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                     Appendix A

                    Input File 1

%  luka completeness of 123 exps.
set(hyper_res).
% assign(max_weight,20).
assign(max_proofs, 0).
clear(print_kept).
clear(back_sub).
% assign(max_seconds, 1200).
assign(max_mem, 128000).
assign(report, 900).
% assign(max_distinct_vars, 4).
% assign(pick_given_ratio, 3).
set(order_history).
set(input_sos_first).
set(sos_queue).
set(print_level).
  
list(usable).
-P(i(x,y)) | -P(x) | P(y).
  
%  The following disjunctions are known axiom systems.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
$ANSWER(step_allFrege_18_35_39_40_46_21).  % 21 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
  
-P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
  
end_of_list.
  
list(sos).
%  The following three are Luka, 1 2 3.
P(i(i(x,y),i(i(y,z),i(x,z)))).
P(i(i(n(x),x),x)).
P(i(x,i(n(x),y))).
  
%  The following are from Frege, 18 35 21 46 39 40, with 21 dependent.
% P(i(x,i(y,x))).  %  axiom F1.
% P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).  %  axiom F2.
% P(i(i(x,i(y,z)),i(y,i(x,z)))).  %  axiom F3.
% P(i(i(x,y),i(n(y),n(x)))).  %  axiom F4.
% P(i(n(n(x)),x)).  %  axiom F5.
% P(i(x,n(n(x)))).  %  axiom f6.
end_of_list.
  
list(passive).
-P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
-P(i(i(n(p),p),p)) | $ANSWER(step_L2).
-P(i(p,i(n(p),q))) | $ANSWER(step_L3).
-P(i(p,i(q,p))) | $ANSWER(step_18).
-P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
-P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
-P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
-P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
-P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
-P(i(n(n(p)),p)) | $ANSWER(step_39).
-P(i(p,n(n(p)))) | $ANSWER(step_40).
-P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
-P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
% list(demodulators).
% % (n(n(x)) = junk).
%  (n(n(n(x))) = junk).
%  (i(i(x,x),y) = junk).
%  (i(y,i(x,x)) = junk).
% (i(junk,x) = junk).
% (i(x,junk) = junk).
% (n(junk) = junk).
% (P(junk) = $T).
% end_of_list.

                   Input File 2

%  luka completeness of 123 exps.
set(hyper_res).
% assign(reduce_weight_limit, 010024).
assign(max_weight,20).
% set(control_memory).
assign(max_proofs, 0).
clear(print_kept).
% set(very_verbose).
% set(ancestor_subsume).
% clear(back_sub).
% assign(max_seconds, 1800).
assign(max_mem, 128000).
assign(report, 900).
assign(max_distinct_vars, 4).
% assign(pick_given_ratio, 3).
set(order_history).
set(input_sos_first).
set(sos_queue).
set(print_level).
  
list(usable).
-P(i(x,y)) | -P(x) | P(y).
  
%  The following disjunctions are known axiom systems.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
$ANSWER(step_allFrege_18_35_39_40_46_21).  % 21 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
  
-P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
  
end_of_list.
  
list(sos).
%  The following three are Luka, 1 2 3.
P(i(i(x,y),i(i(y,z),i(x,z)))).
P(i(i(n(x),x),x)).
P(i(x,i(n(x),y))).
  
%  The following are from Frege, 18 35 21 46 39 40, with 21 dependent.
% P(i(x,i(y,x))).  %  axiom F1.
% P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).  %  axiom F2.
% P(i(i(x,i(y,z)),i(y,i(x,z)))).  %  axiom F3.
% P(i(i(x,y),i(n(y),n(x)))).  %  axiom F4.
% P(i(n(n(x)),x)).  %  axiom F5.
% P(i(x,n(n(x)))).  %  axiom f6.
end_of_list.
  
list(passive).
-P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
-P(i(i(n(p),p),p)) | $ANSWER(step_L2).
-P(i(p,i(n(p),q))) | $ANSWER(step_L3).
-P(i(p,i(q,p))) | $ANSWER(step_18).
-P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
-P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
-P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
-P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
-P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
-P(i(n(n(p)),p)) | $ANSWER(step_39).
-P(i(p,n(n(p)))) | $ANSWER(step_40).
-P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
-P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
% (n(n(x)) = junk).
(n(n(n(x))) = junk).
% (i(i(x,x),y) = junk).
% (i(y,i(x,x)) = junk).
(i(junk,x) = junk).
(i(x,junk) = junk).
(n(junk) = junk).
(P(junk) = $T).
end_of_list.

               Summary of Output 2A

----- OTTER 2.2xa+, January 1992 -----
The job began on cosmo.mcs.anl.gov, Mon Aug 17 08:05:04 1992
The command was "otter4++".
  
set(hyper_res).
assign(max_weight,20).
assign(max_proofs,0).
clear(print_kept).
assign(max_mem,128000).
assign(report,900).
assign(max_distinct_vars,4).
set(order_history).
set(input_sos_first).
set(sos_queue).
set(print_level).
  
list(usable).
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
3 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).
4 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) |
$ANSWER(step_allWos_x_19_37_60).
7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | -P(i(p,i(n(p),q))) | 
$ANSWER(step_allLuka_1_2_3).
8 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
9 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
end_of_list.
  
list(sos).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
end_of_list.
  
list(passive).
13 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
14 [] -P(i(i(n(p),p),p)) | $ANSWER(step_L2).
15 [] -P(i(p,i(n(p),q))) | $ANSWER(step_L3).
16 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
25 [] -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
27 [] -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
29 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
30 [] n(n(n(x)))=junk.
31 [] i(junk,x)=junk.
32 [] i(x,junk)=junk.
33 [] n(junk)=junk.
34 [] P(junk)=$T.
end_of_list.
  
Starting on Level 1, last kept clause of level 0 is 34.
Starting on Level 1, last kept clause of level 0 is 34.
  
  
given clause #1: (wt=-2147483647) 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
-----> EMPTY CLAUSE at   0.30 sec ----> 37 [hyper,7,10,11,12]
$ANSWER(step_allLuka_1_2_3).
Length of proof is 0.  Level of proof is 0.
---------------- PROOF ----------------
  
7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,7,10,11,12] $ANSWER(step_allLuka_1_2_3).
  
length of proof is 0
------------ end of proof -------------
Starting on Level 2, last kept clause of level 1 is 41.
Starting on Level 3, last kept clause of level 2 is 65.
Starting on Level 4, last kept clause of level 3 is 147.
Starting on Level 5, last kept clause of level 4 is 344.
Starting on Level 6, last kept clause of level 5 is 744.
Starting on Level 7, last kept clause of level 6 is 1861.
----> UNIT CONFLICT at 203.96 sec ----> 2216 [binary,2215,17] $ANSWER(step_19).
Length of proof is 19.  Level of proof is 7.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
40 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
49 [hyper,1,36,12] P(i(i(n(x),x),i(n(x),y))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
67 [hyper,1,35,42] P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
107 [hyper,1,39,56] P(i(x,i(y,i(n(x),z)))).
113 [hyper,1,56,40] P(i(x,i(n(i(i(n(y),y),y)),z))).
151 [hyper,1,67,49] P(i(i(x,i(n(y),y)),i(i(i(n(y),z),u),i(x,u)))).
163 [hyper,1,10,70] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,i(n(x),x)),u))).
255 [hyper,1,10,107] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
282 [hyper,1,70,113] P(i(i(i(i(n(x),x),x),y),i(z,y))).
370 [hyper,1,163,42] P(i(i(x,i(n(y),y)),i(i(z,x),i(i(y,u),i(z,u))))).
551 [hyper,1,255,151] P(i(x,i(i(i(n(x),y),z),i(u,z)))).
810 [hyper,1,370,282] P(i(i(x,i(i(i(n(y),y),y),z)),i(i(z,u),i(x,u)))).
2215 [hyper,1,810,551] P(i(i(i(x,y),z),i(y,z))).
2216 [binary,2215,17] $ANSWER(step_19).
  
length of proof is 19
------------ end of proof -------------
----> UNIT CONFLICT at 360.33 sec ----> 3250 [binary,3249,16] $ANSWER(step_18).
Length of proof is 28.  Level of proof is 7.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
16 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
40 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
44 [hyper,1,35,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
45 [hyper,1,36,36] P(i(i(n(i(x,y)),i(x,y)),i(i(n(x),x),y))).
55 [hyper,1,36,39] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
58 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
59 [hyper,1,39,36] P(i(x,i(i(n(n(x)),n(x)),y))).
61 [hyper,1,39,11] P(i(x,x)).
69 [hyper,1,42,39] P(i(i(x,y),i(i(i(n(y),z),u),i(x,u)))).
76 [hyper,1,44,40] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
78 [hyper,1,42,45] P(i(i(x,i(n(y),y)),i(i(n(i(y,z)),i(y,z)),i(x,z)))).
107 [hyper,1,39,56] P(i(x,i(y,i(n(x),z)))).
110 [hyper,1,10,56] P(i(i(i(x,i(y,z)),u),i(i(y,n(x)),u))).
125 [hyper,1,58,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
155 [hyper,1,69,59] P(i(i(i(n(i(i(n(n(x)),n(x)),y)),z),u),i(x,u))).
172 [hyper,1,76,55] P(i(i(x,i(i(n(y),y),y)),i(y,y))).
179 [hyper,1,35,78] P(i(i(n(x),y),i(i(n(i(x,z)),i(x,z)),i(i(y,x),z)))).
256 [hyper,1,107,61] P(i(x,i(n(i(y,y)),z))).
266 [hyper,1,110,78] P(i(i(n(x),n(y)),i(i(n(i(x,z)),i(x,z)),i(y,z)))).
421 [hyper,1,155,172] P(i(x,i(y,y))).
560 [hyper,1,179,256] P(i(i(n(i(x,y)),i(x,y)),i(i(i(n(i(z,z)),u),x),y))).
580 [hyper,1,125,266] P(i(i(i(i(n(i(x,y)),i(x,y)),i(z,y)),u),i(x,u))).
1022 [hyper,1,560,421] P(i(i(i(n(i(x,x)),y),z),z)).
3249 [hyper,1,580,1022] P(i(x,i(y,x))).
3250 [binary,3249,16] $ANSWER(step_18).
  
length of proof is 28
------------ end of proof -------------
----> UNIT CONFLICT at 427.39 sec ----> 3516 [binary,3515,22] $ANSWER(step_37).
Length of proof is 19.  Level of proof is 7.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,10,36] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
58 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
59 [hyper,1,39,36] P(i(x,i(i(n(n(x)),n(x)),y))).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
94 [hyper,1,48,10] P(i(i(x,y),i(i(y,z),i(i(n(x),x),z)))).
110 [hyper,1,10,56] P(i(i(i(x,i(y,z)),u),i(i(y,n(x)),u))).
129 [hyper,1,42,59] P(i(i(x,i(n(n(y)),n(y))),i(y,i(x,z)))).
158 [hyper,1,58,70] P(i(i(i(n(x),y),i(n(z),z)),i(i(z,u),i(x,u)))).
206 [hyper,1,58,94] P(i(i(i(n(x),y),z),i(i(z,u),i(i(n(x),x),u)))).
268 [hyper,1,110,70] P(i(i(n(x),n(y)),i(i(x,z),i(y,z)))).
321 [hyper,1,58,129] P(i(i(i(n(x),y),i(n(n(z)),n(z))),i(z,i(x,u)))).
585 [hyper,1,206,268] P(i(i(i(i(x,y),i(z,y)),u),i(i(n(x),x),u))).
1090 [hyper,1,585,321] P(i(i(n(n(x)),n(x)),i(y,i(x,z)))).
3515 [hyper,1,158,1090] P(i(i(i(x,y),z),i(n(x),z))).
3516 [binary,3515,22] $ANSWER(step_37).
  
length of proof is 19
------------ end of proof -------------
Starting on Level 8, last kept clause of level 7 is 5998.
----> UNIT CONFLICT at 1145.98 sec ----> 6146 [binary,6145,23] $ANSWER(step_39).
Length of proof is 26.  Level of proof is 8.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
40 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,10,36] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
49 [hyper,1,36,12] P(i(i(n(x),x),i(n(x),y))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
58 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
67 [hyper,1,35,42] P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
113 [hyper,1,56,40] P(i(x,i(n(i(i(n(y),y),y)),z))).
114 [hyper,1,48,58] P(i(i(x,y),i(i(i(n(n(x)),z),x),y))).
124 [hyper,1,58,11] P(i(i(i(n(n(x)),y),x),x)).
125 [hyper,1,58,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
151 [hyper,1,67,49] P(i(i(x,i(n(y),y)),i(i(i(n(y),z),u),i(x,u)))).
161 [hyper,1,35,70] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))).
282 [hyper,1,70,113] P(i(i(i(i(n(x),x),x),y),i(z,y))).
288 [hyper,1,42,114] P(i(i(x,i(i(n(n(y)),z),y)),i(i(y,u),i(x,u)))).
316 [hyper,1,36,124] P(i(i(n(i(i(n(n(x)),y),x)),i(i(n(n(x)),y),x)),x)).
360 [hyper,1,10,161] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))).
658 [hyper,1,151,282] P(i(i(i(n(x),y),z),i(i(i(i(n(u),u),u),x),z))).
759 [hyper,1,360,288] P(i(i(n(x),n(n(y))),i(i(y,z),i(i(x,y),z)))).
1340 [hyper,1,658,316] P(i(i(i(i(n(x),x),x),i(i(n(n(y)),z),y)),y)).
1891 [hyper,1,125,759] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(z,u))).
6145 [hyper,1,1891,1340] P(i(n(n(x)),x)).
6146 [binary,6145,23] $ANSWER(step_39).
  
length of proof is 26
------------ end of proof -------------
----> UNIT CONFLICT at 1523.40 sec ----> 7209 [binary,7208,26] $ANSWER(step_49).
Length of proof is 17.  Level of proof is 8.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
61 [hyper,1,39,11] P(i(x,x)).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
107 [hyper,1,39,56] P(i(x,i(y,i(n(x),z)))).
110 [hyper,1,10,56] P(i(i(i(x,i(y,z)),u),i(i(y,n(x)),u))).
163 [hyper,1,10,70] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,i(n(x),x)),u))).
256 [hyper,1,107,61] P(i(x,i(n(i(y,y)),z))).
268 [hyper,1,110,70] P(i(i(n(x),n(y)),i(i(x,z),i(y,z)))).
369 [hyper,1,163,70] P(i(i(n(x),i(n(y),y)),i(i(x,z),i(i(y,x),z)))).
595 [hyper,1,10,268] P(i(i(i(i(x,y),i(z,y)),u),i(i(n(x),n(z)),u))).
804 [hyper,1,369,256] P(i(i(x,y),i(i(i(z,z),x),y))).
2184 [hyper,1,804,61] P(i(i(i(x,x),y),y)).
7208 [hyper,1,595,2184] P(i(i(n(x),n(y)),i(y,x))).
7209 [binary,7208,26] $ANSWER(step_49).
  
length of proof is 17
------------ end of proof -------------
----> UNIT CONFLICT at 1620.15 sec ----> 8745 [binary,8744,18] $ANSWER(step_21).
Length of proof is 18.  Level of proof is 8.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
40 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
107 [hyper,1,39,56] P(i(x,i(y,i(n(x),z)))).
113 [hyper,1,56,40] P(i(x,i(n(i(i(n(y),y),y)),z))).
163 [hyper,1,10,70] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,i(n(x),x)),u))).
255 [hyper,1,10,107] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
282 [hyper,1,70,113] P(i(i(i(i(n(x),x),x),y),i(z,y))).
370 [hyper,1,163,42] P(i(i(x,i(n(y),y)),i(i(z,x),i(i(y,u),i(z,u))))).
372 [hyper,1,163,10] P(i(i(x,i(n(y),y)),i(i(i(x,z),u),i(i(y,z),u)))).
810 [hyper,1,370,282] P(i(i(x,i(i(i(n(y),y),y),z)),i(i(z,u),i(x,u)))).
818 [hyper,1,255,372] P(i(x,i(i(i(y,z),u),i(i(x,z),u)))).
2237 [hyper,1,810,818] P(i(i(i(i(x,y),y),z),i(x,z))).
8744 [hyper,1,35,2237] P(i(i(x,i(y,z)),i(y,i(x,z)))).
8745 [binary,8744,18] $ANSWER(step_21).
  
length of proof is 18
------------ end of proof -------------
----> UNIT CONFLICT at 1621.25 sec ----> 8842 [binary,8841,19] $ANSWER(step_22).
Length of proof is 18.  Level of proof is 8.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
40 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
107 [hyper,1,39,56] P(i(x,i(y,i(n(x),z)))).
113 [hyper,1,56,40] P(i(x,i(n(i(i(n(y),y),y)),z))).
163 [hyper,1,10,70] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,i(n(x),x)),u))).
255 [hyper,1,10,107] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
282 [hyper,1,70,113] P(i(i(i(i(n(x),x),x),y),i(z,y))).
370 [hyper,1,163,42] P(i(i(x,i(n(y),y)),i(i(z,x),i(i(y,u),i(z,u))))).
372 [hyper,1,163,10] P(i(i(x,i(n(y),y)),i(i(i(x,z),u),i(i(y,z),u)))).
810 [hyper,1,370,282] P(i(i(x,i(i(i(n(y),y),y),z)),i(i(z,u),i(x,u)))).
818 [hyper,1,255,372] P(i(x,i(i(i(y,z),u),i(i(x,z),u)))).
2237 [hyper,1,810,818] P(i(i(i(i(x,y),y),z),i(x,z))).
8841 [hyper,1,2237,35] P(i(i(x,y),i(i(z,x),i(z,y)))).
8842 [binary,8841,19] $ANSWER(step_22).
  
length of proof is 18
------------ end of proof -------------
----> UNIT CONFLICT at 4279.70 sec ----> 17626 [binary,17625,24] $ANSWER(step_40).
Length of proof is 25.  Level of proof is 8.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
58 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
59 [hyper,1,39,36] P(i(x,i(i(n(n(x)),n(x)),y))).
61 [hyper,1,39,11] P(i(x,x)).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
107 [hyper,1,39,56] P(i(x,i(y,i(n(x),z)))).
110 [hyper,1,10,56] P(i(i(i(x,i(y,z)),u),i(i(y,n(x)),u))).
125 [hyper,1,58,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
129 [hyper,1,42,59] P(i(i(x,i(n(n(y)),n(y))),i(y,i(x,z)))).
133 [hyper,1,10,59] P(i(i(i(i(n(n(x)),n(x)),y),z),i(x,z))).
163 [hyper,1,10,70] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,i(n(x),x)),u))).
256 [hyper,1,107,61] P(i(x,i(n(i(y,y)),z))).
268 [hyper,1,110,70] P(i(i(n(x),n(y)),i(i(x,z),i(y,z)))).
321 [hyper,1,58,129] P(i(i(i(n(x),y),i(n(n(z)),n(z))),i(z,i(x,u)))).
369 [hyper,1,163,70] P(i(i(n(x),i(n(y),y)),i(i(x,z),i(i(y,x),z)))).
589 [hyper,1,125,268] P(i(i(i(i(x,y),i(z,y)),u),i(x,u))).
804 [hyper,1,369,256] P(i(i(x,y),i(i(i(z,z),x),y))).
1129 [hyper,1,589,321] P(i(n(x),i(y,i(x,z)))).
2169 [hyper,1,804,133] P(i(i(i(x,x),i(i(i(n(n(y)),n(y)),z),u)),i(y,u))).
3584 [hyper,1,369,1129] P(i(i(x,y),i(i(i(x,z),x),y))).
17625 [hyper,1,2169,3584] P(i(x,n(n(x)))).
17626 [binary,17625,24] $ANSWER(step_40).
  
length of proof is 25
------------ end of proof -------------
----> UNIT CONFLICT at 7905.81 sec ----> 29264 [binary,29263,20] $ANSWER(step_30).
Length of proof is 28.  Level of proof is 8.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
40 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
42 [hyper,1,35,35] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,10,36] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
56 [hyper,1,35,39] P(i(i(x,n(y)),i(y,i(x,z)))).
58 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
59 [hyper,1,39,36] P(i(x,i(i(n(n(x)),n(x)),y))).
70 [hyper,1,42,36] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
94 [hyper,1,48,10] P(i(i(x,y),i(i(y,z),i(i(n(x),x),z)))).
110 [hyper,1,10,56] P(i(i(i(x,i(y,z)),u),i(i(y,n(x)),u))).
113 [hyper,1,56,40] P(i(x,i(n(i(i(n(y),y),y)),z))).
114 [hyper,1,48,58] P(i(i(x,y),i(i(i(n(n(x)),z),x),y))).
129 [hyper,1,42,59] P(i(i(x,i(n(n(y)),n(y))),i(y,i(x,z)))).
158 [hyper,1,58,70] P(i(i(i(n(x),y),i(n(z),z)),i(i(z,u),i(x,u)))).
206 [hyper,1,58,94] P(i(i(i(n(x),y),z),i(i(z,u),i(i(n(x),x),u)))).
268 [hyper,1,110,70] P(i(i(n(x),n(y)),i(i(x,z),i(y,z)))).
282 [hyper,1,70,113] P(i(i(i(i(n(x),x),x),y),i(z,y))).
288 [hyper,1,42,114] P(i(i(x,i(i(n(n(y)),z),y)),i(i(y,u),i(x,u)))).
321 [hyper,1,58,129] P(i(i(i(n(x),y),i(n(n(z)),n(z))),i(z,i(x,u)))).
585 [hyper,1,206,268] P(i(i(i(i(x,y),i(z,y)),u),i(i(n(x),x),u))).
664 [hyper,1,35,282] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
1090 [hyper,1,585,321] P(i(i(n(n(x)),n(x)),i(y,i(x,z)))).
1386 [hyper,1,288,664] P(i(i(i(x,y),z),i(i(x,i(n(y),y)),z))).
3515 [hyper,1,158,1090] P(i(i(i(x,y),z),i(n(x),z))).
4656 [hyper,1,1386,35] P(i(i(i(i(x,y),i(z,y)),i(n(u),u)),i(i(z,x),u))).
29263 [hyper,1,4656,3515] P(i(i(x,i(x,y)),i(x,y))).
29264 [binary,29263,20] $ANSWER(step_30).
  
length of proof is 28
------------ end of proof -------------
Starting on Level 9, last kept clause of level 8 is 39675.
------------ END OF SEARCH ------------
  
--------------- options ---------------
set(input_sos_first). set(sos_queue). clear(sos_stack). 
set(print_given). clear(binary_res). set(hyper_res). 
clear(ur_res). clear(para_into). clear(para_from). 
clear(demod_inf). set(para_from_left). set(para_from_right). 
set(para_into_left). set(para_into_right). clear(para_from_vars). 
clear(para_into_vars). clear(para_from_units_only). clear(para_into_units_only). 
clear(para_skip_skolem). clear(para_ones_rule). clear(para_all). 
clear(very_verbose). clear(order_eq). clear(sort_literals). 
clear(delete_identical_nested_skolem). set(for_sub). clear(unit_deletion). 
clear(print_kept). set(print_proofs). set(back_sub). 
set(print_back_sub). clear(factor). set(demod_history). 
clear(demod_linear). clear(demod_out_in). clear(dynamic_demod). 
clear(dynamic_demod_all). set(print_new_demod). clear(back_demod). 
set(print_back_demod). set(symbol_elim). clear(knuth_bendix). 
clear(lex_rpo). clear(dynamic_demod_lex_dep). clear(lex_order_vars). 
clear(for_sub_fpa). clear(no_fapl). clear(no_fanl). 
set(check_arity). clear(prolog_style_variables). clear(process_input). 
clear(simplify_fol). clear(bird_print). clear(free_all_mem). 
clear(atom_wt_max_args). clear(term_wt_max_args). clear(print_lists_at_end). 
clear(really_delete_clauses). clear(prog_synthesis). clear(ancestor_subsume). 
clear(new_functions). clear(linked_ur_res). clear(linked_ur_trace). 
clear(linked_sub_unit_usable). clear(linked_sub_unit_sos).
clear(index_for_back_demod). 
clear(linked_unit_del). clear(linked_target_all). clear(linked_hyper_res). 
clear(control_memory). set(order_history). clear(neg_hyper_res). 
clear(suppress_weight_warning). clear(display_terms). set(print_level). 
  
  
assign(report, 900). assign(max_seconds, 0). assign(max_gen, 0). 
assign(max_kept, 0). assign(max_given, 0). assign(max_mem, 128000). 
assign(max_literals, 0). assign(max_weight,20). assign(fpa_literals, 8). 
assign(fpa_terms, 8). assign(demod_limit, 100). assign(max_proofs, 0). 
assign(neg_weight, 0). assign(stats_level,2). assign(reduce_weight_limit, 0). 
assign(max_ur_depth, 5). assign(max_ur_deduction_size,20).
assign(max_distinct_vars, 4). 
assign(pick_given_ratio, -1). assign(random_ratio, -1). assign(random_seed, 1). 
assign(change_limit_after, 0). assign(new_max_weight, 0). assign(max_sos_size, 0). 
  
