% Prove a distributivity property for median algebras.

lex([A,B,C,D,E,f(x,x,x)]).

set(para_from).
set(para_into).
set(lex_order_vars).
set(order_eq).
 
set(dynamic_demod).
set(back_demod).
assign(dynamic_demod_depth,1).
assign(dynamic_demod_rhs,4).
assign(demod_limit, 200).
clear(dynamic_demod_lex_dep).
 
set(input_sos_first).
assign(bsub_hint_add_wt, -1024).
set(keep_hint_subsumers).
 
assign(pick_given_ratio, 4).
 
assign(max_weight, 45).
assign(change_limit_after, 50).
assign(new_max_weight, 25).
 
assign(max_mem, 750000).
 
%set(print_proof_as_hints).
clear(print_kept).
clear(print_new_demod).
clear(print_back_demod).
clear(print_back_sub).

assign(heat,1).

% flatten out the occurrences of f
weight_list(pick_given).

   weight(f( f($(1),$(1),$(1)) , f($(1),$(1),$(1)) , f($(1),$(1),$(1)) ), 1).

   weight(f(x,x,$(1)),6).
   weight(f(x,$(1),x),6).
   weight(f($(1),x,x),6).

   weight(f(x,$(1),$(1)),3).
   weight(f($(1),x,$(1)),3).
   weight(f($(1),$(1),x),3).

end_of_list.

list(hot).

   f(f(x,w,y),w,z) = f(x,w,f(y,w,z)).

end_of_list.

list(sos).

   f(x,x,y) = x.

   f(x,y,z) = f(y,x,z).
   f(x,y,z) = f(x,z,y).
   f(x,y,z) = f(z,y,x).

   f(f(x,w,y),w,z) = f(x,w,f(y,w,z)).
                                                                                
   f(f(A,B,C),D,E) != f(f(A,D,E),f(B,D,E),f(C,D,E)) # label("original").
   f(f(A,D,E),f(B,D,E),f(C,D,E)) != f(f(A,B,C),D,E) # label("original").
   f(f(A,D,E),f(B,D,E),f(C,D,E)) != f(D,E,f(A,B,C)) # label("original").

end_of_list.

list(demodulators).

   f(x,x,y) = x.
   f(x,y,x) = x.
   f(y,x,x) = x.

   f(x,y,z) = f(y,x,z).
   f(x,y,z) = f(x,z,y).
   f(x,y,z) = f(z,y,x).

end_of_list.

list(hints2).

   % hints generated by hand

   f(x,y,f(x,y,z)) = f(x,y,z).
   f(x,y,f(x,z,y)) = f(x,y,z).
   f(x,y,f(y,x,z)) = f(x,y,z).
   f(x,y,f(y,z,x)) = f(x,y,z).
   f(x,y,f(z,x,y)) = f(x,y,z).
   f(x,y,f(z,y,x)) = f(x,y,z).

   f(x,y,f(x,z,f(y,z,u))) = f(x,y,z).
   f(x,y,f(x,z,f(y,u,z))) = f(x,y,z).
   f(x,y,f(x,z,f(z,y,u))) = f(x,y,z).
   f(x,y,f(x,z,f(z,u,y))) = f(x,y,z).
   f(x,y,f(x,z,f(u,y,z))) = f(x,y,z).
   f(x,y,f(x,z,f(u,z,y))) = f(x,y,z).

   f(x,y,f(z,x,f(y,z,u))) = f(x,y,z).
   f(x,y,f(z,x,f(y,u,z))) = f(x,y,z).
   f(x,y,f(z,x,f(z,y,u))) = f(x,y,z).
   f(x,y,f(z,x,f(z,u,y))) = f(x,y,z).
   f(x,y,f(z,x,f(u,y,z))) = f(x,y,z).
   f(x,y,f(z,x,f(u,z,y))) = f(x,y,z).

   f(y,x,f(x,z,f(y,z,u))) = f(x,y,z).
   f(y,x,f(x,z,f(y,u,z))) = f(x,y,z).
   f(y,x,f(x,z,f(z,y,u))) = f(x,y,z).
   f(y,x,f(x,z,f(z,u,y))) = f(x,y,z).
   f(y,x,f(x,z,f(u,y,z))) = f(x,y,z).
   f(y,x,f(x,z,f(u,z,y))) = f(x,y,z).

   f(y,x,f(z,x,f(y,z,u))) = f(x,y,z).
   f(y,x,f(z,x,f(y,u,z))) = f(x,y,z).
   f(y,x,f(z,x,f(z,y,u))) = f(x,y,z).
   f(y,x,f(z,x,f(z,u,y))) = f(x,y,z).
   f(y,x,f(z,x,f(u,y,z))) = f(x,y,z).
   f(y,x,f(z,x,f(u,z,y))) = f(x,y,z).

end_of_list.


% proof for A = B
list(hints2).  % Hints from process 1092, Wed Jul  6 07:13:20 2005
f(x,x,y)=x.
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(f(A,D,E),f(A,D,E),f(C,D,E))!=f(f(A,A,C),D,E).
f(x,y,x)=x.
f(f(A,D,E),f(A,D,E),f(C,D,E))!=f(f(A,C,A),D,E).
f(f(A,D,E),f(A,D,E),f(C,D,E))!=f(A,D,E).
end_of_list.

% A = C
list(hints2).  % Hints from process 1120, Wed Jul  6 07:20:48 2005
f(x,x,y)=x.
f(x,y,z)=f(x,z,y).
f(f(A,D,E),f(B,D,E),f(A,D,E))!=f(f(A,B,A),D,E).
x=x.
f(x,y,x)=x.
f(f(A,B,A),D,E)!=f(A,D,E).
f(A,D,E)!=f(A,D,E).
end_of_list.

% D = E
list(hints2).  % Hints from process 1126, Wed Jul  6 07:21:49 2005
f(x,x,y)=x.
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(f(A,D,D),f(B,D,D),f(C,D,D))!=f(f(A,B,C),D,D).
x=x.
f(x,y,x)=x.
f(x,y,y)=y.
f(D,f(B,D,D),f(C,D,D))!=f(f(A,B,C),D,D).
f(f(A,B,C),D,D)!=f(D,D,f(C,D,D)).
f(f(A,B,C),D,D)!=f(D,D,D).
f(f(A,B,C),D,D)!=D.
D!=D.
end_of_list.

% B = C
list(hints2).  % Hints from process 1129, Wed Jul  6 07:22:32 2005
f(x,x,y)=x.
f(x,y,z)=f(y,z,x).
f(f(A,D,E),f(B,D,E),f(B,D,E))!=f(f(A,B,B),D,E).
x=x.
f(x,y,y)=y.
f(f(A,B,B),D,E)!=f(B,D,E).
f(B,D,E)!=f(B,D,E).
$F.
end_of_list.

% B = E
list(hints2).  % Hints from process 1133, Wed Jul  6 07:23:21 2005
f(x,x,y)=x.
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,D,B),f(B,D,B),f(C,D,B))!=f(f(A,B,C),D,B).
f(x,y,x)=x.
f(f(A,D,B),B,f(C,D,B))!=f(f(A,B,C),D,B).
f(x,y,z)=f(y,x,z).
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(x,y,z),y,u)=f(x,y,f(z,u,y)).
f(f(x,y,z),y,z)=f(x,y,z).
f(x,y,z)=f(z,x,y).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(f(A,D,B),B,C),B,D)!=f(f(A,B,C),D,B).
$F.
end_of_list.

% A = E
list(hints2).  % Hints from process 1139, Wed Jul  6 07:26:53 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,D,A),f(B,D,A),f(C,D,A))!=f(f(A,B,C),D,A).
f(x,y,x)=x.
f(A,f(B,D,A),f(C,D,A))!=f(f(A,B,C),D,A).
f(f(C,D,A),A,f(B,D,A))!=f(f(A,B,C),D,A).
f(f(C,D,A),A,f(B,D,A))!=f(f(C,A,B),D,A).
f(f(x,y,z),y,u)=f(x,y,f(z,u,y)).
f(f(x,y,z),y,z)=f(x,y,z).
f(x,y,z)=f(z,x,y).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(f(x,y,z),y,u),x,y)=f(f(z,y,u),x,y).
f(f(f(x,y,z),z,u),y,z)=f(f(x,z,u),y,z).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,y,z))=f(f(x,z,u),y,z).
$F.
end_of_list.

% C = E
list(hints2).  % Hints from process 1143, Wed Jul  6 07:28:23 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,D,C),f(B,D,C),f(C,D,C))!=f(f(A,B,C),D,C).
f(x,y,x)=x.
f(f(A,D,C),f(B,D,C),C)!=f(f(A,B,C),D,C).
f(D,C,A)=f(A,D,C).
f(f(D,C,A),f(B,D,C),C)!=f(f(A,B,C),D,C).
f(f(x,y,f(z,y,u)),y,w)=f(f(x,y,z),y,f(u,y,w)).
f(f(x,y,f(z,y,u)),y,w)=f(f(x,y,z),y,f(u,w,y)).
f(f(x,y,f(z,y,u)),y,w)=f(f(x,y,z),f(u,w,y),y).
f(f(x,y,z),y,z)=f(x,y,z).
f(x,y,z)=f(z,x,y).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(D,C,f(A,B,C)),C,D)!=f(f(D,C,A),f(B,D,C),C).
f(f(D,C,f(A,C,B)),C,D)!=f(f(D,C,A),f(B,D,C),C).
$F.
end_of_list.

% B = D
list(hints2).  % Hints from process 13717, Wed Jul  6 07:30:53 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,B,E),f(B,B,E),f(C,B,E))!=f(f(A,B,C),B,E).
f(x,y,x)=x.
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(A,B,E),f(B,B,E),f(C,B,E))!=f(f(A,B,C),E,B).
f(f(A,B,E),f(B,E,B),f(C,B,E))!=f(f(A,B,C),E,B).
f(f(A,B,E),B,f(C,B,E))!=f(f(A,B,C),E,B).
f(f(x,y,z),y,z)=f(x,y,z).
f(x,y,z)=f(z,x,y).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,z,y))=f(f(x,z,u),y,z).
f(f(x,y,z),y,f(u,y,z))=f(f(x,y,u),z,y).
$F.
end_of_list.

% C = D
list(hints2).  % Hints from process 13723, Wed Jul  6 07:31:55 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,C,E),f(B,C,E),f(C,C,E))!=f(f(A,B,C),C,E).
f(x,y,x)=x.
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(z,y,x).
f(x,y,z)=f(z,x,y).
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(A,C,E),f(B,C,E),f(C,C,E))!=f(f(A,B,C),E,C).
f(f(A,C,E),f(B,C,E),f(C,E,C))!=f(f(A,B,C),E,C).
f(f(A,C,E),f(B,C,E),C)!=f(f(A,B,C),E,C).
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),y,x)=f(z,y,x).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,z,y))=f(f(x,z,u),y,z).
f(f(x,y,z),y,f(u,y,z))=f(f(x,y,u),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(u,y,x),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(x,u,y),z,y).
$F.
end_of_list.

