)
(47 (paramod 6 (1) 46 (1 1 1 1)) (= (n (+ (n (c)) (n (+ (d) (n (c)))))) (d)) (204))
(48 (instantiate 3 ((v0 . (c))(v1 . (d))(v2 . v66))) (= (+ (+ (c) (d)) v66) (+ (c) (+ (d) v66))) NIL)
(49 (paramod 6 (1) 48 (1 1)) (= (+ (c) v66) (+ (c) (+ (d) v66))) NIL)
(50 (flip 49 ()) (= (+ (c) (+ (d) v66)) (+ (c) v66)) NIL)
(51 (instantiate 50 ((v66 . v0))) (= (+ (c) (+ (d) v0)) (+ (c) v0)) (206))
(52 (instantiate 34 ((v0 . v64)(v1 . (c))(v2 . (d)))) (= (n (+ (n (+ v64 (+ (c) (d)))) (n (+ (c) (n (+ (d) v64)))))) (c)) NIL)
(53 (paramod 6 (1) 52 (1 1 1 1 2)) (= (n (+ (n (+ v64 (c))) (n (+ (c) (n (+ (d) v64)))))) (c)) NIL)
(54 (instantiate 53 ((v64 . v0))) (= (n (+ (n (+ v0 (c))) (n (+ (c) (n (+ (d) v0)))))) (c)) (244))
(55 (instantiate 2 ((v0 . v65)(v1 . (n (+ v66 v64))))) (= (+ v65 (n (+ v66 v64))) (+ (n (+ v66 v64)) v65)) NIL)
(56 (instantiate 34 ((v0 . v64)(v1 . v65)(v2 . v66))) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v66 v64)))))) v65) NIL)
(57 (paramod 55 (1) 56 (1 1 2 1)) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ (n (+ v66 v64)) v65)))) v65) NIL)
(58 (instantiate 57 ((v64 . v0)(v65 . v1)(v66 . v2))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ (n (+ v2 v0)) v1)))) v1) (272))
(59 (instantiate 38 ((v0 . (+ v0 v1))(v1 . (n (+ (n v0) v1))))) (= (n (+ (n (+ (+ v0 v1) (n (+ (n v0) v1)))) (n (+ (n (+ v0 v1)) (n (+ (n v0) v1)))))) (n (+ (n v0) v1))) NIL)
(60 (paramod 38 (1) 59 (1 1 2)) (= (n (+ (n (+ (+ v0 v1) (n (+ (n v0) v1)))) v1)) (n (+ (n v0) v1))) NIL)
(61 (instantiate 3 ((v0 . v0)(v1 . v1)(v2 . (n (+ (n v0) v1))))) (= (+ (+ v0 v1) (n (+ (n v0) v1))) (+ v0 (+ v1 (n (+ (n v0) v1))))) NIL)
(62 (paramod 61 (1) 60 (1 1 1 1)) (= (n (+ (n (+ v0 (+ v1 (n (+ (n v0) v1))))) v1)) (n (+ (n v0) v1))) NIL)
(63 (instantiate 2 ((v0 . (n (+ v0 (+ v1 (n (+ (n v0) v1))))))(v1 . v1))) (= (+ (n (+ v0 (+ v1 (n (+ (n v0) v1))))) v1) (+ v1 (n (+ v0 (+ v1 (n (+ (n v0) v1))))))) NIL)
(64 (paramod 63 (1) 62 (1 1)) (= (n (+ v1 (n (+ v0 (+ v1 (n (+ (n v0) v1))))))) (n (+ (n v0) v1))) NIL)
(65 (instantiate 64 ((v0 . v1)(v1 . v0))) (= (n (+ v0 (n (+ v1 (+ v0 (n (+ (n v1) v0))))))) (n (+ (n v1) v0))) (338))
(66 (instantiate 4 ((v0 . v65))) (= (+ v65 (+ v1 v2)) (+ v1 (+ v65 v2))) NIL)
(67 (instantiate 42 ((v0 . (+ v1 v2))(v1 . v65))) (= (n (+ (n (+ (+ v1 v2) (n v65))) (n (+ v65 (+ v1 v2))))) (+ v1 v2)) NIL)
(68 (paramod 66 (1) 67 (1 1 2 1)) (= (n (+ (n (+ (+ v1 v2) (n v65))) (n (+ v1 (+ v65 v2))))) (+ v1 v2)) NIL)
(69 (instantiate 3 ((v0 . v1)(v1 . v2)(v2 . (n v65)))) (= (+ (+ v1 v2) (n v65)) (+ v1 (+ v2 (n v65)))) NIL)
(70 (paramod 69 (1) 68 (1 1 1 1)) (= (n (+ (n (+ v1 (+ v2 (n v65)))) (n (+ v1 (+ v65 v2))))) (+ v1 v2)) NIL)
(71 (instantiate 70 ((v1 . v0)(v2 . v1)(v65 . v2))) (= (n (+ (n (+ v0 (+ v1 (n v2)))) (n (+ v0 (+ v2 v1))))) (+ v0 v1)) (376))
(72 (instantiate 22 ((v0 . v64)(v1 . (n (+ v0 (n v1))))(v2 . (+ v1 v0)))) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ (n (+ v0 (n v1))) (+ v1 v0))) (n (+ (n (+ v0 (n v1))) (n (+ v1 v0))))))))) v64) NIL)