------------- memory usage ------------
784 mallocs of 32700 bytes each,25035.9 K.

type (bytes each)	gets	frees	in use	avail	bytes
sym_ent (  96)	131	0	131	0	12.3 K
term (  20)	472819081	472662484	156597	66	3059.8 K
rel (  20)	451241657	450994532	247125	66	4827.9 K
term_ptr (   8)	1246428	73236	1173192	0	9165.6 K
formula_ptr_2 (  28)	0	0	0	0	0.0 K
fpa_head (  12)	5860	117	5743	0	67.3 K
fpa_tree (  28)	735507	735480	27	34	1.7 K
context ( 776)	25043787	25043784	3	6	6.8 K
trail (  12)	42473200	42473197	3	7	0.1 K
imd_tree (  20)	14	0	14	0	0.3 K
imd_pos (2016)	167835301	167835301	0	1	2.0 K
is_tree (  12)	279485	8729	270756	0	3172.9 K
is_pos (1216)	215471952	215471952	0	10	11.9 K
fsub_pos (   8)	6872608	6872608	0	1	0.0 K
literal (  16)	17998482	17945388	53094	1	829.6 K
clause (  32)	17984659	17931625	53034	1	1657.3 K
list (  60)	8	4	4	1	0.3 K
clash_nd (  44)	13843	13842	1	6	0.3 K
clause_ptr (   8)	55418	2384	53034	0	414.3 K
int_ptr (   8)	76015790	75803798	211992	11	1656.3 K
link_node (  68)	0	0	0	0	0.0 K
ans_lit_node(  12)	0	0	0	0	0.0 K
formula_box( 148)	0	0	0	0	0.0 K
formula(  20)	0	0	0	0	0.0 K
formula_ptr(   8)	0	0	0	0	0.0 K
  
-------------- statistics -------------

clauses input	0
clauses given	6879
clauses generated	17984612
  (factors generated)	0
demod & eval rewrites	3570865
clauses wt,lit,sk delete	10605554
tautologies deleted	506449
clauses forward subsumed	6819618
  (subsumed by sos)	2359214
unit deletions	0
clauses kept	52990
empty clauses	10
clauses back subsumed	1861
usable size	6584
sos size	44557
demodulators size	5
Kbytes malloced	25035
  
----------- times (seconds) -----------

run time	22070.93
(run time  6 hr, 7 min, 50 sec)	
system time	5288.30
input time	0.25
  clausify time	0.00
hyper_res time	5995.93
pre_process time	14977.82
  demod time	7178.98
  weigh cl time	668.38
  for_sub time	2981.89
  unit_del timei0.00
  renumber time	3.96
  delete cl time	1923.22
  keep cl time	102.60
  print_cl time	0.00
  conflict time	13.51
post_process time	810.89
  back demod time	0.00
  back_sub time	664.71
  unindex time	144.20
lex_rpo time	0.00

The job finished   Mon Aug 17 17:00:27 1992

                Summary of Output 2B

----- OTTER 2.2xa+, January 1992 -----
The job began on cosmo.mcs.anl.gov, Mon Aug 17 08:08:05 1992
The command was "otter4++".
  
set(hyper_res).
assign(max_weight,20).
assign(max_proofs,0).
clear(print_kept).
assign(max_mem,128000).
assign(report,900).
assign(max_distinct_vars,4).
set(order_history).
set(input_sos_first).
set(print_level).
  
list(usable).
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
3 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).
4 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | -P(i(p,i(n(p),q))) | 
$ANSWER(step_allLuka_1_2_3).
8 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
9 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
end_of_list.
  
list(sos).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
end_of_list.
  
list(passive).
13 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
14 [] -P(i(i(n(p),p),p)) | $ANSWER(step_L2).
15 [] -P(i(p,i(n(p),q))) | $ANSWER(step_L3).
16 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
25 [] -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
27 [] -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
29 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
30 [] n(n(n(x)))=junk.
31 [] i(junk,x)=junk.
32 [] i(x,junk)=junk.
33 [] n(junk)=junk.
34 [] P(junk)=$T.
end_of_list.
  
given clause #1: (wt=-2147483647) 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
-----> EMPTY CLAUSE at   0.27 sec ----> 37 [hyper,7,10,11,12]
$ANSWER(step_allLuka_1_2_3).
Length of proof is 0.  Level of proof is 0.
---------------- PROOF ----------------
  
7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | 
$ANSWER(step_allLuka_1_2_3).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,7,10,11,12] $ANSWER(step_allLuka_1_2_3).
  
length of proof is 0
------------ end of proof -------------
----> UNIT CONFLICT at  17.32 sec ----> 625 [binary,624,16] $ANSWER(step_18).
Length of proof is 23.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
16 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
625 [binary,624,16] $ANSWER(step_18).
  
length of proof is 23
------------ end of proof -------------
----> UNIT CONFLICT at  17.60 sec ----> 641 [binary,640,17] $ANSWER(step_19).
Length of proof is 24.  Level of proof is 18.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
641 [binary,640,17] $ANSWER(step_19).
  
length of proof is 24
------------ end of proof -------------
----> UNIT CONFLICT at  39.60 sec ----> 1698 [binary,1697,18] $ANSWER(step_21).
Length of proof is 35.  Level of proof is 24.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1697 [hyper,1,35,1200] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1698 [binary,1697,18] $ANSWER(step_21).
  
length of proof is 35
------------ end of proof -------------
----> UNIT CONFLICT at  39.65 sec ----> 1714 [binary,1713,23] $ANSWER(step_39).
Length of proof is 40.  Level of proof is 24.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
52 [hyper,1,36,11] P(i(i(n(i(n(x),x)),i(n(x),x)),x)).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
175 [hyper,1,120,52] P(i(i(i(x,x),i(n(y),y)),y)).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
304 [hyper,1,59,175] P(i(i(i(n(i(x,x)),y),i(n(z),z)),z)).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
474 [hyper,1,35,304] P(i(i(n(x),n(i(y,y))),x)).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
503 [hyper,1,59,474] P(i(i(i(n(n(x)),y),n(i(z,z))),x)).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1713 [hyper,1,1200,503] P(i(n(n(x)),x)).
1714 [binary,1713,23] $ANSWER(step_39).
  
length of proof is 40
------------ end of proof -------------
----> UNIT CONFLICT at  39.78 sec ----> 1739 [binary,1738,19] $ANSWER(step_22).
Length of proof is 35.  Level of proof is 24.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1738 [hyper,1,1200,35] P(i(i(x,y),i(i(z,x),i(z,y)))).
1739 [binary,1738,19] $ANSWER(step_22).
  
length of proof is 35
------------ end of proof -------------
----> UNIT CONFLICT at  40.40 sec ----> 1821 [binary,1820,22] $ANSWER(step_37).
Length of proof is 36.  Level of proof is 25.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1736 [hyper,1,1200,39] P(i(n(x),i(x,y))).
1820 [hyper,1,10,1736] P(i(i(i(x,y),z),i(n(x),z))).
1821 [binary,1820,22] $ANSWER(step_37).
  
length of proof is 36
------------ end of proof -------------
----> UNIT CONFLICT at  40.93 sec ----> 1925 [binary,1924,24] $ANSWER(step_40).
Length of proof is 42.  Level of proof is 26.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
52 [hyper,1,36,11] P(i(i(n(i(n(x),x)),i(n(x),x)),x)).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
175 [hyper,1,120,52] P(i(i(i(x,x),i(n(y),y)),y)).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
304 [hyper,1,59,175] P(i(i(i(n(i(x,x)),y),i(n(z),z)),z)).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
474 [hyper,1,35,304] P(i(i(n(x),n(i(y,y))),x)).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
503 [hyper,1,59,474] P(i(i(i(n(n(x)),y),n(i(z,z))),x)).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1713 [hyper,1,1200,503] P(i(n(n(x)),x)).
1747 [hyper,1,1016,1713] P(i(i(x,n(x)),n(x))).
1924 [hyper,1,39,1747] P(i(x,n(n(x)))).
1925 [binary,1924,24] $ANSWER(step_40).
  
length of proof is 42
------------ end of proof -------------
----> UNIT CONFLICT at  42.70 sec ----> 2322 [binary,2321,20] $ANSWER(step_30).
Length of proof is 37.  Level of proof is 26.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1736 [hyper,1,1200,39] P(i(n(x),i(x,y))).
1802 [hyper,1,1016,1736] P(i(i(i(x,y),x),x)).
2321 [hyper,1,35,1802] P(i(i(x,i(x,y)),i(x,y))).
2322 [binary,2321,20] $ANSWER(step_30).
  
length of proof is 37
------------ end of proof -------------
----> UNIT CONFLICT at 155.36 sec ----> 15109 [binary,15108,26] $ANSWER(step_49).
Length of proof is 38.  Level of proof is 27.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1697 [hyper,1,35,1200] P(i(i(x,i(y,z)),i(y,i(x,z)))).
13309 [hyper,1,1697,1016] P(i(i(x,y),i(i(n(y),x),y))).
14726 [hyper,1,39,13309] P(i(x,i(i(n(y),n(x)),y))).
15108 [hyper,1,1697,14726] P(i(i(n(x),n(y)),i(y,x))).
15109 [binary,15108,26] $ANSWER(step_49).
  
length of proof is 38
------------ end of proof -------------
----> UNIT CONFLICT at 1251.81 sec ----> 80809 [binary,80808,25] $ANSWER(step_46).
Length of proof is 46.  Level of proof is 31.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
25 [] -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
48 [hyper,1,10,36] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1697 [hyper,1,35,1200] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1736 [hyper,1,1200,39] P(i(n(x),i(x,y))).
1738 [hyper,1,1200,35] P(i(i(x,y),i(i(z,x),i(z,y)))).
1802 [hyper,1,1016,1736] P(i(i(i(x,y),x),x)).
1820 [hyper,1,10,1736] P(i(i(i(x,y),z),i(n(x),z))).
17025 [hyper,1,1738,1802] P(i(i(x,i(i(y,z),y)),i(x,y))).
50658 [hyper,1,35,17025] P(i(i(i(x,y),z),i(i(z,x),x))).
75070 [hyper,1,1697,50658] P(i(i(x,y),i(i(i(y,z),x),y))).
79753 [hyper,1,1820,75070] P(i(n(x),i(i(i(y,z),x),y))).
80273 [hyper,1,1697,79753] P(i(i(i(x,y),z),i(n(z),x))).
80808 [hyper,1,48,80273] P(i(i(x,y),i(n(y),n(x)))).
80809 [binary,80808,25] $ANSWER(step_46).
  
length of proof is 46
------------ end of proof -------------
----> UNIT CONFLICT at 1901.86 sec ----> 109698 [binary,109697,27] $ANSWER(step_54).
Length of proof is 44.  Level of proof is 30.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
27 [] -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
48 [hyper,1,10,36] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1697 [hyper,1,35,1200] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1736 [hyper,1,1200,39] P(i(n(x),i(x,y))).
1738 [hyper,1,1200,35] P(i(i(x,y),i(i(z,x),i(z,y)))).
1802 [hyper,1,1016,1736] P(i(i(i(x,y),x),x)).
17025 [hyper,1,1738,1802] P(i(i(x,i(i(y,z),y)),i(x,y))).
50658 [hyper,1,35,17025] P(i(i(i(x,y),z),i(i(z,x),x))).
75079 [hyper,1,35,50658] P(i(i(x,y),i(i(i(x,z),y),y))).
86937 [hyper,1,1697,75079] P(i(i(i(x,y),z),i(i(x,z),z))).
109697 [hyper,1,48,86937] P(i(i(x,y),i(i(n(x),y),y))).
109698 [binary,109697,27] $ANSWER(step_54).
  
length of proof is 44
------------ end of proof -------------
-----> EMPTY CLAUSE at 1904.94 sec ----> 109706
[hyper,3,624,1697,1738,12,109697,2321] $ANSWER(step_allHilbert_18_21_22_3_54_30).
Length of proof is 45.  Level of proof is 30.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
35 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
36 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
39 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
48 [hyper,1,10,36] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
59 [hyper,1,10,39] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
62 [hyper,1,39,11] P(i(x,x)).
63 [hyper,1,39,10] P(i(x,i(i(y,z),i(n(x),z)))).
64 [hyper,1,12,62] P(i(n(i(x,x)),y)).
67 [hyper,1,10,64] P(i(i(x,y),i(n(i(z,z)),y))).
86 [hyper,1,10,63] P(i(i(i(i(x,y),i(n(z),y)),u),i(z,u))).
91 [hyper,1,39,67] P(i(x,i(n(i(y,y)),z))).
95 [hyper,1,10,91] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
110 [hyper,1,95,11] P(i(x,i(y,y))).
116 [hyper,1,10,110] P(i(i(i(x,x),y),i(z,y))).
120 [hyper,1,10,116] P(i(i(i(x,y),z),i(i(i(u,u),y),z))).
123 [hyper,1,116,36] P(i(x,i(i(n(y),y),y))).
131 [hyper,1,10,123] P(i(i(i(i(n(x),x),x),y),i(z,y))).
169 [hyper,1,131,120] P(i(x,i(i(i(y,y),z),z))).
186 [hyper,1,10,169] P(i(i(i(i(i(x,x),y),y),z),i(u,z))).
314 [hyper,1,59,10] P(i(i(i(n(x),y),z),i(i(z,u),i(x,u)))).
378 [hyper,1,86,186] P(i(x,i(y,i(n(x),z)))).
389 [hyper,1,10,378] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
485 [hyper,1,35,131] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
598 [hyper,1,485,485] P(i(x,i(i(y,i(n(z),z)),i(y,z)))).
599 [hyper,1,389,485] P(i(x,i(y,i(z,x)))).
617 [hyper,1,485,599] P(i(x,i(y,i(z,y)))).
624 [hyper,1,617,617] P(i(x,i(y,x))).
628 [hyper,1,314,617] P(i(i(i(x,i(y,x)),z),i(u,z))).
640 [hyper,1,10,624] P(i(i(i(x,y),z),i(y,z))).
780 [hyper,1,485,628] P(i(x,i(i(i(y,i(z,y)),u),u))).
821 [hyper,1,780,780] P(i(i(i(x,i(y,x)),z),z)).
1000 [hyper,1,821,598] P(i(i(x,i(n(y),y)),i(x,y))).
1016 [hyper,1,35,1000] P(i(i(n(x),y),i(i(y,x),x))).
1075 [hyper,1,640,1016] P(i(x,i(i(x,y),y))).
1200 [hyper,1,10,1075] P(i(i(i(i(x,y),y),z),i(x,z))).
1697 [hyper,1,35,1200] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1736 [hyper,1,1200,39] P(i(n(x),i(x,y))).
1738 [hyper,1,1200,35] P(i(i(x,y),i(i(z,x),i(z,y)))).
1802 [hyper,1,1016,1736] P(i(i(i(x,y),x),x)).
2321 [hyper,1,35,1802] P(i(i(x,i(x,y)),i(x,y))).
17025 [hyper,1,1738,1802] P(i(i(x,i(i(y,z),y)),i(x,y))).
50658 [hyper,1,35,17025] P(i(i(i(x,y),z),i(i(z,x),x))).
75079 [hyper,1,35,50658] P(i(i(x,y),i(i(i(x,z),y),y))).
86937 [hyper,1,1697,75079] P(i(i(i(x,y),z),i(i(x,z),z))).
109697 [hyper,1,48,86937] P(i(i(x,y),i(i(n(x),y),y))).
109706 [hyper,3,624,1697,1738,12,109697,2321]
$ANSWER(step_allHilbert_18_21_22_3_54_30).
  
length of proof is 45
------------ end of proof -------------
search stopped in tp_alloc by max_mem option.
------------ END OF SEARCH ------------
  
--------------- options ---------------
set(input_sos_first). clear(sos_queue). clear(sos_stack). 
set(print_given). clear(binary_res). set(hyper_res). 
clear(ur_res). clear(para_into). clear(para_from). 
clear(demod_inf). set(para_from_left). set(para_from_right). 
set(para_into_left). set(para_into_right). clear(para_from_vars). 
clear(para_into_vars). clear(para_from_units_only). clear(para_into_units_only). 
clear(para_skip_skolem). clear(para_ones_rule). clear(para_all). 
clear(very_verbose). clear(order_eq). clear(sort_literals). 
clear(delete_identical_nested_skolem). set(for_sub). clear(unit_deletion). 
clear(print_kept). set(print_proofs). set(back_sub). 
set(print_back_sub). clear(factor). set(demod_history). 
clear(demod_linear). clear(demod_out_in). clear(dynamic_demod). 
clear(dynamic_demod_all). set(print_new_demod). clear(back_demod). 
set(print_back_demod). set(symbol_elim). clear(knuth_bendix). 
clear(lex_rpo). clear(dynamic_demod_lex_dep). clear(lex_order_vars). 
clear(for_sub_fpa). clear(no_fapl). clear(no_fanl). 
set(check_arity). clear(prolog_style_variables). clear(process_input). 
clear(simplify_fol). clear(bird_print). clear(free_all_mem). 
clear(atom_wt_max_args). clear(term_wt_max_args). clear(print_lists_at_end). 
clear(really_delete_clauses). clear(prog_synthesis). clear(ancestor_subsume). 
clear(new_functions). clear(linked_ur_res). clear(linked_ur_trace). 
clear(linked_sub_unit_usable). clear(linked_sub_unit_sos).
clear(index_for_back_demod). 
clear(linked_unit_del). clear(linked_target_all). clear(linked_hyper_res). 
clear(control_memory). set(order_history). clear(neg_hyper_res). 
clear(suppress_weight_warning). clear(display_terms). set(print_level). 
  
  
assign(report, 900). assign(max_seconds, 0). assign(max_gen, 0). 
assign(max_kept, 0). assign(max_given, 0). assign(max_mem, 128000). 
assign(max_literals, 0). assign(max_weight,20). assign(fpa_literals, 8). 
assign(fpa_terms, 8). assign(demod_limit, 100). assign(max_proofs, 0). 
assign(neg_weight, 0). assign(stats_level,2). assign(reduce_weight_limit, 0). 
assign(max_ur_depth, 5). assign(max_ur_deduction_size,20).
assign(max_distinct_vars, 4). 
assign(pick_given_ratio, -1). assign(random_ratio, -1). assign(random_seed, 1). 
assign(change_limit_after, 0). assign(new_max_weight, 0). assign(max_sos_size, 0). 
  
  
------------- memory usage ------------
4008 mallocs of 32700 bytes each, 127989.8 K.
  type (bytes each)        gets      frees     in use      avail      bytes
sym_ent (  96)              129          0        129          0     12.1 K
term (  20)            91959436   91077258     882178          2  17230.1 K
rel (  20)             85431755   84156145    1275610          0  24914.3 K
term_ptr (   8)         5820213      60932    5759281          0  44994.4 K
formula_ptr_2 (  28)          0          0          0          0      0.0 K
fpa_head (  12)            8097         36       8061          0     94.5 K
fpa_tree (  28)         2462391    2462373         18         69      2.4 K
context ( 776)          9310961    9310958          3          6      6.8 K
trail (  12)           20917626   20917622          4         10      0.2 K
imd_tree (  20)              14          0         14          0      0.3 K
imd_pos (2016)         30454147   30454147          0          1      2.0 K
is_tree (  12)          1280937       6590    1274347          0  14933.8 K
is_pos (1216)          41244584   41244584          0         10     11.9 K
fsub_pos (   8)         3087815    3087815          0          1      0.0 K
literal (  16)          5322314    5024330     297984          0   4656.0 K
clause (  32)           5315271    5017347     297924          0   9310.1 K
list (  60)                   8          4          4          1      0.3 K
clash_nd (  44)            7121       7120          1          6      0.3 K
clause_ptr (   8)        300735       2812     297923          0   2327.5 K
int_ptr (   8)         22691469   21499916    1191553          0   9309.0 K
link_node (  68)              0          0          0          0      0.0 K
ans_lit_node(  12)            0          0          0          0      0.0 K
formula_box( 148)             0          0          0          0      0.0 K
formula(  20)                 0          0          0          0      0.0 K
formula_ptr(   8)             0          0          0          0      0.0 K
  
-------------- statistics -------------
clauses input                  0
clauses given               3736
clauses generated        5315221
  (factors generated)          0
demod & eval rewrites    1200143
clauses wt,lit,sk delete 1997003
tautologies deleted       230401
clauses forward subsumed 2789939
  (subsumed by sos)       312628
unit deletions                 0
clauses kept              297876
empty clauses                 13
clauses back subsumed       1757
usable size                 3712
sos size                  292419
demodulators size              5
Kbytes malloced           127989
  
----------- times (seconds) -----------
run time         15699.88                   (run time  4 hr,21 min, 39 sec)
system time       2277.57
input time           0.23
  clausify time      0.00
hyper_res time    1354.84
pre_process time  5310.94
  demod time      1480.73
  weigh cl time    244.79
  for_sub time     694.99
  unit_del time      0.00
  renumber time     24.52
  delete cl time   422.75
  keep cl time    1799.98
  print_cl time      0.00
  conflict time     74.83
post_process time 8263.41
  back demod time    0.00
  back_sub time   7650.18
  unindex time     603.54
lex_rpo time         0.00
The job finished        Mon Aug 17 14:26:48 1992

          Input File 5

%  luka completeness of 123 exps.
set(hyper_res).
% assign(reduce_weight_limit, 010024).
assign(max_weight,20).
% set(control_memory).
assign(max_proofs, 0).
clear(print_kept).
% set(very_verbose).
% set(ancestor_subsume).
% clear(back_sub).
% assign(max_seconds, 1800).
assign(max_mem, 128000).
assign(report, 900).
assign(max_distinct_vars, 4).
% assign(pick_given_ratio, 3).
set(order_history).
set(input_sos_first).
% set(sos_queue).
set(print_level).
  
weight_list(pick_and_purge).
%  Following are 68 theses suggested by Scott.
%  They are in reverse order from those numbered by Lukasiewicz 4 to 71.
weight(P(n(i(i(x,x),n(i(y,y))))),2).
weight(P(i(x,i(y,n(i(x,n(y)))))),2).
weight(P(i(x,i(n(y),n(i(x,y))))),2).
weight(P(i(n(i(x,n(y))),y)),2).
weight(P(i(n(i(x,y)),n(y))),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(i(n(x),n(i(y,y))),x)),2).
weight(P(i(n(i(x,x)),y)),2).
weight(P(i(x,i(y,y))),2).
weight(P(i(i(n(n(x)),y),i(x,y))),2).
weight(P(i(i(x,y),i(i(z,y),i(i(n(x),z),y)))),2).
weight(P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))),2).
weight(P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))),2).
weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),2).
weight(P(i(i(n(x),y),i(i(x,z),i(i(z,y),y)))),2).
weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),2).
weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),2).
weight(P(i(i(x,y),i(i(n(x),y),y))),2).
weight(P(i(i(n(x),y),i(i(x,y),y))),2).
weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),2).
weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),2).
weight(P(i(i(i(n(x),y),z),i(i(n(y),x),z))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(x,n(y)),i(y,n(x)))),2).
weight(P(i(i(x,y),i(n(y),n(x)))),2).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
weight(P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))),2).
weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),2).
weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),2).
weight(P(i(i(x,y),i(n(n(x)),y))),2).
weight(P(i(x,n(n(x)))),2).
weight(P(i(n(n(x)),x)),2).
weight(P(i(i(x,n(x)),n(x))),2).
weight(P(i(i(i(x,y),z),i(n(x),z))),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))),2).
weight(P(i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))),2).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))),2).
weight(P(i(i(x,i(x,y)),i(x,y))),2).
weight(P(i(i(i(x,y),z),i(i(x,z),z))),2).
weight(P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))),2).
weight(P(i(i(i(x,y),y),i(i(y,x),x))),2).
weight(P(i(i(i(x,y),z),i(i(z,x),x))),2).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))),2).
weight(P(i(i(i(x,y),x),x)),2).
weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2).
weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(x,i(y,x))),2).
weight(P(i(x,i(i(y,x),x))),2).
weight(P(i(x,x)),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
weight(P(i(x,i(i(n(y),y),y))),2).
weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2).
weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))),2).
weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2).
end_of_list.
  
list(usable).
-P(i(x,y)) | -P(x) | P(y).
  
%  The following disjunctions are known axiom systems.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
$ANSWER(step_allFrege_18_35_39_40_46_21).  % 21 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
  
-P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
  
end_of_list.
  
list(sos).
%  The following three are Luka, 1 2 3.
P(i(i(x,y),i(i(y,z),i(x,z)))).
P(i(i(n(x),x),x)).
P(i(x,i(n(x),y))).
  
%  The following are from Frege, 18 35 21 46 39 40, with 21 dependent.
% P(i(x,i(y,x))).  %  axiom F1.
% P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).  %  axiom F2.
% P(i(i(x,i(y,z)),i(y,i(x,z)))).  %  axiom F3.
% P(i(i(x,y),i(n(y),n(x)))).  %  axiom F4.
% P(i(n(n(x)),x)).  %  axiom F5.
% P(i(x,n(n(x)))).  %  axiom f6.
end_of_list.
  
list(passive).
-P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
-P(i(i(n(p),p),p)) | $ANSWER(step_L2).
-P(i(p,i(n(p),q))) | $ANSWER(step_L3).
-P(i(p,i(q,p))) | $ANSWER(step_18).
-P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
-P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
-P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
-P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
-P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
-P(i(n(n(p)),p)) | $ANSWER(step_39).
-P(i(p,n(n(p)))) | $ANSWER(step_40).
-P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
-P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
% (n(n(x)) = junk).
(n(n(n(x))) = junk).
(i(i(x,x),y) = junk).
(i(y,i(x,x)) = junk).
(i(junk,x) = junk).
(i(x,junk) = junk).
(n(junk) = junk).
(P(junk) = $T).
end_of_list.

                      Summary of Experiment 5

----- OTTER 2.2xa+, January 1992 -----
The job began on cosmo.mcs.anl.gov, Wed Aug 19 16:57:51 1992
The command was "otter4++".
  
set(hyper_res).
assign(max_weight,20).
assign(max_proofs,0).
clear(print_kept).
assign(max_mem,128000).
assign(report,900).
assign(max_distinct_vars,4).
set(order_history).
set(input_sos_first).
set(print_level).
  
weight_list(pick_and_purge).
weight(P(n(i(i(x,x),n(i(y,y))))),2).
weight(P(i(x,i(y,n(i(x,n(y)))))),2).
weight(P(i(x,i(n(y),n(i(x,y))))),2).
weight(P(i(n(i(x,n(y))),y)),2).
weight(P(i(n(i(x,y)),n(y))),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(i(n(x),n(i(y,y))),x)),2).
weight(P(i(n(i(x,x)),y)),2).
weight(P(i(x,i(y,y))),2).
weight(P(i(i(n(n(x)),y),i(x,y))),2).
weight(P(i(i(x,y),i(i(z,y),i(i(n(x),z),y)))),2).
weight(P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))),2).
weight(P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))),2).
weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),2).
weight(P(i(i(n(x),y),i(i(x,z),i(i(z,y),y)))),2).
weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),2).
weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),2).
weight(P(i(i(x,y),i(i(n(x),y),y))),2).
weight(P(i(i(n(x),y),i(i(x,y),y))),2).
weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),2).
weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),2).
weight(P(i(i(i(n(x),y),z),i(i(n(y),x),z))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(x,n(y)),i(y,n(x)))),2).
weight(P(i(i(x,y),i(n(y),n(x)))),2).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
weight(P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))),2).
weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),2).
weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),2).
weight(P(i(i(x,y),i(n(n(x)),y))),2).
weight(P(i(x,n(n(x)))),2).
weight(P(i(n(n(x)),x)),2).
weight(P(i(i(x,n(x)),n(x))),2).
weight(P(i(i(i(x,y),z),i(n(x),z))),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))),2).
weight(P(i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))),2).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))),2).
weight(P(i(i(x,i(x,y)),i(x,y))),2).
weight(P(i(i(i(x,y),z),i(i(x,z),z))),2).
weight(P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))),2).
weight(P(i(i(i(x,y),y),i(i(y,x),x))),2).
weight(P(i(i(i(x,y),z),i(i(z,x),x))),2).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))),2).
weight(P(i(i(i(x,y),x),x)),2).
weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2).
weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(x,i(y,x))),2).
weight(P(i(x,i(i(y,x),x))),2).
weight(P(i(x,x)),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
weight(P(i(x,i(i(n(y),y),y))),2).
weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2).
weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))),2).
weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2).
end_of_list.
  
list(usable).
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
3 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).
4 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | -P(i(p,i(n(p),q))) | 
$ANSWER(step_allLuka_1_2_3).
8 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
9 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
end_of_list.
  
list(sos).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
end_of_list.
  
list(passive).
13 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
14 [] -P(i(i(n(p),p),p)) | $ANSWER(step_L2).
15 [] -P(i(p,i(n(p),q))) | $ANSWER(step_L3).
16 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
25 [] -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
27 [] -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
29 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
30 [] n(n(n(x)))=junk.
31 [] i(i(x,x),y)=junk.
32 [] i(y,i(x,x))=junk.
33 [] i(junk,x)=junk.
34 [] i(x,junk)=junk.
35 [] n(junk)=junk.
36 [] P(junk)=$T.
end_of_list.
  
given clause #1: (wt=-2147483647) 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
-----> EMPTY CLAUSE at   0.49 sec ----> 39 [hyper,7,10,11,12]
$ANSWER(step_allLuka_1_2_3).
Length of proof is 0.  Level of proof is 0.
---------------- PROOF ----------------
  
7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
39 [hyper,7,10,11,12] $ANSWER(step_allLuka_1_2_3).
  
length of proof is 0
------------ end of proof -------------
----> UNIT CONFLICT at   7.93 sec ----> 486 [binary,485,26] $ANSWER(step_49).
Length of proof is 13.  Level of proof is 8.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
486 [binary,485,26] $ANSWER(step_49).
  
length of proof is 13
------------ end of proof -------------
----> UNIT CONFLICT at   9.21 sec ----> 618 [binary,617,16] $ANSWER(step_18).
Length of proof is 14.  Level of proof is 9.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
16 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
618 [binary,617,16] $ANSWER(step_18).
  
length of proof is 14
------------ end of proof -------------
----> UNIT CONFLICT at   9.97 sec ----> 666 [binary,665,17] $ANSWER(step_19).
Length of proof is 15.  Level of proof is 10.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
666 [binary,665,17] $ANSWER(step_19).
  
length of proof is 15
------------ end of proof -------------
----> UNIT CONFLICT at  11.13 sec ----> 812 [binary,811,18] $ANSWER(step_21).
Length of proof is 23.  Level of proof is 12.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
812 [binary,811,18] $ANSWER(step_21).
  