% A = D
list(hints2).  % Hints from process 1158, Wed Jul  6 07:36:26 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(y,z,x).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,A,E),f(B,A,E),f(C,A,E))!=f(f(A,B,C),A,E).
f(x,y,x)=x.
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(z,y,x).
f(x,y,z)=f(z,x,y).
f(f(x,y,f(z,y,u)),y,w)=f(f(x,y,z),y,f(u,y,w)).
f(f(A,A,E),f(B,A,E),f(C,A,E))!=f(f(A,B,C),E,A).
f(f(A,E,A),f(B,A,E),f(C,A,E))!=f(f(A,B,C),E,A).
f(A,f(B,A,E),f(C,A,E))!=f(f(A,B,C),E,A).
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),y,x)=f(z,y,x).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(x,y,z),y,f(u,y,x))=f(f(z,y,u),x,y).
f(f(x,y,z),z,f(u,z,y))=f(f(x,z,u),y,z).
f(f(x,y,z),y,f(u,y,z))=f(f(x,y,u),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(u,y,x),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(y,x,u),z,y).
f(x,f(y,x,z),f(u,x,z))=f(f(x,y,u),z,x).
$F.
end_of_list.

% D = E
list(hints2).  % Hints from process 25002, Wed Jul  6 11:53:02 2005
f(x,y,z)=f(z,y,x).
f(x,x,y)=x.
f(f(A,D,D),f(B,D,D),f(C,D,D))!=f(f(A,B,C),D,D).
f(x,y,y)=y.
f(x,x,y)=f(z,x,x).
f(x,f(y,x,x),z)=f(u,x,x).
f(f(x,y,y),f(z,y,y),u)=f(w,y,y).
$F.
end_of_list.


% B = E
list(hints2).  % Hints from process 25013, Wed Jul  6 11:53:45 2005
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,D,B),f(B,D,B),f(C,D,B))!=f(f(A,B,C),D,B).
f(x,y,z)=f(y,z,x).
f(x,y,z)=f(z,x,y).
f(x,y,x)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,u,y)).
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,y,z))=f(f(x,z,u),y,z).
f(f(x,y,z),f(z,u,z),f(w,y,z))=f(f(x,z,w),y,z).
$F.
end_of_list.


% A = E
list(hints2).  % Hints from process 25025, Wed Jul  6 11:54:32 2005
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,D,A),f(B,D,A),f(C,D,A))!=f(f(A,B,C),D,A).
f(x,y,z)=f(y,z,x).
f(x,y,z)=f(z,x,y).
f(x,y,x)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,u,y)).
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,y,z))=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,y,z))=f(f(z,u,x),y,z).
f(x,f(y,z,x),f(u,z,x))=f(f(x,y,u),z,x).
f(f(x,y,x),f(z,u,x),f(w,u,x))=f(f(x,z,w),u,x).
$F.
end_of_list.


% B = D
list(hints2).  % Hints from process 25033, Wed Jul  6 11:55:09 2005
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,B,E),f(B,B,E),f(C,B,E))!=f(f(A,B,C),B,E).
f(x,y,z)=f(y,z,x).
f(x,y,z)=f(z,x,y).
f(x,y,x)=x.
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,z,y))=f(f(x,z,u),y,z).
f(f(x,y,z),y,f(u,y,z))=f(f(x,y,u),z,y).
f(f(x,y,z),f(y,y,u),f(w,y,z))=f(f(x,y,w),z,y).
f(f(x,y,z),f(y,y,u),f(w,y,z))=f(f(x,y,w),y,z).
$F.
end_of_list.


% C = D
list(hints2).  % Hints from process 25045, Wed Jul  6 11:55:56 2005
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,C,E),f(B,C,E),f(C,C,E))!=f(f(A,B,C),C,E).
f(x,y,z)=f(y,z,x).
f(x,y,z)=f(z,x,y).
f(x,y,x)=x.
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,z,y))=f(f(x,z,u),y,z).
f(f(x,y,z),y,f(u,y,z))=f(f(x,y,u),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(u,y,x),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(x,u,y),z,y).
f(f(x,y,z),f(u,y,z),f(y,y,w))=f(f(x,u,y),z,y).
f(f(x,y,z),f(u,y,z),f(y,y,w))=f(f(x,u,y),y,z).
$F.
end_of_list.

% A = D
list(hints2).  % Hints from process 25072, Wed Jul  6 11:57:47 2005
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,A,E),f(B,A,E),f(C,A,E))!=f(f(A,B,C),A,E).
f(x,y,z)=f(y,z,x).
f(x,y,z)=f(z,x,y).
f(x,y,x)=x.
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),z,u)=f(y,z,f(x,z,u)).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(f(x,y,z),z,u),z,y)=f(f(x,z,u),y,z).
f(f(x,y,z),z,f(u,z,y))=f(f(x,z,u),y,z).
f(f(x,y,z),y,f(u,y,z))=f(f(x,y,u),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(u,y,x),z,y).
f(f(x,y,z),f(u,y,z),y)=f(f(y,x,u),z,y).
f(x,f(y,x,z),f(u,x,z))=f(f(x,y,u),z,x).
f(f(x,x,y),f(z,x,u),f(w,x,u))=f(f(x,z,w),u,x).
f(f(x,x,y),f(z,x,u),f(w,x,u))=f(f(x,z,w),x,u).
$F.
end_of_list.

% C = E
list(hints2).  % Hints from process 25083, Wed Jul  6 11:58:37 2005
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,x,y)=x.
f(f(x,y,z),y,u)=f(x,y,f(z,y,u)).
f(f(A,D,C),f(B,D,C),f(C,D,C))!=f(f(A,B,C),D,C).
f(x,f(y,z,u),w)=f(x,w,f(y,u,z)).
f(x,y,z)=f(y,z,x).
f(x,y,z)=f(z,x,y).
f(x,y,x)=x.
f(f(x,y,f(z,y,u)),y,w)=f(f(x,y,z),y,f(u,y,w)).
f(f(x,y,z),y,z)=f(x,y,z).
f(f(x,y,z),x,y)=f(z,x,y).
f(f(x,y,z),y,x)=f(z,x,y).
f(f(x,y,f(z,y,u)),y,w)=f(f(x,y,z),f(u,w,y),y).
f(f(x,y,f(z,u,y)),y,w)=f(f(x,y,z),f(u,w,y),y).
f(f(x,y,z),f(u,x,y),y)=f(f(z,u,y),x,y).
f(f(x,y,z),f(u,y,z),z)=f(f(x,u,z),y,z).
f(f(x,y,z),f(u,y,z),f(z,w,z))=f(f(x,u,z),y,z).
$F.
end_of_list.


% A = C
list(hints2).  % Hints from process 25094, Wed Jul  6 12:00:15 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(z,y,x).
f(x,x,y)=x.
f(f(A,D,E),f(B,D,E),f(A,D,E))!=f(f(A,B,A),D,E).
f(f(x,y,z),u,w)=f(w,u,f(x,z,y)).
f(x,y,x)=x.
f(x,y,f(z,z,u))=f(z,y,x).
f(f(x,y,x),z,u)=f(x,z,u).
f(f(x,y,z),u,f(x,y,z))=f(f(x,w,x),y,z).
$F.
end_of_list.

% B = C
list(hints2).  % Hints from process 25143, Wed Jul  6 12:02:46 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(z,y,x).
f(x,x,y)=x.
f(f(A,D,E),f(B,D,E),f(B,D,E))!=f(f(A,B,B),D,E).
f(f(x,y,z),u,w)=f(w,u,f(x,z,y)).
f(x,y,y)=y.
f(x,y,f(z,z,u))=f(z,y,x).
f(x,x,y)=f(z,x,x).
f(x,f(y,x,x),z)=f(u,x,x).
f(f(x,y,x),z,u)=f(x,z,u).
f(f(x,y,y),z,u)=f(y,z,u).
f(x,f(y,z,u),f(y,z,u))=f(f(w,y,y),z,u).
$F.
end_of_list.

% A = B
list(hints2).  % Hints from process 25150, Wed Jul  6 12:03:15 2005
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(z,y,x).
f(x,x,y)=x.
f(f(A,D,E),f(A,D,E),f(C,D,E))!=f(f(A,A,C),D,E).
f(f(x,y,z),u,w)=f(w,u,f(x,z,y)).
f(x,y,y)=y.
f(x,y,f(z,z,u))=f(z,y,x).
f(x,x,y)=f(z,x,x).
f(f(x,y,x),z,u)=f(x,z,u).
f(f(x,y,z),f(x,y,z),u)=f(f(x,w,x),y,z).
f(x,x,x)=f(x,x,y).
f(f(x,y,z),f(x,y,z),u)=f(f(x,x,w),y,z).
$F.
end_of_list.

