----- Otter 3.2-beta, May 2001 -----
The process was started by mccune on theorem.mcs.anl.gov,
Tue Jul 10 11:45:29 2001
The command was "otter".  The process ID is 19599.

set(hyper_res).
clear(back_sub).
assign(pick_given_ratio,3).
assign(max_proofs,3).
assign(max_weight,16).
clear(print_kept).
set(order_history).
assign(max_mem,1500).
op(800,yfx,->).

list(usable).
1 [] -P(x->y)| -P(x)|P(y).
end_of_list.

list(sos).
2 [] P(x->y-> (y->z-> (x->z))).
3 [] P(-x->x->x).
4 [] P(x-> (-x->y)).
end_of_list.

list(passive).
5 [] -P(a->a)|$Ans(CN_16).
6 [] -P(b-> (a->b))|$Ans(CN_18).
7 [] -P(a->b->c-> (b->c))|$Ans(CN_19).
end_of_list.

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

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

given clause #1: (wt=12) 2 [] P(x->y-> (y->z-> (x->z))).

given clause #2: (wt=7) 3 [] P(-x->x->x).

given clause #3: (wt=7) 4 [] P(x-> (-x->y)).

given clause #4: (wt=10) 10 [hyper,1,4,4] P(-(x-> (-x->y))->z).

given clause #5: (wt=16) 8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)).

given clause #6: (wt=10) 12 [hyper,1,4,3] P(-(-x->x->x)->y).

given clause #7: (wt=11) 9 [hyper,1,2,3] P(x->y-> (-x->x->y)).

given clause #8: (wt=10) 24 [hyper,1,9,4] P(-x->x-> (-x->y)).

given clause #9: (wt=11) 11 [hyper,1,2,4] P(-x->y->z-> (x->z)).

----> UNIT CONFLICT at   0.00 sec ----> 35 [binary,34.1,5.1] $Ans(CN_16).

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

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

1 [] -P(x->y)| -P(x)|P(y).
2 [] P(x->y-> (y->z-> (x->z))).
3 [] P(-x->x->x).
4 [] P(x-> (-x->y)).
5 [] -P(a->a)|$Ans(CN_16).
11 [hyper,1,2,4] P(-x->y->z-> (x->z)).
34 [hyper,1,11,3] P(x->x).
35 [binary,34.1,5.1] $Ans(CN_16).

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


given clause #10: (wt=4) 34 [hyper,1,11,3] P(x->x).

given clause #11: (wt=7) 37 [hyper,1,4,34] P(-(x->x)->y).

given clause #12: (wt=10) 33 [hyper,1,11,4] P(x-> (-(-x->y)->z)).

given clause #13: (wt=15) 13 [hyper,1,4,2] P(-(x->y-> (y->z-> (x->z)))->u).

given clause #14: (wt=10) 39 [hyper,1,4,37] P(-(-(x->x)->y)->z).

given clause #15: (wt=11) 29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))).

given clause #16: (wt=9) 52 [hyper,1,11,29] P(x-> (y-> (-x->z))).

given clause #17: (wt=13) 14 [hyper,1,4,10] P(-(-(x-> (-x->y))->z)->u).

given clause #18: (wt=9) 56 [hyper,1,29,37] P(x-> (-(y->y)->z)).

given clause #19: (wt=11) 32 [hyper,1,11,9] P(x-> (-(-x)-> -x->y)).

given clause #20: (wt=11) 36 [hyper,1,11,2] P(x-> (y->z-> (-x->z))).

given clause #21: (wt=14) 15 [hyper,1,2,10] P(x->y-> (-(z-> (-z->u))->y)).

given clause #22: (wt=11) 40 [hyper,1,2,37] P(x->y-> (-(z->z)->y)).

given clause #23: (wt=12) 55 [hyper,1,29,39] P(x-> (-(-(y->y)->z)->u)).

given clause #24: (wt=12) 57 [hyper,1,29,12] P(x-> (-(-y->y->y)->z)).

given clause #25: (wt=16) 16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))).