length of proof is 23
------------ end of proof -------------
----> UNIT CONFLICT at  11.80 sec ----> 910 [binary,909,22] $ANSWER(step_37).
Length of proof is 17.  Level of proof is 12.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
909 [hyper,1,10,712] P(i(i(i(x,y),z),i(n(x),z))).
910 [binary,909,22] $ANSWER(step_37).
  
length of proof is 17
------------ end of proof -------------
----> UNIT CONFLICT at  12.18 sec ----> 965 [binary,964,19] $ANSWER(step_22).
Length of proof is 24.  Level of proof is 13.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
965 [binary,964,19] $ANSWER(step_22).
  
length of proof is 24
------------ end of proof -------------
----> UNIT CONFLICT at  12.70 sec ----> 1017 [binary,1016,20] $ANSWER(step_30).
Length of proof is 20.  Level of proof is 13.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
1016 [hyper,1,37,890] P(i(i(x,i(x,y)),i(x,y))).
1017 [binary,1016,20] $ANSWER(step_30).
  
length of proof is 20
------------ end of proof -------------
----> UNIT CONFLICT at  12.94 sec ----> 1053 [binary,1052,23] $ANSWER(step_39).
Length of proof is 20.  Level of proof is 13.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
1052 [hyper,1,891,60] P(i(n(n(x)),x)).
1053 [binary,1052,23] $ANSWER(step_39).
  
length of proof is 20
------------ end of proof -------------
----> UNIT CONFLICT at  16.88 sec ----> 1608 [binary,1607,24] $ANSWER(step_40).
Length of proof is 22.  Level of proof is 14.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
50 [hyper,1,10,38] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
1011 [hyper,1,50,890] P(i(i(x,n(x)),n(x))).
1607 [hyper,1,41,1011] P(i(x,n(n(x)))).
1608 [binary,1607,24] $ANSWER(step_40).
  
length of proof is 22
------------ end of proof -------------
----> UNIT CONFLICT at  18.20 sec ----> 1802 [binary,1801,25] $ANSWER(step_46).
Length of proof is 21.  Level of proof is 14.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
25 [] -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
900 [hyper,1,65,712] P(i(i(x,y),i(n(n(x)),y))).
1083 [hyper,1,10,900] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))).
1801 [hyper,1,1083,891] P(i(i(x,y),i(n(y),n(x)))).
1802 [binary,1801,25] $ANSWER(step_46).
  
length of proof is 21
------------ end of proof -------------
----> UNIT CONFLICT at  27.49 sec ----> 2852 [binary,2851,27] $ANSWER(step_54).
Length of proof is 25.  Level of proof is 15.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
27 [] -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
900 [hyper,1,65,712] P(i(i(x,y),i(n(n(x)),y))).
1041 [hyper,1,10,891] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
1083 [hyper,1,10,900] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))).
1678 [hyper,1,1041,481] P(i(i(n(x),y),i(i(x,y),y))).
2851 [hyper,1,1083,1678] P(i(i(x,y),i(i(n(x),y),y))).
2852 [binary,2851,27] $ANSWER(step_54).
  
length of proof is 25
------------ end of proof -------------
-----> EMPTY CLAUSE at  42.66 sec ----> 4289
[hyper,3,617,811,964,12,2851,1016] $ANSWER(step_allHilbert_18_21_22_3_54_30).
Length of proof is 37.  Level of proof is 15.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
900 [hyper,1,65,712] P(i(i(x,y),i(n(n(x)),y))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1016 [hyper,1,37,890] P(i(i(x,i(x,y)),i(x,y))).
1041 [hyper,1,10,891] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
1083 [hyper,1,10,900] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))).
1678 [hyper,1,1041,481] P(i(i(n(x),y),i(i(x,y),y))).
2851 [hyper,1,1083,1678] P(i(i(x,y),i(i(n(x),y),y))).
4289 [hyper,3,617,811,964,12,2851,1016] $ANSWER(step_allHilbert_18_21_22_3_54_30).
  
length of proof is 37
------------ end of proof -------------
----> UNIT CONFLICT at  46.19 sec ----> 4599 [binary,4598,28] $ANSWER(step_59).
Length of proof is 36.  Level of proof is 16.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1041 [hyper,1,10,891] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
1678 [hyper,1,1041,481] P(i(i(n(x),y),i(i(x,y),y))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
2879 [hyper,1,10,1678] P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))).
4598 [hyper,1,2879,2412] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
4599 [binary,4598,28] $ANSWER(step_59).
  
length of proof is 36
------------ end of proof -------------
----> UNIT CONFLICT at  64.71 sec ----> 6005 [binary,6004,21] $ANSWER(step_35).
Length of proof is 35.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
930 [hyper,1,10,811] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1016 [hyper,1,37,890] P(i(i(x,i(x,y)),i(x,y))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
3859 [hyper,1,2412,1016] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
6004 [hyper,1,930,3859] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
6005 [binary,6004,21] $ANSWER(step_35).
  
length of proof is 35
------------ end of proof -------------
-----> EMPTY CLAUSE at  75.80 sec ----> 6819 [hyper,5,665,909,4598]
$ANSWER(step_allLuka_x_19_37_59).
Length of proof is 37.  Level of proof is 16.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
909 [hyper,1,10,712] P(i(i(i(x,y),z),i(n(x),z))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1041 [hyper,1,10,891] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
1678 [hyper,1,1041,481] P(i(i(n(x),y),i(i(x,y),y))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
2879 [hyper,1,10,1678] P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))).
4598 [hyper,1,2879,2412] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
6819 [hyper,5,665,909,4598] $ANSWER(step_allLuka_x_19_37_59).
  
length of proof is 37
------------ end of proof -------------
----> UNIT CONFLICT at  75.95 sec ----> 6831 [binary,6830,29] $ANSWER(step_60).
Length of proof is 37.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
29 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1041 [hyper,1,10,891] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
1678 [hyper,1,1041,481] P(i(i(n(x),y),i(i(x,y),y))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
2879 [hyper,1,10,1678] P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))).
4598 [hyper,1,2879,2412] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
6830 [hyper,1,964,4598] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))).
6831 [binary,6830,29] $ANSWER(step_60).
  
length of proof is 37
------------ end of proof -------------
-----> EMPTY CLAUSE at  99.16 sec ----> 8547
[hyper,9,60,617,811,890,6004,1052,1607,485]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
Length of proof is 41.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
50 [hyper,1,10,38] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
930 [hyper,1,10,811] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1011 [hyper,1,50,890] P(i(i(x,n(x)),n(x))).
1016 [hyper,1,37,890] P(i(i(x,i(x,y)),i(x,y))).
1052 [hyper,1,891,60] P(i(n(n(x)),x)).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
1607 [hyper,1,41,1011] P(i(x,n(n(x)))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
3859 [hyper,1,2412,1016] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
6004 [hyper,1,930,3859] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
8547 [hyper,9,60,617,811,890,6004,1052,1607,485]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
  
length of proof is 41
------------ end of proof -------------
-----> EMPTY CLAUSE at  99.20 sec ----> 8548
[hyper,8,60,617,811,890,6004,1052,1607,1801]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
Length of proof is 44.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
8 [] -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
50 [hyper,1,10,38] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
900 [hyper,1,65,712] P(i(i(x,y),i(n(n(x)),y))).
930 [hyper,1,10,811] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1011 [hyper,1,50,890] P(i(i(x,n(x)),n(x))).
1016 [hyper,1,37,890] P(i(i(x,i(x,y)),i(x,y))).
1052 [hyper,1,891,60] P(i(n(n(x)),x)).
1083 [hyper,1,10,900] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
1607 [hyper,1,41,1011] P(i(x,n(n(x)))).
1801 [hyper,1,1083,891] P(i(i(x,y),i(n(y),n(x)))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
3859 [hyper,1,2412,1016] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
6004 [hyper,1,930,3859] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
8548 [hyper,8,60,617,811,890,6004,1052,1607,1801]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
  
length of proof is 44
------------ end of proof -------------
-----> EMPTY CLAUSE at  99.25 sec ----> 8549 [hyper,4,617,6004,485]
$ANSWER(step_allBEH_Church_FL_18_35_49).
Length of proof is 35.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
4 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
930 [hyper,1,10,811] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1016 [hyper,1,37,890] P(i(i(x,i(x,y)),i(x,y))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
3859 [hyper,1,2412,1016] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
6004 [hyper,1,930,3859] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
8549 [hyper,4,617,6004,485] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 35
------------ end of proof -------------
-----> EMPTY CLAUSE at  99.29 sec ----> 8550
[hyper,2,617,6004,1052,1607,1801,811]
$ANSWER(step_allFrege_18_35_39_40_46_21).
Length of proof is 44.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
50 [hyper,1,10,38] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
890 [hyper,1,481,712] P(i(i(i(x,y),x),x)).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
900 [hyper,1,65,712] P(i(i(x,y),i(n(n(x)),y))).
930 [hyper,1,10,811] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1011 [hyper,1,50,890] P(i(i(x,n(x)),n(x))).
1016 [hyper,1,37,890] P(i(i(x,i(x,y)),i(x,y))).
1052 [hyper,1,891,60] P(i(n(n(x)),x)).
1083 [hyper,1,10,900] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
1607 [hyper,1,41,1011] P(i(x,n(n(x)))).
1801 [hyper,1,1083,891] P(i(i(x,y),i(n(y),n(x)))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
3859 [hyper,1,2412,1016] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
6004 [hyper,1,930,3859] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
8550 [hyper,2,617,6004,1052,1607,1801,811]
$ANSWER(step_allFrege_18_35_39_40_46_21).
  
length of proof is 44
------------ end of proof -------------
-----> EMPTY CLAUSE at 106.26 sec ----> 8893 [hyper,6,665,909,6830]
$ANSWER(step_allWos_x_19_37_60).
Length of proof is 38.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) |
$ANSWER(step_allWos_x_19_37_60).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
51 [hyper,1,38,12] P(i(i(n(x),x),i(n(x),y))).
55 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
57 [hyper,1,10,41] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))).
60 [hyper,1,41,11] P(i(x,x)).
65 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
72 [hyper,1,10,51] P(i(i(i(n(x),y),z),i(i(n(x),x),z))).
118 [hyper,1,55,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
309 [hyper,1,65,118] P(i(i(i(i(n(x),x),x),y),i(z,y))).
377 [hyper,1,37,309] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
417 [hyper,1,37,377] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
440 [hyper,1,72,417] P(i(i(n(x),x),i(y,i(i(z,x),x)))).
441 [hyper,1,65,417] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
452 [hyper,1,65,440] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))).
463 [hyper,1,37,441] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
481 [hyper,1,441,60] P(i(i(n(x),y),i(i(y,x),x))).
485 [hyper,1,441,41] P(i(i(n(x),n(y)),i(y,x))).
578 [hyper,1,57,481] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))).
617 [hyper,1,41,485] P(i(x,i(y,x))).
632 [hyper,1,452,578] P(i(i(n(x),x),i(i(x,y),y))).
665 [hyper,1,10,617] P(i(i(i(x,y),z),i(y,z))).
697 [hyper,1,41,632] P(i(x,i(i(x,y),y))).
712 [hyper,1,665,485] P(i(n(x),i(x,y))).
811 [hyper,1,44,697] P(i(i(x,i(y,z)),i(y,i(x,z)))).
891 [hyper,1,463,712] P(i(i(n(x),y),i(n(y),x))).
909 [hyper,1,10,712] P(i(i(i(x,y),z),i(n(x),z))).
964 [hyper,1,811,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
1041 [hyper,1,10,891] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
1480 [hyper,1,44,964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
1678 [hyper,1,1041,481] P(i(i(n(x),y),i(i(x,y),y))).
2412 [hyper,1,1480,964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
2879 [hyper,1,10,1678] P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))).
4598 [hyper,1,2879,2412] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
6830 [hyper,1,964,4598] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))).
8893 [hyper,6,665,909,6830] $ANSWER(step_allWos_x_19_37_60).
  
length of proof is 38
------------ end of proof -------------
------------ END OF SEARCH ------------
  
--------------- options ---------------
set(input_sos_first). clear(sos_queue). clear(sos_stack). 
set(print_given). clear(binary_res). set(hyper_res). 
clear(ur_res). clear(para_into). clear(para_from). 
clear(demod_inf). set(para_from_left). set(para_from_right). 
set(para_into_left). set(para_into_right). clear(para_from_vars). 
clear(para_into_vars). clear(para_from_units_only). clear(para_into_units_only). 
clear(para_skip_skolem). clear(para_ones_rule). clear(para_all). 
clear(very_verbose). clear(order_eq). clear(sort_literals). 
clear(delete_identical_nested_skolem). set(for_sub). clear(unit_deletion). 
clear(print_kept). set(print_proofs). set(back_sub). 
set(print_back_sub). clear(factor). set(demod_history). 
clear(demod_linear). clear(demod_out_in). clear(dynamic_demod). 
clear(dynamic_demod_all). set(print_new_demod). clear(back_demod). 
set(print_back_demod). set(symbol_elim). clear(knuth_bendix). 
clear(lex_rpo). clear(dynamic_demod_lex_dep). clear(lex_order_vars). 
clear(for_sub_fpa). clear(no_fapl). clear(no_fanl). 
set(check_arity). clear(prolog_style_variables). clear(process_input). 
clear(simplify_fol). clear(bird_print). clear(free_all_mem). 
clear(atom_wt_max_args). clear(term_wt_max_args). clear(print_lists_at_end). 
clear(really_delete_clauses). clear(prog_synthesis). clear(ancestor_subsume). 
clear(new_functions). clear(linked_ur_res). clear(linked_ur_trace). 
clear(linked_sub_unit_usable). clear(linked_sub_unit_sos).
clear(index_for_back_demod). 
clear(linked_unit_del). clear(linked_target_all). clear(linked_hyper_res). 
clear(control_memory). set(order_history). clear(neg_hyper_res). 
clear(suppress_weight_warning). clear(display_terms). set(print_level). 
  
  
assign(report, 900). assign(max_seconds, 0). assign(max_gen, 0). 
assign(max_kept, 0). assign(max_given, 0). assign(max_mem, 128000). 
assign(max_literals, 0). assign(max_weight,20). assign(fpa_literals, 8). 
assign(fpa_terms, 8). assign(demod_limit, 100). assign(max_proofs, 0). 
assign(neg_weight, 0). assign(stats_level,2). assign(reduce_weight_limit, 0). 
assign(max_ur_depth, 5). assign(max_ur_deduction_size,20).
assign(max_distinct_vars, 4). 
assign(pick_given_ratio, -1). assign(random_ratio, -1). assign(random_seed, 1). 
assign(change_limit_after, 0). assign(new_max_weight, 0). assign(max_sos_size, 0). 
  
  
------------- memory usage ------------
144 mallocs of 32700 bytes each, 4598.4 K.
  type (bytes each)        gets      frees     in use      avail      bytes
sym_ent (  96)              136          0        136          0     12.8 K
term (  20)             1105676    1074955      30721         29    600.6 K
rel (  20)              1045080     996558      48522         27    948.2 K
term_ptr (   8)          203665      11316     192349          0   1502.7 K
formula_ptr_2 (  28)          0          0          0          0      0.0 K
fpa_head (  12)            2383         23       2360          0     27.7 K
fpa_tree (  28)          114226     114226          0         94      2.6 K
context ( 776)           106743     106743          0         10      7.6 K
trail (  12)             426761     426761          0         15      0.2 K
imd_tree (  20)              21          0         21          0      0.4 K
imd_pos (2016)           769302     769302          0          3      5.9 K
is_tree (  12)            51281       1592      49689          0    582.3 K
is_pos (1216)            481510     481510          0         10     11.9 K
fsub_pos (   8)           23135      23135          0          1      0.0 K
literal (  16)            53748      43874       9874          2    154.3 K
clause (  32)             53047      43232       9815          1    306.8 K
list (  60)                   8          4          4          1      0.3 K
clash_nd (  44)             798        798          0          7      0.3 K
clause_ptr (   8)         11625       1810       9815          0     76.7 K
int_ptr (   8)           216614     177488      39126          4    305.7 K
link_node (  68)              0          0          0          0      0.0 K
ans_lit_node(  12)            0          0          0          0      0.0 K
formula_box( 148)             0          0          0          0      0.0 K
formula(  20)                 0          0          0          0      0.0 K
formula_ptr(   8)             0          0          0          0      0.0 K
  
-------------- statistics -------------
clauses input                  0
clauses given                301
clauses generated          52993
  (factors generated)          0
demod & eval rewrites       3760
clauses wt,lit,sk delete   29034
tautologies deleted          816
clauses forward subsumed   13378
  (subsumed by sos)         5999
unit deletions                 0
clauses kept                9757
empty clauses                 22
clauses back subsumed        338
usable size                  298
sos size                    9133
demodulators size              7
Kbytes malloced             4598
  
----------- times (seconds) -----------
run time           128.66                   (run time  0 hr,2 min, 8 sec)
system time         20.44
input time           0.43
  clausify time      0.00
hyper_res time      16.75
pre_process time    76.01
  demod time        20.42
  weigh cl time     20.68
  for_sub time       7.46
  unit_del time      0.00
  renumber time      0.56
  delete cl time     3.42
  keep cl time      14.33
  print_cl time      0.00
  conflict time      2.62
post_process time   32.97
  back demod time    0.00
  back_sub time     30.37
  unindex time       2.39
lex_rpo time         0.00
The job finished        Wed Aug 19 17:00:25 1992

                  Summary of Experiment 6

----- OTTER 2.2xa+, January 1992 -----
The job began on cosmo.mcs.anl.gov, Fri Aug 21 18:52:47 1992
The command was "otter4++".
  
set(hyper_res).
assign(max_weight,20).
assign(max_proofs,0).
clear(print_kept).
set(ancestor_subsume).
assign(max_seconds,7500).
assign(max_mem,128000).
assign(report,900).
assign(max_distinct_vars,4).
assign(pick_given_ratio,3).
set(order_history).
set(input_sos_first).
set(print_level).
  
weight_list(pick_and_purge).
weight(P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)),2).
weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2).
weight(P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2).
weight(P(i(i(i(x,y),x),x)),2).
weight(P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2).
weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2).
weight(P(i(i(x,i(x,y)),i(x,y))),2).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))),2).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))),2).
weight(P(i(x,i(i(n(y),y),y))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(x,i(y,x))),2).
weight(P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)),3).
weight(P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))),3).
weight(P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))),3).
weight(P(i(i(n(x),y),i(n(y),x))),3).
weight(P(i(i(x,i(x,y)),i(x,y))),3).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))),3).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),3).
weight(P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))),3).
weight(P(i(n(i(x,y)),x)),3).
weight(P(i(n(x),i(x,y))),3).
weight(P(i(i(i(i(y,z),i(x,z)),u),i(i(x,y),u))),4).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),4).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),4).
weight(P(i(i(v,i(i(x,z),u)),i(i(x,y),i(v,i(i(y,z),u))))),4).
weight(P(i(i(y,z),i(i(x,y),i(i(z,u),i(x,u))))),4).
weight(P(i(i(i(n(x),y),z),i(x,z))),4).
weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),4).
weight(P(i(i(y,i(i(n(x),x),x)),i(i(n(x),x),x))),4).
weight(P(i(v,i(i(n(x),x),x))),4).
weight(P(i(i(n(x),y),i(v,i(i(y,x),x)))),4).
weight(P(i(i(i(v,i(i(y,x),x)),z),i(i(n(x),y),z))),4).
weight(P(i(i(n(x),y),i(i(y,x),x))),4).
weight(P(i(x,x)),4).
weight(P(i(x,i(i(y,x),x))),4).
weight(P(i(x,i(y,x))),4).
weight(P(i(i(i(x,y),z),i(y,z))),4).
weight(P(i(x,i(i(x,y),y))),4).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),4).
weight(P(i(i(y,z),i(i(x,y),i(x,z)))),4).
weight(P(i(i(i(y,i(x,z)),u),i(i(x,i(y,z)),u))),4).
weight(P(i(i(i(x,y),x),x)),4).
weight(P(i(i(i(x,z),u),i(i(x,y),i(i(y,z),u)))),4).
weight(P(i(i(i(x,y),z),i(i(z,x),x))),4).
weight(P(i(i(i(x,y),y),i(i(y,x),x))),4).
weight(P(i(i(i(i(z,x),x),u),i(i(i(x,y),z),u))),4).
weight(P(i(i(i(x,y),z),i(i(x,z),z))),4).
weight(P(i(i(x,i(x,y)),i(x,y))),4).
weight(P(i(i(x,u),i(i(i(x,y),z),i(i(u,z),z)))),4).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),4).
weight(P(i(i(x,u),i(i(u,i(y,i(x,z))),i(y,i(x,z))))),4).
weight(P(i(i(u,i(y,i(x,z))),i(i(x,u),i(y,i(x,z))))),4).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),4).
weight(P(i(n(x),i(x,y))),4).
weight(P(i(i(i(x,y),z),i(n(x),z))),4).
weight(P(i(i(x,n(x)),n(x))),4).
weight(P(i(n(n(x)),x)),4).
weight(P(i(x,n(n(x)))),4).
weight(P(i(i(x,y),i(n(n(x)),y))),4).
weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),4).
weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),4).
weight(P(i(i(u,i(y,n(x))),i(i(x,y),i(u,n(x))))),4).
weight(P(i(i(u,i(y,x)),i(i(n(x),y),i(u,x)))),4).
weight(P(i(i(x,y),i(n(y),n(x)))),4).
weight(P(i(i(x,n(y)),i(y,n(x)))),4).
weight(P(i(i(n(x),y),i(n(y),x))),4).
weight(P(i(i(n(x),n(y)),i(y,x))),4).
weight(P(i(i(i(n(y),x),z),i(i(n(x),y),z))),4).
weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),4).
weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),4).
weight(P(i(i(n(x),y),i(i(x,y),y))),4).
weight(P(i(i(x,y),i(i(n(x),y),y))),4).
weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),4).
weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),4).
weight(P(i(i(n(x),z),i(i(x,y),i(i(y,z),z)))),4).
weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),4).
weight(P(i(i(n(x),z),i(i(y,z),i(i(x,y),z)))),4).
weight(P(i(i(u,i(n(x),z)),i(u,i(i(y,z),i(i(x,y),z))))),4).
weight(P(i(i(x,y),i(i(z,y),i(i(n(x),z),y)))),4).
weight(P(i(i(n(n(x)),y),i(x,y))),4).
weight(P(i(y,i(x,x))),4).
weight(P(i(n(i(x,x)),y)),4).
weight(P(i(i(n(y),n(i(x,x))),y)),4).
weight(P(i(n(i(x,y)),x)),4).
weight(P(i(n(i(x,y)),n(y))),4).
weight(P(i(n(i(x,n(y))),y)),4).
weight(P(i(x,i(n(y),n(i(x,y))))),4).
weight(P(i(x,i(y,n(i(x,n(y)))))),4).
weight(P(n(i(i(x,x),n(i(y,y))))),4).
end_of_list.
  
list(usable).
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
end_of_list.
  
list(sos).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
end_of_list.
  
list(passive).
6 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
7 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
8 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
end_of_list.
  
list(demodulators).
9 [] n(n(n(x)))=junk.
10 [] i(junk,x)=junk.
11 [] i(x,junk)=junk.
12 [] n(junk)=junk.
13 [] P(junk)=$T.
end_of_list.
  
given clause #1: (wt=-2147483647) 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
----> UNIT CONFLICT at   3.20 sec ----> 246 [binary,245,8] $ANSWER(step_49).
Length of proof is 14.  Level of proof is 10.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
8 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
246 [binary,245,8] $ANSWER(step_49).
  
length of proof is 14
------------ end of proof -------------
----> UNIT CONFLICT at   3.60 sec ----> 280 [binary,279,6] $ANSWER(step_18).
Length of proof is 15.  Level of proof is 11.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
6 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
279 [hyper,1,17,245] P(i(x,i(y,x))).
280 [binary,279,6] $ANSWER(step_18).
  
length of proof is 15
------------ end of proof -------------
----> UNIT CONFLICT at  12.49 sec ----> 1216 [binary,1215,7] $ANSWER(step_35).
Length of proof is 28.  Level of proof is 19.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
7 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
252 [hyper,1,218,4] P(i(i(n(x),y),i(i(y,x),x))).
279 [hyper,1,17,245] P(i(x,i(y,x))).
345 [hyper,1,3,279] P(i(i(i(x,y),z),i(y,z))).
421 [hyper,1,345,252] P(i(x,i(i(x,y),y))).
422 [hyper,1,345,245] P(i(n(x),i(x,y))).
474 [hyper,1,20,421] P(i(i(x,i(y,z)),i(y,i(x,z)))).
515 [hyper,1,252,422] P(i(i(i(x,y),x),x)).
559 [hyper,1,3,474] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
579 [hyper,1,474,3] P(i(i(x,y),i(i(z,x),i(z,y)))).
650 [hyper,1,14,515] P(i(i(x,i(x,y)),i(x,y))).
727 [hyper,1,3,579] P(i(i(i(i(x,y),i(x,z)),u),i(i(y,z),u))).
1035 [hyper,1,727,727] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
1140 [hyper,1,1035,650] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
1215 [hyper,1,559,1140] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
1216 [binary,1215,7] $ANSWER(step_35).
  
length of proof is 28
------------ end of proof -------------
-----> EMPTY CLAUSE at  13.70 sec ----> 1329 [hyper,2,279,1215,245]
$ANSWER(step_allBEH_Church_FL_18_35_49).
Length of proof is 28.  Level of proof is 19.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
252 [hyper,1,218,4] P(i(i(n(x),y),i(i(y,x),x))).
279 [hyper,1,17,245] P(i(x,i(y,x))).
345 [hyper,1,3,279] P(i(i(i(x,y),z),i(y,z))).
421 [hyper,1,345,252] P(i(x,i(i(x,y),y))).
422 [hyper,1,345,245] P(i(n(x),i(x,y))).
474 [hyper,1,20,421] P(i(i(x,i(y,z)),i(y,i(x,z)))).
515 [hyper,1,252,422] P(i(i(i(x,y),x),x)).
559 [hyper,1,3,474] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
579 [hyper,1,474,3] P(i(i(x,y),i(i(z,x),i(z,y)))).
650 [hyper,1,14,515] P(i(i(x,i(x,y)),i(x,y))).
727 [hyper,1,3,579] P(i(i(i(i(x,y),i(x,z)),u),i(i(y,z),u))).
1035 [hyper,1,727,727] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
1140 [hyper,1,1035,650] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
1215 [hyper,1,559,1140] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
1329 [hyper,2,279,1215,245] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 28
------------ end of proof -------------
----> UNIT CONFLICT at 987.70 sec ----> 21637 [binary,21636,7] $ANSWER(step_35).
Length of proof is 27.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
7 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
252 [hyper,1,218,4] P(i(i(n(x),y),i(i(y,x),x))).
279 [hyper,1,17,245] P(i(x,i(y,x))).
313 [hyper,1,20,252] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
345 [hyper,1,3,279] P(i(i(i(x,y),z),i(y,z))).
373 [hyper,1,20,313] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
421 [hyper,1,345,252] P(i(x,i(i(x,y),y))).
422 [hyper,1,345,245] P(i(n(x),i(x,y))).
511 [hyper,1,421,3] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
513 [hyper,1,313,422] P(i(i(n(x),y),i(n(y),x))).
623 [hyper,1,513,422] P(i(n(i(x,y)),x)).
21341 [hyper,1,14,373] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
21372 [hyper,1,21341,623] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
21636 [hyper,1,511,21372] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
21637 [binary,21636,7] $ANSWER(step_35).
  