% Length of proof is 249.  Level of proof is 40.
% 
% ---------------- PROOF ----------------
% 
% 1 [] f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
% 2 [] f(x,y,z)=f(y,x,z).
% 5 [] f(x,x,y)=x.
% 6 [] f(x,y,x)=x.
% 7 [] f(y,x,x)=x.
% 8 [] f(x,y,z)=f(y,x,z).
% 9 [] f(x,y,z)=f(x,z,y).
% 10 [] f(x,y,z)=f(z,y,x).
% 11 [] f(x,y,f(x,y,z))=f(x,y,z).
% 12 [] f(x,y,f(x,z,y))=f(x,y,z).
% 15 [] f(x,y,f(z,x,y))=f(x,y,z).
% 17 [] f(x,y,f(x,z,f(y,z,u)))=f(x,y,z).
% 19 [] f(x,y,f(x,z,f(z,y,u)))=f(x,y,z).
% 22 [] f(x,y,f(x,z,f(u,z,y)))=f(x,y,z).
% 29 [] f(y,x,f(x,z,f(y,z,u)))=f(x,y,z).
% 30 [] f(y,x,f(x,z,f(y,u,z)))=f(x,y,z).
% 33 [] f(y,x,f(x,z,f(u,y,z)))=f(x,y,z).
% 35 [] f(y,x,f(z,x,f(y,z,u)))=f(x,y,z).
% 39 [] f(y,x,f(z,x,f(u,y,z)))=f(x,y,z).
% 40 [] f(y,x,f(z,x,f(u,z,y)))=f(x,y,z).
% 41 [] f(x,x,y)=x.
% 42 [] f(x,y,z)=f(y,x,z).
% 43 [] f(x,y,z)=f(x,z,y).
% 44 [] f(x,y,z)=f(z,y,x).
% 45 [] f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
% 48 [] f(f(A,D,E),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C))   # label("original").
% 768 [para_into,2.1.1,2.1.2] f(x,y,z)=f(x,y,z).
% 769 (heat=1) [para_into,768.1.1,1.1.2,demod,10,8,8] f(x,y,f(z,x,u))=f(z,x,f(x,u,y)).
% 770 [para_into,41.1.1,41.1.1] x=x.
% 771 [para_into,45.1.1.1,45.1.2,demod,10,8,10,8,8,10,8] f(x,y,f(x,z,f(u,x,w)))=f(u,x,f(x,y,f(x,w,z))).
% 772 [para_into,45.1.1.1,45.1.1,demod,8,10,8,8,8,flip.1] f(x,f(y,x,z),f(x,u,w))=f(x,w,f(y,x,f(x,z,u))).
% 773 [para_into,45.1.1.1,44.1.2,demod,10,8,8] f(x,y,f(z,x,u))=f(x,u,f(z,x,y)).
% 774 [para_into,45.1.1.1,43.1.2,demod,10,8] f(x,y,f(z,u,x))=f(z,x,f(u,x,y)).
% 775 [para_into,45.1.1.1,42.1.2,demod,10,8,8,8] f(x,y,f(x,z,u))=f(x,z,f(x,u,y)).
% 776 [para_into,45.1.1,45.1.2,demod,10,8,10,8,8,8] f(x,y,f(x,z,f(u,x,w)))=f(u,x,f(x,w,f(x,z,y))).
% 777 [para_into,45.1.1,44.1.2,demod,8,10,8,flip.1] f(x,y,f(z,x,u))=f(z,x,f(x,y,u)).
% 778 [para_into,45.1.2.3,45.1.2,demod,8,8,8,10,8] f(x,f(y,x,z),f(x,u,w))=f(y,x,f(x,w,f(x,z,u))).
% 784 (heat=1) [para_into,771.1.1,1.1.1,demod,9,8,8,10,8,flip.1] f(x,f(y,z,u),f(z,f(y,z,u),f(w,w5,f(y,z,u))))=f(y,z,f(z,u,f(w,f(y,z,u),f(x,w5,f(y,z,u))))).
% 785 (heat=1) [para_into,771.1.2.3.3,1.1.2,demod,10,8,9,9,10,8,8,flip.1] f(x,y,f(x,z,f(u,w,f(x,w5,u))))=f(x,z,f(x,f(x,u,y),f(w5,u,w))).
% 791 (heat=1) [para_from,771.1.1,1.1.1.1,demod,10,8,10,8] f(x,y,f(z,u,f(u,x,f(u,w,w5))))=f(u,x,f(x,y,f(u,w5,f(z,u,w)))).
% 797 (heat=1) [para_into,772.1.1.3,1.1.2,demod,8,10,8,8,8,9,flip.1] f(x,f(x,y,f(x,z,u)),f(u,w,w5))=f(x,f(x,y,z),f(u,w5,f(x,u,w))).
% 805 (heat=1) [para_from,772.1.2,1.1.2.3,demod,8,8,8,10,9,9] f(x,f(y,x,z),f(z,u,f(z,w,w5)))=f(y,x,f(z,f(x,z,w5),f(z,u,w))).
% 809 (heat=1) [para_into,773.1.1,1.1.1,demod,9,8,10,9,8,flip.1] f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(w,x,f(y,z,u)))).
% 812 (heat=1) [para_into,773.1.2,1.1.1,demod,10,9,8,10,9,8] f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(x,w,f(y,z,u)))).
% 813 (heat=1) [para_from,773.1.1,1.1.2.3,demod,8,8,10] f(x,f(y,x,z),f(z,u,w))=f(y,x,f(z,w,f(x,z,u))).
% 814 (heat=1) [para_from,773.1.1,1.1.1.1,demod,8,10,8,10,8,10,8] f(x,y,f(z,u,f(z,w,x)))=f(z,x,f(x,y,f(z,u,w))).
% 815 (heat=1) [para_into,774.1.1.3,1.1.2,demod,10,10,8,8,9,flip.1] f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(w,f(y,z,u),f(z,u,f(y,z,x))).
% 823 (heat=1) [para_into,775.1.1.3,1.1.1,demod,8,8,10,8] f(x,f(y,z,u),f(y,z,f(z,u,w)))=f(z,f(y,z,u),f(x,w,f(y,z,u))).
% 843 (heat=1) [para_from,777.1.1,1.1.1.1,demod,10,8,10,8] f(x,y,f(z,u,f(u,x,w)))=f(u,x,f(x,y,f(z,u,w))).
% 873 [para_into,769.1.1.3,769.1.1,demod,10,9,9,8,flip.1] f(x,y,f(x,z,f(u,y,w)))=f(x,z,f(u,y,f(x,y,w))).
% 874 [para_into,769.1.2.3,769.1.2,demod,10,8,9,8] f(x,f(x,y,z),f(y,u,w))=f(x,z,f(y,w,f(x,y,u))).
% 875 [para_into,769.1.2.3,769.1.1,demod,8,8,8,8] f(x,f(x,y,z),f(x,u,w))=f(x,u,f(x,y,f(x,z,w))).
% 885 (heat=1) [para_into,873.1.1,1.1.2,demod,6,8,8,flip.1] f(x,y,f(y,z,f(x,y,u)))=f(x,y,f(y,z,u)).
% 890 (heat=1) [para_into,873.1.2,1.1.2,demod,8,11,8,flip.1] f(x,f(y,x,z),f(y,x,u))=f(y,x,f(x,z,u)).
% 901,900 (heat=1) [para_into,874.1.1,1.1.2,demod,9,11,5,11,flip.1] f(x,y,f(z,u,f(x,z,y)))=f(x,z,y).
% 905 (heat=1) [para_into,874.1.2,1.1.2,demod,9,9,8,flip.1] f(x,f(y,z,x),f(y,z,u))=f(y,f(y,z,x),f(z,x,u)).
% 919 (heat=1) [para_into,875.1.2,1.1.2,demod,6] f(x,f(x,y,z),f(x,y,u))=f(x,y,f(x,z,u)).
% 957 [para_from,773.1.1,769.1.1.3,demod,10,10,8,9,8,flip.1] f(x,y,f(x,z,f(y,u,w)))=f(x,z,f(y,u,f(x,y,w))).
% 964,963 (heat=1) [para_into,957.1.2,1.1.2,demod,17,9,8,flip.1] f(x,f(y,z,x),f(y,z,u))=f(y,z,x).
% 968,967 (heat=1) [para_from,957.1.2,1.1.2,demod,8,8,19,9] f(x,f(y,x,z),f(y,z,u))=f(y,x,z).
% 970,969 [back_demod,905,demod,10,9,10,9,8,968] f(x,f(x,y,z),f(y,z,u))=f(x,y,z).
% 972 (heat=1) [para_into,969.1.1.2,1.1.1,demod,8,10,8] f(f(x,y,z),f(x,y,f(y,z,u)),f(y,u,w))=f(y,u,f(x,y,z)).
% 979,978 (heat=1) [para_from,969.1.1,1.1.2.3,demod,9,7] f(f(x,y,f(y,z,u)),f(y,z,u),f(z,u,w))=f(y,z,u).
% 992 [para_into,978.1.1.1,769.1.2,demod,8,9,8,8,9] f(f(x,y,z),f(x,y,f(x,u,z)),f(y,z,w))=f(x,y,z).
% 996 [para_into,978.1.1.1,44.1.2,demod,10,8,8] f(f(x,y,z),f(x,u,f(x,y,z)),f(y,z,w))=f(x,y,z).
% 998 [para_into,978.1.1.1,42.1.2] f(f(x,y,f(x,z,u)),f(x,z,u),f(z,u,w))=f(x,z,u).
% 1009 [para_into,978.1.1,44.1.2,demod,10,8,10,8,8,10,8] f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,u)))=f(x,y,u).
% 1242 (heat=1) [para_into,1009.1.1.1,1.1.2,demod,10,8,8] f(f(x,y,z),f(y,u,f(x,y,w)),f(z,w5,f(x,y,z)))=f(x,y,z).
% 1314 [para_from,978.1.2,42.1.2,demod,8,8,8,10,8,flip.1] f(f(x,y,z),f(x,z,u),f(y,w,f(x,y,z)))=f(x,y,z).
% 1406 (heat=1) [para_into,1314.1.1.2,1.1.2,demod,10,8,9] f(f(x,y,z),f(y,u,f(x,y,z)),f(z,w,f(x,z,w5)))=f(x,y,z).
% 1617 [para_from,771.1.2,44.1.2,demod,10,8,10,8] f(x,y,f(x,z,f(x,u,w)))=f(x,z,f(x,w,f(x,u,y))).
% 1741 (heat=1) [para_into,1617.1.1.3,1.1.2,demod,6,9,flip.1] f(x,y,f(x,z,f(x,u,y)))=f(x,u,f(x,y,z)).