(73 (paramod 42 (1) 72 (1 1 2 1 2 2)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ (n (+ v0 (n v1))) (+ v1 v0))) v0))))) v64) NIL)
(74 (instantiate 4 ((v0 . (n (+ v0 (n v1))))(v1 . v1)(v2 . v0))) (= (+ (n (+ v0 (n v1))) (+ v1 v0)) (+ v1 (+ (n (+ v0 (n v1))) v0))) NIL)
(75 (paramod 74 (1) 73 (1 1 2 1 2 1 1)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ v1 (+ (n (+ v0 (n v1))) v0))) v0))))) v64) NIL)
(76 (instantiate 2 ((v0 . (n (+ v0 (n v1))))(v1 . v0))) (= (+ (n (+ v0 (n v1))) v0) (+ v0 (n (+ v0 (n v1))))) NIL)
(77 (paramod 76 (1) 75 (1 1 2 1 2 1 1 2)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ v1 (+ v0 (n (+ v0 (n v1)))))) v0))))) v64) NIL)
(78 (instantiate 2 ((v0 . (n (+ v1 (+ v0 (n (+ v0 (n v1)))))))(v1 . v0))) (= (+ (n (+ v1 (+ v0 (n (+ v0 (n v1)))))) v0) (+ v0 (n (+ v1 (+ v0 (n (+ v0 (n v1)))))))) NIL)
(79 (paramod 78 (1) 77 (1 1 2 1 2)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ v0 (n (+ v1 (+ v0 (n (+ v0 (n v1))))))))))) v64) NIL)
(80 (instantiate 79 ((v0 . v1)(v1 . v2)(v64 . v0))) (= (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2))))))))))) v0) (378))
(81 (instantiate 45 ((v0 . (d))(v1 . v65)(v2 . (c)))) (= (n (+ (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))) (n (+ (c) (d))))) (d)) NIL)
(82 (paramod 6 (1) 81 (1 1 2 1)) (= (n (+ (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))) (n (c)))) (d)) NIL)
(83 (instantiate 2 ((v0 . (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))))(v1 . (n (c))))) (= (+ (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))) (n (c))) (+ (n (c)) (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))))) NIL)
(84 (paramod 83 (1) 82 (1 1)) (= (n (+ (n (c)) (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))))) (d)) NIL)
(85 (instantiate 84 ((v65 . v0))) (= (n (+ (n (c)) (n (+ (d) (+ (n (+ v0 (c))) (n (+ (c) (n v0)))))))) (d)) (432))
(86 (instantiate 38 ((v0 . (c))(v1 . (n (+ (d) (n (c))))))) (= (n (+ (n (+ (c) (n (+ (d) (n (c)))))) (n (+ (n (c)) (n (+ (d) (n (c)))))))) (n (+ (d) (n (c))))) NIL)
(87 (paramod 47 (1) 86 (1 1 2)) (= (n (+ (n (+ (c) (n (+ (d) (n (c)))))) (d))) (n (+ (d) (n (c))))) NIL)
(88 (instantiate 2 ((v0 . (n (+ (c) (n (+ (d) (n (c)))))))(v1 . (d)))) (= (+ (n (+ (c) (n (+ (d) (n (c)))))) (d)) (+ (d) (n (+ (c) (n (+ (d) (n (c)))))))) NIL)
(89 (paramod 88 (1) 87 (1 1)) (= (n (+ (d) (n (+ (c) (n (+ (d) (n (c)))))))) (n (+ (d) (n (c))))) (496))
(90 (instantiate 30 ((v0 . v64)(v1 . (c))(v2 . (+ (d) v0)))) (= (n (+ (n (+ v64 (+ (c) (+ (d) v0)))) (n (+ (+ (d) v0) (n (+ v64 (c))))))) (+ (d) v0)) NIL)
(91 (paramod 51 (1) 90 (1 1 1 1 2)) (= (n (+ (n (+ v64 (+ (c) v0))) (n (+ (+ (d) v0) (n (+ v64 (c))))))) (+ (d) v0)) NIL)
(92 (instantiate 3 ((v0 . (d))(v1 . v0)(v2 . (n (+ v64 (c)))))) (= (+ (+ (d) v0) (n (+ v64 (c)))) (+ (d) (+ v0 (n (+ v64 (c)))))) NIL)