length of proof is 27
------------ end of proof -------------
----> UNIT CONFLICT at 989.67 sec ----> 21749 [binary,21748,7] $ANSWER(step_35).
Length of proof is 25.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
7 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
252 [hyper,1,218,4] P(i(i(n(x),y),i(i(y,x),x))).
279 [hyper,1,17,245] P(i(x,i(y,x))).
313 [hyper,1,20,252] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
345 [hyper,1,3,279] P(i(i(i(x,y),z),i(y,z))).
373 [hyper,1,20,313] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
422 [hyper,1,345,245] P(i(n(x),i(x,y))).
513 [hyper,1,313,422] P(i(i(n(x),y),i(n(y),x))).
623 [hyper,1,513,422] P(i(n(i(x,y)),x)).
21341 [hyper,1,14,373] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
21372 [hyper,1,21341,623] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
21748 [hyper,1,21372,3] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
21749 [binary,21748,7] $ANSWER(step_35).
  
length of proof is 25
------------ end of proof -------------
-----> EMPTY CLAUSE at 1027.72 sec ----> 21977 [hyper,2,279,21636,245]
$ANSWER(step_allBEH_Church_FL_18_35_49).
Length of proof is 27.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
252 [hyper,1,218,4] P(i(i(n(x),y),i(i(y,x),x))).
279 [hyper,1,17,245] P(i(x,i(y,x))).
313 [hyper,1,20,252] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
345 [hyper,1,3,279] P(i(i(i(x,y),z),i(y,z))).
373 [hyper,1,20,313] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
421 [hyper,1,345,252] P(i(x,i(i(x,y),y))).
422 [hyper,1,345,245] P(i(n(x),i(x,y))).
511 [hyper,1,421,3] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
513 [hyper,1,313,422] P(i(i(n(x),y),i(n(y),x))).
623 [hyper,1,513,422] P(i(n(i(x,y)),x)).
21341 [hyper,1,14,373] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
21372 [hyper,1,21341,623] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
21636 [hyper,1,511,21372] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
21977 [hyper,2,279,21636,245] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 27
------------ end of proof -------------
----> UNIT CONFLICT at 6208.57 sec ----> 89216 [binary,89215,6] $ANSWER(step_18).
Length of proof is 14.  Level of proof is 10.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
6 [] -P(i(p,i(q,p))) | $ANSWER(step_18).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
31 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
72 [hyper,1,22,65] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
120 [hyper,1,17,31] P(i(x,i(y,i(n(x),z)))).
133 [hyper,1,3,120] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
999 [hyper,1,72,4] P(i(i(i(i(n(x),x),x),y),y)).
65972 [hyper,1,14,999] P(i(i(x,i(n(y),y)),i(x,y))).
89215 [hyper,1,133,65972] P(i(x,i(y,x))).
89216 [binary,89215,6] $ANSWER(step_18).
  
length of proof is 14
------------ end of proof -------------
----> UNIT CONFLICT at 6208.60 sec ----> 89218 [binary,89217,8] $ANSWER(step_49).
Length of proof is 13.  Level of proof is 10.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
8 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
31 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
72 [hyper,1,22,65] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
123 [hyper,1,3,31] P(i(i(i(x,i(y,z)),u),i(i(y,n(x)),u))).
999 [hyper,1,72,4] P(i(i(i(i(n(x),x),x),y),y)).
65972 [hyper,1,14,999] P(i(i(x,i(n(y),y)),i(x,y))).
89217 [hyper,1,123,65972] P(i(i(n(x),n(y)),i(y,x))).
89218 [binary,89217,8] $ANSWER(step_49).
  
length of proof is 13
------------ end of proof -------------
-----> EMPTY CLAUSE at 6249.04 sec ----> 89458 [hyper,2,89215,21636,89217]
$ANSWER(step_allBEH_Church_FL_18_35_49).
Length of proof is 36.  Level of proof is 17.
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
22 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
30 [hyper,1,15,17] P(i(i(n(i(i(n(x),y),z)),i(i(n(x),y),z)),i(x,z))).
31 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
42 [hyper,1,17,22] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
53 [hyper,1,42,4] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
57 [hyper,1,53,4] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
65 [hyper,1,17,57] P(i(x,i(i(n(y),y),y))).
72 [hyper,1,22,65] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
73 [hyper,1,20,65] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
120 [hyper,1,17,31] P(i(x,i(y,i(n(x),z)))).
123 [hyper,1,3,31] P(i(i(i(x,i(y,z)),u),i(i(y,n(x)),u))).
133 [hyper,1,3,120] P(i(i(i(x,i(n(y),z)),u),i(y,u))).
196 [hyper,1,14,73] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
218 [hyper,1,3,196] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
245 [hyper,1,218,30] P(i(i(n(x),n(y)),i(y,x))).
252 [hyper,1,218,4] P(i(i(n(x),y),i(i(y,x),x))).
279 [hyper,1,17,245] P(i(x,i(y,x))).
313 [hyper,1,20,252] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
345 [hyper,1,3,279] P(i(i(i(x,y),z),i(y,z))).
373 [hyper,1,20,313] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
421 [hyper,1,345,252] P(i(x,i(i(x,y),y))).
422 [hyper,1,345,245] P(i(n(x),i(x,y))).
511 [hyper,1,421,3] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
513 [hyper,1,313,422] P(i(i(n(x),y),i(n(y),x))).
623 [hyper,1,513,422] P(i(n(i(x,y)),x)).
999 [hyper,1,72,4] P(i(i(i(i(n(x),x),x),y),y)).
21341 [hyper,1,14,373] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
21372 [hyper,1,21341,623] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
21636 [hyper,1,511,21372] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
65972 [hyper,1,14,999] P(i(i(x,i(n(y),y)),i(x,y))).
89215 [hyper,1,133,65972] P(i(x,i(y,x))).
89217 [hyper,1,123,65972] P(i(i(n(x),n(y)),i(y,x))).
89458 [hyper,2,89215,21636,89217] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 36
------------ end of proof -------------
------------ END OF SEARCH ------------
  
--------------- options ---------------
set(input_sos_first). clear(sos_queue). clear(sos_stack). 
set(print_given). clear(binary_res). set(hyper_res). 
clear(ur_res). clear(para_into). clear(para_from). 
clear(demod_inf). set(para_from_left). set(para_from_right). 
set(para_into_left). set(para_into_right). clear(para_from_vars). 
clear(para_into_vars). clear(para_from_units_only). clear(para_into_units_only). 
clear(para_skip_skolem). clear(para_ones_rule). clear(para_all). 
clear(very_verbose). clear(order_eq). clear(sort_literals). 
clear(delete_identical_nested_skolem). set(for_sub). clear(unit_deletion). 
clear(print_kept). set(print_proofs). set(back_sub). 
set(print_back_sub). clear(factor). set(demod_history). 
clear(demod_linear). clear(demod_out_in). clear(dynamic_demod). 
clear(dynamic_demod_all). set(print_new_demod). clear(back_demod). 
set(print_back_demod). set(symbol_elim). clear(knuth_bendix). 
clear(lex_rpo). clear(dynamic_demod_lex_dep). clear(lex_order_vars). 
clear(for_sub_fpa). clear(no_fapl). clear(no_fanl). 
set(check_arity). clear(prolog_style_variables). clear(process_input). 
clear(simplify_fol). clear(bird_print). clear(free_all_mem). 
clear(atom_wt_max_args). clear(term_wt_max_args). clear(print_lists_at_end). 
clear(really_delete_clauses). clear(prog_synthesis). set(ancestor_subsume). 
clear(new_functions). clear(linked_ur_res). clear(linked_ur_trace). 
clear(linked_sub_unit_usable). clear(linked_sub_unit_sos).
clear(index_for_back_demod). 
clear(linked_unit_del). clear(linked_target_all). clear(linked_hyper_res). 
clear(control_memory). set(order_history). clear(neg_hyper_res). 
clear(suppress_weight_warning). clear(display_terms). set(print_level). 
  
  
assign(report, 900). assign(max_seconds, 7500). assign(max_gen, 0). 
assign(max_kept, 0). assign(max_given, 0). assign(max_mem, 128000). 
assign(max_literals, 0). assign(max_weight,20). assign(fpa_literals, 8). 
assign(fpa_terms, 8). assign(demod_limit, 100). assign(max_proofs, 0). 
assign(neg_weight, 0). assign(stats_level,2). assign(reduce_weight_limit, 0). 
assign(max_ur_depth, 5). assign(max_ur_deduction_size,20).
assign(max_distinct_vars, 4). 
assign(pick_given_ratio, 3). assign(random_ratio, -1). assign(random_seed, 1). 
assign(change_limit_after, 0). assign(new_max_weight, 0). assign(max_sos_size, 0). 
  
  
------------- memory usage ------------
951 mallocs of 32700 bytes each, 30368.8 K.
  type (bytes each)        gets      frees     in use      avail      bytes
sym_ent (  96)              119          0        119          0     11.2 K
term (  20)            18736737   18528107     208630         21   4075.2 K
rel (  20)             17783573   17475632     307941         21   6014.9 K
term_ptr (   8)         2303196    1149287    1153909       1041   9023.0 K
formula_ptr_2 (  28)          0          0          0          0      0.0 K
fpa_head (  12)            5606        151       5455         14     64.1 K
fpa_tree (  28)          868324     868324          0         47      1.3 K
context ( 776)          1891011    1891011          0          5      3.8 K
trail (  12)            9299078    9299078          0         10      0.1 K
imd_tree (  20)              14          0         14          0      0.3 K
imd_pos (2016)          7427287    7427287          0          1      2.0 K
is_tree (  12)           297852      16208     281644         11   3300.6 K
is_pos (1216)           8013739    8013739          0         10     11.9 K
fsub_pos (   8)          387843     387843          0          1      0.0 K
literal (  16)           905043     815284      89759          2   1402.5 K
clause (  32)            901772     812021      89751          1   2804.8 K
list (  60)                   8          4          4          1      0.3 K
clash_nd (  44)            3269       3269          0          2      0.1 K
clause_ptr (   8)      15556098   15466346      89752         37    701.5 K
int_ptr (   8)          3659553    3300605     358948          4   2804.3 K
link_node (  68)              0          0          0          0      0.0 K
ans_lit_node(  12)            0          0          0          0      0.0 K
formula_box( 148)             0          0          0          0      0.0 K
formula(  20)                 0          0          0          0      0.0 K
formula_ptr(   8)             0          0          0          0      0.0 K
  
-------------- statistics -------------
clauses input                  0
clauses given               1658
clauses generated         901748
  (factors generated)          0
demod & eval rewrites      44206
clauses wt,lit,sk delete  505571
tautologies deleted         8331
clauses forward subsumed  298115
cl not subsumed due to ancestor_subsume   30862
  (subsumed by sos)       129147
unit deletions                 0
clauses kept               89728
empty clauses                 10
clauses back subsumed      32704
usable size                 1031
sos size                   55999
demodulators size              5
Kbytes malloced            30368
  
----------- times (seconds) -----------
run time          6360.88                   (run time  1 hr, 46 min, 0 sec)
system time        367.02
input time           0.41
  clausify time      0.00
hyper_res time     268.25
pre_process time  1850.03
  demod time       277.57
  weigh cl time    524.71
  for_sub time     567.07
  unit_del time      0.00
  renumber time     23.49
  delete cl time    73.15
  keep cl time     268.40
  print_cl time      0.00
  conflict time     21.11
post_process time 4191.67
  back demod time    0.00
  back_sub time   1166.42
  unindex time    3016.68
lex_rpo time         0.00
The job finished        Fri Aug 21 22:07:24 1992

\end{verbatim}
\begin{verbatim}

                 Appendix B

        Input File for Stage 1 of Example 1

%  luka completeness of 123 exps.
set(hyper_res).
% assign(reduce_weight_limit, 010024).
assign(max_weight,20).
% set(control_memory).
assign(max_proofs, 0).
clear(print_kept).
% set(very_verbose).
% set(ancestor_subsume).
clear(back_sub).
% assign(max_seconds, 1200).
assign(max_mem, 128000).
assign(report, 900).
% assign(max_distinct_vars, 4).
% assign(pick_given_ratio, 3).
set(order_history).
set(input_sos_first).
% set(sos_queue).
  
% weight_list(pick_and_purge).
%  Following are 68 theses suggested by Scott.
%  They are in reverse order from those numbered by Lukasiewicz 4 to 71.
% weight(P(i(i(i(i(y,z),i(x,z)),u),i(i(x,y),u))),2).
% weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
% weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
% weight(P(i(i(v,i(i(x,z),u)),i(i(x,y),i(v,i(i(y,z),u))))),2).
% weight(P(i(i(y,z),i(i(x,y),i(i(z,u),i(x,u))))),2).
% weight(P(i(i(i(n(x),y),z),i(x,z))),2).
% weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),2).
% weight(P(i(i(y,i(i(n(x),x),x)),i(i(n(x),x),x))),2).
% weight(P(i(v,i(i(n(x),x),x))),2).
% weight(P(i(i(n(x),y),i(v,i(i(y,x),x)))),2).
% weight(P(i(i(i(v,i(i(y,x),x)),z),i(i(n(x),y),z))),2).
% weight(P(i(i(n(x),y),i(i(y,x),x))),2).
% weight(P(i(x,x)),2).
% weight(P(i(x,i(i(y,x),x))),2).
% weight(P(i(y,i(x,y))),2).
% weight(P(i(i(i(x,y),z),i(y,z))),2).
% weight(P(i(x,i(i(x,y),y))),2).
% weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
% weight(P(i(i(y,z),i(i(x,y),i(x,z)))),2).
% weight(P(i(i(i(y,i(x,z)),u),i(i(x,i(y,z)),u))),2).
% weight(P(i(i(i(x,y),x),x)),2).
% weight(P(i(i(i(x,z),u),i(i(x,y),i(i(y,z),u)))),2).
% weight(P(i(i(i(x,y),z),i(i(z,x),x))),2).
% weight(P(i(i(i(x,y),y),i(i(y,x),x))),2).
% weight(P(i(i(i(i(z,x),x),u),i(i(i(x,y),z),u))),2).
% weight(P(i(i(i(x,y),z),i(i(x,z),z))),2).
% weight(P(i(i(x,i(x,y)),i(x,y))),2).
% weight(P(i(i(x,u),i(i(i(x,y),z),i(i(u,z),z)))),2).
% weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2).
% weight(P(i(i(x,u),i(i(u,i(y,i(x,z))),i(y,i(x,z))))),2).
% weight(P(i(i(u,i(y,i(x,z))),i(i(x,u),i(y,i(x,z))))),2).
% weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
% weight(P(i(n(x),i(x,y))),2).
% weight(P(i(i(i(x,y),z),i(n(x),z))),2).
% weight(P(i(i(x,n(x)),n(x))),2).
% weight(P(i(n(n(x)),x)),2).
% weight(P(i(x,n(n(x)))),2).
% weight(P(i(i(x,y),i(n(n(x)),y))),2).
% weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),2).
% weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),2).
% weight(P(i(i(u,i(y,n(x))),i(i(x,y),i(u,n(x))))),2).
% weight(P(i(i(u,i(y,x)),i(i(n(x),y),i(u,x)))),2).
% weight(P(i(i(x,y),i(n(y),n(x)))),2).
% weight(P(i(i(x,n(y)),i(y,n(x)))),2).
% weight(P(i(i(n(x),y),i(n(y),x))),2).
% weight(P(i(i(n(x),n(y)),i(y,x))),2).
% weight(P(i(i(i(n(y),x),z),i(i(n(x),y),z))),2).
% weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),2).
% weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),2).
% weight(P(i(i(n(x),y),i(i(x,y),y))),2).
% weight(P(i(i(x,y),i(i(n(x),y),y))),2).
% weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),2).
% weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),2).
% weight(P(i(i(n(x),z),i(i(x,y),i(i(y,z),z)))),2).
% weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),2).
% weight(P(i(i(n(x),z),i(i(y,z),i(i(x,y),z)))),2).
% weight(P(i(i(u,i(n(x),z)),i(u,i(i(y,z),i(i(x,y),z))))),2).
% weight(P(i(i(x,z),i(i(y,z),i(i(n(x),y),z)))),2).
% weight(P(i(i(n(n(x)),y),i(x,y))),2).
% weight(P(i(y,i(x,x))),2).
% weight(P(i(n(i(x,x)),y)),2).
% weight(P(i(i(n(y),n(i(x,x))),y)),2).
% weight(P(i(n(i(x,y)),x)),2).
% weight(P(i(n(i(x,y)),n(y))),2).
% weight(P(i(n(i(x,n(y))),y)),2).
% weight(P(i(x,i(n(y),n(i(x,y))))),2).
% weight(P(i(x,i(y,n(i(x,n(y)))))),2).
% weight(P(n(i(i(x,x),n(i(y,y))))),2).
% end_of_list.
  
list(usable).
-P(i(x,y)) | -P(x) | P(y).
  
%  The following disjunctions are known axiom systems.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
$ANSWER(step_allFrege_18_35_39_40_46_21).  % 21 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
  
-P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
  
end_of_list.
  
list(sos).
%  The following three are Luka, 1 2 3.
P(i(i(x,y),i(i(y,z),i(x,z)))).
P(i(i(n(x),x),x)).
P(i(x,i(n(x),y))).
  
%  The following are from Frege, 18 35 21 46 39 40, with 21 dependent.
% P(i(x,i(y,x))).  %  axiom F1.
% P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).  %  axiom F2.
% P(i(i(x,i(y,z)),i(y,i(x,z)))).  %  axiom F3.
% P(i(i(x,y),i(n(y),n(x)))).  %  axiom F4.
% P(i(n(n(x)),x)).  %  axiom F5.
% P(i(x,n(n(x)))).  %  axiom f6.
end_of_list.
  
list(passive).
-P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
-P(i(i(n(p),p),p)) | $ANSWER(step_L2).
-P(i(p,i(n(p),q))) | $ANSWER(step_L3).
-P(i(q,i(p,q))) | $ANSWER(step_18).
-P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
-P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
-P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
-P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
-P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
-P(i(n(n(p)),p)) | $ANSWER(step_39).
-P(i(p,n(n(p)))) | $ANSWER(step_40).
-P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
-P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
% (n(n(x)) = junk).
(n(n(n(x))) = junk).
% (i(i(x,x),y) = junk).
% (i(y,i(x,x)) = junk).
(i(junk,x) = junk).
(i(x,junk) = junk).
(n(junk) = junk).
(P(junk) = $T).
end_of_list.

           Summary of Output File for Stage 2 of Example 1

----- OTTER 2.2xa+, January 1992 -----
The job began on cosmo.mcs.anl.gov, Sun Aug 30 08:13:48 1992
The command was "otter4++".
  
set(hyper_res).
assign(max_weight,20).
assign(max_proofs,0).
clear(print_kept).
set(ancestor_subsume).
assign(max_seconds,600).
assign(max_mem,22000).
assign(report,900).
set(print_level).
set(order_history).
set(input_sos_first).
  
weight_list(pick_and_purge).
weight(P(i(i(i(i(y,z),i(x,z)),u),i(i(x,y),u))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(v,i(i(x,z),u)),i(i(x,y),i(v,i(i(y,z),u))))),2).
weight(P(i(i(y,z),i(i(x,y),i(i(z,u),i(x,u))))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),2).
weight(P(i(i(y,i(i(n(x),x),x)),i(i(n(x),x),x))),2).
weight(P(i(v,i(i(n(x),x),x))),2).
weight(P(i(i(n(x),y),i(v,i(i(y,x),x)))),2).
weight(P(i(i(i(v,i(i(y,x),x)),z),i(i(n(x),y),z))),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(x,x)),2).
weight(P(i(x,i(i(y,x),x))),2).
weight(P(i(y,i(x,y))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(i(y,z),i(i(x,y),i(x,z)))),2).
weight(P(i(i(i(y,i(x,z)),u),i(i(x,i(y,z)),u))),2).
weight(P(i(i(i(x,y),x),x)),2).
weight(P(i(i(i(x,z),u),i(i(x,y),i(i(y,z),u)))),2).
weight(P(i(i(i(x,y),z),i(i(z,x),x))),2).
weight(P(i(i(i(x,y),y),i(i(y,x),x))),2).
weight(P(i(i(i(i(z,x),x),u),i(i(i(x,y),z),u))),2).
weight(P(i(i(i(x,y),z),i(i(x,z),z))),2).
weight(P(i(i(x,i(x,y)),i(x,y))),2).
weight(P(i(i(x,u),i(i(i(x,y),z),i(i(u,z),z)))),2).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2).
weight(P(i(i(x,u),i(i(u,i(y,i(x,z))),i(y,i(x,z))))),2).
weight(P(i(i(u,i(y,i(x,z))),i(i(x,u),i(y,i(x,z))))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(i(i(x,y),z),i(n(x),z))),2).
weight(P(i(i(x,n(x)),n(x))),2).
weight(P(i(n(n(x)),x)),2).
weight(P(i(x,n(n(x)))),2).
weight(P(i(i(x,y),i(n(n(x)),y))),2).
weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),2).
weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),2).
weight(P(i(i(u,i(y,n(x))),i(i(x,y),i(u,n(x))))),2).
weight(P(i(i(u,i(y,x)),i(i(n(x),y),i(u,x)))),2).
weight(P(i(i(x,y),i(n(y),n(x)))),2).
weight(P(i(i(x,n(y)),i(y,n(x)))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(i(n(y),x),z),i(i(n(x),y),z))),2).
weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),2).
weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),2).
weight(P(i(i(n(x),y),i(i(x,y),y))),2).
weight(P(i(i(x,y),i(i(n(x),y),y))),2).
weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),2).
weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),2).
weight(P(i(i(n(x),z),i(i(x,y),i(i(y,z),z)))),2).
weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),2).
weight(P(i(i(n(x),z),i(i(y,z),i(i(x,y),z)))),2).
weight(P(i(i(u,i(n(x),z)),i(u,i(i(y,z),i(i(x,y),z))))),2).
weight(P(i(i(x,z),i(i(y,z),i(i(n(x),y),z)))),2).
weight(P(i(i(n(n(x)),y),i(x,y))),2).
weight(P(i(y,i(x,x))),2).
weight(P(i(n(i(x,x)),y)),2).
weight(P(i(i(n(y),n(i(x,x))),y)),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(n(i(x,y)),n(y))),2).
weight(P(i(n(i(x,n(y))),y)),2).
weight(P(i(x,i(n(y),n(i(x,y))))),2).
weight(P(i(x,i(y,n(i(x,n(y)))))),2).
weight(P(n(i(i(x,x),n(i(y,y))))),2).
end_of_list.
  
list(usable).
1 [] -P(i(x,y))| -P(x)|P(y).
2 [] -P(i(q,i(p,q)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|
-P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49).
end_of_list.
  
list(sos).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
end_of_list.
  
list(passive).
6 [] -P(i(q,i(p,q)))|$ANSWER(step_18).
7 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|$ANSWER(step_35).
8 [] -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_49).
end_of_list.
  
list(demodulators).
9 [] n(n(n(x)))=junk.
10 [] i(junk,x)=junk.
11 [] i(x,junk)=junk.
12 [] n(junk)=junk.
13 [] P(junk)=$T.
end_of_list.
  
given clause #1: (wt=-2147483647) 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
----> UNIT CONFLICT at   6.12 sec ----> 722 [binary,721,8] $ANSWER(step_49).
Length of proof is 20.  Level of proof is 12.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
8 [] -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_49).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
74 [hyper,1,48,15] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))).
106 [hyper,1,3,74] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
463 [hyper,1,106,456] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
502 [hyper,1,3,463] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
559 [hyper,1,502,4] P(i(i(n(x),y),i(i(y,x),x))).
622 [hyper,1,20,559] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
721 [hyper,1,622,5] P(i(i(n(x),n(y)),i(y,x))).
722 [binary,721,8] $ANSWER(step_49).
  
length of proof is 20
------------ end of proof -------------
----> UNIT CONFLICT at   7.15 sec ----> 819 [binary,818,6] $ANSWER(step_18).
Length of proof is 21.  Level of proof is 13.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
6 [] -P(i(q,i(p,q)))|$ANSWER(step_18).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
74 [hyper,1,48,15] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))).
106 [hyper,1,3,74] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
463 [hyper,1,106,456] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
502 [hyper,1,3,463] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
559 [hyper,1,502,4] P(i(i(n(x),y),i(i(y,x),x))).
622 [hyper,1,20,559] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
721 [hyper,1,622,5] P(i(i(n(x),n(y)),i(y,x))).
818 [hyper,1,17,721] P(i(x,i(y,x))).
819 [binary,818,6] $ANSWER(step_18).
  
length of proof is 21
------------ end of proof -------------
----> UNIT CONFLICT at   7.69 sec ----> 874 [binary,873,8] $ANSWER(step_49).
Length of proof is 19.  Level of proof is 13.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
8 [] -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_49).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
478 [hyper,1,456,15] P(i(x,i(i(n(y),y),y))).
528 [hyper,1,48,478] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
583 [hyper,1,3,528] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
666 [hyper,1,583,4] P(i(i(n(x),y),i(i(y,x),x))).
789 [hyper,1,20,666] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
873 [hyper,1,789,5] P(i(i(n(x),n(y)),i(y,x))).
874 [binary,873,8] $ANSWER(step_49).
  
length of proof is 19
------------ end of proof -------------
----> UNIT CONFLICT at   8.76 sec ----> 980 [binary,979,6] $ANSWER(step_18).
Length of proof is 20.  Level of proof is 14.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
6 [] -P(i(q,i(p,q)))|$ANSWER(step_18).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
478 [hyper,1,456,15] P(i(x,i(i(n(y),y),y))).
528 [hyper,1,48,478] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
583 [hyper,1,3,528] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
666 [hyper,1,583,4] P(i(i(n(x),y),i(i(y,x),x))).
789 [hyper,1,20,666] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
873 [hyper,1,789,5] P(i(i(n(x),n(y)),i(y,x))).
979 [hyper,1,17,873] P(i(x,i(y,x))).
980 [binary,979,6] $ANSWER(step_18).
  
length of proof is 20
------------ end of proof -------------
----> UNIT CONFLICT at  66.36 sec ----> 5854 [binary,5853,7] $ANSWER(step_35).
Length of proof is 42.  Level of proof is 20.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
7 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|$ANSWER(step_35).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
74 [hyper,1,48,15] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))).
106 [hyper,1,3,74] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
463 [hyper,1,106,456] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
478 [hyper,1,456,15] P(i(x,i(i(n(y),y),y))).
502 [hyper,1,3,463] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
528 [hyper,1,48,478] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
559 [hyper,1,502,4] P(i(i(n(x),y),i(i(y,x),x))).
583 [hyper,1,3,528] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
622 [hyper,1,20,559] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
666 [hyper,1,583,4] P(i(i(n(x),y),i(i(y,x),x))).
721 [hyper,1,622,5] P(i(i(n(x),n(y)),i(y,x))).
789 [hyper,1,20,666] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
818 [hyper,1,17,721] P(i(x,i(y,x))).
873 [hyper,1,789,5] P(i(i(n(x),n(y)),i(y,x))).
919 [hyper,1,3,818] P(i(i(i(x,y),z),i(y,z))).
979 [hyper,1,17,873] P(i(x,i(y,x))).
1000 [hyper,1,919,666] P(i(x,i(i(x,y),y))).
1041 [hyper,1,3,979] P(i(i(i(x,y),z),i(y,z))).
1107 [hyper,1,20,1000] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1179 [hyper,1,1041,873] P(i(n(x),i(x,y))).
1181 [hyper,1,1041,666] P(i(x,i(i(x,y),y))).
1311 [hyper,1,1107,666] P(i(i(x,y),i(i(n(y),x),y))).
1344 [hyper,1,789,1179] P(i(i(n(x),y),i(n(y),x))).
1382 [hyper,1,20,1181] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1653 [hyper,1,48,1311] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
1969 [hyper,1,1344,1179] P(i(n(i(x,y)),x)).
2081 [hyper,1,3,1382] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
3354 [hyper,1,1653,1969] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
5853 [hyper,1,2081,3354] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
5854 [binary,5853,7] $ANSWER(step_35).
  