% 1762 [para_into,992.1.1.1,44.1.2,demod,10,9,8,8,9,10] f(f(x,y,z),f(x,y,u),f(y,z,f(x,z,w)))=f(x,y,z).
% 1785 [para_into,992.1.1,44.1.2,demod,10,9,8,10,8,9,10,8] f(f(x,y,z),f(x,y,u),f(x,u,f(y,u,w)))=f(x,y,u).
% 2146 [para_into,996.1.2,773.1.2,demod,8,8,8,9,10,8] f(f(x,y,f(x,z,u)),f(x,w,f(x,y,f(x,z,u))),f(y,w5,f(x,z,u)))=f(x,u,f(x,y,z)).
% 2280 (heat=1) [para_into,2146.1.1,1.1.2,demod,10,9,10] f(f(x,y,z),f(x,u,f(x,w,f(x,y,z))),f(w,f(x,w,f(x,y,z)),f(x,u,f(x,w,f(x,y,z)))))=f(x,z,f(x,w,y)).
% 2468 [para_into,1009.1.1.1,44.1.2,demod,8,8,8] f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u)))=f(y,z,u).
% 2470 [para_into,1009.1.1.1,43.1.2] f(f(x,y,z),f(x,z,u),f(u,w,f(x,z,u)))=f(x,z,u).
% 2495,2494 [para_into,1009.1.1.3,41.1.1,demod,10,9] f(x,f(y,z,u),f(y,z,x))=f(y,z,x).
% 2725 (heat=1) [para_into,2494.1.1,1.1.1,demod,9,9] f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,f(x,w,f(y,z,u)))))=f(y,z,f(x,w,f(y,z,u))).
% 2730 (heat=1) [para_from,2494.1.2,1.1.1.1,demod,10,9,9,970,10,8] f(x,y,f(z,u,x))=f(u,x,f(z,x,y)).
% 2776 [para_from,1009.1.1,771.1.1.3,demod,8,7,8,flip.1] f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,x)))=f(w,f(y,z,u),f(y,z,x)).
% 2832 (heat=1) [para_into,2776.1.1,1.1.2,demod,9,10,9,10,9,10,9,9] f(f(x,y,z),f(x,u,f(y,z,w)),f(y,z,w))=f(u,f(x,y,z),f(y,z,w)).
% 4319 [para_into,1762.1.1,42.1.2] f(f(x,y,z),f(x,y,u),f(y,u,f(x,u,w)))=f(x,y,u).
% 4792 [para_into,774.1.2,771.1.1,demod,5,9,10,9,8,11,flip.1] f(x,y,f(z,y,u))=f(z,y,f(x,y,u)).
% 4915 [back_demod,2280,demod,9,40,10,9] f(x,f(y,z,u),f(y,w,f(y,x,f(y,z,u))))=f(y,u,f(y,z,x)).
% 4959,4958 (heat=1) [para_from,4915.1.2,1.1.2,demod,6,7,7,9,8,flip.1] f(x,y,f(z,u,f(z,x,y)))=f(z,x,y).
% 5872 [para_into,1785.1.1.1,44.1.2,demod,8,8] f(f(x,y,z),f(y,z,u),f(z,u,f(y,u,w)))=f(y,z,u).
% 5874 [para_into,1785.1.1.1,43.1.2] f(f(x,y,z),f(x,z,u),f(x,u,f(z,u,w)))=f(x,z,u).
% 6539,6538 [para_into,2468.1.1.3,774.1.1] f(f(x,y,z),f(y,z,u),f(y,u,f(z,u,w)))=f(y,z,u).
% 6541,6540 [para_into,2468.1.1.3,41.1.1,demod,10,9] f(x,f(y,z,u),f(z,u,x))=f(z,u,x).
% 6555,6554 [para_into,2468.1.1,769.1.1,demod,10,9,10,9,7,9,10,9] f(x,f(x,y,z),f(u,y,z))=f(x,y,z).
% 6863 [para_from,2468.1.1,771.1.1.3,demod,8,7,8,flip.1] f(x,f(y,z,u),f(w,f(y,z,u),f(z,u,x)))=f(w,f(y,z,u),f(z,u,x)).
% 6918 (heat=1) [para_into,6863.1.1,1.1.2,demod,9,10,9,10,9,10,9,9] f(f(x,y,z),f(x,u,f(w,y,z)),f(w,y,z))=f(u,f(x,y,z),f(w,y,z)).
% 7249 [para_into,2470.1.1.3,978.1.1,demod,10,8,10,8,9,10,8] f(f(x,y,z),f(x,z,u),f(x,z,f(w,u,f(x,z,u))))=f(x,z,f(w,u,f(x,z,u))).
% 7250 [para_into,2470.1.1.3,41.1.1,demod,10,9] f(x,f(y,z,u),f(y,u,x))=f(y,u,x).
% 7265,7264 [para_into,2470.1.1,769.1.1,demod,10,9,10,9,7,9,10,9] f(x,f(x,y,z),f(y,u,z))=f(x,y,z).
% 7380,7379 (heat=1) [para_from,7249.1.1,1.1.1,demod,35,10,8,11] f(x,y,f(z,u,f(x,y,u)))=f(x,y,u).
% 8193,8192 [para_into,4319.1.1.1,43.1.2] f(f(x,y,z),f(x,z,u),f(z,u,f(x,u,w)))=f(x,z,u).
% 8505 [para_into,776.1.2.3.3,769.1.2,demod,8,9,8] f(x,f(x,y,f(x,z,u)),f(y,w,w5))=f(x,z,f(x,u,f(y,w5,f(x,y,w)))).
% 8893 (heat=1) [para_into,8505.1.2.3,1.1.2,demod,9,9,8,964] f(x,f(x,y,f(x,z,u)),f(y,u,w))=f(x,z,f(x,y,u)).
% 9797 [para_into,5872.1.1.3.3,2470.1.1,demod,9,8,7,9,8] f(f(x,y,f(z,u,w)),f(z,w,w5),f(y,f(z,u,w),f(z,w,w5)))=f(y,f(z,u,w),f(z,w,w5)).
% 9972 (heat=1) [para_into,9797.1.1.1,1.1.2,demod,10,8,8,970,10,9,8,970] f(f(x,y,z),f(x,z,f(u,x,y)),f(y,z,w))=f(x,y,z).
% 11581 [para_into,9972.1.1.2.3,774.1.1,demod,9,10,9,10,8,9] f(f(x,y,f(z,u,w)),f(x,y,f(z,w,f(x,u,w))),f(y,w5,f(z,u,w)))=f(x,y,f(z,u,w)).
% 11634 (heat=1) [para_into,11581.1.1.1,1.1.2,demod,10,8,7380,8,8,8] f(f(x,y,z),f(y,z,f(x,y,u)),f(y,w,f(y,u,z)))=f(x,y,f(y,u,z)).
% 13015 [para_into,963.1.1.2,774.1.1] f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,w))=f(z,u,f(x,y,z)).
% 13462 [para_from,963.1.1,777.1.2.3,demod,10,9,8,10,9,8] f(x,f(x,y,z),f(x,u,f(y,z,w)))=f(x,u,f(x,y,z)).
% 13472 [para_from,963.1.1,45.1.2.3,demod,9,7] f(f(x,y,f(z,u,y)),f(z,u,y),f(z,u,w))=f(z,u,y).
% 13778 [para_into,13472.1.1.1.3,11634.1.2,demod,10,8,10,8,8,8,9,8] f(f(x,f(y,z,u),f(f(y,u,w),f(y,u,f(y,z,w)),f(y,w5,f(y,z,u)))),f(y,w,w6),f(y,w,f(y,z,u)))=f(y,w,f(y,z,u)).
% 13831 (heat=1) [para_into,13778.1.1.1.3.2,1.1.2,demod,7,6,7,9,5,7,9,9,7,9] f(f(x,y,f(z,y,u)),f(z,y,u),f(z,u,w))=f(z,y,u).
% 15000 [para_from,778.1.1,998.1.1.1,demod,9,8,9] f(f(x,y,f(y,z,f(y,u,w))),f(y,z,w),f(z,w,w5))=f(y,z,w).
% 16404 [para_into,13015.1.1.1,13831.1.2,demod,8,8,979,8] f(f(x,y,z),f(y,z,f(x,z,u)),f(z,u,w))=f(z,u,f(x,y,z)).
% 17222 [para_from,13015.1.2,777.1.1.3,demod,10,9,8,10,9,8] f(x,y,f(f(x,z,u),f(w,w5,z),f(w,z,f(x,w5,z))))=f(x,z,f(x,y,f(w,w5,z))).
% 17900 (heat=1) [para_into,17222.1.2.3,1.1.2,demod,10,8,8,10,8,35,10,8] f(x,y,f(f(x,z,u),f(y,z,w),f(z,w,f(x,y,z))))=f(x,y,z).
% 17973 [para_into,15000.1.1.1.3,963.1.2,demod,9,2495,9,8,9] f(f(x,y,f(y,z,f(y,u,w))),f(y,w,z),f(w,z,w5))=f(y,w,z).
% 18596 [para_from,15000.1.1,2470.1.1.3,demod,10,9,8,10,8,9,10,9,8] f(f(x,y,z),f(x,z,u),f(x,z,f(w,u,f(x,u,f(z,u,w5)))))=f(x,z,f(w,u,f(x,u,f(z,u,w5)))).
% 18723 (heat=1) [para_from,18596.1.1,1.1.1,demod,35,10,8,11] f(x,y,f(z,u,f(x,u,f(y,u,w))))=f(x,y,u).
% 19118 [para_into,16404.1.1.3,13472.1.2,demod,10,8] f(f(x,y,z),f(y,z,f(x,z,u)),f(f(z,u,w),f(z,u,w5),f(w6,w,f(z,u,w))))=f(z,u,f(x,y,z)).
% 19318 (heat=1) [para_into,19118.1.1.3.3,1.1.2,demod,7,10,7,6,10,9] f(x,f(y,z,u),f(z,u,f(y,u,x)))=f(u,x,f(y,z,u)).
% 20322 [para_from,17900.1.2,13472.1.2,demod,10,9,10,9,979,8,8,10,9,flip.1] f(x,y,f(f(z,x,u),f(z,y,w),f(z,w,f(z,x,y))))=f(z,x,y).
% 20439 [para_from,18723.1.1,17973.1.1,demod,9,10,9,9] f(x,f(y,z,f(z,x,f(z,u,w))),f(z,x,w))=f(z,x,w).
% 20459,20458 [para_from,18723.1.2,13831.1.2,demod,8,8,979,8,8,flip.1] f(x,y,f(z,u,f(y,z,f(x,z,w))))=f(x,y,z).
% 20465,20464 (heat=1) [para_into,20439.1.1.2.3,1.1.2,demod,6,8,8,9,8] f(x,f(x,y,z),f(u,y,f(x,y,z)))=f(x,y,z).
% 20581 [para_into,19318.1.1.2,44.1.2,demod,10,8,10,8] f(x,f(y,z,u),f(y,z,f(x,y,u)))=f(x,y,f(y,z,u)).