given clause #26: (wt=12) 58 [hyper,1,29,10] P(x-> (-(y-> (-y->z))->u)).

given clause #27: (wt=12) 61 [hyper,1,11,52] P(x-> (y-> (-(-x->z)->u))).

given clause #28: (wt=12) 62 [hyper,1,9,52] P(-x->x-> (y-> (-x->z))).

given clause #29: (wt=15) 17 [hyper,1,8,4] P(x->y-> (-(y->z-> (x->z))->u)).

given clause #30: (wt=12) 63 [hyper,1,4,52] P(-(x-> (y-> (-x->z)))->u).

given clause #31: (wt=12) 75 [hyper,1,4,56] P(-(x-> (-(y->y)->z))->u).

given clause #32: (wt=13) 19 [hyper,1,4,12] P(-(-(-x->x->x)->y)->z).

given clause #33: (wt=16) 18 [hyper,1,8,2] P(x->y-> (x->z->u-> (y->z->u))).

given clause #34: (wt=13) 25 [hyper,1,9,3] P(-(-x->x)-> (-x->x)->x).

given clause #35: (wt=13) 27 [hyper,1,4,24] P(-(-x->x-> (-x->y))->z).

given clause #36: (wt=13) 38 [hyper,1,9,37] P(-(-(x->x))-> -(x->x)->y).

given clause #37: (wt=14) 20 [hyper,1,2,12] P(x->y-> (-(-z->z->z)->y)).

given clause #38: (wt=13) 42 [hyper,1,11,33] P(x-> (-(-(-x->y)->z)->u)).

given clause #39: (wt=13) 43 [hyper,1,9,33] P(-x->x-> (-(-x->y)->z)).

given clause #40: (wt=13) 44 [hyper,1,4,33] P(-(x-> (-(-x->y)->z))->u).

given clause #41: (wt=16) 21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)).

given clause #42: (wt=13) 46 [hyper,1,33,37] P(-(-(-(x->x)->y)->z)->u).

given clause #43: (wt=13) 64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)).

given clause #44: (wt=12) 122 [hyper,1,64,4] P(x-> (-(y-> (-x->z))->u)).

given clause #45: (wt=14) 22 [hyper,1,4,9] P(-(x->y-> (-x->x->y))->z).

given clause #46: (wt=13) 76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)).

given clause #47: (wt=6) 132 [hyper,1,76,3] P(x-> (y->y)).

given clause #48: (wt=9) 131 [hyper,1,76,21] P(x-> (-y->y->y)).

given clause #49: (wt=15) 23 [hyper,1,2,9] P(-x->x->y->z-> (x->y->z)).

given clause #50: (wt=9) 141 [hyper,1,4,132] P(-(x-> (y->y))->z).

given clause #51: (wt=10) 140 [hyper,1,16,132] P(x->y-> (z-> (x->y))).

given clause #52: (wt=8) 162 [hyper,1,140,132] P(x-> (y-> (z->z))).

given clause #53: (wt=16) 26 [hyper,1,9,24] P(-(-x->x)-> (-x->x)-> (-x->y)).

given clause #54: (wt=9) 181 [hyper,1,140,4] P(x-> (y-> (-y->z))).

given clause #55: (wt=10) 142 [hyper,1,2,132] P(x->x->y-> (z->y)).

given clause #56: (wt=10) 183 [hyper,1,140,162] P(x-> (y-> (z-> (u->u)))).

given clause #57: (wt=14) 28 [hyper,1,2,24] P(-x->y->z-> (-x->x->z)).

given clause #58: (wt=11) 129 [hyper,1,76,62] P(x-> (y-> (-(z->z)->u))).

given clause #59: (wt=11) 135 [hyper,1,52,132] P(x-> (-(y-> (z->z))->u)).

given clause #60: (wt=11) 154 [hyper,1,64,140] P(x-> (y-> (z-> (-x->u)))).

given clause #61: (wt=14) 30 [hyper,1,4,11] P(-(-x->y->z-> (x->z))->u).