(93 (paramod 92 (1) 91 (1 1 2 1)) (= (n (+ (n (+ v64 (+ (c) v0))) (n (+ (d) (+ v0 (n (+ v64 (c)))))))) (+ (d) v0)) NIL)
(94 (instantiate 93 ((v0 . v1)(v64 . v0))) (= (n (+ (n (+ v0 (+ (c) v1))) (n (+ (d) (+ v1 (n (+ v0 (c)))))))) (+ (d) v1)) (548))
(95 (instantiate 65 ((v0 . (n (+ (d) (n (c)))))(v1 . (c)))) (= (n (+ (n (+ (d) (n (c)))) (n (+ (c) (+ (n (+ (d) (n (c)))) (n (+ (n (c)) (n (+ (d) (n (c))))))))))) (n (+ (n (c)) (n (+ (d) (n (c))))))) NIL)
(96 (paramod 47 (1) 95 (1 1 2 1 2 2)) (= (n (+ (n (+ (d) (n (c)))) (n (+ (c) (+ (n (+ (d) (n (c)))) (d)))))) (n (+ (n (c)) (n (+ (d) (n (c))))))) NIL)
(97 (instantiate 2 ((v0 . (n (+ (d) (n (c)))))(v1 . (d)))) (= (+ (n (+ (d) (n (c)))) (d)) (+ (d) (n (+ (d) (n (c)))))) NIL)
(98 (paramod 97 (1) 96 (1 1 2 1 2)) (= (n (+ (n (+ (d) (n (c)))) (n (+ (c) (+ (d) (n (+ (d) (n (c))))))))) (n (+ (n (c)) (n (+ (d) (n (c))))))) NIL)
(99 (instantiate 51 ((v0 . (n (+ (d) (n (c))))))) (= (+ (c) (+ (d) (n (+ (d) (n (c)))))) (+ (c) (n (+ (d) (n (c)))))) NIL)
(100 (paramod 99 (1) 98 (1 1 2 1)) (= (n (+ (n (+ (d) (n (c)))) (n (+ (c) (n (+ (d) (n (c)))))))) (n (+ (n (c)) (n (+ (d) (n (c))))))) NIL)
(101 (paramod 47 (1) 100 (2)) (= (n (+ (n (+ (d) (n (c)))) (n (+ (c) (n (+ (d) (n (c)))))))) (d)) (832))
(102 (instantiate 80 ((v0 . (n (c)))(v1 . (d))(v2 . (c)))) (= (n (+ (n (+ (n (c)) (n (+ (d) (n (c)))))) (n (+ (n (c)) (+ (d) (n (+ (c) (+ (d) (n (+ (d) (n (c)))))))))))) (n (c))) NIL)
(103 (paramod 47 (1) 102 (1 1 1)) (= (n (+ (d) (n (+ (n (c)) (+ (d) (n (+ (c) (+ (d) (n (+ (d) (n (c)))))))))))) (n (c))) NIL)
(104 (instantiate 51 ((v0 . (n (+ (d) (n (c))))))) (= (+ (c) (+ (d) (n (+ (d) (n (c)))))) (+ (c) (n (+ (d) (n (c)))))) NIL)
(105 (paramod 104 (1) 103 (1 1 2 1 2 2 1)) (= (n (+ (d) (n (+ (n (c)) (+ (d) (n (+ (c) (n (+ (d) (n (c))))))))))) (n (c))) NIL)
(106 (instantiate 4 ((v0 . (n (c)))(v1 . (d))(v2 . (n (+ (c) (n (+ (d) (n (c))))))))) (= (+ (n (c)) (+ (d) (n (+ (c) (n (+ (d) (n (c)))))))) (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))) NIL)
(107 (paramod 106 (1) 105 (1 1 2 1)) (= (n (+ (d) (n (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))))) (n (c))) (1042))
(108 (instantiate 54 ((v0 . (n (+ (c) (n (+ (d) (n (c))))))))) (= (n (+ (n (+ (n (+ (c) (n (+ (d) (n (c)))))) (c))) (n (+ (c) (n (+ (d) (n (+ (c) (n (+ (d) (n (c)))))))))))) (c)) NIL)
(109 (paramod 89 (1) 108 (1 1 2 1 2)) (= (n (+ (n (+ (n (+ (c) (n (+ (d) (n (c)))))) (c))) (n (+ (c) (n (+ (d) (n (c)))))))) (c)) NIL)
(110 (instantiate 2 ((v0 . (n (+ (c) (n (+ (d) (n (c)))))))(v1 . (c)))) (= (+ (n (+ (c) (n (+ (d) (n (c)))))) (c)) (+ (c) (n (+ (c) (n (+ (d) (n (c)))))))) NIL)
(111 (paramod 110 (1) 109 (1 1 1 1)) (= (n (+ (n (+ (c) (n (+ (c) (n (+ (d) (n (c)))))))) (n (+ (c) (n (+ (d) (n (c)))))))) (c)) NIL)
(112 (instantiate 2 ((v0 . (n (+ (c) (n (+ (c) (n (+ (d) (n (c)))))))))(v1 . (n (+ (c) (n (+ (d) (n (c))))))))) (= (+ (n (+ (c) (n (+ (c) (n (+ (d) (n (c)))))))) (n (+ (c) (n (+ (d) (n (c))))))) (+ (n (+ (c) (n (+ (d) (n (c)))))) (n (+ (c) (n (+ (c) (n (+ (d) (n (c)))))))))) NIL)