% 20636 [para_from,967.1.1,5874.1.1.1,demod,9,10,8,9] f(f(x,y,z),f(y,u,f(x,z,w)),f(y,u,f(u,w5,f(x,z,w))))=f(y,u,f(x,z,w)).
% 20639 (heat=1) [para_into,20636.1.1.3,1.1.2,demod,7,5,10,9] f(x,f(y,z,u),f(z,x,f(y,u,w)))=f(z,x,f(y,u,w)).
% 20653 [para_into,20639.1.1,773.1.2,demod,9,8,9,8] f(x,f(x,y,f(z,u,y)),f(z,u,w))=f(x,y,f(z,u,w)).
% 20737 [para_from,969.1.2,48.1.1.1,demod,10,9,9] f(f(A,f(x,D,E),f(A,D,E)),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
% 20738 (heat=1) [para_into,20737.1.1.1.2,1.1.1] f(f(A,f(x,D,f(y,D,E)),f(A,D,E)),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
% 20762,20761 [para_into,2494.1.1.2,777.1.1,demod,10,9,9,10,9] f(x,f(x,y,z),f(u,y,f(y,z,w)))=f(x,y,z).
% 20767 (heat=1) [para_into,20761.1.1.3.3,1.1.2,demod,10,8,8] f(x,f(x,y,z),f(y,u,f(z,w,f(y,z,w5))))=f(x,y,z).
% 20782,20781 [para_into,20761.1.1,44.1.2,demod,10,8,10,9,10,8] f(x,f(y,z,f(z,u,w)),f(z,u,x))=f(z,u,x).
% 20855 [para_into,20767.1.1.3.3,2470.1.1,demod,10,9] f(x,f(x,y,f(z,u,w)),f(y,w5,f(y,z,w)))=f(x,y,f(z,u,w)).
% 20856 [para_into,20767.1.1.3.3,2468.1.1,demod,10,9] f(x,f(x,y,f(z,u,w)),f(y,w5,f(y,u,w)))=f(x,y,f(z,u,w)).
% 20861 (heat=1) [para_into,20855.1.1.3,1.1.2,demod,6] f(x,f(x,y,f(z,u,w)),f(y,z,w))=f(x,y,f(z,u,w)).
% 20862 (heat=1) [para_into,20856.1.1.3,1.1.2,demod,6] f(x,f(x,y,f(z,u,w)),f(y,u,w))=f(x,y,f(z,u,w)).
% 20890 [para_from,20862.1.2,20781.1.2,demod,20782,10,8,9,flip.1] f(x,f(y,z,u),f(x,u,f(w,y,z)))=f(x,u,f(w,y,z)).
% 20902 [para_into,20890.1.1.3,2470.1.1,demod,7,7,8,flip.1] f(f(x,y,z),f(x,z,u),f(w,u,f(x,z,u)))=f(x,z,u).
% 20904 [para_into,20890.1.1.3,2468.1.1,demod,7,7,8,flip.1] f(f(x,y,z),f(y,z,u),f(w,u,f(y,z,u)))=f(y,z,u).
% 20906 [para_into,20890.1.1.3,1009.1.1,demod,7,7,8,flip.1] f(f(x,y,z),f(x,y,u),f(w,u,f(x,y,u)))=f(x,y,u).
% 21001 [para_into,20904.1.1,785.1.2,demod,10,8,10,8,10,8,15,10,9,9,12,9,20782,8,15,10,9,10,8,flip.1] f(x,y,f(y,z,f(u,x,y)))=f(y,z,f(u,x,y)).
% 21019,21018 [para_into,6540.1.1,20862.1.2,demod,10,9,9,6555,10,10,9] f(x,f(x,y,z),f(x,z,f(u,y,z)))=f(x,y,z).
% 21183 [para_into,2730.1.1,13015.1.2] f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,w))=f(y,z,f(x,z,u)).
% 21228 [para_from,791.1.2,784.1.2,demod,5,10,9,11,7,7,11,flip.1] f(x,y,f(z,u,f(u,x,y)))=f(u,x,y).
% 21256,21255 [para_into,21228.1.1,21228.1.2,demod,10,9,10,9,8,8,901,10,9] f(x,y,f(z,u,f(x,u,y)))=f(x,u,y).
% 21263 [para_into,21228.1.1,900.1.2,demod,8,8,21256,8] f(x,f(y,z,f(x,z,u)),f(u,w,f(x,z,u)))=f(x,z,u).
% 21272 [para_into,21228.1.2,2730.1.1,demod,8,8,901,10,9,flip.1] f(x,y,f(z,u,y))=f(z,y,f(u,x,y)).
% 21273 [para_into,21228.1.2,774.1.1,demod,8,8,901,10,9,flip.1] f(x,y,f(z,u,y))=f(z,y,f(x,u,y)).
% 21317 [para_into,21263.1.1.3,20862.1.1,demod,10,8,8,9] f(x,f(x,y,f(z,y,u)),f(w,z,f(x,z,y)))=f(x,z,y).
% 21324,21323 [para_into,21263.1.1,44.1.2,demod,10,9,10,9,8,10,9,10,9] f(x,f(y,z,f(y,x,u)),f(u,w,f(y,x,u)))=f(y,x,u).
% 21332,21331 (heat=1) [para_into,21317.1.1.3,1.1.2,demod,8,10,10,9] f(x,f(x,y,f(y,z,u)),f(y,z,f(x,z,w)))=f(x,y,z).
% 21368,21367 [para_into,21317.1.1.2.3,21263.1.2,demod,8,8,8,21324,9,8,9] f(x,f(x,y,f(y,z,u)),f(z,w,f(x,y,z)))=f(x,y,z).
% 21370,21369 [para_into,21317.1.1.2.3,21228.1.2,demod,10,8,7380,9,8,9] f(x,f(x,y,f(y,z,u)),f(u,w,f(x,y,u)))=f(x,y,u).
% 21516 [para_into,4792.1.2,21183.1.2,demod,8,9,8,flip.1] f(f(x,y,z),f(x,y,f(y,z,u)),f(y,u,w))=f(x,y,f(y,z,u)).
% 21543 [para_from,21516.1.2,21228.1.1.3,demod,10,9,10,8,8,9,10,8] f(x,y,f(f(x,z,u),f(y,u,w),f(z,u,f(x,y,u))))=f(x,y,u).
% 21623 [para_from,972.1.2,21228.1.2,demod,8,8,901,10,9,8,10,9,flip.1] f(f(x,y,z),f(u,y,w),f(u,y,f(x,y,w)))=f(x,y,f(u,y,w)).
% 21624 (heat=1) [para_into,21623.1.2,1.1.2,demod,8,8,10,8] f(f(x,y,z),f(y,u,w),f(y,u,f(x,y,w)))=f(y,w,f(x,y,u)).
% 21635 [para_from,797.1.1,2468.1.1.3,demod,10,8,12,9,9] f(f(x,y,z),f(y,z,u),f(u,f(y,z,u),f(u,w,w5)))=f(y,z,u).
% 21646,21645 [para_from,797.1.2,21272.1.2,demod,11,7,9,11,10,9,9,flip.1] f(x,f(y,z,u),f(x,z,u))=f(x,z,u).
% 21670 [para_into,21645.1.1,13462.1.2,demod,10,8] f(x,f(x,y,z),f(x,f(y,z,u),f(y,z,w)))=f(x,y,z).
% 21696 [para_from,21623.1.2,4792.1.2,demod,8,8,8,10,8,flip.1] f(f(x,y,z),f(x,y,f(y,u,z)),f(y,u,w))=f(x,y,f(y,u,z)).
% 21699 [para_into,21624.1.1.1,21228.1.2,demod,10,8,7380,8,8] f(f(x,y,z),f(x,u,w),f(x,u,f(x,z,w)))=f(x,w,f(x,z,u)).
% 21701 [para_into,21624.1.1.1,44.1.2,demod,8,8] f(f(x,y,z),f(y,u,w),f(y,u,f(y,z,w)))=f(y,w,f(y,z,u)).
% 21711,21710 [para_into,21635.1.1,4792.1.2,demod,10,9,10,8,10,9,10,8,10,9] f(x,f(x,y,z),f(f(x,y,z),f(x,u,w),f(y,z,w5)))=f(x,y,z).
% 21712 [para_into,21635.1.1,44.1.2,demod,10,9,10,9,10,8,8,10,9] f(f(x,y,z),f(x,f(x,y,z),f(x,u,w)),f(y,z,w5))=f(x,y,z).
% 21720 [para_from,21635.1.1,21183.1.1.2,demod,8,6541,10,9,5,flip.1] f(x,f(y,z,x),f(f(u,y,z),f(y,z,x),f(x,w,w5)))=f(y,z,x).
% 21745 [para_from,21696.1.1,21255.1.1,demod,8,flip.1] f(x,f(y,z,u),f(y,z,f(z,x,u)))=f(y,z,f(z,x,u)).
% 21778 [para_from,21670.1.1,20322.1.1.3.3,demod,9,10,8,2495,10,8,7] f(f(x,y,z),f(x,y,u),f(x,y,w))=f(w,f(x,y,z),f(x,y,u)).
% 21783 [para_into,21778.1.1.1,21720.1.2,demod,10,9,10,8,10,9,10,8,21711,10,9] f(f(x,y,z),f(y,z,u),f(y,z,w))=f(w,f(x,y,z),f(y,z,u)).
% 21784 [para_into,21778.1.1.1,21317.1.2,demod,8,9,8,21368,9] f(f(x,y,z),f(x,z,u),f(x,z,w))=f(w,f(x,y,z),f(x,z,u)).
% 21786 [para_into,21778.1.1,21699.1.1,demod,9,9,9,9,flip.1] f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,y,f(x,z,u)).
% 21787 [para_into,21778.1.1,7250.1.2,demod,8,10,9,21646] f(f(x,y,z),f(x,y,u),f(x,y,w))=f(z,f(x,y,u),f(x,y,w)).
% 21795 [para_from,21778.1.1,21699.1.1,demod,9,9] f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,z,f(x,y,u)).
% 21807 [para_into,21786.1.1.1,21228.1.2,demod,10,8,7380,8,8,8,8] f(f(x,y,z),f(x,z,u),f(y,z,u))=f(x,z,f(y,z,u)).
% 21813 [para_into,21786.1.1,7250.1.2,demod,9,9,8,9,9,10,9,21646] f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,u,f(x,y,z)).
% 21818 (heat=1) [para_into,21807.1.2,1.1.2,demod,9,10,8] f(f(x,y,z),f(x,z,u),f(y,z,u))=f(z,u,f(x,y,z)).