length of proof is 42
------------ end of proof -------------
-----> EMPTY CLAUSE at 187.84 sec ----> 9779 [hyper,2,979,5853,873]
$ANSWER(step_allBEH_Church_FL_18_35_49).
Length of proof is 42.  Level of proof is 20.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
2 [] -P(i(q,i(p,q)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|
-P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
74 [hyper,1,48,15] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))).
106 [hyper,1,3,74] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
463 [hyper,1,106,456] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
478 [hyper,1,456,15] P(i(x,i(i(n(y),y),y))).
502 [hyper,1,3,463] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
528 [hyper,1,48,478] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
559 [hyper,1,502,4] P(i(i(n(x),y),i(i(y,x),x))).
583 [hyper,1,3,528] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
622 [hyper,1,20,559] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
666 [hyper,1,583,4] P(i(i(n(x),y),i(i(y,x),x))).
721 [hyper,1,622,5] P(i(i(n(x),n(y)),i(y,x))).
789 [hyper,1,20,666] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
818 [hyper,1,17,721] P(i(x,i(y,x))).
873 [hyper,1,789,5] P(i(i(n(x),n(y)),i(y,x))).
919 [hyper,1,3,818] P(i(i(i(x,y),z),i(y,z))).
979 [hyper,1,17,873] P(i(x,i(y,x))).
1000 [hyper,1,919,666] P(i(x,i(i(x,y),y))).
1041 [hyper,1,3,979] P(i(i(i(x,y),z),i(y,z))).
1107 [hyper,1,20,1000] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1179 [hyper,1,1041,873] P(i(n(x),i(x,y))).
1181 [hyper,1,1041,666] P(i(x,i(i(x,y),y))).
1311 [hyper,1,1107,666] P(i(i(x,y),i(i(n(y),x),y))).
1344 [hyper,1,789,1179] P(i(i(n(x),y),i(n(y),x))).
1382 [hyper,1,20,1181] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1653 [hyper,1,48,1311] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
1969 [hyper,1,1344,1179] P(i(n(i(x,y)),x)).
2081 [hyper,1,3,1382] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
3354 [hyper,1,1653,1969] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
5853 [hyper,1,2081,3354] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
9779 [hyper,2,979,5853,873] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 42
------------ end of proof -------------
----> UNIT CONFLICT at 239.37 sec ----> 11206 [binary,11205,7] $ANSWER(step_35).
Length of proof is 31.  Level of proof is 21.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
7 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|$ANSWER(step_35).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
478 [hyper,1,456,15] P(i(x,i(i(n(y),y),y))).
528 [hyper,1,48,478] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
583 [hyper,1,3,528] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
666 [hyper,1,583,4] P(i(i(n(x),y),i(i(y,x),x))).
789 [hyper,1,20,666] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
873 [hyper,1,789,5] P(i(i(n(x),n(y)),i(y,x))).
979 [hyper,1,17,873] P(i(x,i(y,x))).
1041 [hyper,1,3,979] P(i(i(i(x,y),z),i(y,z))).
1179 [hyper,1,1041,873] P(i(n(x),i(x,y))).
1181 [hyper,1,1041,666] P(i(x,i(i(x,y),y))).
1344 [hyper,1,789,1179] P(i(i(n(x),y),i(n(y),x))).
1382 [hyper,1,20,1181] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1969 [hyper,1,1344,1179] P(i(n(i(x,y)),x)).
2081 [hyper,1,3,1382] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
2088 [hyper,1,1382,666] P(i(i(x,y),i(i(n(y),x),y))).
3666 [hyper,1,48,2088] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
7099 [hyper,1,3666,1969] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
11205 [hyper,1,2081,7099] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
11206 [binary,11205,7] $ANSWER(step_35).
  
length of proof is 31
------------ end of proof -------------
-----> EMPTY CLAUSE at 547.00 sec ----> 16956 [hyper,2,979,11205,873]
$ANSWER(step_allBEH_Church_FL_18_35_49).
Length of proof is 31.  Level of proof is 21.
---------------- PROOF ----------------
  
1 [] -P(i(x,y))| -P(x)|P(y).
2 [] -P(i(q,i(p,q)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|
-P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49).
3 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
4 [] P(i(i(n(x),x),x)).
5 [] P(i(x,i(n(x),y))).
14 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
15 [hyper,1,3,4] P(i(i(x,y),i(i(n(x),x),y))).
17 [hyper,1,3,5] P(i(i(i(n(x),y),z),i(x,z))).
20 [hyper,1,14,14] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
24 [hyper,1,14,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
33 [hyper,1,14,17] P(i(i(x,n(y)),i(y,i(x,z)))).
38 [hyper,1,17,4] P(i(x,x)).
48 [hyper,1,20,24] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
60 [hyper,1,5,38] P(i(n(i(x,x)),y)).
182 [hyper,1,33,60] P(i(x,i(n(i(y,y)),z))).
222 [hyper,1,3,182] P(i(i(i(n(i(x,x)),y),z),i(u,z))).
442 [hyper,1,222,4] P(i(x,i(y,y))).
456 [hyper,1,3,442] P(i(i(i(x,x),y),i(z,y))).
478 [hyper,1,456,15] P(i(x,i(i(n(y),y),y))).
528 [hyper,1,48,478] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
583 [hyper,1,3,528] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
666 [hyper,1,583,4] P(i(i(n(x),y),i(i(y,x),x))).
789 [hyper,1,20,666] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
873 [hyper,1,789,5] P(i(i(n(x),n(y)),i(y,x))).
979 [hyper,1,17,873] P(i(x,i(y,x))).
1041 [hyper,1,3,979] P(i(i(i(x,y),z),i(y,z))).
1179 [hyper,1,1041,873] P(i(n(x),i(x,y))).
1181 [hyper,1,1041,666] P(i(x,i(i(x,y),y))).
1344 [hyper,1,789,1179] P(i(i(n(x),y),i(n(y),x))).
1382 [hyper,1,20,1181] P(i(i(x,i(y,z)),i(y,i(x,z)))).
1969 [hyper,1,1344,1179] P(i(n(i(x,y)),x)).
2081 [hyper,1,3,1382] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
2088 [hyper,1,1382,666] P(i(i(x,y),i(i(n(y),x),y))).
3666 [hyper,1,48,2088] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
7099 [hyper,1,3666,1969] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))).
11205 [hyper,1,2081,7099] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
16956 [hyper,2,979,11205,873] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 31
------------ end of proof -------------
search stopped by max_seconds option.
------------ END OF SEARCH ------------
  
--------------- options ---------------
set(input_sos_first). clear(sos_queue). clear(sos_stack). 
set(print_given). clear(binary_res). set(hyper_res). 
clear(ur_res). clear(para_into). clear(para_from). 
clear(demod_inf). set(para_from_left). set(para_from_right). 
set(para_into_left). set(para_into_right). clear(para_from_vars). 
clear(para_into_vars). clear(para_from_units_only). clear(para_into_units_only). 
clear(para_skip_skolem). clear(para_ones_rule). clear(para_all). 
clear(very_verbose). clear(order_eq). clear(sort_literals). 
clear(delete_identical_nested_skolem). set(for_sub). clear(unit_deletion). 
clear(print_kept). set(print_proofs). set(back_sub). 
set(print_back_sub). clear(factor). set(demod_history). 
clear(demod_linear). clear(demod_out_in). clear(dynamic_demod). 
clear(dynamic_demod_all). set(print_new_demod). clear(back_demod). 
set(print_back_demod). set(symbol_elim). clear(knuth_bendix). 
clear(lex_rpo). clear(dynamic_demod_lex_dep). clear(lex_order_vars). 
clear(for_sub_fpa). clear(no_fapl). clear(no_fanl). 
set(check_arity). clear(prolog_style_variables). clear(process_input). 
clear(simplify_fol). clear(bird_print). clear(free_all_mem). 
clear(atom_wt_max_args). clear(term_wt_max_args). clear(print_lists_at_end). 
clear(really_delete_clauses). clear(prog_synthesis). set(ancestor_subsume). 
clear(new_functions). clear(linked_ur_res). clear(linked_ur_trace). 
clear(linked_sub_unit_usable). clear(linked_sub_unit_sos).
clear(index_for_back_demod). 
clear(linked_unit_del). clear(linked_target_all). clear(linked_hyper_res). 
clear(control_memory). set(order_history). clear(neg_hyper_res). 
clear(suppress_weight_warning). clear(display_terms). set(print_level). 
  
  
assign(report, 900). assign(max_seconds, 600). assign(max_gen, 0). 
assign(max_kept, 0). assign(max_given, 0). assign(max_mem,22000). 
assign(max_literals, 0). assign(max_weight,20). assign(fpa_literals, 8). 
assign(fpa_terms, 8). assign(demod_limit, 100). assign(max_proofs, 0). 
assign(neg_weight, 0). assign(stats_level,2). assign(reduce_weight_limit, 0). 
assign(max_ur_depth, 5). assign(max_ur_deduction_size,20).
assign(max_distinct_vars, -1). 
assign(pick_given_ratio, -1). assign(random_ratio, -1). assign(random_seed, 1). 
assign(change_limit_after, 0). assign(new_max_weight, 0). assign(max_sos_size, 0). 
  
  
------------- memory usage ------------
190 mallocs of 32700 bytes each, 6067.4 K.
  type (bytes each)        gets      frees     in use      avail      bytes
sym_ent (  96)              114          0        114          0     10.7 K
term (  20)             1188461    1146224      42237         19    825.3 K
rel (  20)              1124118    1060398      63720         18   1244.9 K
term_ptr (   8)          481472     266828     214644       1333   1687.3 K
formula_ptr_2 (  28)          0          0          0          0      0.0 K
fpa_head (  12)            2099         64       2035          3     23.9 K
fpa_tree (  28)          192792     192792          0         45      1.2 K
context ( 776)           174927     174927          0          5      3.8 K
trail (  12)            1178409    1178409          0         13      0.2 K
imd_tree (  20)              14          0         14          0      0.3 K
imd_pos (2016)           474830     474830          0          1      2.0 K
is_tree (  12)            57123       1996      55127          0    646.0 K
is_pos (1216)            958007     958007          0         10     11.9 K
fsub_pos (   8)           35465      35465          0          1      0.0 K
literal (  16)            60481      42581      17900          2    279.7 K
clause (  32)             59647      41755      17892          1    559.2 K
list (  60)                   8          4          4          1      0.3 K
clash_nd (  44)             832        832          0          2      0.1 K
clause_ptr (   8)       1254753    1236861      17892         43    140.1 K
int_ptr (   8)           240786     169274      71512          7    558.7 K
link_node (  68)              0          0          0          0      0.0 K
ans_lit_node(  12)            0          0          0          0      0.0 K
formula_box( 148)             0          0          0          0      0.0 K
formula(  20)                 0          0          0          0      0.0 K
formula_ptr(   8)             0          0          0          0      0.0 K
  
-------------- statistics -------------
clauses input                  0
clauses given                410
clauses generated          59624
  (factors generated)          0
demod & eval rewrites       1902
clauses wt,lit,sk delete   23789
tautologies deleted          368
clauses forward subsumed   17594
cl not subsumed due to ancestor_subsume    7249
  (subsumed by sos)        10245
unit deletions                 0
clauses kept               17871
empty clauses                  8
clauses back subsumed       7543
usable size                  211
sos size                   10122
demodulators size              5
Kbytes malloced             6067
  
----------- times (seconds) -----------
run time           604.73                   (run time  0 hr, 10 min, 4 sec)
system time         26.61
input time           0.26
  clausify time      0.00
hyper_res time      17.25
pre_process time   146.06
  demod time        16.33
  weigh cl time     39.59
  for_sub time      50.62
  unit_del time      0.00
  renumber time      2.83
  delete cl time     3.53
  keep cl time      26.76
  print_cl time      0.00
  conflict time      4.04
post_process time  437.23
  back demod time    0.00
  back_sub time    102.66
  unindex time     333.04
lex_rpo time         0.00
The job finished        Sun Aug 30 08:24:23 1992

\end{verbatim}
\begin{verbatim}

          Input File for Cursory Proof Checking


%  luka completeness of 123 exps.
set(hyper_res).
% assign(reduce_weight_limit, 010024).
assign(max_weight,2).
% set(control_memory).
assign(max_proofs, 0).
clear(print_kept).
% set(very_verbose).
% set(ancestor_subsume).
clear(back_sub).
% assign(max_seconds, 600).
assign(max_mem,22000).
assign(report, 900).
% assign(max_distinct_vars, 4).
% assign(pick_given_ratio, 3).
set(order_history).
set(input_sos_first).
% set(sos_queue).
  
weight_list(pick_and_purge).
%  Following are the steps of a 42-step proof, including duplicates.
weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2).
weight(P(i(i(x,y),i(i(n(x),x),y))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(x,n(y)),i(y,i(x,z)))),2).
weight(P(i(x,x)),2).
weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2).
weight(P(i(n(i(x,x)),y)),2).
weight(P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))),2).
weight(P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))),2).
weight(P(i(x,i(n(i(y,y)),z))),2).
weight(P(i(i(i(n(i(x,x)),y),z),i(u,z))),2).
weight(P(i(x,i(y,y))),2).
weight(P(i(i(i(x,x),y),i(z,y))),2).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
weight(P(i(x,i(i(n(y),y),y))),2).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
weight(P(i(x,i(y,x))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(x,i(y,x))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(i(x,y),i(i(n(y),x),y))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
end_of_list.
  
list(usable).
-P(i(x,y)) | -P(x) | P(y).
  
%  The following disjunctions are known axiom systems.
  
% -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
% -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
% $ANSWER(step_allFrege_18_35_39_40_46_21).  % 21 is dependent.
   
% -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
% -P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
% -P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
% $ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
   
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
   
% -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
% -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
   
% -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
% -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) |
$ANSWER(step_allWos_x_19_37_60).
   
% -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
% -P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
   
% -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
% -P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
% -P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
% $ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
   
% -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
% -P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
% -P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
% $ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
   
end_of_list.
  
list(sos).
%  P(i(x,i(i(n(y),y),y))).
%  The following three are Luka, 1 2 3.
P(i(i(x,y),i(i(y,z),i(x,z)))).
P(i(i(n(x),x),x)).
P(i(x,i(n(x),y))).
  
%  The following are from Frege, 18 35 21 46 39 40, with 21 dependent.
% P(i(x,i(y,x))).  %  axiom F1.
% P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).  %  axiom F2.
% P(i(i(x,i(y,z)),i(y,i(x,z)))).  %  axiom F3.
% P(i(i(x,y),i(n(y),n(x)))).  %  axiom F4.
% P(i(n(n(x)),x)).  %  axiom F5.
% P(i(x,n(n(x)))).  %  axiom f6.
end_of_list.
  
list(passive).
% -P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
% -P(i(i(n(p),p),p)) | $ANSWER(step_L2).
% -P(i(p,i(n(p),q))) | $ANSWER(step_L3).
-P(i(q,i(p,q))) | $ANSWER(step_18).
% -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
% -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
% -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
% -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
-P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
% -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
% -P(i(n(n(p)),p)) | $ANSWER(step_39).
% -P(i(p,n(n(p)))) | $ANSWER(step_40).
% -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
% -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
% -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
% -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
% (n(n(x)) = junk).
(n(n(n(x))) = junk).
% (i(i(x,x),y) = junk).
% (i(y,i(x,x)) = junk).
(i(junk,x) = junk).
(i(x,junk) = junk).
(n(junk) = junk).
(P(junk) = $T).
end_of_list.

Input File for Stage 4 of Example 1

%  luka completeness of 123 exps.
set(hyper_res).
% assign(reduce_weight_limit,010024).
assign(max_weight,20).
% set(control_memory).
assign(max_proofs, 0).
clear(print_kept).
% set(very_verbose).
set(ancestor_subsume).
% clear(back_sub).
% assign(max_seconds, 600).
assign(max_mem, 100000).
assign(report, 900).
assign(max_distinct_vars, 5).
assign(pick_given_ratio, 3).
set(order_history).
set(input_sos_first).
% set(sos_queue).
  
weight_list(pick_and_purge).
%  Following are the union of earlier shorter proofs, lengths 31 29 28.
weight(P(i(i(i(i(n(x),x),x),y),i(z,y))),1).
weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),1).
weight(P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))),1).
weight(P(i(i(i(i(x,y),y),z),i(x,z))),1).
weight(P(i(i(i(n(i(x,x)),y),z),i(u,z))),1).
weight(P(i(i(i(n(x),y),z),i(x,z))),1).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),1).
weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),1).
weight(P(i(i(i(x,x),y),i(z,y))),1).
weight(P(i(i(i(x,y),x),x)),1).
weight(P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))),1).
weight(P(i(i(i(x,y),z),i(y,z))),1).
weight(P(i(i(n(x),n(y)),i(y,x))),1).
weight(P(i(i(n(x),y),i(i(y,x),x))),1).
weight(P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))),1).
weight(P(i(i(n(x),y),i(n(y),x))),1).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),1).
weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),1).
weight(P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))),1).
weight(P(i(i(x,i(n(y),y)),i(z,i(x,y)))),1).
weight(P(i(i(x,i(x,y)),i(x,y))),1).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),1).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),1).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),1).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),1).
weight(P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))),1).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),1).
weight(P(i(i(x,n(y)),i(y,i(x,z)))),1).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),1).
weight(P(i(i(x,y),i(i(n(x),x),y))),1).
weight(P(i(i(x,y),i(i(n(y),x),y))),1).
weight(P(i(i(x,y),i(i(z,x),i(z,y)))),1).
weight(P(i(n(i(i(n(x),x),x)),y)),1).
weight(P(i(n(i(x,x)),y)),1).
weight(P(i(n(i(x,y)),x)),1).
weight(P(i(n(x),i(x,y))),1).
weight(P(i(x,i(i(i(y,z),y),y))),1).
weight(P(i(x,i(i(n(y),y),y))),1).
weight(P(i(x,i(i(x,y),y))),1).
weight(P(i(x,i(n(i(i(n(y),y),y)),z))),1).
weight(P(i(x,i(n(i(y,y)),z))),1).
weight(P(i(x,i(y,i(i(x,z),z)))),1).
weight(P(i(x,i(y,x))),1).
weight(P(i(x,i(y,y))),1).
weight(P(i(x,x)),1).
%  Following are 68 theses suggested by Scott.
weight(P(i(i(i(i(y,z),i(x,z)),u),i(i(x,y),u))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(v,i(i(x,z),u)),i(i(x,y),i(v,i(i(y,z),u))))),2).
weight(P(i(i(y,z),i(i(x,y),i(i(z,u),i(x,u))))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),2).
weight(P(i(i(y,i(i(n(x),x),x)),i(i(n(x),x),x))),2).
weight(P(i(v,i(i(n(x),x),x))),2).
weight(P(i(i(n(x),y),i(v,i(i(y,x),x)))),2).
weight(P(i(i(i(v,i(i(y,x),x)),z),i(i(n(x),y),z))),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(x,x)),2).
weight(P(i(x,i(i(y,x),x))),2).
weight(P(i(y,i(x,y))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(i(y,z),i(i(x,y),i(x,z)))),2).
weight(P(i(i(i(y,i(x,z)),u),i(i(x,i(y,z)),u))),2).
weight(P(i(i(i(x,y),x),x)),2).
weight(P(i(i(i(x,z),u),i(i(x,y),i(i(y,z),u)))),2).
weight(P(i(i(i(x,y),z),i(i(z,x),x))),2).
weight(P(i(i(i(x,y),y),i(i(y,x),x))),2).
weight(P(i(i(i(i(z,x),x),u),i(i(i(x,y),z),u))),2).
weight(P(i(i(i(x,y),z),i(i(x,z),z))),2).
weight(P(i(i(x,i(x,y)),i(x,y))),2).
weight(P(i(i(x,u),i(i(i(x,y),z),i(i(u,z),z)))),2).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2).
weight(P(i(i(x,u),i(i(u,i(y,i(x,z))),i(y,i(x,z))))),2).
weight(P(i(i(u,i(y,i(x,z))),i(i(x,u),i(y,i(x,z))))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(i(i(x,y),z),i(n(x),z))),2).
weight(P(i(i(x,n(x)),n(x))),2).
weight(P(i(n(n(x)),x)),2).
weight(P(i(x,n(n(x)))),2).
weight(P(i(i(x,y),i(n(n(x)),y))),2).
weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),2).
weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),2).
weight(P(i(i(u,i(y,n(x))),i(i(x,y),i(u,n(x))))),2).
weight(P(i(i(u,i(y,x)),i(i(n(x),y),i(u,x)))),2).
weight(P(i(i(x,y),i(n(y),n(x)))),2).
weight(P(i(i(x,n(y)),i(y,n(x)))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(i(n(y),x),z),i(i(n(x),y),z))),2).
weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),2).
weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),2).
weight(P(i(i(n(x),y),i(i(x,y),y))),2).
weight(P(i(i(x,y),i(i(n(x),y),y))),2).
weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),2).
weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),2).
weight(P(i(i(n(x),z),i(i(x,y),i(i(y,z),z)))),2).
weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),2).
weight(P(i(i(n(x),z),i(i(y,z),i(i(x,y),z)))),2).
weight(P(i(i(u,i(n(x),z)),i(u,i(i(y,z),i(i(x,y),z))))),2).
weight(P(i(i(x,z),i(i(y,z),i(i(n(x),y),z)))),2).
weight(P(i(i(n(n(x)),y),i(x,y))),2).
weight(P(i(y,i(x,x))),2).
weight(P(i(n(i(x,x)),y)),2).
weight(P(i(i(n(y),n(i(x,x))),y)),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(n(i(x,y)),n(y))),2).
weight(P(i(n(i(x,n(y))),y)),2).
weight(P(i(x,i(n(y),n(i(x,y))))),2).
weight(P(i(x,i(y,n(i(x,n(y)))))),2).
weight(P(n(i(i(x,x),n(i(y,y))))),2).
end_of_list.
  
list(usable).
-P(i(x,y)) | -P(x) | P(y).
  
%  The following disjunctions are known axiom systems.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | 
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
$ANSWER(step_allFrege_18_35_39_40_46_21).  % 21 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | 
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
  
-P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | 
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) |
$ANSWER(step_allWos_x_19_37_60).
  
-P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | 
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | 
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
  
-P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | 
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
  
end_of_list.
  
list(sos).
%  The following three are Luka, 1 2 3.
P(i(i(x,y),i(i(y,z),i(x,z)))).
P(i(i(n(x),x),x)).
P(i(x,i(n(x),y))).
  
%  The following are from Frege, 18 35 21 46 39 40, with 21 dependent.
% P(i(x,i(y,x))).  %  axiom F1.
% P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).  %  axiom F2.
% P(i(i(x,i(y,z)),i(y,i(x,z)))).  %  axiom F3.
% P(i(i(x,y),i(n(y),n(x)))).  %  axiom F4.
% P(i(n(n(x)),x)).  %  axiom F5.
% P(i(x,n(n(x)))).  %  axiom f6.
end_of_list.
  
list(passive).
-P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
-P(i(i(n(p),p),p)) | $ANSWER(step_L2).
-P(i(p,i(n(p),q))) | $ANSWER(step_L3).
-P(i(q,i(p,q))) | $ANSWER(step_18).
-P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
-P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
-P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
-P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
-P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
-P(i(n(n(p)),p)) | $ANSWER(step_39).
-P(i(p,n(n(p)))) | $ANSWER(step_40).
-P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
-P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
% (n(n(x)) = junk).
(n(n(n(x))) = junk).
(i(i(x,x),y) = junk).
(i(y,i(x,x)) = junk).
(i(junk,x) = junk).
(i(x,junk) = junk).
(n(junk) = junk).
(P(junk) = $T).
end_of_list.

                 Proof for Stage 4 of Example 1

-----> EMPTY CLAUSE at 6422.88 sec ----> 90903 [hyper,4,284,90712,228]
$ANSWER(step_allBEH_Church_FL_18_35_49).
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
4 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
57 [hyper,1,37,41] P(i(i(x,n(y)),i(y,i(x,z)))).
74 [hyper,1,44,38] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
100 [hyper,1,57,42] P(i(x,i(n(i(i(n(y),y),y)),z))).
118 [hyper,1,74,100] P(i(i(i(i(n(x),x),x),y),i(z,y))).
144 [hyper,1,37,118] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
164 [hyper,1,37,144] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
200 [hyper,1,74,164] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
217 [hyper,1,37,200] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
228 [hyper,1,200,41] P(i(i(n(x),n(y)),i(y,x))).
263 [hyper,1,44,217] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
284 [hyper,1,41,228] P(i(x,i(y,x))).
374 [hyper,1,10,284] P(i(i(i(x,y),z),i(y,z))).
434 [hyper,1,374,228] P(i(n(x),i(x,y))).
531 [hyper,1,10,434] P(i(i(i(x,y),z),i(n(x),z))).
8071 [hyper,1,531,531] P(i(n(i(x,y)),i(n(x),z))).
54057 [hyper,1,74,8071] P(i(i(x,y),i(n(i(x,z)),y))).
89816 [hyper,1,263,54057] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
90712 [hyper,1,89816,10] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
90903 [hyper,4,284,90712,228] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 23

             Shortest Proof of Church Found in Example 1

-----> EMPTY CLAUSE at  20.96 sec ----> 287 [hyper,4,76,269,64]
$ANSWER(step_allBEH_Church_FL_18_35_49).
---------------- PROOF ----------------
  
1 [] -P(i(x,y)) | -P(x) | P(y).
4 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
34 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
35 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
37 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
38 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
39 [hyper,1,34,34] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
43 [hyper,1,34,37] P(i(i(x,n(y)),i(y,i(x,z)))).
44 [hyper,1,39,35] P(i(i(x,i(n(y),y)),i(i(y,z),i(x,z)))).
46 [hyper,1,43,38] P(i(x,i(n(i(i(n(y),y),y)),z))).
48 [hyper,1,44,46] P(i(i(i(i(n(x),x),x),y),i(z,y))).
50 [hyper,1,34,48] P(i(i(x,i(n(y),y)),i(z,i(x,y)))).
52 [hyper,1,34,50] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
56 [hyper,1,44,52] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
64 [hyper,1,56,37] P(i(i(n(x),n(y)),i(y,x))).
66 [hyper,1,56,34] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
76 [hyper,1,37,64] P(i(x,i(y,x))).
88 [hyper,1,10,76] P(i(i(i(x,y),z),i(y,z))).
109 [hyper,1,88,64] P(i(n(x),i(x,y))).
134 [hyper,1,10,109] P(i(i(i(x,y),z),i(n(x),z))).
165 [hyper,1,134,134] P(i(n(i(x,y)),i(n(x),z))).
210 [hyper,1,44,165] P(i(i(x,y),i(n(i(x,z)),y))).
243 [hyper,1,10,210] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
269 [hyper,1,243,66] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
287 [hyper,4,76,269,64] $ANSWER(step_allBEH_Church_FL_18_35_49).
  
length of proof is 22
\end{verbatim}
\begin{verbatim}

                        Appendix C

The following input file was successfully used to proof check the original
33-step Lukasiewicz proof of Church and of related theorems.