(113 (paramod 112 (1) 111 (1 1)) (= (n (+ (n (+ (c) (n (+ (d) (n (c)))))) (n (+ (c) (n (+ (c) (n (+ (d) (n (c)))))))))) (c)) (1112))
(114 (instantiate 58 ((v0 . (n (c)))(v1 . (n (+ (c) (n (+ (d) (n (c)))))))(v2 . (d)))) (= (n (+ (n (+ (n (c)) (+ (n (+ (c) (n (+ (d) (n (c)))))) (d)))) (n (+ (n (+ (d) (n (c)))) (n (+ (c) (n (+ (d) (n (c)))))))))) (n (+ (c) (n (+ (d) (n (c))))))) NIL)
(115 (paramod 101 (1) 114 (1 1 2)) (= (n (+ (n (+ (n (c)) (+ (n (+ (c) (n (+ (d) (n (c)))))) (d)))) (d))) (n (+ (c) (n (+ (d) (n (c))))))) NIL)
(116 (instantiate 2 ((v0 . (n (+ (c) (n (+ (d) (n (c)))))))(v1 . (d)))) (= (+ (n (+ (c) (n (+ (d) (n (c)))))) (d)) (+ (d) (n (+ (c) (n (+ (d) (n (c)))))))) NIL)
(117 (paramod 116 (1) 115 (1 1 1 1 2)) (= (n (+ (n (+ (n (c)) (+ (d) (n (+ (c) (n (+ (d) (n (c))))))))) (d))) (n (+ (c) (n (+ (d) (n (c))))))) NIL)
(118 (instantiate 4 ((v0 . (n (c)))(v1 . (d))(v2 . (n (+ (c) (n (+ (d) (n (c))))))))) (= (+ (n (c)) (+ (d) (n (+ (c) (n (+ (d) (n (c)))))))) (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))) NIL)
(119 (paramod 118 (1) 117 (1 1 1 1)) (= (n (+ (n (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))) (d))) (n (+ (c) (n (+ (d) (n (c))))))) NIL)
(120 (instantiate 2 ((v0 . (n (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))))(v1 . (d)))) (= (+ (n (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))) (d)) (+ (d) (n (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))))) NIL)
(121 (paramod 120 (1) 119 (1 1)) (= (n (+ (d) (n (+ (d) (+ (n (c)) (n (+ (c) (n (+ (d) (n (c))))))))))) (n (+ (c) (n (+ (d) (n (c))))))) NIL)
(122 (paramod 107 (1) 121 (1)) (= (n (c)) (n (+ (c) (n (+ (d) (n (c))))))) NIL)
(123 (flip 122 ()) (= (n (+ (c) (n (+ (d) (n (c)))))) (n (c))) (1278))
(124 (paramod 123 (1) 113 (1 1 1)) (= (n (+ (n (c)) (n (+ (c) (n (+ (c) (n (+ (d) (n (c)))))))))) (c)) NIL)
(125 (paramod 123 (1) 124 (1 1 2 1 2)) (= (n (+ (n (c)) (n (+ (c) (n (c)))))) (c)) (1298))
(126 (instantiate 80 ((v0 . (n (c)))(v1 . (c))(v2 . (c)))) (= (n (+ (n (+ (n (c)) (n (+ (c) (n (c)))))) (n (+ (n (c)) (+ (c) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))))) (n (c))) NIL)
(127 (paramod 125 (1) 126 (1 1 1)) (= (n (+ (c) (n (+ (n (c)) (+ (c) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))))) (n (c))) NIL)
(128 (instantiate 4 ((v0 . (n (c)))(v1 . (c))(v2 . (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))) (= (+ (n (c)) (+ (c) (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))) (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))) NIL)
(129 (paramod 128 (1) 127 (1 1 2 1)) (= (n (+ (c) (n (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))))) (n (c))) (1404))
(130 (instantiate 65 ((v0 . (n (+ (c) (n (c)))))(v1 . (c)))) (= (n (+ (n (+ (c) (n (c)))) (n (+ (c) (+ (n (+ (c) (n (c)))) (n (+ (n (c)) (n (+ (c) (n (c))))))))))) (n (+ (n (c)) (n (+ (c) (n (c))))))) NIL)