% 21824 [para_from,21786.1.2,20639.1.1.3,demod,5,8,8,8] f(x,y,f(f(x,y,z),f(x,y,u),f(y,z,u)))=f(x,y,f(y,z,u)).
% 21868 [para_into,21783.1.1,21255.1.2,demod,9,7380] f(f(x,y,z),f(y,z,u),f(y,z,w))=f(u,f(x,y,z),f(y,z,w)).
% 21869 [para_into,21783.1.2,21624.1.2,demod,7,10,9,15,10,9,7] f(x,f(y,z,x),f(z,x,u))=f(x,u,f(y,z,x)).
% 21870 [para_into,21783.1.2,19318.1.1,demod,9] f(f(x,y,z),f(y,z,u),f(y,z,f(x,z,u)))=f(z,u,f(x,y,z)).
% 21879 [para_into,21784.1.1,21255.1.2,demod,9,7380] f(f(x,y,z),f(x,z,u),f(x,z,w))=f(u,f(x,y,z),f(x,z,w)).
% 21880 [para_into,21784.1.2,21624.1.2,demod,7,10,9,12,9,7] f(x,f(y,z,x),f(y,x,u))=f(x,u,f(y,z,x)).
% 21899 [para_into,21787.1.1.1,21317.1.2,demod,8,9,8,21368] f(f(x,y,z),f(x,z,u),f(x,z,w))=f(y,f(x,z,u),f(x,z,w)).
% 21902 [para_into,21868.1.1,21783.1.1,demod,10,9,9,flip.1] f(x,f(y,z,u),f(w,z,u))=f(y,f(w,z,u),f(z,u,x)).
% 21907 [para_from,21879.1.1,20581.1.1,demod,10,901,10,9,10,8,flip.1] f(x,f(y,x,z),f(x,u,z))=f(y,x,f(x,u,z)).
% 21922 [para_from,21870.1.2,21228.1.2,demod,8,8,901,10,9,10,9,8,flip.1] f(f(x,y,z),f(u,y,z),f(y,z,f(x,u,z)))=f(x,z,f(u,y,z)).
% 21970,21969 [para_into,21922.1.1.3,21787.1.2,demod,8,9,11,7,9,8,20465] f(f(x,y,f(x,z,u)),f(x,z,u),f(y,z,f(x,z,u)))=f(x,z,u).
% 22020 [para_into,21869.1.2,21818.1.2,demod,10,9,8,10,9,8,8,flip.1] f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,f(x,y,z),f(x,z,u)).
% 22039 [para_from,21869.1.2,19318.1.2,demod,10,9,10,9,9] f(x,f(y,z,u),f(z,u,f(x,y,u)))=f(u,f(x,z,u),f(y,z,u)).
% 22079 [para_from,21880.1.2,21879.1.2,demod,7,flip.1] f(x,f(y,z,x),f(y,x,f(y,u,z)))=f(y,z,x).
% 22114,22113 [para_into,22079.1.1,21624.1.2,demod,9,9,9,11,9,7,9] f(x,f(y,x,z),f(y,u,z))=f(y,x,z).
% 22115 [para_into,22079.1.2,17973.1.1,demod,10,9,8,10,8,10,10,9,8,10,9,8,10,8,10,8,8,21019,10,8] f(f(x,y,z),f(x,y,u),f(w,u,f(y,u,f(x,u,w5))))=f(x,y,u).
% 22129 [para_into,22115.1.1.1,22079.1.2,demod,10,9,9,8,20762,8] f(f(x,y,z),f(y,z,u),f(u,w,f(z,u,f(y,u,w5))))=f(y,z,u).
% 22168 [para_into,22129.1.1,21624.1.2,demod,9,8,8,10,9,10,8,8,10,9,9,6555,10,7,10,9] f(f(x,y,z),f(x,z,f(x,y,u)),f(w,y,z))=f(x,y,z).
% 22224 [para_into,21745.1.1,21868.1.1,demod,10,9,21256,10,9,flip.1] f(x,y,f(z,y,f(u,x,y)))=f(z,y,f(u,x,y)).
% 22279,22278 [para_into,809.1.2.3.3,7264.1.1,demod,9,9,8,9,8,39,10,8] f(f(x,y,z),f(x,u,f(y,z,u)),f(y,z,u))=f(y,z,u).
% 22286 [para_into,809.1.2.3.3,773.1.2,demod,5,9,10,9,11,flip.1] f(x,y,f(y,z,f(u,x,y)))=f(u,y,f(x,y,z)).
% 22337 [para_into,22278.1.1,22113.1.2,demod,10,9,10,9,10,9,8,10,9,8,9,21646,10,9] f(f(x,y,f(y,z,u)),f(x,z,u),f(y,z,u))=f(y,z,u).
% 22502,22501 [para_from,21795.1.2,2494.1.1.2,demod,10,9,9,10,9] f(x,f(x,y,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(x,y,z).
% 22535 [para_into,21807.1.2,22286.1.2] f(f(x,y,z),f(x,z,u),f(y,z,u))=f(y,z,f(z,u,f(x,y,z))).
% 22542,22541 [para_from,21813.1.2,2494.1.1.2,demod,10,9,9,10,9] f(x,f(x,y,z),f(f(y,u,w),f(y,u,z),f(y,w,z)))=f(x,y,z).
% 22570,22569 [para_from,813.1.2,21870.1.2,demod,8,8,9,8,8,9,11,7,9,21970,8,10,11,9,9,flip.1] f(x,f(y,z,u),f(y,x,u))=f(y,x,u).
% 22621 [para_into,814.1.2.3,21623.1.2,demod,10,9,8,29,8,8,8,8,flip.1] f(x,y,f(f(x,z,u),f(z,y,w),f(z,y,f(x,z,w))))=f(x,z,y).
% 22671 [para_from,22621.1.2,22569.1.2,demod,8,9,7265,8,8,flip.1] f(x,y,f(f(z,x,u),f(z,y,w),f(z,y,f(z,x,w))))=f(z,x,y).
% 22681 [para_into,22671.1.1.3.3.3,20639.1.1,demod,9,8,8,7,8,10,9] f(x,f(y,z,u),f(x,w,f(z,w,f(y,u,w5))))=f(x,w,f(y,z,u)).
% 22688 (heat=1) [para_into,22681.1.1.3,1.1.2,demod,9,8] f(x,f(y,z,u),f(w,f(x,z,w),f(y,u,w5)))=f(x,w,f(y,z,u)).
% 22691 [para_into,22688.1.1.3,22039.1.2,demod,7,7,9] f(x,y,f(x,f(z,y,u),f(y,u,f(x,z,u))))=f(x,y,u).
% 22768 [para_into,815.1.2.3,812.1.2,demod,6,6,6,9,8,6,6,6,10,8,8] f(x,f(y,z,u),f(u,x,w))=f(x,w,f(y,u,f(z,u,x))).
% 22770 [para_into,815.1.2.3,805.1.2,demod,8,9,11,8,8,9,11,6,7,8,9,11,8,10,11,9,flip.1] f(x,f(y,z,u),f(z,f(y,w,f(y,w5,u)),f(y,z,u)))=f(y,z,u).
% 22807 [para_from,22770.1.1,21635.1.1.3.3] f(f(x,y,z),f(y,z,u),f(u,f(y,z,u),f(w,w5,w6)))=f(y,z,u).
% 22813 [para_from,22770.1.1,21712.1.1.2.3] f(f(x,y,z),f(x,f(x,y,z),f(u,w,w5)),f(y,z,w6))=f(x,y,z).
% 22899,22898 [para_into,22807.1.1.1,41.1.1] f(x,f(x,y,z),f(z,f(x,y,z),f(u,w,w5)))=f(x,y,z).
% 22918 [para_from,22813.1.1,21543.1.1.3.3,demod,10,8,10,8,22899,10,8,9,10,8,6,11,10,8,flip.1] f(x,y,f(z,f(x,y,z),f(u,w,w5)))=f(x,y,z).
% 22953 [para_into,22918.1.1.3.2,21255.1.1,demod,9,9,8,9,7380] f(x,y,f(f(x,y,z),f(u,z,f(x,y,z)),f(w,w5,w6)))=f(x,y,z).
% 23010 [para_into,22953.1.1.3.2,21273.1.2,demod,10,8] f(x,y,f(f(x,y,z),f(x,z,f(y,z,u)),f(w,w5,w6)))=f(x,y,z).
% 23329 [para_into,22681.1.1.3.3,21813.1.2,demod,5,9,8,5,9] f(x,y,f(x,z,f(f(y,u,z),f(y,u,w),f(y,z,w))))=f(x,y,z).
% 23424 [para_into,823.1.2.3,22113.1.1,demod,8,33,8,7,8,9,flip.1] f(x,f(y,z,u),f(z,x,u))=f(z,x,u).
% 23557 [para_into,21899.1.1,21879.1.1,demod,10,9,flip.1] f(x,f(y,z,u),f(z,u,w))=f(y,f(z,x,u),f(z,u,w)).
% 23566 [para_into,22020.1.1,23424.1.2,demod,9,9,8,21646,9] f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,f(x,y,u),f(x,z,u)).
% 23649 [para_from,23566.1.2,809.1.2.3.3,demod,9,9,8,12,9,7,9,8,8,flip.1] f(x,y,f(z,y,f(f(x,u,z),f(x,u,y),f(x,z,y))))=f(x,z,y).
% 23754,23753 [para_into,1242.1.1,2730.1.2,demod,8,8,8,8,9,15,10,9,8] f(x,f(y,z,f(y,u,w)),f(y,u,x))=f(y,u,x).
% 24390 [para_from,21824.1.2,21228.1.1.3,demod,10,9,10,9,10,8,10,9,10,8] f(x,y,f(z,u,f(f(x,y,u),f(x,z,u),f(y,z,u))))=f(x,y,u).
% 24423 [para_from,885.1.2,22337.1.1.1] f(f(x,y,f(y,z,f(x,y,u))),f(x,z,u),f(y,z,u))=f(y,z,u).
% 24439 [para_into,24423.1.1.1.3,23753.1.2,demod,23754,9,9,9] f(f(x,y,f(y,z,f(x,y,u))),f(x,u,z),f(y,u,z))=f(y,u,z).
% 24578 [para_into,890.1.2,20581.1.2,demod,8,8,8,flip.1] f(x,f(y,z,u),f(y,z,f(y,x,u)))=f(y,f(y,x,z),f(y,x,u)).
% 24614 [para_from,24578.1.2,21701.1.2,demod,11,7,9,flip.1] f(x,f(y,z,u),f(y,u,f(y,x,z)))=f(y,z,f(y,x,u)).
% 24635 [para_into,24614.1.1.3,22691.1.1,demod,10,8,10,9,22,9,10,8,7,10,8,10,9,flip.1] f(x,f(y,z,f(u,z,x)),f(y,x,f(u,y,z)))=f(y,z,x).