          Input File for Rigorous Proof Checking

set(hyper_res).
% clear(print_kept).
assign(report,60).
assign(max_mem,8000).
assign(max_weight,80).
assign(max_proofs,0).
set(input_sos_first).
set(order_history).
  
weight_list(pick_and_purge).
weight(P(rew(*0,*0),*1),99).
end_of_list.
  
list(usable).
-P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y).
-P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(z,i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
-P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(z,i(n(n(p)),p)) | -P(u,i(p,n(n(p)))) | -P(v,i(i(p,q),i(n(q),n(p)))) | 
-P(w,i(i(p,i(q,r)),i(q,i(p,r)))) | 
$ANSWER(step_allFrege_18_35_39_40_46_21).  % 21 is dependent.
-P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(z,i(i(q,r),i(i(p,q),i(p,r)))) | -P(u,i(p,i(n(p),q))) | 
-P(v,i(i(p,q),i(i(n(p),q),q))) | -P(w,i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
-P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) | 
-P(z,i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
-P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) | 
-P(z,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | 
$ANSWER(step_allWos_x_19_37_60).
end_of_list.
  
list(sos).
P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
P(c2,i(i(n(x),x),x)).
P(c3,i(x,i(n(x),y))).
end_of_list.
  
list(passive).
% -P(x,i(i(i(i(q,r),i(p,r)),s),i(i(p,q),s))) | $ANS(neg_th_04).
% -P(x,i(i(p,i(q,r)),i(i(s,q),i(p,i(s,r))))) | $ANS(neg_th_05).
% -P(x,i(i(p,q),i(i(i(p,r),s),i(i(q,r),s)))) | $ANS(neg_th_06).
% -P(x,i(i(t,i(i(p,r),s)),i(i(p,q),i(t,i(i(q,r),s))))) | $ANS(neg_th_07).
% -P(x,i(i(q,r),i(i(p,q),i(i(r,s),i(p,s))))) | $ANS(neg_th_08).
% -P(x,i(i(i(n(p),q),r),i(p,r))) | $ANS(neg_th_09).
% -P(x,i(p,i(i(i(n(p),p),p),i(i(q,p),p)))) | $ANS(neg_th_10).
% -P(x,i(i(q,i(i(n(p),p),p)),i(i(n(p),p),p))) | $ANS(neg_th_11).
% -P(x,i(t,i(i(n(p),p),p))) | $ANS(neg_th_12).
% -P(x,i(i(n(p),q),i(t,i(i(q,p),p)))) | $ANS(neg_th_13).
% -P(x,i(i(i(t,i(i(q,p),p)),r),i(i(n(p),q),r))) | $ANS(neg_th_14).
% -P(x,i(i(n(p),q),i(i(q,p),p))) | $ANS(neg_th_15).
% -P(x,i(p,p)) | $ANS(neg_th_16).
% -P(x,i(p,i(i(q,p),p))) | $ANS(neg_th_17).
% -P(x,i(q,i(p,q))) | $ANS(neg_th_18).
% -P(x,i(i(i(p,q),r),i(q,r))) | $ANS(neg_th_19).
% -P(x,i(p,i(i(p,q),q))) | $ANS(neg_th_20).
% -P(x,i(i(p,i(q,r)),i(q,i(p,r)))) | $ANS(neg_th_21).
% -P(x,i(i(q,r),i(i(p,q),i(p,r)))) | $ANS(neg_th_22).
% -P(x,i(i(i(q,i(p,r)),s),i(i(p,i(q,r)),s))) | $ANS(neg_th_23).
% -P(x,i(i(i(p,q),p),p)) | $ANS(neg_th_24).
% -P(x,i(i(i(p,r),s),i(i(p,q),i(i(q,r),s)))) | $ANS(neg_th_25).
% -P(x,i(i(i(p,q),r),i(i(r,p),p))) | $ANS(neg_th_26).
% -P(x,i(i(i(p,q),q),i(i(q,p),p))) | $ANS(neg_th_27).
% -P(x,i(i(i(i(r,p),p),s),i(i(i(p,q),r),s))) | $ANS(neg_th_28).
% -P(x,i(i(i(p,q),r),i(i(p,r),r))) | $ANS(neg_th_29).
% -P(x,i(i(p,i(p,q)),i(p,q))) | $ANS(neg_th_30).
% -P(x,i(i(p,s),i(i(i(p,q),r),i(i(s,r),r)))) | $ANS(neg_th_31).
% -P(x,i(i(i(p,q),r),i(i(p,s),i(i(s,r),r)))) | $ANS(neg_th_32).
% -P(x,i(i(p,s),i(i(s,i(q,i(p,r))),i(q,i(p,r))))) | $ANS(neg_th_33).
% -P(x,i(i(s,i(q,i(p,r))),i(i(p,s),i(q,i(p,r))))) | $ANS(neg_th_34).
% -P(x,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANS(neg_th_35).
% -P(x,i(n(p),i(p,q))) | $ANS(neg_th_36).
% -P(x,i(i(i(p,q),r),i(n(p),r))) | $ANS(neg_th_37).
% -P(x,i(i(p,n(p)),n(p))) | $ANS(neg_th_38).
% -P(x,i(n(n(p)),p)) | $ANS(neg_th_39).
% -P(x,i(p,n(n(p)))) | $ANS(neg_th_40).
% -P(x,i(i(p,q),i(n(n(p)),q))) | $ANS(neg_th_41).
% -P(x,i(i(i(n(n(p)),q),r),i(i(p,q),r))) | $ANS(neg_th_42).
% -P(x,i(i(p,q),i(i(q,n(p)),n(p)))) | $ANS(neg_th_43).
% -P(x,i(i(s,i(q,n(p))),i(i(p,q),i(s,n(p))))) | $ANS(neg_th_44).
% -P(x,i(i(s,i(q,p)),i(i(n(p),q),i(s,p)))) | $ANS(neg_th_45).
% -P(x,i(i(p,q),i(n(q),n(p)))) | $ANS(neg_th_46).
% -P(x,i(i(p,n(q)),i(q,n(p)))) | $ANS(neg_th_47).
% -P(x,i(i(n(p),q),i(n(q),p))) | $ANS(neg_th_48).
% -P(x,i(i(n(p),n(q)),i(q,p))) | $ANS(neg_th_49).
% -P(x,i(i(i(n(q),p),r),i(i(n(p),q),r))) | $ANS(neg_th_50).
% -P(x,i(i(p,i(q,r)),i(p,i(n(r),n(q))))) | $ANS(neg_th_51).
% -P(x,i(i(p,i(q,n(r))),i(p,i(r,n(q))))) | $ANS(neg_th_52).
% -P(x,i(i(n(p),q),i(i(p,q),q))) | $ANS(neg_th_53).
% -P(x,i(i(p,q),i(i(n(p),q),q))) | $ANS(neg_th_54).
% -P(x,i(i(p,q),i(i(p,n(q)),n(p)))) | $ANS(neg_th_55).
% -P(x,i(i(i(i(p,q),q),r),i(i(n(p),q),r))) | $ANS(neg_th_56).
% -P(x,i(i(n(p),r),i(i(p,q),i(i(q,r),r)))) | $ANS(neg_th_57).
% -P(x,i(i(i(i(p,q),i(i(q,r),r)),s),i(i(n(p),r),s))) | $ANS(neg_th_58).
% -P(x,i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANS(neg_th_59).
% -P(x,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANS(neg_th_60).
% -P(x,i(i(p,r),i(i(q,r),i(i(n(p),q),r)))) | $ANS(neg_th_61).
% -P(x,i(i(n(n(p)),q),i(p,q))) | $ANS(neg_th_62).
% -P(x,i(q,i(p,p))) | $ANS(neg_th_63).
% -P(x,i(n(i(p,p)),q)) | $ANS(neg_th_64).
% -P(x,i(i(n(q),n(i(p,p))),q)) | $ANS(neg_th_65).
% -P(x,i(n(i(p,q)),p)) | $ANS(neg_th_66).
% -P(x,i(n(i(p,q)),n(q))) | $ANS(neg_th_67).
% -P(x,i(n(i(p,n(q))),q)) | $ANS(neg_th_68).
% -P(x,i(p,i(n(q),n(i(p,q))))) | $ANS(neg_th_69).
% -P(x,i(p,i(q,n(i(p,n(q)))))) | $ANS(neg_th_70).
% -P(x,n(i(i(p,p),n(i(q,q))))) | $ANS(neg_th_71).
end_of_list.
  
list(demodulators).
%  Following mirror Lukasiewicz proof with history.
EQ(rew(c1,c1),c4).
EQ(rew(c4,c4),c5).
EQ(rew(c4,c1),c6).
EQ(rew(c5,c6),c7).
EQ(rew(c7,c1),c8).
EQ(rew(c1,c3),c9).
EQ(rew(c9,c6),c10).
EQ(rew(c10,c2),c10a).
EQ(rew(c10a,c2),c11).
EQ(rew(c9,c11),c12).
EQ(rew(c7,c12),c13).
EQ(rew(c1,c13),c14).
EQ(rew(c14,c2),c15).
EQ(rew(c9,c2),c16).
EQ(rew(c9,c15),c17).
EQ(rew(c5,c17),c17a).
EQ(rew(c17a,c3),c18).
EQ(rew(c1,c18),c19).
EQ(rew(c19,c15),c20).
EQ(rew(c5,c20),c21).
EQ(rew(c21,c1),c22).
EQ(rew(c1,c21),c23).
EQ(rew(c23,c15),c24a).
EQ(rew(c24a,c3),c24).
EQ(rew(c21,c6),c25).
EQ(rew(c25,c24),c26).
EQ(rew(c1,c26),c28).
EQ(rew(c28,c26),c29).
EQ(rew(c29,c16),c30).
EQ(rew(c7,c29),c31).
EQ(rew(c21,c31),c32).
EQ(rew(c32,c18),c33).
EQ(rew(c21,c33),c34).
EQ(rew(c34,c22),c35).
EQ(rew(c21,c3),c36).
EQ(rew(c1,c36),c37).
EQ(rew(c26,c2),c38).
EQ(rew(c37,c2),c39).
EQ(rew(c9,c38),c40).
EQ(rew(c1,c39),c41).
EQ(rew(c1,c41),c42).
EQ(rew(c42,c15),c43).
EQ(rew(c5,c43),c44).
EQ(rew(c5,c15),c45).
EQ(rew(c44,c36),c46).
EQ(rew(c44,c3),c47).
EQ(rew(c45,c36),c48).
EQ(rew(c45,c3),c49).
EQ(rew(c1,c48),c50).
EQ(rew(c22,c46),c51).
EQ(rew(c22,c47),c52).
EQ(rew(c50,c15),c53).
EQ(rew(c21,c53),c54).
EQ(rew(c44,c47),c55).
EQ(rew(c1,c53),c56).
EQ(rew(c56,c32),c57).
EQ(rew(c1,c57),c58).
EQ(rew(c58,c21),c59).
EQ(rew(c22,c59),c60).
EQ(rew(c60,c41),c61).
EQ(rew(c1,c40),c62).
EQ(rew(c21,c18),c63).
EQ(rew(c48,c63),c64).
EQ(rew(c61,c16),c64a).
EQ(rew(c64a,c64),c65).
EQ(rew(c48,c36),c66).
EQ(rew(c46,c18),c67).
EQ(rew(c48,c18),c68).
EQ(rew(c51,c20),c69).
EQ(rew(c52,c20),c70).
EQ(rew(c70,c16),c70a).
EQ(rew(c70a,c16),c71).
end_of_list.

         Summary of Output for Rigorous Proof Checking

----- OTTER 2.2, July 1991 -----
The job began on cosmo.mcs.anl.gov, Sun Aug  9 15:34:06 1992
The command was "otter4+".

set(hyper_res).
assign(report,60).
assign(max_mem,8000).
assign(max_weight,80).
assign(max_proofs,0).
set(input_sos_first).
set(order_history).

weight_list(pick_and_purge).
weight(P(rew(*0,*0),*1),99).
end_of_list.

list(usable).
1 [] -P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y).
2 [] -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(z,i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
3 [] -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(z,i(n(n(p)),p)) | -P(u,i(p,n(n(p)))) | -P(v,i(i(p,q),i(n(q),n(p)))) | 
-P(w,i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
4 [] -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(q,i(p,r)))) | 
-P(z,i(i(q,r),i(i(p,q),i(p,r)))) | -P(u,i(p,i(n(p),q))) | 
-P(v,i(i(p,q),i(i(n(p),q),q))) | -P(w,i(i(p,i(p,q)),i(p,q))) | 
$ANSWER(step_allHilbert_18_21_22_3_54_30).
5 [] -P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) | 
-P(z,i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
6 [] -P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) | 
-P(z,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | 
$ANSWER(step_allWos_x_19_37_60).
end_of_list.

list(sos).
7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
8 [] P(c2,i(i(n(x),x),x)).
9 [] P(c3,i(x,i(n(x),y))).
end_of_list.

list(passive).
end_of_list.

list(demodulators).
10 [] EQ(rew(c1,c1),c4).
11 [] EQ(rew(c4,c4),c5).
12 [] EQ(rew(c4,c1),c6).
13 [] EQ(rew(c5,c6),c7).
14 [] EQ(rew(c7,c1),c8).
15 [] EQ(rew(c1,c3),c9).
16 [] EQ(rew(c9,c6),c10).
17 [] EQ(rew(c10,c2),c10a).
18 [] EQ(rew(c10a,c2),c11).
19 [] EQ(rew(c9,c11),c12).
20 [] EQ(rew(c7,c12),c13).
21 [] EQ(rew(c1,c13),c14).
22 [] EQ(rew(c14,c2),c15).
23 [] EQ(rew(c9,c2),c16).
24 [] EQ(rew(c9,c15),c17).
25 [] EQ(rew(c5,c17),c17a).
26 [] EQ(rew(c17a,c3),c18).
27 [] EQ(rew(c1,c18),c19).
28 [] EQ(rew(c19,c15),c20).
29 [] EQ(rew(c5,c20),c21).
30 [] EQ(rew(c21,c1),c22).
31 [] EQ(rew(c1,c21),c23).
32 [] EQ(rew(c23,c15),c24a).
33 [] EQ(rew(c24a,c3),c24).
34 [] EQ(rew(c21,c6),c25).
35 [] EQ(rew(c25,c24),c26).
36 [] EQ(rew(c1,c26),c28).
37 [] EQ(rew(c28,c26),c29).
38 [] EQ(rew(c29,c16),c30).
39 [] EQ(rew(c7,c29),c31).
40 [] EQ(rew(c21,c31),c32).
41 [] EQ(rew(c32,c18),c33).
42 [] EQ(rew(c21,c33),c34).
43 [] EQ(rew(c34,c22),c35).
44 [] EQ(rew(c21,c3),c36).
45 [] EQ(rew(c1,c36),c37).
46 [] EQ(rew(c26,c2),c38).
47 [] EQ(rew(c37,c2),c39).
48 [] EQ(rew(c9,c38),c40).
49 [] EQ(rew(c1,c39),c41).
50 [] EQ(rew(c1,c41),c42).
51 [] EQ(rew(c42,c15),c43).
52 [] EQ(rew(c5,c43),c44).
53 [] EQ(rew(c5,c15),c45).
54 [] EQ(rew(c44,c36),c46).
55 [] EQ(rew(c44,c3),c47).
56 [] EQ(rew(c45,c36),c48).
57 [] EQ(rew(c45,c3),c49).
58 [] EQ(rew(c1,c48),c50).
59 [] EQ(rew(c22,c46),c51).
60 [] EQ(rew(c22,c47),c52).
61 [] EQ(rew(c50,c15),c53).
62 [] EQ(rew(c21,c53),c54).
63 [] EQ(rew(c44,c47),c55).
64 [] EQ(rew(c1,c53),c56).
65 [] EQ(rew(c56,c32),c57).
66 [] EQ(rew(c1,c57),c58).
67 [] EQ(rew(c58,c21),c59).
68 [] EQ(rew(c22,c59),c60).
69 [] EQ(rew(c60,c41),c61).
70 [] EQ(rew(c1,c40),c62).
71 [] EQ(rew(c21,c18),c63).
72 [] EQ(rew(c48,c63),c64).
73 [] EQ(rew(c61,c16),c64a).
74 [] EQ(rew(c64a,c64),c65).
75 [] EQ(rew(c48,c36),c66).
76 [] EQ(rew(c46,c18),c67).
77 [] EQ(rew(c48,c18),c68).
78 [] EQ(rew(c51,c20),c69).
79 [] EQ(rew(c52,c20),c70).
80 [] EQ(rew(c70,c16),c70a).
81 [] EQ(rew(c70a,c16),c71).
end_of_list.

given clause #1: (wt=-2147483647) 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
-----> EMPTY CLAUSE at   1.84 sec ----> 143 [hyper,4,99,102,107,9,121,142]
$ANSWER(step_allHilbert_18_21_22_3_54_30).  Length of proof is 34.
---------------- PROOF ----------------

1 [] -P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y).
4 [] -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(z,i(i(q,r),i(i(p,q),i(p,r)))) | -P(u,i(p,i(n(p),q))) |
-P(v,i(i(p,q),i(i(n(p),q),q))) | -P(w,i(i(p,i(p,q)),i(p,q))) |
$ANSWER(step_allHilbert_18_21_22_3_54_30).
7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
8 [] P(c2,i(i(n(x),x),x)).
9 [] P(c3,i(x,i(n(x),y))).
10 [] EQ(rew(c1,c1),c4).
11 [] EQ(rew(c4,c4),c5).
12 [] EQ(rew(c4,c1),c6).
13 [] EQ(rew(c5,c6),c7).
15 [] EQ(rew(c1,c3),c9).
16 [] EQ(rew(c9,c6),c10).
17 [] EQ(rew(c10,c2),c10a).
18 [] EQ(rew(c10a,c2),c11).
19 [] EQ(rew(c9,c11),c12).
20 [] EQ(rew(c7,c12),c13).
21 [] EQ(rew(c1,c13),c14).
22 [] EQ(rew(c14,c2),c15).
23 [] EQ(rew(c9,c2),c16).
24 [] EQ(rew(c9,c15),c17).
25 [] EQ(rew(c5,c17),c17a).
26 [] EQ(rew(c17a,c3),c18).
27 [] EQ(rew(c1,c18),c19).
28 [] EQ(rew(c19,c15),c20).
29 [] EQ(rew(c5,c20),c21).
30 [] EQ(rew(c21,c1),c22).
31 [] EQ(rew(c1,c21),c23).
32 [] EQ(rew(c23,c15),c24a).
33 [] EQ(rew(c24a,c3),c24).
34 [] EQ(rew(c21,c6),c25).
35 [] EQ(rew(c25,c24),c26).
36 [] EQ(rew(c1,c26),c28).
37 [] EQ(rew(c28,c26),c29).
38 [] EQ(rew(c29,c16),c30).
44 [] EQ(rew(c21,c3),c36).
53 [] EQ(rew(c5,c15),c45).
56 [] EQ(rew(c45,c36),c48).
58 [] EQ(rew(c1,c48),c50).
61 [] EQ(rew(c50,c15),c53).
62 [] EQ(rew(c21,c53),c54).
82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))).
84 [hyper,1,83,8,demod,23] P(c16,i(x,x)).
85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))).
92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))).
94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))).
96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))).
98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))).
99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))).
100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))).
101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))).
102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))).
103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))).
106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))).
107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))).
114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))).
116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))).
120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))).
121 [hyper,1,102,120,demod,62] P(c54,i(i(x,y),i(i(n(x),y),y))).
123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))).
124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)).
125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))).
126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))).
140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))).
142 [hyper,1,140,84,demod,38] P(c30,i(i(x,i(x,y)),i(x,y))).
143 [hyper,4,99,102,107,9,121,142] $ANSWER(step_allHilbert_18_21_22_3_54_30).

length of proof is 34
------------ end of proof -------------
-----> EMPTY CLAUSE at   2.30 sec ----> 150 [hyper,3,99,149,109,128,130,102]
$ANSWER(step_allFrege_18_35_39_40_46_21).  Length of proof is 41.
---------------- PROOF ----------------

1 [] -P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y).
3 [] -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(z,i(n(n(p)),p)) | -P(u,i(p,n(n(p)))) | -P(v,i(i(p,q),i(n(q),n(p)))) | 
-P(w,i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
8 [] P(c2,i(i(n(x),x),x)).
9 [] P(c3,i(x,i(n(x),y))).
10 [] EQ(rew(c1,c1),c4).
11 [] EQ(rew(c4,c4),c5).
12 [] EQ(rew(c4,c1),c6).
13 [] EQ(rew(c5,c6),c7).
15 [] EQ(rew(c1,c3),c9).
16 [] EQ(rew(c9,c6),c10).
17 [] EQ(rew(c10,c2),c10a).
18 [] EQ(rew(c10a,c2),c11).
19 [] EQ(rew(c9,c11),c12).
20 [] EQ(rew(c7,c12),c13).
21 [] EQ(rew(c1,c13),c14).
22 [] EQ(rew(c14,c2),c15).
24 [] EQ(rew(c9,c15),c17).
25 [] EQ(rew(c5,c17),c17a).
26 [] EQ(rew(c17a,c3),c18).
27 [] EQ(rew(c1,c18),c19).
28 [] EQ(rew(c19,c15),c20).
29 [] EQ(rew(c5,c20),c21).
30 [] EQ(rew(c21,c1),c22).
31 [] EQ(rew(c1,c21),c23).
32 [] EQ(rew(c23,c15),c24a).
33 [] EQ(rew(c24a,c3),c24).
34 [] EQ(rew(c21,c6),c25).
35 [] EQ(rew(c25,c24),c26).
36 [] EQ(rew(c1,c26),c28).
37 [] EQ(rew(c28,c26),c29).
39 [] EQ(rew(c7,c29),c31).
40 [] EQ(rew(c21,c31),c32).
41 [] EQ(rew(c32,c18),c33).
42 [] EQ(rew(c21,c33),c34).
43 [] EQ(rew(c34,c22),c35).
44 [] EQ(rew(c21,c3),c36).
45 [] EQ(rew(c1,c36),c37).
46 [] EQ(rew(c26,c2),c38).
47 [] EQ(rew(c37,c2),c39).
48 [] EQ(rew(c9,c38),c40).
49 [] EQ(rew(c1,c39),c41).
50 [] EQ(rew(c1,c41),c42).
51 [] EQ(rew(c42,c15),c43).
52 [] EQ(rew(c5,c43),c44).
54 [] EQ(rew(c44,c36),c46).
82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))).
85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))).
92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))).
94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))).
97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))).
98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))).
99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))).
100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))).
101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))).
102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))).
103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))).
106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))).
107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))).
108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))).
109 [hyper,1,108,8,demod,47] P(c39,i(n(n(x)),x)).
110 [hyper,1,7,109,demod,49] P(c41,i(i(x,y),i(n(n(x)),y))).
111 [hyper,1,7,110,demod,50] P(c42,i(i(i(n(n(x)),y),z),i(i(x,y),z))).
112 [hyper,1,111,95,demod,51] P(c43,i(i(x,y),i(i(y,n(x)),n(x)))).
113 [hyper,1,85,112,demod,52] P(c44,i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))).
124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)).
125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))).
126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))).
127 [hyper,1,125,8,demod,46] P(c38,i(i(x,n(x)),n(x))).
128 [hyper,1,83,127,demod,48] P(c40,i(x,n(n(x)))).
130 [hyper,1,113,106,demod,54] P(c46,i(i(x,y),i(n(y),n(x)))).
140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))).
141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))).
144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))).
146 [hyper,1,144,99,demod,41] P(c33,i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))).
148 [hyper,1,102,146,demod,42] P(c34,i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))).
149 [hyper,1,148,107,demod,43] P(c35,i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
150 [hyper,3,99,149,109,128,130,102] $ANSWER(step_allFrege_18_35_39_40_46_21).

length of proof is 41
------------ end of proof -------------
-----> EMPTY CLAUSE at   2.36 sec ----> 151 [hyper,2,99,149,115]
$ANSWER(step_allBEH_Church_FL_18_35_49).  Length of proof is 33.
---------------- PROOF ----------------

1 [] -P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y).
2 [] -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | 
-P(z,i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
8 [] P(c2,i(i(n(x),x),x)).
9 [] P(c3,i(x,i(n(x),y))).
10 [] EQ(rew(c1,c1),c4).
11 [] EQ(rew(c4,c4),c5).
12 [] EQ(rew(c4,c1),c6).
13 [] EQ(rew(c5,c6),c7).
15 [] EQ(rew(c1,c3),c9).
16 [] EQ(rew(c9,c6),c10).
17 [] EQ(rew(c10,c2),c10a).
18 [] EQ(rew(c10a,c2),c11).
19 [] EQ(rew(c9,c11),c12).
20 [] EQ(rew(c7,c12),c13).
21 [] EQ(rew(c1,c13),c14).
22 [] EQ(rew(c14,c2),c15).
24 [] EQ(rew(c9,c15),c17).
25 [] EQ(rew(c5,c17),c17a).
26 [] EQ(rew(c17a,c3),c18).
27 [] EQ(rew(c1,c18),c19).
28 [] EQ(rew(c19,c15),c20).
29 [] EQ(rew(c5,c20),c21).
30 [] EQ(rew(c21,c1),c22).
31 [] EQ(rew(c1,c21),c23).
32 [] EQ(rew(c23,c15),c24a).
33 [] EQ(rew(c24a,c3),c24).
34 [] EQ(rew(c21,c6),c25).
35 [] EQ(rew(c25,c24),c26).
36 [] EQ(rew(c1,c26),c28).
37 [] EQ(rew(c28,c26),c29).
39 [] EQ(rew(c7,c29),c31).
40 [] EQ(rew(c21,c31),c32).
41 [] EQ(rew(c32,c18),c33).
42 [] EQ(rew(c21,c33),c34).
43 [] EQ(rew(c34,c22),c35).
53 [] EQ(rew(c5,c15),c45).
57 [] EQ(rew(c45,c3),c49).
82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))).
85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))).
92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))).
94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))).
96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))).
98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))).
99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))).
100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))).
101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))).
102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))).
103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))).
107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))).
115 [hyper,1,96,9,demod,57] P(c49,i(i(n(x),n(y)),i(y,x))).
123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))).
124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)).
125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))).
126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))).
140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))).
141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))).
144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))).
146 [hyper,1,144,99,demod,41] P(c33,i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))).
148 [hyper,1,102,146,demod,42] P(c34,i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))).
149 [hyper,1,148,107,demod,43] P(c35,i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
151 [hyper,2,99,149,115] $ANSWER(step_allBEH_Church_FL_18_35_49).

length of proof is 33
------------ end of proof -------------
-----> EMPTY CLAUSE at   2.56 sec ----> 153 [hyper,5,100,108,152]
$ANSWER(step_allLuka_x_19_37_59).  Length of proof is 37.
---------------- PROOF ----------------

1 [] -P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y).
5 [] -P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) | 
-P(z,i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
8 [] P(c2,i(i(n(x),x),x)).
9 [] P(c3,i(x,i(n(x),y))).
10 [] EQ(rew(c1,c1),c4).
11 [] EQ(rew(c4,c4),c5).
12 [] EQ(rew(c4,c1),c6).
13 [] EQ(rew(c5,c6),c7).
15 [] EQ(rew(c1,c3),c9).
16 [] EQ(rew(c9,c6),c10).
17 [] EQ(rew(c10,c2),c10a).
18 [] EQ(rew(c10a,c2),c11).
19 [] EQ(rew(c9,c11),c12).
20 [] EQ(rew(c7,c12),c13).
21 [] EQ(rew(c1,c13),c14).
22 [] EQ(rew(c14,c2),c15).
24 [] EQ(rew(c9,c15),c17).
25 [] EQ(rew(c5,c17),c17a).
26 [] EQ(rew(c17a,c3),c18).
27 [] EQ(rew(c1,c18),c19).
28 [] EQ(rew(c19,c15),c20).
29 [] EQ(rew(c5,c20),c21).
31 [] EQ(rew(c1,c21),c23).
32 [] EQ(rew(c23,c15),c24a).
33 [] EQ(rew(c24a,c3),c24).
34 [] EQ(rew(c21,c6),c25).
35 [] EQ(rew(c25,c24),c26).
36 [] EQ(rew(c1,c26),c28).
37 [] EQ(rew(c28,c26),c29).
39 [] EQ(rew(c7,c29),c31).
40 [] EQ(rew(c21,c31),c32).
44 [] EQ(rew(c21,c3),c36).
45 [] EQ(rew(c1,c36),c37).
53 [] EQ(rew(c5,c15),c45).
56 [] EQ(rew(c45,c36),c48).
58 [] EQ(rew(c1,c48),c50).
61 [] EQ(rew(c50,c15),c53).
64 [] EQ(rew(c1,c53),c56).
65 [] EQ(rew(c56,c32),c57).
66 [] EQ(rew(c1,c57),c58).
67 [] EQ(rew(c58,c21),c59).
82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))).
85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))).
92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))).
94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))).
96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))).
98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))).
99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))).
100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))).
101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))).
102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))).
103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))).
106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))).
108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))).
114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))).
116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))).
120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))).
122 [hyper,1,7,120,demod,64] P(c56,i(i(i(i(x,y),y),z),i(i(n(x),y),z))).
123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))).
124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)).
125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))).
126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))).
140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))).
141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))).
144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))).
145 [hyper,1,122,144,demod,65] P(c57,i(i(n(x),y),i(i(x,z),i(i(z,y),y)))).
147 [hyper,1,7,145,demod,66] P(c58,i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))).
152 [hyper,1,147,102,demod,67] P(c59,i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
153 [hyper,5,100,108,152] $ANSWER(step_allLuka_x_19_37_59).