(131 (paramod 125 (1) 130 (1 1 2 1 2 2)) (= (n (+ (n (+ (c) (n (c)))) (n (+ (c) (+ (n (+ (c) (n (c)))) (c)))))) (n (+ (n (c)) (n (+ (c) (n (c))))))) NIL)
(132 (instantiate 2 ((v0 . (n (+ (c) (n (c)))))(v1 . (c)))) (= (+ (n (+ (c) (n (c)))) (c)) (+ (c) (n (+ (c) (n (c)))))) NIL)
(133 (paramod 132 (1) 131 (1 1 2 1 2)) (= (n (+ (n (+ (c) (n (c)))) (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))) (n (+ (n (c)) (n (+ (c) (n (c))))))) NIL)
(134 (paramod 125 (1) 133 (2)) (= (n (+ (n (+ (c) (n (c)))) (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))) (c)) (1420))
(135 (instantiate 58 ((v0 . (n (c)))(v1 . (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))(v2 . (c)))) (= (n (+ (n (+ (n (c)) (+ (n (+ (c) (+ (c) (n (+ (c) (n (c))))))) (c)))) (n (+ (n (+ (c) (n (c)))) (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))))) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))) NIL)
(136 (paramod 134 (1) 135 (1 1 2)) (= (n (+ (n (+ (n (c)) (+ (n (+ (c) (+ (c) (n (+ (c) (n (c))))))) (c)))) (c))) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))) NIL)
(137 (instantiate 2 ((v0 . (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))(v1 . (c)))) (= (+ (n (+ (c) (+ (c) (n (+ (c) (n (c))))))) (c)) (+ (c) (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))) NIL)
(138 (paramod 137 (1) 136 (1 1 1 1 2)) (= (n (+ (n (+ (n (c)) (+ (c) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))) (c))) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))) NIL)
(139 (instantiate 4 ((v0 . (n (c)))(v1 . (c))(v2 . (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))) (= (+ (n (c)) (+ (c) (n (+ (c) (+ (c) (n (+ (c) (n (c))))))))) (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))) NIL)
(140 (paramod 139 (1) 138 (1 1 1 1)) (= (n (+ (n (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))) (c))) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))) NIL)
(141 (instantiate 2 ((v0 . (n (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))))(v1 . (c)))) (= (+ (n (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))) (c)) (+ (c) (n (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))))) NIL)
(142 (paramod 141 (1) 140 (1 1)) (= (n (+ (c) (n (+ (c) (+ (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))))))) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))) NIL)
(143 (paramod 129 (1) 142 (1)) (= (n (c)) (n (+ (c) (+ (c) (n (+ (c) (n (c)))))))) NIL)
(144 (flip 143 ()) (= (n (+ (c) (+ (c) (n (+ (c) (n (c))))))) (n (c))) (1482))
(145 (instantiate 94 ((v0 . (c))(v1 . (n (+ (c) (n (c))))))) (= (n (+ (n (+ (c) (+ (c) (n (+ (c) (n (c))))))) (n (+ (d) (+ (n (+ (c) (n (c)))) (n (+ (c) (c)))))))) (+ (d) (n (+ (c) (n (c)))))) NIL)
(146 (paramod 144 (1) 145 (1 1 1)) (= (n (+ (n (c)) (n (+ (d) (+ (n (+ (c) (n (c)))) (n (+ (c) (c)))))))) (+ (d) (n (+ (c) (n (c)))))) NIL)
(147 (instantiate 2 ((v0 . (n (+ (c) (n (c)))))(v1 . (n (+ (c) (c)))))) (= (+ (n (+ (c) (n (c)))) (n (+ (c) (c)))) (+ (n (+ (c) (c))) (n (+ (c) (n (c)))))) NIL)