given clause #62: (wt=11) 163 [hyper,1,140,131] P(x-> (y-> (-z->z->z))).

given clause #63: (wt=11) 171 [hyper,1,140,52] P(x-> (y-> (z-> (-y->u)))).

given clause #64: (wt=11) 190 [hyper,1,4,162] P(-(x-> (y-> (z->z)))->u).

given clause #65: (wt=15) 31 [hyper,1,2,11] P(x->y->z-> (-x->u->y->z)).

given clause #66: (wt=10) 249 [hyper,1,31,3] P(-(-x)->y->x->x).

given clause #67: (wt=11) 192 [hyper,1,140,181] P(x-> (y-> (z-> (-z->u)))).

given clause #68: (wt=12) 137 [hyper,1,33,132] P(-(-(x-> (y->y))->z)->u).

given clause #69: (wt=16) 41 [hyper,1,33,33] P(-(-(x-> (-(-x->y)->z))->u)->v).

given clause #70: (wt=12) 147 [hyper,1,4,131] P(-(x-> (-y->y->y))->z).

given clause #71: (wt=12) 153 [hyper,1,140,140] P(x-> (y->z-> (u-> (y->z)))).

given clause #72: (wt=12) 174 [hyper,1,140,33] P(x-> (y-> (-(-y->z)->u))).

given clause #73: (wt=14) 45 [hyper,1,2,33] P(-(-x->y)->z->u-> (x->u)).

given clause #74: (wt=12) 178 [hyper,1,140,24] P(x-> (-y->y-> (-y->z))).

given clause #75: (wt=12) 191 [hyper,1,2,162] P(x-> (y->y)->z-> (u->z)).

given clause #76: (wt=12) 197 [hyper,1,4,181] P(-(x-> (y-> (-y->z)))->u).

given clause #77: (wt=16) 47 [hyper,1,33,24] P(-(-(-x->x-> (-x->y))->z)->u).

given clause #78: (wt=12) 199 [hyper,1,140,142] P(x-> (y->y->z-> (u->z))).

given clause #79: (wt=12) 202 [hyper,1,140,183] P(x-> (y-> (z-> (u-> (v->v))))).

given clause #80: (wt=12) 251 [hyper,1,140,249] P(x-> (-(-y)->z->y->y)).

given clause #81: (wt=16) 48 [hyper,1,33,12] P(-(-(-(-x->x->x)->y)->z)->u).

given clause #82: (wt=12) 256 [hyper,1,8,249] P(x-> -(-(x->y))-> (x->y)).

given clause #83: (wt=13) 87 [hyper,1,16,56] P(x-> -(y->y)-> (z-> (x->u))).

given clause #84: (wt=13) 89 [hyper,1,16,52] P(x->y-> (z-> (x-> (-z->u)))).

given clause #85: (wt=16) 49 [hyper,1,33,10] P(-(-(-(x-> (-x->y))->z)->u)->v).

given clause #86: (wt=13) 121 [hyper,1,64,16] P(x-> (y-> -x-> (z-> (y->u)))).

given clause #87: (wt=13) 123 [hyper,1,64,2] P(x-> (-x->y->z-> (u->z))).

given clause #88: (wt=13) 139 [hyper,1,17,132] P(-(x->x->y-> (z->y))->u).

given clause #89: (wt=16) 50 [hyper,1,33,39] P(-(-(-(-(x->x)->y)->z)->u)->v).

given clause #90: (wt=13) 146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))).

given clause #91: (wt=8) 308 [hyper,1,64,146] P(x-> (y-> (z->x))).

given clause #92: (wt=8) 322 [hyper,1,146,308] P(x-> (y-> (z->y))).

----> UNIT CONFLICT at   0.06 sec ----> 361 [binary,360.1,6.1] $Ans(CN_18).

Length of proof is 17.  Level of proof is 10.