length of proof is 37
------------ end of proof -------------
-----> EMPTY CLAUSE at   2.65 sec ----> 155 [hyper,6,100,108,154]
$ANSWER(step_allWos_x_19_37_60).  Length of proof is 39.
---------------- PROOF ----------------

1 [] -P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y).
6 [] -P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) |
-P(z,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) |
$ANSWER(step_allWos_x_19_37_60).
7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))).
8 [] P(c2,i(i(n(x),x),x)).
9 [] P(c3,i(x,i(n(x),y))).
10 [] EQ(rew(c1,c1),c4).
11 [] EQ(rew(c4,c4),c5).
12 [] EQ(rew(c4,c1),c6).
13 [] EQ(rew(c5,c6),c7).
15 [] EQ(rew(c1,c3),c9).
16 [] EQ(rew(c9,c6),c10).
17 [] EQ(rew(c10,c2),c10a).
18 [] EQ(rew(c10a,c2),c11).
19 [] EQ(rew(c9,c11),c12).
20 [] EQ(rew(c7,c12),c13).
21 [] EQ(rew(c1,c13),c14).
22 [] EQ(rew(c14,c2),c15).
24 [] EQ(rew(c9,c15),c17).
25 [] EQ(rew(c5,c17),c17a).
26 [] EQ(rew(c17a,c3),c18).
27 [] EQ(rew(c1,c18),c19).
28 [] EQ(rew(c19,c15),c20).
29 [] EQ(rew(c5,c20),c21).
30 [] EQ(rew(c21,c1),c22).
31 [] EQ(rew(c1,c21),c23).
32 [] EQ(rew(c23,c15),c24a).
33 [] EQ(rew(c24a,c3),c24).
34 [] EQ(rew(c21,c6),c25).
35 [] EQ(rew(c25,c24),c26).
36 [] EQ(rew(c1,c26),c28).
37 [] EQ(rew(c28,c26),c29).
39 [] EQ(rew(c7,c29),c31).
40 [] EQ(rew(c21,c31),c32).
44 [] EQ(rew(c21,c3),c36).
45 [] EQ(rew(c1,c36),c37).
53 [] EQ(rew(c5,c15),c45).
56 [] EQ(rew(c45,c36),c48).
58 [] EQ(rew(c1,c48),c50).
61 [] EQ(rew(c50,c15),c53).
64 [] EQ(rew(c1,c53),c56).
65 [] EQ(rew(c56,c32),c57).
66 [] EQ(rew(c1,c57),c58).
67 [] EQ(rew(c58,c21),c59).
68 [] EQ(rew(c22,c59),c60).
82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))).
85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))).
89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))).
92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))).
94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))).
96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))).
98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))).
99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))).
100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))).
101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))).
102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))).
103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))).
105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))).
106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))).
107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))).
108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))).
114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))).
116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))).
120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))).
122 [hyper,1,7,120,demod,64] P(c56,i(i(i(i(x,y),y),z),i(i(n(x),y),z))).
123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))).
124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)).
125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))).
126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))).
140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))).
141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))).
144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))).
145 [hyper,1,122,144,demod,65] P(c57,i(i(n(x),y),i(i(x,z),i(i(z,y),y)))).
147 [hyper,1,7,145,demod,66] P(c58,i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))).
152 [hyper,1,147,102,demod,67] P(c59,i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
154 [hyper,1,107,152,demod,68] P(c60,i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))).
155 [hyper,6,100,108,154] $ANSWER(step_allWos_x_19_37_60).

length of proof is 39
------------ end of proof -------------
------------ END OF SEARCH ------------

--------------- options ---------------
set(input_sos_first). clear(sos_queue). clear(sos_stack). 
set(print_given). clear(binary_res). set(hyper_res). 
clear(ur_res). clear(para_into). clear(para_from). 
clear(demod_inf). set(para_from_left). set(para_from_right). 
set(para_into_left). set(para_into_right). clear(para_from_vars). 
clear(para_into_vars). clear(para_from_units_only). clear(para_into_units_only). 
clear(para_skip_skolem). clear(para_ones_rule). clear(para_all). 
clear(very_verbose). clear(order_eq). clear(sort_literals). 
clear(delete_identical_nested_skolem). set(for_sub). clear(unit_deletion). 
set(print_kept). set(print_proofs). set(back_sub). 
set(print_back_sub). clear(factor). set(demod_history). 
clear(demod_linear). clear(demod_out_in). clear(dynamic_demod). 
clear(dynamic_demod_all). set(print_new_demod). clear(back_demod). 
set(print_back_demod). set(symbol_elim). clear(knuth_bendix). 
clear(lex_rpo). clear(dynamic_demod_lex_dep). clear(lex_order_vars). 
clear(for_sub_fpa). clear(no_fapl). clear(no_fanl). 
set(check_arity). clear(prolog_style_variables). clear(process_input). 
clear(simplify_fol). clear(bird_print). clear(free_all_mem). 
clear(atom_wt_max_args). clear(term_wt_max_args). clear(print_lists_at_end). 
clear(really_delete_clauses). clear(prog_synthesis). clear(ancestor_subsume). 
clear(new_functions). clear(linked_ur_res). clear(linked_ur_trace). 
clear(linked_sub_unit_usable). clear(linked_sub_unit_sos).
clear(index_for_back_demod). 
clear(linked_unit_del). clear(linked_target_all). clear(linked_hyper_res). 
clear(control_memory). clear(n_resolution). set(order_history). 
clear(neg_hyper_res). clear(suppress_weight_warning). clear(print_level). 


assign(report, 60). assign(max_seconds, 0). assign(max_gen, 0). 
assign(max_kept, 0). assign(max_given, 0). assign(max_mem, 8000). 
assign(max_literals, 0). assign(max_weight, 80). assign(fpa_literals, 8). 
assign(fpa_terms, 8). assign(demod_limit, 100). assign(max_proofs, 0). 
assign(neg_weight, 0). assign(stats_level, 2). assign(reduce_weight_limit, 0). 
assign(max_ur_depth, 5). assign(max_ur_deduction_size, 20).
assign(max_distinct_vars, -1). 
assign(pick_given_ratio, -1). assign(random_ratio, -1). assign(random_seed, 1). 


------------- memory usage ------------
5 mallocs of 32700 bytes each, 159.7 K.
  type (bytes each)        gets      frees     in use      avail      bytes
sym_ent (  84)              127          0        127          0     10.4 K
term (  20)               76118      75443        675         36     13.9 K
rel (  20)                71936      70961        975         35     19.7 K
term_ptr (   8)            3124          0       3124          0     24.4 K
formula_ptr_2 (  28)          0          0          0          0      0.0 K
fpa_head (  12)             554          0        554          0      6.5 K
fpa_tree (  28)            3827       3827          0         91      2.5 K
context ( 776)             4462       4462          0          8      6.1 K
trail (  12)              15831      15831          0         20      0.2 K
imd_tree (  20)             111          0        111          0      2.2 K
imd_pos (2016)                0          0          0          0      0.0 K
is_tree (  12)             1049          0       1049          0     12.3 K
is_pos (1216)                16         16          0          8      9.5 K
fsub_pos (   8)               2          2          0          1      0.0 K
literal (  16)             4064       3883        181          2      2.9 K
clause (  32)              3875       3717        158          1      5.0 K
list (  60)                   8          4          4          1      0.3 K
clash_nd (  44)             227        227          0          5      0.2 K
clause_ptr (   8)           954        796        158         81      1.9 K
int_ptr (   8)            15319      14856        463          4      3.6 K
link_node (  68)              0          0          0          0      0.0 K
ans_lit_node(  12)            0          0          0          0      0.0 K
formula_box( 148)             0          0          0          0      0.0 K
formula(  20)                 0          0          0          0      0.0 K
formula_ptr(   8)             0          0          0          0      0.0 K

-------------- statistics -------------
clauses input                 81
clauses given                 75
clauses generated           3790
demod & eval rewrites         74
clauses wt,lit,sk delete    3711
tautologies deleted            0
clauses forward subsumed       2
  (subsumed by sos)            2
clauses kept                  72
empty clauses                  5
clauses back subsumed          0
sos size                       0
Kbytes malloced              159

----------- times (seconds) -----------
run time             2.98                   (run time  0 hr, 0 min, 2 sec)
system time          1.17
input time           0.08
  clausify time      0.00
hyper_res time       1.02
pre_process time     1.68
  demod time         0.55
  weigh cl time      0.41
  for_sub time       0.01
  renumber time      0.00
  keep cl time       0.06
  print_cl time      0.03
  conflict time      0.04
post_process time    0.02
  back_sub time      0.01
lex_rpo time         0.00
The job finished        Sun Aug  9 15:34:11 1992

            Key Input File for Example 2

%  luka completeness of 123 exps.
set(hyper_res).
% assign(reduce_weight_limit, 010024).
assign(max_weight, 20).
% set(control_memory).
assign(max_proofs, 0).
clear(print_kept).
% set(very_verbose).
set(ancestor_subsume).
% clear(back_sub).
% assign(max_seconds, 1200).
assign(max_mem, 128000).
assign(report, 900).
assign(max_distinct_vars, 5).
assign(pick_given_ratio, 3).
set(order_history).
set(input_sos_first).
% set(sos_queue).
  
weight_list(pick_and_purge).
%  Following are union of best proofs of Church, lengths 27 24,
%  from experiments 12 through 12e.
weight(P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)),2).
weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2).
weight(P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2).
weight(P(i(i(i(x,y),x),x)),2).
weight(P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2).
weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2).
weight(P(i(i(x,i(x,y)),i(x,y))),2).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))),2).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))),2).
weight(P(i(x,i(i(n(y),y),y))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(x,i(y,x))),2).
%  Following are steps from Luka orig not in preceding union.
weight(P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)),3).
weight(P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))),3).
weight(P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))),3).
weight(P(i(i(n(x),y),i(n(y),x))),3).
weight(P(i(i(x,i(x,y)),i(x,y))),3).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))),3).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),3).
weight(P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))),3).
weight(P(i(n(i(x,y)),x)),3).
weight(P(i(n(x),i(x,y))),3).
% %  Following are the steps from Lukasiewicz original proof.
%  weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2).
%  weight(P(i(i(i(n(x),y),z),i(x,z))),2).
%  weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
%  weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
%  weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2).
%  weight(P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))),2).
%  weight(P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))),2).
%  weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2).
%  weight(P(i(x,i(i(n(y),y),y))),2).
%  weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
%  weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
%  weight(P(i(i(n(x),y),i(i(y,x),x))),2).
%  weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
%  weight(P(i(x,i(i(y,x),x))),2).
%  weight(P(i(i(x,i(y,z)),i(z,i(x,z)))),2).
%  weight(P(i(x,i(y,x))),2).
%  weight(P(i(i(i(x,y),z),i(y,z))),2).
%  weight(P(i(x,i(i(x,y),y))),2).
%  weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
%  weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2).
%  weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))),2).
%  weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2).
%  weight(P(i(i(n(x),n(y)),i(y,x))),2).
%  weight(P(i(i(x,i(n(y),z)),i(i(i(x,z),y),y))),2).
%  weight(P(i(i(i(x,y),x),x)),2).
%  weight(P(i(i(i(x,y),z),i(i(z,x),x))),2).
%  weight(P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))),2).
%  weight(P(i(i(i(x,y),z),i(i(x,z),z))),2).
%  weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))),2).
%  weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2).
%  weight(P(i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))),2).
%  weight(P(i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))),2).
%  weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
%  Following are 68 theses suggested by Scott.
weight(P(i(i(i(i(y,z),i(x,z)),u),i(i(x,y),u))),4).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),4).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),4).
weight(P(i(i(v,i(i(x,z),u)),i(i(x,y),i(v,i(i(y,z),u))))),4).
weight(P(i(i(y,z),i(i(x,y),i(i(z,u),i(x,u))))),4).
weight(P(i(i(i(n(x),y),z),i(x,z))),4).
weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),4).
weight(P(i(i(y,i(i(n(x),x),x)),i(i(n(x),x),x))),4).
weight(P(i(v,i(i(n(x),x),x))),4).
weight(P(i(i(n(x),y),i(v,i(i(y,x),x)))),4).
weight(P(i(i(i(v,i(i(y,x),x)),z),i(i(n(x),y),z))),4).
weight(P(i(i(n(x),y),i(i(y,x),x))),4).
weight(P(i(x,x)),4).
weight(P(i(x,i(i(y,x),x))),4).
weight(P(i(y,i(x,y))),4).
weight(P(i(i(i(x,y),z),i(y,z))),4).
weight(P(i(x,i(i(x,y),y))),4).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),4).
weight(P(i(i(y,z),i(i(x,y),i(x,z)))),4).
weight(P(i(i(i(y,i(x,z)),u),i(i(x,i(y,z)),u))),4).
weight(P(i(i(i(x,y),x),x)),4).
weight(P(i(i(i(x,z),u),i(i(x,y),i(i(y,z),u)))),4).
weight(P(i(i(i(x,y),z),i(i(z,x),x))),4).
weight(P(i(i(i(x,y),y),i(i(y,x),x))),4).
weight(P(i(i(i(i(z,x),x),u),i(i(i(x,y),z),u))),4).
weight(P(i(i(i(x,y),z),i(i(x,z),z))),4).
weight(P(i(i(x,i(x,y)),i(x,y))),4).
weight(P(i(i(x,u),i(i(i(x,y),z),i(i(u,z),z)))),4).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),4).
weight(P(i(i(x,u),i(i(u,i(y,i(x,z))),i(y,i(x,z))))),4).
weight(P(i(i(u,i(y,i(x,z))),i(i(x,u),i(y,i(x,z))))),4).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),4).
weight(P(i(n(x),i(x,y))),4).
weight(P(i(i(i(x,y),z),i(n(x),z))),4).
weight(P(i(i(x,n(x)),n(x))),4).
weight(P(i(n(n(x)),x)),4).
weight(P(i(x,n(n(x)))),4).
weight(P(i(i(x,y),i(n(n(x)),y))),4).
weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),4).
weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),4).
weight(P(i(i(u,i(y,n(x))),i(i(x,y),i(u,n(x))))),4).
weight(P(i(i(u,i(y,x)),i(i(n(x),y),i(u,x)))),4).
weight(P(i(i(x,y),i(n(y),n(x)))),4).
weight(P(i(i(x,n(y)),i(y,n(x)))),4).
weight(P(i(i(n(x),y),i(n(y),x))),4).
weight(P(i(i(n(x),n(y)),i(y,x))),4).
weight(P(i(i(i(n(y),x),z),i(i(n(x),y),z))),4).
weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),4).
weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),4).
weight(P(i(i(n(x),y),i(i(x,y),y))),4).
weight(P(i(i(x,y),i(i(n(x),y),y))),4).
weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),4).
weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),4).
weight(P(i(i(n(x),z),i(i(x,y),i(i(y,z),z)))),4).
weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),4).
weight(P(i(i(n(x),z),i(i(y,z),i(i(x,y),z)))),4).
weight(P(i(i(u,i(n(x),z)),i(u,i(i(y,z),i(i(x,y),z))))),4).
weight(P(i(i(x,z),i(i(y,z),i(i(n(x),y),z)))),4).
weight(P(i(i(n(n(x)),y),i(x,y))),4).
weight(P(i(y,i(x,x))),4).
weight(P(i(n(i(x,x)),y)),4).
weight(P(i(i(n(y),n(i(x,x))),y)),4).
weight(P(i(n(i(x,y)),x)),4).
weight(P(i(n(i(x,y)),n(y))),4).
weight(P(i(n(i(x,n(y))),y)),4).
weight(P(i(x,i(n(y),n(i(x,y))))),4).
weight(P(i(x,i(y,n(i(x,n(y)))))),4).
weight(P(n(i(i(x,x),n(i(y,y))))),4).
end_of_list.
  
list(usable).
-P(i(x,y)) | -P(x) | P(y).
  
%  The following disjunctions are known axiom systems.
  
-P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
% 21 is dependent.
  
-P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) |
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) |
$ANSWER(step_allHilbert_18_21_22_3_54_30).  % 30 is dependent.
  
-P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
  
-P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
  
-P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) |
-P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3).
  
-P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
  
-P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
  
end_of_list.
  
list(sos).
%  The following three are Luka, 1 2 3.
P(i(i(x,y),i(i(y,z),i(x,z)))).
P(i(i(n(x),x),x)).
P(i(x,i(n(x),y))).
  
%  The following are from Frege, 18 35 21 46 39 40, with 21 dependent.
% P(i(x,i(y,x))).  %  axiom F1.
% P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).  %  axiom F2.
% P(i(i(x,i(y,z)),i(y,i(x,z)))).  %  axiom F3.
% P(i(i(x,y),i(n(y),n(x)))).  %  axiom F4.
% P(i(n(n(x)),x)).  %  axiom F5.
% P(i(x,n(n(x)))).  %  axiom f6.
end_of_list.
  
list(passive).
-P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
-P(i(i(n(p),p),p)) | $ANSWER(step_L2).
-P(i(p,i(n(p),q))) | $ANSWER(step_L3).
-P(i(q,i(p,q))) | $ANSWER(step_18).
-P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
-P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
-P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
-P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
-P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
-P(i(n(n(p)),p)) | $ANSWER(step_39).
-P(i(p,n(n(p)))) | $ANSWER(step_40).
-P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
-P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.
  
list(demodulators).
% (n(n(x)) = junk).
(n(n(n(x))) = junk).
(i(i(x,x),y) = junk).
(i(y,i(x,x)) = junk).
(i(junk,x) = junk).
(i(x,junk) = junk).
(n(junk) = junk).
(P(junk) = $T).
end_of_list.

      Summary of Output for Success with Example 2

----- OTTER 2.2, July 1991 -----
The job began on cosmo.mcs.anl.gov, Sat Aug  8 17:37:00 1992
The command was "otter4+".

set(hyper_res).
assign(max_weight,20).
assign(max_proofs,0).
clear(print_kept).
set(ancestor_subsume).
assign(max_mem,128000).
assign(report,900).
assign(max_distinct_vars,5).
assign(pick_given_ratio,3).
set(order_history).
set(input_sos_first).

weight_list(pick_and_purge).
weight(P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)),2).
weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2).
weight(P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))),2).
weight(P(i(i(i(n(x),y),z),i(x,z))),2).
weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2).
weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2).
weight(P(i(i(i(x,y),x),x)),2).
weight(P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))),2).
weight(P(i(i(i(x,y),z),i(y,z))),2).
weight(P(i(i(n(x),n(y)),i(y,x))),2).
weight(P(i(i(n(x),y),i(i(y,x),x))),2).
weight(P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))),2).
weight(P(i(i(n(x),y),i(n(y),x))),2).
weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2).
weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2).
weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2).
weight(P(i(i(x,i(x,y)),i(x,y))),2).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))),2).
weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),2).
weight(P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))),2).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2).
weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2).
weight(P(i(n(i(x,y)),x)),2).
weight(P(i(n(x),i(x,y))),2).
weight(P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))),2).
weight(P(i(x,i(i(n(y),y),y))),2).
weight(P(i(x,i(i(x,y),y))),2).
weight(P(i(x,i(y,x))),2).
weight(P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)),3).
weight(P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))),3).
weight(P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))),3).
weight(P(i(i(n(x),y),i(n(y),x))),3).
weight(P(i(i(x,i(x,y)),i(x,y))),3).
weight(P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))),3).
weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),3).
weight(P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))),3).
weight(P(i(n(i(x,y)),x)),3).
weight(P(i(n(x),i(x,y))),3).
weight(P(i(i(i(i(y,z),i(x,z)),u),i(i(x,y),u))),4).
weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),4).
weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),4).
weight(P(i(i(v,i(i(x,z),u)),i(i(x,y),i(v,i(i(y,z),u))))),4).
weight(P(i(i(y,z),i(i(x,y),i(i(z,u),i(x,u))))),4).
weight(P(i(i(i(n(x),y),z),i(x,z))),4).
weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),4).
weight(P(i(i(y,i(i(n(x),x),x)),i(i(n(x),x),x))),4).
weight(P(i(v,i(i(n(x),x),x))),4).
weight(P(i(i(n(x),y),i(v,i(i(y,x),x)))),4).
weight(P(i(i(i(v,i(i(y,x),x)),z),i(i(n(x),y),z))),4).
weight(P(i(i(n(x),y),i(i(y,x),x))),4).
weight(P(i(x,x)),4).
weight(P(i(x,i(i(y,x),x))),4).
weight(P(i(y,i(x,y))),4).
weight(P(i(i(i(x,y),z),i(y,z))),4).
weight(P(i(x,i(i(x,y),y))),4).
weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),4).
weight(P(i(i(y,z),i(i(x,y),i(x,z)))),4).
weight(P(i(i(i(y,i(x,z)),u),i(i(x,i(y,z)),u))),4).
weight(P(i(i(i(x,y),x),x)),4).
weight(P(i(i(i(x,z),u),i(i(x,y),i(i(y,z),u)))),4).
weight(P(i(i(i(x,y),z),i(i(z,x),x))),4).
weight(P(i(i(i(x,y),y),i(i(y,x),x))),4).
weight(P(i(i(i(i(z,x),x),u),i(i(i(x,y),z),u))),4).
weight(P(i(i(i(x,y),z),i(i(x,z),z))),4).
weight(P(i(i(x,i(x,y)),i(x,y))),4).
weight(P(i(i(x,u),i(i(i(x,y),z),i(i(u,z),z)))),4).
weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),4).
weight(P(i(i(x,u),i(i(u,i(y,i(x,z))),i(y,i(x,z))))),4).
weight(P(i(i(u,i(y,i(x,z))),i(i(x,u),i(y,i(x,z))))),4).
weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),4).
weight(P(i(n(x),i(x,y))),4).
weight(P(i(i(i(x,y),z),i(n(x),z))),4).
weight(P(i(i(x,n(x)),n(x))),4).
weight(P(i(n(n(x)),x)),4).
weight(P(i(x,n(n(x)))),4).
weight(P(i(i(x,y),i(n(n(x)),y))),4).
weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),4).
weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),4).
weight(P(i(i(u,i(y,n(x))),i(i(x,y),i(u,n(x))))),4).
weight(P(i(i(u,i(y,x)),i(i(n(x),y),i(u,x)))),4).
weight(P(i(i(x,y),i(n(y),n(x)))),4).
weight(P(i(i(x,n(y)),i(y,n(x)))),4).
weight(P(i(i(n(x),y),i(n(y),x))),4).
weight(P(i(i(n(x),n(y)),i(y,x))),4).
weight(P(i(i(i(n(y),x),z),i(i(n(x),y),z))),4).
weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),4).
weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),4).
weight(P(i(i(n(x),y),i(i(x,y),y))),4).
weight(P(i(i(x,y),i(i(n(x),y),y))),4).
weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),4).
weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),4).
weight(P(i(i(n(x),z),i(i(x,y),i(i(y,z),z)))),4).
weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),4).
weight(P(i(i(n(x),z),i(i(y,z),i(i(x,y),z)))),4).
weight(P(i(i(u,i(n(x),z)),i(u,i(i(y,z),i(i(x,y),z))))),4).
weight(P(i(i(x,z),i(i(y,z),i(i(n(x),y),z)))),4).
weight(P(i(i(n(n(x)),y),i(x,y))),4).
weight(P(i(y,i(x,x))),4).
weight(P(i(n(i(x,x)),y)),4).
weight(P(i(i(n(y),n(i(x,x))),y)),4).
weight(P(i(n(i(x,y)),x)),4).
weight(P(i(n(i(x,y)),n(y))),4).
weight(P(i(n(i(x,n(y))),y)),4).
weight(P(i(x,i(n(y),n(i(x,y))))),4).
weight(P(i(x,i(y,n(i(x,n(y)))))),4).
weight(P(n(i(i(x,x),n(i(y,y))))),4).
end_of_list.

list(usable).
1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
$ANSWER(step_allFrege_18_35_39_40_46_21).
3 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) |
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) |
$ANSWER(step_allHilbert_18_21_22_3_54_30).
4 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) |
$ANSWER(step_allWos_x_19_37_60).
7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | -P(i(p,i(n(p),q))) |
$ANSWER(step_allLuka_1_2_3).
8 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
end_of_list.

list(sos).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
end_of_list.

list(passive).
13 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1).
14 [] -P(i(i(n(p),p),p)) | $ANSWER(step_L2).
15 [] -P(i(p,i(n(p),q))) | $ANSWER(step_L3).
16 [] -P(i(q,i(p,q))) | $ANSWER(step_18).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
25 [] -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
27 [] -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
29 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
end_of_list.

list(demodulators).
30 [] (n(n(n(x))) = junk).
31 [] (i(i(x,x),y) = junk).
32 [] (i(y,i(x,x)) = junk).
33 [] (i(junk,x) = junk).
34 [] (i(x,junk) = junk).
35 [] (n(junk) = junk).
36 [] (P(junk) = $T).
end_of_list.

given clause #1: (wt=-2147483647) 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
-----> EMPTY CLAUSE at   0.22 sec ----> 39 [hyper,7,10,11,12]
$ANSWER(step_allLuka_1_2_3).
---------------- PROOF ----------------

7 [] -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | -P(i(p,i(n(p),q))) |
$ANSWER(step_allLuka_1_2_3).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
39 [hyper,7,10,11,12] $ANSWER(step_allLuka_1_2_3).

length of proof is 0
------------ end of proof -------------
----> UNIT CONFLICT at   1.15 sec ----> 176 [binary,175,26] $ANSWER(step_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
176 [binary,175,26] $ANSWER(step_49).

length of proof is 14
------------ end of proof -------------
----> UNIT CONFLICT at   1.44 sec ----> 204 [binary,203,16] $ANSWER(step_18).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
16 [] -P(i(q,i(p,q))) | $ANSWER(step_18).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
204 [binary,203,16] $ANSWER(step_18).

length of proof is 15
------------ end of proof -------------
----> UNIT CONFLICT at   1.86 sec ----> 260 [binary,259,17] $ANSWER(step_19).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
260 [binary,259,17] $ANSWER(step_19).

length of proof is 16
------------ end of proof -------------
----> UNIT CONFLICT at   2.80 sec ----> 361 [binary,360,22] $ANSWER(step_37).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
361 [binary,360,22] $ANSWER(step_37).

length of proof is 18
------------ end of proof -------------
----> UNIT CONFLICT at   2.90 sec ----> 379 [binary,378,18] $ANSWER(step_21).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
379 [binary,378,18] $ANSWER(step_21).

length of proof is 18
------------ end of proof -------------
----> UNIT CONFLICT at   3.26 sec ----> 438 [binary,437,20] $ANSWER(step_30).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
437 [hyper,1,37,350] P(i(i(x,i(x,y)),i(x,y))).
438 [binary,437,20] $ANSWER(step_30).

length of proof is 19
------------ end of proof -------------
----> UNIT CONFLICT at   3.48 sec ----> 475 [binary,474,19] $ANSWER(step_22).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
474 [hyper,1,378,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
475 [binary,474,19] $ANSWER(step_22).

length of proof is 19
------------ end of proof -------------
----> UNIT CONFLICT at   5.31 sec ----> 704 [binary,703,21] $ANSWER(step_35).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
409 [hyper,1,321,10] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
519 [hyper,1,159,421] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
703 [hyper,1,409,519] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
704 [binary,703,21] $ANSWER(step_35).