(148 (paramod 147 (1) 146 (1 1 2 1 2)) (= (n (+ (n (c)) (n (+ (d) (+ (n (+ (c) (c))) (n (+ (c) (n (c))))))))) (+ (d) (n (+ (c) (n (c)))))) NIL)
(149 (instantiate 85 ((v0 . (c)))) (= (n (+ (n (c)) (n (+ (d) (+ (n (+ (c) (c))) (n (+ (c) (n (c))))))))) (d)) NIL)
(150 (paramod 149 (1) 148 (1)) (= (d) (+ (d) (n (+ (c) (n (c)))))) NIL)
(151 (flip 150 ()) (= (+ (d) (n (+ (c) (n (c))))) (d)) (1520))
(152 (instantiate 71 ((v0 . v64)(v1 . (n (+ (c) (n (c)))))(v2 . (d)))) (= (n (+ (n (+ v64 (+ (n (+ (c) (n (c)))) (n (d))))) (n (+ v64 (+ (d) (n (+ (c) (n (c))))))))) (+ v64 (n (+ (c) (n (c)))))) NIL)
(153 (paramod 151 (1) 152 (1 1 2 1 2)) (= (n (+ (n (+ v64 (+ (n (+ (c) (n (c)))) (n (d))))) (n (+ v64 (d))))) (+ v64 (n (+ (c) (n (c)))))) NIL)
(154 (instantiate 2 ((v0 . (n (+ (c) (n (c)))))(v1 . (n (d))))) (= (+ (n (+ (c) (n (c)))) (n (d))) (+ (n (d)) (n (+ (c) (n (c)))))) NIL)
(155 (paramod 154 (1) 153 (1 1 1 1 2)) (= (n (+ (n (+ v64 (+ (n (d)) (n (+ (c) (n (c))))))) (n (+ v64 (d))))) (+ v64 (n (+ (c) (n (c)))))) NIL)
(156 (instantiate 2 ((v0 . (n (+ v64 (+ (n (d)) (n (+ (c) (n (c))))))))(v1 . (n (+ v64 (d)))))) (= (+ (n (+ v64 (+ (n (d)) (n (+ (c) (n (c))))))) (n (+ v64 (d)))) (+ (n (+ v64 (d))) (n (+ v64 (+ (n (d)) (n (+ (c) (n (c))))))))) NIL)
(157 (paramod 156 (1) 155 (1 1)) (= (n (+ (n (+ v64 (d))) (n (+ v64 (+ (n (d)) (n (+ (c) (n (c))))))))) (+ v64 (n (+ (c) (n (c)))))) NIL)
(158 (instantiate 157 ((v64 . v0))) (= (n (+ (n (+ v0 (d))) (n (+ v0 (+ (n (d)) (n (+ (c) (n (c))))))))) (+ v0 (n (+ (c) (n (c)))))) (1628))
(159 (instantiate 22 ((v0 . v64)(v1 . (d))(v2 . (+ (c) (n (c)))))) (= (n (+ (n (+ v64 (d))) (n (+ v64 (+ (n (+ (d) (+ (c) (n (c))))) (n (+ (d) (n (+ (c) (n (c))))))))))) v64) NIL)
(160 (paramod 151 (1) 159 (1 1 2 1 2 2 1)) (= (n (+ (n (+ v64 (d))) (n (+ v64 (+ (n (+ (d) (+ (c) (n (c))))) (n (d))))))) v64) NIL)
(161 (instantiate 4 ((v0 . (d))(v1 . (c))(v2 . (n (c))))) (= (+ (d) (+ (c) (n (c)))) (+ (c) (+ (d) (n (c))))) NIL)
(162 (paramod 161 (1) 160 (1 1 2 1 2 1 1)) (= (n (+ (n (+ v64 (d))) (n (+ v64 (+ (n (+ (c) (+ (d) (n (c))))) (n (d))))))) v64) NIL)
(163 (instantiate 51 ((v0 . (n (c))))) (= (+ (c) (+ (d) (n (c)))) (+ (c) (n (c)))) NIL)
(164 (paramod 163 (1) 162 (1 1 2 1 2 1 1)) (= (n (+ (n (+ v64 (d))) (n (+ v64 (+ (n (+ (c) (n (c)))) (n (d))))))) v64) NIL)
(165 (instantiate 2 ((v0 . (n (+ (c) (n (c)))))(v1 . (n (d))))) (= (+ (n (+ (c) (n (c)))) (n (d))) (+ (n (d)) (n (+ (c) (n (c)))))) NIL)
(166 (paramod 165 (1) 164 (1 1 2 1 2)) (= (n (+ (n (+ v64 (d))) (n (+ v64 (+ (n (d)) (n (+ (c) (n (c))))))))) v64) NIL)
(167 (instantiate 158 ((v0 . v64))) (= (n (+ (n (+ v64 (d))) (n (+ v64 (+ (n (d)) (n (+ (c) (n (c))))))))) (+ v64 (n (+ (c) (n (c)))))) NIL)
(168 (paramod 167 (1) 166 (1)) (= (+ v64 (n (+ (c) (n (c))))) v64) NIL)
(169 (instantiate 168 ((v64 . v0))) (= (+ v0 (n (+ (c) (n (c))))) v0) (1642))