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

1 [] -P(x->y)| -P(x)|P(y).
2 [] P(x->y-> (y->z-> (x->z))).
3 [] P(-x->x->x).
4 [] P(x-> (-x->y)).
6 [] -P(b-> (a->b))|$Ans(CN_18).
8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)).
9 [hyper,1,2,3] P(x->y-> (-x->x->y)).
11 [hyper,1,2,4] P(-x->y->z-> (x->z)).
16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))).
21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)).
29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))).
34 [hyper,1,11,3] P(x->x).
37 [hyper,1,4,34] P(-(x->x)->y).
52 [hyper,1,11,29] P(x-> (y-> (-x->z))).
56 [hyper,1,29,37] P(x-> (-(y->y)->z)).
64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)).
76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)).
131 [hyper,1,76,21] P(x-> (-y->y->y)).
146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))).
308 [hyper,1,64,146] P(x-> (y-> (z->x))).
322 [hyper,1,146,308] P(x-> (y-> (z->y))).
360 [hyper,1,322,322] P(x-> (y->x)).
361 [binary,360.1,6.1] $Ans(CN_18).

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


given clause #93: (wt=14) 51 [hyper,1,2,39] P(x->y-> (-(-(z->z)->u)->y)).

given clause #94: (wt=6) 360 [hyper,1,322,322] P(x-> (y->x)).

----> UNIT CONFLICT at   0.07 sec ----> 387 [binary,386.1,7.1] $Ans(CN_19).

Length of proof is 18.  Level of proof is 11.

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

1 [] -P(x->y)| -P(x)|P(y).
2 [] P(x->y-> (y->z-> (x->z))).
3 [] P(-x->x->x).
4 [] P(x-> (-x->y)).
7 [] -P(a->b->c-> (b->c))|$Ans(CN_19).
8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)).
9 [hyper,1,2,3] P(x->y-> (-x->x->y)).
11 [hyper,1,2,4] P(-x->y->z-> (x->z)).
16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))).
21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)).
29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))).
34 [hyper,1,11,3] P(x->x).
37 [hyper,1,4,34] P(-(x->x)->y).
52 [hyper,1,11,29] P(x-> (y-> (-x->z))).
56 [hyper,1,29,37] P(x-> (-(y->y)->z)).
64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)).
76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)).
131 [hyper,1,76,21] P(x-> (-y->y->y)).
146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))).
308 [hyper,1,64,146] P(x-> (y-> (z->x))).
322 [hyper,1,146,308] P(x-> (y-> (z->y))).
360 [hyper,1,322,322] P(x-> (y->x)).
386 [hyper,1,2,360] P(x->y->z-> (y->z)).
387 [binary,386.1,7.1] $Ans(CN_19).

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


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                 94
clauses generated           5345
  hyper_res generated       5345
demod & eval rewrites          0
clauses wt,lit,sk delete    1477
tautologies deleted            0
clauses forward subsumed    3491
  (subsumed by sos)          447
unit deletions                 0
factor simplifications         0
clauses kept                 377
new demodulators               0
empty clauses                  3
clauses back demodulated       0
clauses back subsumed          0
usable size                   95
sos size                     286
demodulators size              0
passive size                   3
hot size                       0
Kbytes malloced              319

----------- times (seconds) -----------
user CPU time          0.07          (0 hr, 0 min, 0 sec)
system CPU time        0.04          (0 hr, 0 min, 0 sec)
wall-clock time        0             (0 hr, 0 min, 0 sec)
input time             0.00
  clausify time        0.00
pick given time        0.00
hyper_res time         0.02
pre_process time       0.05
  renumber time        0.01
  demod time           0.00
  order equalities     0.00
  unit deleletion      0.00
  factor simplify      0.00
  weigh cl time        0.01
  hints keep time      0.00
  sort lits time       0.00
  forward subsume      0.01
  delete cl time       0.00
  keep cl time         0.00
    hints time         0.00
  print_cl time        0.00
  conflict time        0.00
  new demod time       0.00
post_process time      0.00
  back demod time      0.00
  back subsume         0.00
  factor time          0.00
  unindex time         0.00

That finishes the proof of the theorem.

Process 19599 finished Tue Jul 10 11:45:29 2001