% 24957 [para_from,22535.1.2,809.1.2.3,demod,15,10,9,7,10,9,10,9,10,8,flip.1] f(x,y,f(f(z,x,u),f(z,y,u),f(x,y,u)))=f(x,y,u).
% 25040 [para_into,23010.1.1.3,21879.1.1,demod,10,8] f(x,y,f(f(x,y,z),f(x,z,u),f(y,z,w)))=f(x,y,z).
% 25073,25072 [para_from,25040.1.2,24635.1.2,demod,10,10,8,8,9,21332,10,9,8,8,flip.1] f(x,y,f(f(z,x,y),f(z,x,u),f(z,y,w)))=f(z,x,y).
% 25251,25250 [para_into,919.1.2,21645.1.1,demod,9,9] f(x,f(x,y,f(z,y,u)),f(x,u,f(z,y,u)))=f(x,y,u).
% 25269 [para_from,23649.1.1,24439.1.1.2,demod,9,9,10,9,25073,9,22114,11,9,9,10,9,25073,9,9,10,9,25073] f(f(x,y,z),f(x,u,z),f(y,z,f(x,u,z)))=f(y,z,f(x,u,z)).
% 25284,25283 [para_into,25269.1.2,20906.1.1,demod,10,9,8,21646] f(f(x,y,f(z,u,y)),f(z,u,w),f(z,u,y))=f(z,u,y).
% 25287 [para_into,25269.1.2,20902.1.1,demod,10,9,8,21646] f(f(x,y,f(z,u,y)),f(z,w,u),f(z,u,y))=f(z,u,y).
% 25290,25289 [para_from,25269.1.2,843.1.2.3,demod,10,8,7380,10,8,10,9,10,9,9,8,flip.1] f(x,y,f(f(x,z,u),f(x,z,f(z,u,y)),f(z,u,y)))=f(x,z,y).
% 25406 [para_into,24390.1.1,25289.1.2,demod,9,10,8,8,9,10,8,8,9,10,8,8,25290,9] f(x,y,f(z,u,f(f(x,z,u),f(x,u,y),f(z,u,y))))=f(x,u,y).
% 25408 [para_into,24390.1.1,25287.1.2,demod,10,9,10,8,10,8,10,8,10,9,10,8,10,8,10,8,9,10,9,10,8,10,8,10,8,25284,10,9] f(x,y,f(z,u,f(f(z,u,x),f(z,u,y),f(u,x,y))))=f(u,x,y).
% 25714,25713 [para_from,25406.1.1,20890.1.1.3,demod,9,8,9,9,970,9,8,8,flip.1] f(x,y,f(z,u,f(f(x,z,u),f(x,z,y),f(z,u,y))))=f(x,z,y).
% 26295 [para_into,1741.1.1.3,23329.1.1,demod,9,22502,9,flip.1] f(x,y,f(x,z,f(f(z,u,y),f(z,u,w),f(z,y,w))))=f(x,z,y).
% 26300 [para_from,26295.1.1,24614.1.1.3,demod,9,8,9,970,8,9,flip.1] f(x,f(y,x,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(y,x,z).
% 26302 [para_into,26300.1.1,20890.1.2,demod,9,8,10,9,8,9,8,22542,9,8] f(x,f(x,y,z),f(f(x,y,z),f(y,u,w),f(y,w,z)))=f(x,y,z).
% 26304 [para_from,26302.1.1,21745.1.1.3,demod,8,9,22570,8,7,8,8,10,8,flip.1] f(x,f(y,x,z),f(f(y,u,w),f(y,w,z),f(y,x,z)))=f(y,x,z).
% 26962 [para_into,22224.1.1.3,26304.1.1,demod,9,9,7,9,9,9,8,flip.1] f(x,f(y,z,x),f(f(y,u,z),f(y,u,w),f(y,z,x)))=f(y,z,x).
% 26970 [para_into,26962.1.1,20890.1.2,demod,10,9,10,9,7,10,9,10,9,10,11,10,9] f(x,f(x,y,z),f(f(x,y,z),f(y,u,w),f(y,u,z)))=f(x,y,z).
% 26973,26972 [para_from,26970.1.1,21745.1.1.3,demod,8,9,22570,8,7,8,8,10,8,flip.1] f(x,f(y,x,z),f(f(y,u,w),f(y,u,z),f(y,x,z)))=f(y,x,z).
% 27318 [para_from,2832.1.2,21001.1.2,demod,10,9,10,8,9,22114,11,10,9,10,8,8,10,8,10,9,flip.1] f(f(x,y,z),f(x,u,z),f(y,u,f(x,y,z)))=f(x,y,z).
% 27325,27324 [para_from,27318.1.1,21001.1.1.3,demod,7,8,8,10,8,flip.1] f(f(x,y,z),f(x,u,f(y,u,z)),f(y,u,z))=f(y,u,z).
% 27338 [para_into,27324.1.1.2,1406.1.1,demod,8,9,8,968,9,flip.1] f(x,f(y,x,z),f(u,w,f(y,u,x)))=f(x,f(y,u,x),f(y,x,z)).
% 27408,27407 [para_into,6918.1.1.2,24957.1.1,demod,9,6555,8,9,5,9,6555,8,9,flip.1] f(x,f(y,x,z),f(f(y,u,z),f(y,x,z),f(u,x,z)))=f(y,x,z).
% 27414 [para_into,6918.1.2,13462.1.2,demod,10,8,10,8,22279,10,8,flip.1] f(x,f(y,z,x),f(x,f(u,y,z),f(y,z,w)))=f(y,z,x).
% 27433 [para_into,27414.1.1,27324.1.2,demod,10,9,10,9,10,9,27325,10,9] f(x,f(x,y,z),f(x,f(u,y,z),f(y,z,w)))=f(x,y,z).
% 28654 [para_into,21902.1.1,26962.1.2,demod,10,8,9,10,8,10,8,9,8,26973,flip.1] f(x,f(y,z,u),f(z,u,w))=f(w,f(y,z,u),f(z,u,x)).
% 28682 [para_from,21902.1.1,20738.1.1,demod,4959,9] f(B,f(A,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
% 28688 [para_into,28682.1.1,21902.1.1,demod,10,9,9] f(A,f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
% 28918 [para_from,23557.1.2,27407.1.2,demod,27408,10,8] f(x,f(y,z,u),f(y,u,w))=f(z,f(y,u,x),f(y,u,w)).
% 30051,30050 [para_into,8893.1.2,27433.1.1,demod,970,9,6555,10,9] f(x,f(x,y,z),f(u,f(w,y,z),f(y,z,w5)))=f(x,y,z).
% 30978 [para_into,20653.1.1.2,21273.1.2,demod,9] f(x,f(y,z,f(x,z,u)),f(y,u,w))=f(x,z,f(y,u,w)).
% 31157 [para_into,20861.1.1,874.1.1,demod,9,8] f(x,f(y,z,u),f(u,w,f(x,y,w)))=f(x,w,f(y,z,u)).
% 32765 [para_into,22768.1.2,21907.1.2,demod,10,8,9,7265,10,9,10,9,flip.1] f(x,f(y,x,f(y,z,u)),f(x,u,f(y,z,u)))=f(y,x,u).
% 35658 [para_into,30978.1.1,25408.1.1,demod,10,9,7380,10,8,10,9,8,30,8,10,9,7380,9,8,flip.1] f(x,y,f(z,u,f(f(z,x,u),f(z,x,y),f(z,u,y))))=f(z,x,y).
% 35743 [para_from,31157.1.2,35658.1.2,demod,8,8,25714,10,8,9,flip.1] f(x,f(y,z,f(y,u,x)),f(u,w,z))=f(y,x,f(u,w,z)).
% 41522 [para_from,27338.1.2,35743.1.2,demod,8,12,9,9,6541,flip.1] f(x,f(y,x,z),f(u,w,f(y,u,x)))=f(x,z,f(y,u,x)).
% 41526 [para_from,41522.1.2,28918.1.2,demod,9,7,10,9,9,flip.1] f(x,f(y,x,f(z,y,u)),f(u,w,f(y,x,u)))=f(y,x,u).
% 42212 [para_from,2725.1.2,2832.1.1.2,demod,9,6539,flip.1] f(x,f(y,z,u),f(z,u,f(y,x,w)))=f(z,u,f(y,x,w)).
% 42527 [para_into,42212.1.1.3,22168.1.1,demod,8,8,8,9,30051,8,8,8,10,9,flip.1] f(f(x,y,z),f(x,u,z),f(u,z,f(x,u,w)))=f(x,u,z).
% 42542 [para_into,42212.1.1,28654.1.2,demod,10,9] f(f(x,y,z),f(x,u,w),f(y,u,w))=f(u,w,f(x,y,z)).
% 42570 [para_into,42542.1.1.1,42527.1.2,demod,9,8,8193,9] f(f(x,y,z),f(x,u,w),f(z,u,w))=f(u,w,f(x,y,z)).
% 42573 [para_into,42542.1.1.1,21645.1.1,demod,10,8,10,8,10,8,9,970] f(f(x,y,z),f(x,u,w),f(u,w,f(y,z,w5)))=f(u,w,f(x,y,z)).
% 42672 [para_into,42570.1.1,32765.1.2,demod,10,8,8,8,10,8,10,8,8,25251] f(f(x,y,z),f(x,u,w),f(y,z,w))=f(y,z,f(x,u,w)).
% 42745 [para_into,42672.1.1.1,41526.1.2,demod,8,8,8,21370,9] f(f(x,y,z),f(x,z,u),f(y,w,u))=f(x,z,f(y,w,u)).
% 42864 [para_into,42573.1.1.3,2730.1.1] f(f(x,y,z),f(x,u,w),f(z,u,f(y,u,w)))=f(u,w,f(x,y,z)).
% 42887 [para_from,42864.1.2,28688.1.1,demod,8,8,8,22,9,10,8] f(f(A,C,f(B,D,E)),f(A,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
% 42888 [para_into,42887.1.1,42542.1.1] f(D,E,f(A,C,f(B,D,E)))!=f(D,E,f(A,B,C)).
% 42890 [para_into,42888.1.1.3,42745.1.2] f(D,E,f(f(A,B,C),f(A,C,E),f(B,D,E)))!=f(D,E,f(A,B,C)).
% 42986 [para_into,42890.1.1.3,42864.1.2,demod,968,8,20459] f(D,E,f(A,B,C))!=f(D,E,f(A,B,C)).
% 42987 [binary,42986.1,770.1] $F.
% 
% ------------ end of proof -------------