(170 (instantiate 2 ((v0 . v64)(v1 . (n (+ (c) (n (c))))))) (= (+ v64 (n (+ (c) (n (c))))) (+ (n (+ (c) (n (c)))) v64)) NIL)
(171 (instantiate 169 ((v0 . v64))) (= (+ v64 (n (+ (c) (n (c))))) v64) NIL)
(172 (paramod 170 (1) 171 (1)) (= (+ (n (+ (c) (n (c)))) v64) v64) NIL)
(173 (instantiate 172 ((v64 . v0))) (= (+ (n (+ (c) (n (c)))) v0) v0) (1698))
(174 (instantiate 169 ((v0 . (n v65)))) (= (+ (n v65) (n (+ (c) (n (c))))) (n v65)) NIL)
(175 (instantiate 65 ((v0 . (n (+ (c) (n (c)))))(v1 . v65))) (= (n (+ (n (+ (c) (n (c)))) (n (+ v65 (+ (n (+ (c) (n (c)))) (n (+ (n v65) (n (+ (c) (n (c))))))))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL)
(176 (paramod 174 (1) 175 (1 1 2 1 2 2 1)) (= (n (+ (n (+ (c) (n (c)))) (n (+ v65 (+ (n (+ (c) (n (c)))) (n (n v65))))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL)
(177 (instantiate 173 ((v0 . (n (n v65))))) (= (+ (n (+ (c) (n (c)))) (n (n v65))) (n (n v65))) NIL)
(178 (paramod 177 (1) 176 (1 1 2 1 2)) (= (n (+ (n (+ (c) (n (c)))) (n (+ v65 (n (n v65)))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL)
(179 (instantiate 173 ((v0 . (n (+ v65 (n (n v65))))))) (= (+ (n (+ (c) (n (c)))) (n (+ v65 (n (n v65))))) (n (+ v65 (n (n v65))))) NIL)
(180 (paramod 179 (1) 178 (1 1)) (= (n (n (+ v65 (n (n v65))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL)
(181 (instantiate 169 ((v0 . (n v65)))) (= (+ (n v65) (n (+ (c) (n (c))))) (n v65)) NIL)
(182 (paramod 181 (1) 180 (2 1)) (= (n (n (+ v65 (n (n v65))))) (n (n v65))) NIL)
(183 (instantiate 182 ((v65 . v0))) (= (n (n (+ v0 (n (n v0))))) (n (n v0))) (1752))
(184 (instantiate 173 ((v0 . (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))))) (= (+ (n (+ (c) (n (c)))) (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) NIL)
(185 (instantiate 17 ((v0 . (n (+ (c) (n (c)))))(v1 . v65))) (= (n (+ (n (+ (c) (n (c)))) (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65)))))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL)
(186 (paramod 184 (1) 185 (1 1)) (= (n (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL)
(187 (instantiate 173 ((v0 . v65))) (= (+ (n (+ (c) (n (c)))) v65) v65) NIL)
(188 (paramod 187 (1) 186 (1 1 1 1 1)) (= (n (n (+ (n v65) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL)
(189 (instantiate 173 ((v0 . (n v65)))) (= (+ (n (+ (c) (n (c)))) (n v65)) (n v65)) NIL)
(190 (paramod 189 (1) 188 (1 1 1 2 1 1)) (= (n (n (+ (n v65) (n (n (n v65)))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL)
(191 (instantiate 183 ((v0 . (n v65)))) (= (n (n (+ (n v65) (n (n (n v65)))))) (n (n (n v65)))) NIL)
(192 (paramod 191 (1) 190 (1)) (= (n (n (n v65))) (n (+ (n (+ (c) (n (c)))) v65))) NIL)
(193 (instantiate 173 ((v0 . v65))) (= (+ (n (+ (c) (n (c)))) v65) v65) NIL)
(194 (paramod 193 (1) 192 (2 1)) (= (n (n (n v65))) (n v65)) NIL)
(195 (instantiate 194 ((v65 . v0))) (= (n (n (n v0))) (n v0)) (1961))
