----- Otter 3.3, August 2003 -----
The process was started by mccune on gyro.thornwood,
Wed Aug  6 14:26:48 2003
The command was "../../bin/otter".  The process ID is 6360.

set(para_from).
set(para_into).
set(para_from_vars).
set(order_eq).
set(geometric_rule).
set(geometric_rewrite_before).
set(lrpo).

lex([a,b,f(x,x,x)]).
assign(max_mem,1500).
clear(print_kept).
clear(print_back_sub).

list(usable).
1 [] x=x.
end_of_list.

list(sos).
2 [] f(x,x,y)=x.
3 [] f(x,y,x)=x.
4 [] f(y,x,x)=x.
end_of_list.

list(passive).
5 [] a!=b.
end_of_list.

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

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

given clause #1: (wt=6) 2 [] f(x,x,y)=x.

given clause #2: (wt=6) 3 [] f(x,y,x)=x.

given clause #3: (wt=6) 4 [] f(y,x,x)=x.

given clause #4: (wt=12) 6 [para_into,2.1.1,2.1.2] f(f(x,x,y),f(x,x,y),z)=x.

given clause #5: (wt=18) 16 [para_into,6.1.1.1,6.1.1,gL-id] f(x,f(f(y,y,z),f(y,y,z),u),v)=f(x,y,z).

given clause #6: (wt=6) 65 [para_into,16.1.1,3.1.1,flip.1] f(x,y,z)=x.

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

----> UNIT CONFLICT at   0.01 sec ----> 83 [binary,82.1,5.1] $F.

Length of proof is 4.  Level of proof is 4.

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

2 [] f(x,x,y)=x.
3 [] f(x,y,x)=x.
4 [] f(y,x,x)=x.
5 [] a!=b.
6 [para_into,2.1.1,2.1.2] f(f(x,x,y),f(x,x,y),z)=x.
16 [para_into,6.1.1.1,6.1.1,gL-id] f(x,f(f(y,y,z),f(y,y,z),u),v)=f(x,y,z).
65 [para_into,16.1.1,3.1.1,flip.1] f(x,y,z)=x.
82 [para_into,65.1.1,4.1.1] x=y.
83 [binary,82.1,5.1] $F.

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


Search stopped by max_proofs option.


Search stopped by max_proofs option.

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

-------------- statistics -------------
clauses given                  6
clauses generated            138
  para_from generated         42
  para_into generated         94
  gL rule generated            2
demod & eval rewrites          0
clauses wt,lit,sk delete       0
tautologies deleted            0
clauses forward subsumed      61
  (subsumed by sos)           34
unit deletions                 0
factor simplifications         0
clauses kept                  77
new demodulators               0
empty clauses                  1
clauses back demodulated       0
clauses back subsumed          7
usable size                    5
sos size                      69
demodulators size              0
passive size                   1
hot size                       0
Kbytes malloced              287

----------- times (seconds) -----------
user CPU time          0.01          (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)
input time             0.00
  clausify time        0.00
pick given time        0.00
para_into time         0.01
para_from time         0.00
pre_process time       0.00
  renumber time        0.00
  demod time           0.00
  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      0.00
  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 6360 finished Wed Aug  6 14:26:48 2003