length of proof is 24
------------ end of proof -------------
----> UNIT CONFLICT at   5.53 sec ----> 731 [binary,730,21] $ANSWER(step_35).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
519 [hyper,1,159,421] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
730 [hyper,1,519,10] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
731 [binary,730,21] $ANSWER(step_35).

length of proof is 22
------------ end of proof -------------
-----> EMPTY CLAUSE at   9.56 sec ----> 1122 [hyper,4,203,703,175]
$ANSWER(step_allBEH_Church_FL_18_35_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
4 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
409 [hyper,1,321,10] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
519 [hyper,1,159,421] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
703 [hyper,1,409,519] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
1122 [hyper,4,203,703,175] $ANSWER(step_allBEH_Church_FL_18_35_49).

length of proof is 24
------------ end of proof -------------
----> UNIT CONFLICT at  12.54 sec ----> 1403 [binary,1402,23] $ANSWER(step_39).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
1402 [hyper,1,349,62] P(i(n(n(x)),x)).
1403 [binary,1402,23] $ANSWER(step_39).

length of proof is 20
------------ end of proof -------------
----> UNIT CONFLICT at  76.05 sec ----> 4523 [binary,4522,23] $ANSWER(step_39).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
4523 [binary,4522,23] $ANSWER(step_39).

length of proof is 19
------------ end of proof -------------
----> UNIT CONFLICT at  80.79 sec ----> 4699 [binary,4698,27] $ANSWER(step_54).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
27 [] -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
4604 [hyper,1,419,143] P(i(i(n(x),y),i(i(x,y),y))).
4698 [hyper,1,378,4604] P(i(i(x,y),i(i(n(x),y),y))).
4699 [binary,4698,27] $ANSWER(step_54).

length of proof is 23
------------ end of proof -------------
----> UNIT CONFLICT at 107.27 sec ----> 5946 [binary,5945,24] $ANSWER(step_40).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
38 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
52 [hyper,1,10,38] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
496 [hyper,1,52,350] P(i(i(x,n(x)),n(x))).
5945 [hyper,1,41,496] P(i(x,n(n(x)))).
5946 [binary,5945,24] $ANSWER(step_40).

length of proof is 22
------------ end of proof -------------
----> UNIT CONFLICT at 131.44 sec ----> 6570 [binary,6569,18] $ANSWER(step_21).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
18 [] -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6570 [binary,6569,18] $ANSWER(step_21).

length of proof is 17
------------ end of proof -------------
----> UNIT CONFLICT at 147.57 sec ----> 6965 [binary,6964,19] $ANSWER(step_22).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
19 [] -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
6965 [binary,6964,19] $ANSWER(step_22).

length of proof is 18
------------ end of proof -------------
----> UNIT CONFLICT at 284.41 sec ----> 9689 [binary,9688,28] $ANSWER(step_59).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
64 [hyper,1,44,44] P(i(i(x,i(y,z)),i(i(u,i(z,v)),i(x,i(u,i(y,v)))))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
152 [hyper,1,10,143] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
470 [hyper,1,378,48] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))).
602 [hyper,1,470,350] P(i(i(i(x,y),z),i(i(z,x),x))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
7422 [hyper,1,64,6964] P(i(i(x,i(i(y,z),u)),i(i(v,z),i(x,i(i(y,v),u))))).
8681 [hyper,1,7422,602] P(i(i(x,y),i(i(i(y,z),u),i(i(u,x),y)))).
9012 [hyper,1,6569,8681] P(i(i(i(x,y),z),i(i(u,x),i(i(z,u),x)))).
9688 [hyper,1,152,9012] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
9689 [binary,9688,28] $ANSWER(step_59).

length of proof is 31
------------ end of proof -------------
----> UNIT CONFLICT at 555.94 sec ----> 15361 [binary,15360,24] $ANSWER(step_40).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15361 [binary,15360,24] $ANSWER(step_40).

length of proof is 20
------------ end of proof -------------
-----> EMPTY CLAUSE at 567.88 sec ----> 15734
[hyper,3,203,6569,6964,12,4698,437] $ANSWER(step_allHilbert_18_21_22_3_54_30).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) |
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) |
$ANSWER(step_allHilbert_18_21_22_3_54_30).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
437 [hyper,1,37,350] P(i(i(x,i(x,y)),i(x,y))).
4604 [hyper,1,419,143] P(i(i(n(x),y),i(i(x,y),y))).
4698 [hyper,1,378,4604] P(i(i(x,y),i(i(n(x),y),y))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
15734 [hyper,3,203,6569,6964,12,4698,437]
$ANSWER(step_allHilbert_18_21_22_3_54_30).

length of proof is 28
------------ end of proof -------------
----> UNIT CONFLICT at 580.65 sec ----> 16023 [binary,16022,28] $ANSWER(step_59).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
4604 [hyper,1,419,143] P(i(i(n(x),y),i(i(x,y),y))).
4720 [hyper,1,10,4604] P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
7426 [hyper,1,44,6964] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))).
7929 [hyper,1,7426,6964] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))).
16022 [hyper,1,4720,7929] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
16023 [binary,16022,28] $ANSWER(step_59).

length of proof is 27
------------ end of proof -------------
----> UNIT CONFLICT at 594.34 sec ----> 16381 [binary,16380,28] $ANSWER(step_59).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
28 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
16381 [binary,16380,28] $ANSWER(step_59).

length of proof is 24
------------ end of proof -------------
-----> EMPTY CLAUSE at 1491.20 sec ----> 26454
[hyper,9,62,203,6569,350,703,4522,15360,175]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
409 [hyper,1,321,10] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
519 [hyper,1,159,421] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
703 [hyper,1,409,519] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
26454 [hyper,9,62,203,6569,350,703,4522,15360,175]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).

length of proof is 31
------------ end of proof -------------
----> UNIT CONFLICT at 1497.15 sec ----> 26995 [binary,26994,25] $ANSWER(step_46).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
25 [] -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
26995 [binary,26994,25] $ANSWER(step_46).

length of proof is 22
------------ end of proof -------------
-----> EMPTY CLAUSE at 1599.61 sec ----> 28728 [hyper,5,259,360,16380]
$ANSWER(step_allLuka_x_19_37_59).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
28728 [hyper,5,259,360,16380] $ANSWER(step_allLuka_x_19_37_59).

length of proof is 25
------------ end of proof -------------
----> UNIT CONFLICT at 1599.96 sec ----> 28753 [binary,28752,29] $ANSWER(step_60).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
29 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
28752 [hyper,1,6964,16380] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))).
28753 [binary,28752,29] $ANSWER(step_60).

length of proof is 28
------------ end of proof -------------
-----> EMPTY CLAUSE at 2092.43 sec ----> 33787
[hyper,8,62,203,6569,350,703,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
8 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
409 [hyper,1,321,10] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
519 [hyper,1,159,421] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
703 [hyper,1,409,519] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
33787 [hyper,8,62,203,6569,350,703,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).

length of proof is 33
------------ end of proof -------------
-----> EMPTY CLAUSE at 2092.46 sec ----> 33788
[hyper,2,203,703,4522,15360,26994,6569] $ANSWER(step_allFrege_18_35_39_40_46_21).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
-P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
409 [hyper,1,321,10] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
519 [hyper,1,159,421] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))).
703 [hyper,1,409,519] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
33788 [hyper,2,203,703,4522,15360,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).

length of proof is 31
------------ end of proof -------------
-----> EMPTY CLAUSE at 2310.45 sec ----> 36877 [hyper,6,259,360,28752]
$ANSWER(step_allWos_x_19_37_60).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
28752 [hyper,1,6964,16380] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))).
36877 [hyper,6,259,360,28752] $ANSWER(step_allWos_x_19_37_60).

length of proof is 29
------------ end of proof -------------
----> UNIT CONFLICT at 2831.65 sec ----> 48451 [binary,48450,21] $ANSWER(step_35).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
21 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
48451 [binary,48450,21] $ANSWER(step_35).

length of proof is 22
------------ end of proof -------------
-----> EMPTY CLAUSE at 2843.21 sec ----> 48479
[hyper,9,62,203,6569,350,48450,4522,15360,175]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
48479 [hyper,9,62,203,6569,350,48450,4522,15360,175]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).

length of proof is 29
------------ end of proof -------------
-----> EMPTY CLAUSE at 2843.23 sec ----> 48480
[hyper,8,62,203,6569,350,48450,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
8 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
48480 [hyper,8,62,203,6569,350,48450,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).

length of proof is 32
------------ end of proof -------------
-----> EMPTY CLAUSE at 2843.26 sec ----> 48481 [hyper,4,203,48450,175]
$ANSWER(step_allBEH_Church_FL_18_35_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
4 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
48481 [hyper,4,203,48450,175] $ANSWER(step_allBEH_Church_FL_18_35_49).

length of proof is 22
------------ end of proof -------------
-----> EMPTY CLAUSE at 2843.28 sec ----> 48482
[hyper,2,203,48450,4522,15360,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
$ANSWER(step_allFrege_18_35_39_40_46_21).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
48482 [hyper,2,203,48450,4522,15360,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).

length of proof is 30
------------ end of proof -------------
----> UNIT CONFLICT at 4879.26 sec ----> 74476 [binary,74475,26] $ANSWER(step_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
26 [] -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74476 [binary,74475,26] $ANSWER(step_49).

length of proof is 13
------------ end of proof -------------
-----> EMPTY CLAUSE at 4885.00 sec ----> 74479
[hyper,9,62,203,6569,350,48450,4522,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74479 [hyper,9,62,203,6569,350,48450,4522,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).

length of proof is 35
------------ end of proof -------------
-----> EMPTY CLAUSE at 4885.04 sec ----> 74480 [hyper,4,203,48450,74475]
$ANSWER(step_allBEH_Church_FL_18_35_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
4 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allBEH_Church_FL_18_35_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74480 [hyper,4,203,48450,74475] $ANSWER(step_allBEH_Church_FL_18_35_49).

length of proof is 28
------------ end of proof -------------
----> UNIT CONFLICT at 4886.58 sec ----> 74488 [binary,74487,16] $ANSWER(step_18).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
16 [] -P(i(q,i(p,q))) | $ANSWER(step_18).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74488 [binary,74487,16] $ANSWER(step_18).

length of proof is 14
------------ end of proof -------------
-----> EMPTY CLAUSE at 4894.84 sec ----> 74498
[hyper,9,62,74487,6569,350,48450,4522,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74498 [hyper,9,62,74487,6569,350,48450,4522,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).

length of proof is 36
------------ end of proof -------------
-----> EMPTY CLAUSE at 4894.90 sec ----> 74499
[hyper,8,62,74487,6569,350,48450,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
8 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74499 [hyper,8,62,74487,6569,350,48450,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).

length of proof is 39
------------ end of proof -------------
-----> EMPTY CLAUSE at 4894.94 sec ----> 74500 [hyper,4,74487,48450,74475]
$ANSWER(step_allBEH_Church_FL_18_35_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
4 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74500 [hyper,4,74487,48450,74475] $ANSWER(step_allBEH_Church_FL_18_35_49).

length of proof is 29
------------ end of proof -------------
-----> EMPTY CLAUSE at 4894.98 sec ----> 74501
[hyper,3,74487,6569,6964,12,4698,437]
$ANSWER(step_allHilbert_18_21_22_3_54_30).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) |
-P(i(i(p,q),i(i(n(p),q),q))) |
-P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_allHilbert_18_21_22_3_54_30).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
350 [hyper,1,143,318] P(i(i(i(x,y),x),x)).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
437 [hyper,1,37,350] P(i(i(x,i(x,y)),i(x,y))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4604 [hyper,1,419,143] P(i(i(n(x),y),i(i(x,y),y))).
4698 [hyper,1,378,4604] P(i(i(x,y),i(i(n(x),y),y))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74501 [hyper,3,74487,6569,6964,12,4698,437]
$ANSWER(step_allHilbert_18_21_22_3_54_30).

length of proof is 35
------------ end of proof -------------
-----> EMPTY CLAUSE at 4895.02 sec ----> 74502
[hyper,2,74487,48450,4522,15360,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
$ANSWER(step_allFrege_18_35_39_40_46_21).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74502 [hyper,2,74487,48450,4522,15360,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).

length of proof is 37
------------ end of proof -------------
----> UNIT CONFLICT at 4897.23 sec ----> 74523 [binary,74522,17]
$ANSWER(step_19).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
17 [] -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74523 [binary,74522,17] $ANSWER(step_19).

length of proof is 15
------------ end of proof -------------
-----> EMPTY CLAUSE at 4920.18 sec ----> 74576 [hyper,6,74522,360,28752]
$ANSWER(step_allWos_x_19_37_60).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) |
$ANSWER(step_allWos_x_19_37_60).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
28752 [hyper,1,6964,16380] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74576 [hyper,6,74522,360,28752] $ANSWER(step_allWos_x_19_37_60).

length of proof is 37
------------ end of proof -------------
-----> EMPTY CLAUSE at 4920.22 sec ----> 74577 [hyper,5,74522,360,16380]
$ANSWER(step_allLuka_x_19_37_59).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74577 [hyper,5,74522,360,16380] $ANSWER(step_allLuka_x_19_37_59).

length of proof is 33
------------ end of proof -------------
----> UNIT CONFLICT at 4933.60 sec ----> 74606 [binary,74605,22] $ANSWER(step_37).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
22 [] -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74606 [binary,74605,22] $ANSWER(step_37).

length of proof is 17
------------ end of proof -------------
-----> EMPTY CLAUSE at 4973.70 sec ----> 74744
[hyper,9,62,74487,6569,74595,48450,4522,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74744 [hyper,9,62,74487,6569,74595,48450,4522,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).

length of proof is 38
------------ end of proof -------------
-----> EMPTY CLAUSE at 4973.74 sec ----> 74745
[hyper,8,62,74487,6569,74595,48450,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
8 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74745 [hyper,8,62,74487,6569,74595,48450,4522,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).

length of proof is 41
------------ end of proof -------------
----> UNIT CONFLICT at 4975.40 sec ----> 74755 [binary,74754,20] $ANSWER(step_30).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
20 [] -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74754 [hyper,1,37,74595] P(i(i(x,i(x,y)),i(x,y))).
74755 [binary,74754,20] $ANSWER(step_30).

length of proof is 18
------------ end of proof -------------
-----> EMPTY CLAUSE at 4999.18 sec ----> 74819
[hyper,3,74487,6569,6964,12,4698,74754]
$ANSWER(step_allHilbert_18_21_22_3_54_30).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
3 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) |
-P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) |
$ANSWER(step_allHilbert_18_21_22_3_54_30).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4604 [hyper,1,419,143] P(i(i(n(x),y),i(i(x,y),y))).
4698 [hyper,1,378,4604] P(i(i(x,y),i(i(n(x),y),y))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74754 [hyper,1,37,74595] P(i(i(x,i(x,y)),i(x,y))).
74819 [hyper,3,74487,6569,6964,12,4698,74754]
$ANSWER(step_allHilbert_18_21_22_3_54_30).

length of proof is 37
------------ end of proof -------------
-----> EMPTY CLAUSE at 5020.70 sec ----> 74942 [hyper,6,74522,74605,28752]
$ANSWER(step_allWos_x_19_37_60).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
6 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
6964 [hyper,1,6569,10] P(i(i(x,y),i(i(z,x),i(z,y)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
28752 [hyper,1,6964,16380] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74942 [hyper,6,74522,74605,28752] $ANSWER(step_allWos_x_19_37_60).

length of proof is 38
------------ end of proof -------------
-----> EMPTY CLAUSE at 5020.75 sec ----> 74943 [hyper,5,74522,74605,16380]
$ANSWER(step_allLuka_x_19_37_59).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
5 [] -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) |
-P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
321 [hyper,1,259,143] P(i(x,i(i(x,y),y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
378 [hyper,1,44,321] P(i(i(x,i(y,z)),i(y,i(x,z)))).
419 [hyper,1,10,349] P(i(i(i(n(x),y),z),i(i(n(y),x),z))).
464 [hyper,1,378,143] P(i(i(x,y),i(i(n(y),x),y))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
5591 [hyper,1,72,464] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))).
16380 [hyper,1,419,5591] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74943 [hyper,5,74522,74605,16380] $ANSWER(step_allLuka_x_19_37_59).

length of proof is 34
------------ end of proof -------------
----> UNIT CONFLICT at 5021.73 sec ----> 74948 [binary,74947,23] $ANSWER(step_39).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
23 [] -P(i(n(n(p)),p)) | $ANSWER(step_39).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
74948 [binary,74947,23] $ANSWER(step_39).

length of proof is 18
------------ end of proof -------------
-----> EMPTY CLAUSE at 5074.51 sec ----> 75088
[hyper,9,62,74487,6569,74595,48450,74947,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
75088 [hyper,9,62,74487,6569,74595,48450,74947,15360,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).

length of proof is 40
------------ end of proof -------------
-----> EMPTY CLAUSE at 5074.55 sec ----> 75089
[hyper,8,62,74487,6569,74595,48450,74947,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
8 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
75089 [hyper,8,62,74487,6569,74595,48450,74947,15360,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).

length of proof is 43
------------ end of proof -------------
-----> EMPTY CLAUSE at 5074.60 sec ----> 75090
[hyper,2,74487,48450,74947,15360,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
$ANSWER(step_allFrege_18_35_39_40_46_21).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15360 [hyper,1,175,4522] P(i(x,n(n(x)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
75090 [hyper,2,74487,48450,74947,15360,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).

length of proof is 41
------------ end of proof -------------
----> UNIT CONFLICT at 5074.65 sec ----> 75093 [binary,75092,24]
$ANSWER(step_40).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
24 [] -P(i(p,n(n(p)))) | $ANSWER(step_40).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
75092 [hyper,1,74475,74947] P(i(x,n(n(x)))).
75093 [binary,75092,24] $ANSWER(step_40).

length of proof is 19
------------ end of proof -------------
-----> EMPTY CLAUSE at 5087.57 sec ----> 75117
[hyper,9,62,74487,6569,74595,48450,74947,75092,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
9 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) |
-P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) |
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
75092 [hyper,1,74475,74947] P(i(x,n(n(x)))).
75117 [hyper,9,62,74487,6569,74595,48450,74947,75092,74475]
$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49).

length of proof is 38
------------ end of proof -------------
-----> EMPTY CLAUSE at 5087.62 sec ----> 75118
[hyper,8,62,74487,6569,74595,48450,74947,75092,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
8 [] -P(i(p,p)) | -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
-P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) |
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
62 [hyper,1,41,11] P(i(x,x)).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74595 [hyper,1,74180,74582] P(i(i(i(x,y),x),x)).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
75092 [hyper,1,74475,74947] P(i(x,n(n(x)))).
75118 [hyper,8,62,74487,6569,74595,48450,74947,75092,26994]
$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46).

length of proof is 43
------------ end of proof -------------
-----> EMPTY CLAUSE at 5087.67 sec ----> 75119
[hyper,2,74487,48450,74947,75092,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).
---------------- PROOF ----------------

1 [] -P(i(x,y)) | -P(x) | P(y).
2 [] -P(i(q,i(p,q))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) |
-P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) |
$ANSWER(step_allFrege_18_35_39_40_46_21).
10 [] P(i(i(x,y),i(i(y,z),i(x,z)))).
11 [] P(i(i(n(x),x),x)).
12 [] P(i(x,i(n(x),y))).
37 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))).
41 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))).
42 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)).
44 [hyper,1,37,37] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))).
48 [hyper,1,37,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))).
72 [hyper,1,44,48] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))).
76 [hyper,1,10,48] P(i(i(i(i(i(x,y),z),i(i(u,y),z)),v),i(i(x,u),v))).
103 [hyper,1,48,42] P(i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))).
111 [hyper,1,103,11] P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))).
115 [hyper,1,41,111] P(i(x,i(i(n(y),y),y))).
119 [hyper,1,72,115] P(i(i(n(x),y),i(z,i(i(y,x),x)))).
120 [hyper,1,48,115] P(i(i(i(x,y),z),i(i(i(i(n(u),u),u),y),z))).
131 [hyper,1,10,119] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))).
143 [hyper,1,131,11] P(i(i(n(x),y),i(i(y,x),x))).
148 [hyper,1,44,143] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))).
159 [hyper,1,72,148] P(i(i(n(x),y),i(i(z,i(u,x)),i(i(y,u),i(z,x))))).
160 [hyper,1,44,148] P(i(i(x,i(n(y),z)),i(i(u,i(z,y)),i(x,i(u,y))))).
175 [hyper,1,148,12] P(i(i(n(x),n(y)),i(y,x))).
178 [hyper,1,148,10] P(i(i(n(i(x,y)),i(z,y)),i(i(x,z),i(x,y)))).
203 [hyper,1,41,175] P(i(x,i(y,x))).
259 [hyper,1,10,203] P(i(i(i(x,y),z),i(y,z))).
318 [hyper,1,259,175] P(i(n(x),i(x,y))).
349 [hyper,1,148,318] P(i(i(n(x),y),i(n(y),x))).
360 [hyper,1,10,318] P(i(i(i(x,y),z),i(n(x),z))).
421 [hyper,1,349,318] P(i(n(i(x,y)),x)).
525 [hyper,1,48,421] P(i(i(i(n(i(x,y)),z),u),i(i(x,z),u))).
4080 [hyper,1,120,11] P(i(i(i(i(n(x),x),x),y),y)).
4522 [hyper,1,360,11] P(i(n(n(x)),x)).
6569 [hyper,1,160,203] P(i(i(x,i(y,z)),i(y,i(x,z)))).
15366 [hyper,1,159,4522] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))).
26994 [hyper,1,15366,318] P(i(i(x,y),i(n(y),n(x)))).
48450 [hyper,1,525,178] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))).
74180 [hyper,1,76,4080] P(i(i(n(x),y),i(i(y,x),x))).
74203 [hyper,1,10,74180] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))).
74475 [hyper,1,74203,41] P(i(i(n(x),n(y)),i(y,x))).
74487 [hyper,1,41,74475] P(i(x,i(y,x))).
74522 [hyper,1,10,74487] P(i(i(i(x,y),z),i(y,z))).
74582 [hyper,1,74522,74475] P(i(n(x),i(x,y))).
74605 [hyper,1,10,74582] P(i(i(i(x,y),z),i(n(x),z))).
74947 [hyper,1,4080,74605] P(i(n(n(x)),x)).
75092 [hyper,1,74475,74947] P(i(x,n(n(x)))).
75119 [hyper,2,74487,48450,74947,75092,26994,6569]
$ANSWER(step_allFrege_18_35_39_40_46_21).

length of proof is 41
------------ end of proof -------------
------------ END OF SEARCH ------------

--------------- options ---------------
set(input_sos_first). clear(sos_queue). clear(sos_stack). 
set(print_given). clear(binary_res). set(hyper_res). 
clear(ur_res). clear(para_into). clear(para_from). 
clear(demod_inf). set(para_from_left). set(para_from_right). 
set(para_into_left). set(para_into_right). clear(para_from_vars). 
clear(para_into_vars). clear(para_from_units_only). clear(para_into_units_only). 
clear(para_skip_skolem). clear(para_ones_rule). clear(para_all). 
clear(very_verbose). clear(order_eq). clear(sort_literals). 
clear(delete_identical_nested_skolem). set(for_sub). clear(unit_deletion). 
clear(print_kept). set(print_proofs). set(back_sub). 
set(print_back_sub). clear(factor). set(demod_history). 
clear(demod_linear). clear(demod_out_in). clear(dynamic_demod). 
clear(dynamic_demod_all). set(print_new_demod). clear(back_demod). 
set(print_back_demod). set(symbol_elim). clear(knuth_bendix). 
clear(lex_rpo). clear(dynamic_demod_lex_dep). clear(lex_order_vars). 
clear(for_sub_fpa). clear(no_fapl). clear(no_fanl). 
set(check_arity). clear(prolog_style_variables). clear(process_input). 
clear(simplify_fol). clear(bird_print). clear(free_all_mem). 
clear(atom_wt_max_args). clear(term_wt_max_args). clear(print_lists_at_end). 
clear(really_delete_clauses). clear(prog_synthesis). set(ancestor_subsume). 
clear(new_functions). clear(linked_ur_res). clear(linked_ur_trace). 
clear(linked_sub_unit_usable). clear(linked_sub_unit_sos).
clear(index_for_back_demod). 
clear(linked_unit_del). clear(linked_target_all). clear(linked_hyper_res). 
clear(control_memory). clear(n_resolution). set(order_history). 
clear(neg_hyper_res). clear(suppress_weight_warning). clear(print_level). 


assign(report, 900). assign(max_seconds, 0). assign(max_gen, 0). 
assign(max_kept, 0). assign(max_given, 0). assign(max_mem, 128000). 
assign(max_literals, 0). assign(max_weight, 20). assign(fpa_literals, 8). 
assign(fpa_terms, 8). assign(demod_limit, 100). assign(max_proofs, 0). 
assign(neg_weight, 0). assign(stats_level, 2). assign(reduce_weight_limit, 0). 
assign(max_ur_depth, 5). assign(max_ur_deduction_size, 20).
assign(max_distinct_vars, 5). 
assign(pick_given_ratio, 3). assign(random_ratio, -1). assign(random_seed, 1). 


------------- memory usage ------------
3003 mallocs of 32700 bytes each, 95896.6 K.
  type (bytes each)        gets      frees     in use      avail      bytes
sym_ent (  84)               79          0         79          0      6.5 K
term (  20)            38316875   37648572     668303         28  13053.3 K
rel (  20)             36319608   35323618     995990         28  19453.5 K
term_ptr (   8)         5889855    1943284    3946571        281  30834.8 K
formula_ptr_2 (  28)          0          0          0          0      0.0 K
fpa_head (  12)            7746        330       7416          0     86.9 K
fpa_tree (  28)         2354026    2354021          5         99      2.8 K
context ( 776)          4055182    4055181          1          9      7.6 K
trail (  12)           22746660   22746660          0         15      0.2 K
imd_tree (  20)              21          0         21          0      0.4 K
imd_pos (2016)         26781056   26781056          0          3      5.9 K
is_tree (  12)           947432      32230     915202          7  10725.1 K
is_pos (1216)          20272314   20272314          0         10     11.9 K
fsub_pos (   8)          862994     862994          0          1      0.0 K
literal (  16)          1799413    1548923     250490          2   3913.9 K
clause (  32)           1794522    1544091     250431          1   7826.0 K
list (  60)                   8          4          4          1      0.3 K
clash_nd (  44)            5113       5113          0          7      0.3 K
clause_ptr (   8)      31803282   31552850     250432         55   1956.9 K
int_ptr (   8)          7415932    6414260    1001672          4   7825.6 K
link_node (  68)              0          0          0          0      0.0 K
ans_lit_node(  12)            0          0          0          0      0.0 K
formula_box( 148)             0          0          0          0      0.0 K
formula(  20)                 0          0          0          0      0.0 K
formula_ptr(   8)             0          0          0          0      0.0 K

-------------- statistics -------------
clauses input                 36
clauses given               2446
clauses generated        1794453
demod & eval rewrites     197538
clauses wt,lit,sk delete  909501
tautologies deleted        40374
clauses forward subsumed  594212
cl not subsumed due to ancestor_subsume   48856
  (subsumed by sos)       227064
clauses kept              250334
empty clauses                 61
clauses back subsumed      53962
sos size                  194741
Kbytes malloced            95896

----------- times (seconds) -----------
run time         24332.94                   (run time  6 hr, 45 min, 32 sec)
system time        699.54
input time           0.17
  clausify time      0.00
hyper_res time     617.48
pre_process time  6192.13
  demod time       732.68
  weigh cl time   1824.35
  for_sub time    1807.41
  renumber time     61.99
  keep cl time    1479.34
  print_cl time      0.00
  conflict time     68.29
post_process time17345.90
  back_sub time   6985.20
lex_rpo time         0.00
The job finished        Sun Aug  9 09:12:51 1992

\end{verbatim}
\end{document}