(196 (instantiate 195 ((v0 . (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2))))))))))))) (= (n (n (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2))))))))))))) (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2)))))))))))) NIL)
(197 (paramod 80 (1) 196 (1 1 1)) (= (n (n v0)) (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2)))))))))))) NIL)
(198 (paramod 80 (1) 197 (2)) (= (n (n v0)) v0) (2031))
(199 (instantiate 198 ((v0 . (+ (n (+ v0 v1)) (n (+ (n v0) v1)))))) (= (n (n (+ (n (+ v0 v1)) (n (+ (n v0) v1))))) (+ (n (+ v0 v1)) (n (+ (n v0) v1)))) NIL)
(200 (paramod 38 (1) 199 (1 1)) (= (n v1) (+ (n (+ v0 v1)) (n (+ (n v0) v1)))) NIL)
(201 (flip 200 ()) (= (+ (n (+ v0 v1)) (n (+ (n v0) v1))) (n v1)) (2143))
(202 (instantiate 201 ((v0 . (A))(v1 . (n (B))))) (= (+ (n (+ (A) (n (B)))) (n (+ (n (A)) (n (B))))) (n (n (B)))) NIL)
(203 (paramod 202 (1) 7 (1 1)) (not (= (n (n (B))) (B))) NIL)
(204 (instantiate 198 ((v0 . (B)))) (= (n (n (B))) (B)) NIL)
(205 (paramod 204 (1) 203 (1 1)) (not (= (B) (B))) (2173))
(206 (instantiate 1 ((v0 . (B)))) (= (B) (B)) NIL)
(207 (resolve 205 () 206 ()) false (2174))
)
;; END OF PROOF OBJECT

Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                 48
clauses generated           3063
  para_from generated       1790
  para_into generated       1273
demod & eval rewrites       6647
clauses wt,lit,sk delete     773
tautologies deleted            0
clauses forward subsumed    1669
  (subsumed by sos)           16
unit deletions                 0
factor simplifications         0
clauses kept                1073
new demodulators            1067
empty clauses                  1
clauses back demodulated     423
clauses back subsumed          2
usable size                   24
sos size                     624
demodulators size            645
passive size                   0
hot size                       0
Kbytes malloced             2682

----------- times (seconds) -----------
user CPU time          1.00          (0 hr, 0 min, 1 sec)
system CPU time        0.05          (0 hr, 0 min, 0 sec)
wall-clock time        1             (0 hr, 0 min, 1 sec)
input time             0.01
  clausify time        0.00
  process input        0.00
pick given time        0.00
para_into time         0.04
para_from time         0.02
pre_process time       0.59
  renumber time        0.02
  demod time           0.35
  order equalities     0.00
  unit deleletion      0.00
  factor simplify      0.00
  weigh cl time        0.00
  hints keep time      0.00
  sort lits time       0.00
  forward subsume      0.03
  delete cl time       0.02
  keep cl time         0.11
    hints time         0.03
  print_cl time        0.00
  conflict time        0.02
  new demod time       0.02
post_process time      0.31
  back demod time      0.27
  back subsume         0.03
  factor time          0.00
  unindex time         0.04

That finishes the proof of the theorem.

Process 10624 finished Tue Jul  1 16:24:13 2003