list(hints2).

f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
f(x,y,z)=f(y,x,z).
f(x,x,y)=x.
f(x,y,x)=x.
f(y,x,x)=x.
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(z,y,x).
f(x,y,f(x,y,z))=f(x,y,z).
f(x,y,f(x,z,y))=f(x,y,z).
f(x,y,f(z,x,y))=f(x,y,z).
f(x,y,f(x,z,f(y,z,u)))=f(x,y,z).
f(x,y,f(x,z,f(z,y,u)))=f(x,y,z).
f(x,y,f(x,z,f(u,z,y)))=f(x,y,z).
f(y,x,f(x,z,f(y,z,u)))=f(x,y,z).
f(y,x,f(x,z,f(y,u,z)))=f(x,y,z).
f(y,x,f(x,z,f(u,y,z)))=f(x,y,z).
f(y,x,f(z,x,f(y,z,u)))=f(x,y,z).
f(y,x,f(z,x,f(u,y,z)))=f(x,y,z).
f(y,x,f(z,x,f(u,z,y)))=f(x,y,z).
f(x,x,y)=x.
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(z,y,x).
f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
f(f(A,D,E),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C))   # label("original").
f(x,y,z)=f(x,y,z).
f(x,y,f(z,x,u))=f(z,x,f(x,u,y)).
x=x.
f(x,y,f(x,z,f(u,x,w)))=f(u,x,f(x,y,f(x,w,z))).
f(x,f(y,x,z),f(x,u,w))=f(x,w,f(y,x,f(x,z,u))).
f(x,y,f(z,x,u))=f(x,u,f(z,x,y)).
f(x,y,f(z,u,x))=f(z,x,f(u,x,y)).
f(x,y,f(x,z,u))=f(x,z,f(x,u,y)).
f(x,y,f(x,z,f(u,x,w)))=f(u,x,f(x,w,f(x,z,y))).
f(x,y,f(z,x,u))=f(z,x,f(x,y,u)).
f(x,f(y,x,z),f(x,u,w))=f(y,x,f(x,w,f(x,z,u))).
f(x,f(y,z,u),f(z,f(y,z,u),f(w,w5,f(y,z,u))))=f(y,z,f(z,u,f(w,f(y,z,u),f(x,w5,f(y,z,u))))).
f(x,y,f(x,z,f(u,w,f(x,w5,u))))=f(x,z,f(x,f(x,u,y),f(w5,u,w))).
f(x,y,f(z,u,f(u,x,f(u,w,w5))))=f(u,x,f(x,y,f(u,w5,f(z,u,w)))).
f(x,f(x,y,f(x,z,u)),f(u,w,w5))=f(x,f(x,y,z),f(u,w5,f(x,u,w))).
f(x,f(y,x,z),f(z,u,f(z,w,w5)))=f(y,x,f(z,f(x,z,w5),f(z,u,w))).
f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(w,x,f(y,z,u)))).
f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(x,w,f(y,z,u)))).
f(x,f(y,x,z),f(z,u,w))=f(y,x,f(z,w,f(x,z,u))).
f(x,y,f(z,u,f(z,w,x)))=f(z,x,f(x,y,f(z,u,w))).
f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(w,f(y,z,u),f(z,u,f(y,z,x))).
f(x,f(y,z,u),f(y,z,f(z,u,w)))=f(z,f(y,z,u),f(x,w,f(y,z,u))).
f(x,y,f(z,u,f(u,x,w)))=f(u,x,f(x,y,f(z,u,w))).
f(x,y,f(x,z,f(u,y,w)))=f(x,z,f(u,y,f(x,y,w))).
f(x,f(x,y,z),f(y,u,w))=f(x,z,f(y,w,f(x,y,u))).
f(x,f(x,y,z),f(x,u,w))=f(x,u,f(x,y,f(x,z,w))).
f(x,y,f(y,z,f(x,y,u)))=f(x,y,f(y,z,u)).
f(x,f(y,x,z),f(y,x,u))=f(y,x,f(x,z,u)).
f(x,y,f(z,u,f(x,z,y)))=f(x,z,y).
f(x,f(y,z,x),f(y,z,u))=f(y,f(y,z,x),f(z,x,u)).
f(x,f(x,y,z),f(x,y,u))=f(x,y,f(x,z,u)).
f(x,y,f(x,z,f(y,u,w)))=f(x,z,f(y,u,f(x,y,w))).
f(x,f(y,z,x),f(y,z,u))=f(y,z,x).
f(x,f(y,x,z),f(y,z,u))=f(y,x,z).
f(x,f(x,y,z),f(y,z,u))=f(x,y,z).
f(f(x,y,z),f(x,y,f(y,z,u)),f(y,u,w))=f(y,u,f(x,y,z)).
f(f(x,y,f(y,z,u)),f(y,z,u),f(z,u,w))=f(y,z,u).
f(f(x,y,z),f(x,y,f(x,u,z)),f(y,z,w))=f(x,y,z).
f(f(x,y,z),f(x,u,f(x,y,z)),f(y,z,w))=f(x,y,z).
f(f(x,y,f(x,z,u)),f(x,z,u),f(z,u,w))=f(x,z,u).
f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,u)))=f(x,y,u).
f(f(x,y,z),f(y,u,f(x,y,w)),f(z,w5,f(x,y,z)))=f(x,y,z).
f(f(x,y,z),f(x,z,u),f(y,w,f(x,y,z)))=f(x,y,z).
f(f(x,y,z),f(y,u,f(x,y,z)),f(z,w,f(x,z,w5)))=f(x,y,z).
f(x,y,f(x,z,f(x,u,w)))=f(x,z,f(x,w,f(x,u,y))).
f(x,y,f(x,z,f(x,u,y)))=f(x,u,f(x,y,z)).
f(f(x,y,z),f(x,y,u),f(y,z,f(x,z,w)))=f(x,y,z).
f(f(x,y,z),f(x,y,u),f(x,u,f(y,u,w)))=f(x,y,u).
f(f(x,y,f(x,z,u)),f(x,w,f(x,y,f(x,z,u))),f(y,w5,f(x,z,u)))=f(x,u,f(x,y,z)).
f(f(x,y,z),f(x,u,f(x,w,f(x,y,z))),f(w,f(x,w,f(x,y,z)),f(x,u,f(x,w,f(x,y,z)))))=f(x,z,f(x,w,y)).
f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u)))=f(y,z,u).
f(f(x,y,z),f(x,z,u),f(u,w,f(x,z,u)))=f(x,z,u).
f(x,f(y,z,u),f(y,z,x))=f(y,z,x).
f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,f(x,w,f(y,z,u)))))=f(y,z,f(x,w,f(y,z,u))).
f(x,y,f(z,u,x))=f(u,x,f(z,x,y)).
f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,x)))=f(w,f(y,z,u),f(y,z,x)).
f(f(x,y,z),f(x,u,f(y,z,w)),f(y,z,w))=f(u,f(x,y,z),f(y,z,w)).
f(f(x,y,z),f(x,y,u),f(y,u,f(x,u,w)))=f(x,y,u).
f(x,y,f(z,y,u))=f(z,y,f(x,y,u)).
f(x,f(y,z,u),f(y,w,f(y,x,f(y,z,u))))=f(y,u,f(y,z,x)).
f(x,y,f(z,u,f(z,x,y)))=f(z,x,y).
f(f(x,y,z),f(y,z,u),f(z,u,f(y,u,w)))=f(y,z,u).
f(f(x,y,z),f(x,z,u),f(x,u,f(z,u,w)))=f(x,z,u).
f(f(x,y,z),f(y,z,u),f(y,u,f(z,u,w)))=f(y,z,u).
f(x,f(y,z,u),f(z,u,x))=f(z,u,x).
f(x,f(x,y,z),f(u,y,z))=f(x,y,z).
f(x,f(y,z,u),f(w,f(y,z,u),f(z,u,x)))=f(w,f(y,z,u),f(z,u,x)).
f(f(x,y,z),f(x,u,f(w,y,z)),f(w,y,z))=f(u,f(x,y,z),f(w,y,z)).
f(f(x,y,z),f(x,z,u),f(x,z,f(w,u,f(x,z,u))))=f(x,z,f(w,u,f(x,z,u))).
f(x,f(y,z,u),f(y,u,x))=f(y,u,x).
f(x,f(x,y,z),f(y,u,z))=f(x,y,z).
f(x,y,f(z,u,f(x,y,u)))=f(x,y,u).
f(f(x,y,z),f(x,z,u),f(z,u,f(x,u,w)))=f(x,z,u).
f(x,f(x,y,f(x,z,u)),f(y,w,w5))=f(x,z,f(x,u,f(y,w5,f(x,y,w)))).
f(x,f(x,y,f(x,z,u)),f(y,u,w))=f(x,z,f(x,y,u)).
f(f(x,y,f(z,u,w)),f(z,w,w5),f(y,f(z,u,w),f(z,w,w5)))=f(y,f(z,u,w),f(z,w,w5)).
f(f(x,y,z),f(x,z,f(u,x,y)),f(y,z,w))=f(x,y,z).
f(f(x,y,f(z,u,w)),f(x,y,f(z,w,f(x,u,w))),f(y,w5,f(z,u,w)))=f(x,y,f(z,u,w)).
f(f(x,y,z),f(y,z,f(x,y,u)),f(y,w,f(y,u,z)))=f(x,y,f(y,u,z)).
f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,w))=f(z,u,f(x,y,z)).
f(x,f(x,y,z),f(x,u,f(y,z,w)))=f(x,u,f(x,y,z)).
f(f(x,y,f(z,u,y)),f(z,u,y),f(z,u,w))=f(z,u,y).
f(f(x,f(y,z,u),f(f(y,u,w),f(y,u,f(y,z,w)),f(y,w5,f(y,z,u)))),f(y,w,w6),f(y,w,f(y,z,u)))=f(y,w,f(y,z,u)).
f(f(x,y,f(z,y,u)),f(z,y,u),f(z,u,w))=f(z,y,u).
f(f(x,y,f(y,z,f(y,u,w))),f(y,z,w),f(z,w,w5))=f(y,z,w).
f(f(x,y,z),f(y,z,f(x,z,u)),f(z,u,w))=f(z,u,f(x,y,z)).
f(x,y,f(f(x,z,u),f(w,w5,z),f(w,z,f(x,w5,z))))=f(x,z,f(x,y,f(w,w5,z))).
f(x,y,f(f(x,z,u),f(y,z,w),f(z,w,f(x,y,z))))=f(x,y,z).
f(f(x,y,f(y,z,f(y,u,w))),f(y,w,z),f(w,z,w5))=f(y,w,z).
f(f(x,y,z),f(x,z,u),f(x,z,f(w,u,f(x,u,f(z,u,w5)))))=f(x,z,f(w,u,f(x,u,f(z,u,w5)))).
f(x,y,f(z,u,f(x,u,f(y,u,w))))=f(x,y,u).
f(f(x,y,z),f(y,z,f(x,z,u)),f(f(z,u,w),f(z,u,w5),f(w6,w,f(z,u,w))))=f(z,u,f(x,y,z)).
f(x,f(y,z,u),f(z,u,f(y,u,x)))=f(u,x,f(y,z,u)).
f(x,y,f(f(z,x,u),f(z,y,w),f(z,w,f(z,x,y))))=f(z,x,y).
f(x,f(y,z,f(z,x,f(z,u,w))),f(z,x,w))=f(z,x,w).
f(x,y,f(z,u,f(y,z,f(x,z,w))))=f(x,y,z).
f(x,f(x,y,z),f(u,y,f(x,y,z)))=f(x,y,z).
f(x,f(y,z,u),f(y,z,f(x,y,u)))=f(x,y,f(y,z,u)).
f(f(x,y,z),f(y,u,f(x,z,w)),f(y,u,f(u,w5,f(x,z,w))))=f(y,u,f(x,z,w)).
f(x,f(y,z,u),f(z,x,f(y,u,w)))=f(z,x,f(y,u,w)).
f(x,f(x,y,f(z,u,y)),f(z,u,w))=f(x,y,f(z,u,w)).
f(f(A,f(x,D,E),f(A,D,E)),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
f(f(A,f(x,D,f(y,D,E)),f(A,D,E)),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
f(x,f(x,y,z),f(u,y,f(y,z,w)))=f(x,y,z).
f(x,f(x,y,z),f(y,u,f(z,w,f(y,z,w5))))=f(x,y,z).
f(x,f(y,z,f(z,u,w)),f(z,u,x))=f(z,u,x).
f(x,f(x,y,f(z,u,w)),f(y,w5,f(y,z,w)))=f(x,y,f(z,u,w)).
f(x,f(x,y,f(z,u,w)),f(y,w5,f(y,u,w)))=f(x,y,f(z,u,w)).
f(x,f(x,y,f(z,u,w)),f(y,z,w))=f(x,y,f(z,u,w)).
f(x,f(x,y,f(z,u,w)),f(y,u,w))=f(x,y,f(z,u,w)).
f(x,f(y,z,u),f(x,u,f(w,y,z)))=f(x,u,f(w,y,z)).
f(f(x,y,z),f(x,z,u),f(w,u,f(x,z,u)))=f(x,z,u).
f(f(x,y,z),f(y,z,u),f(w,u,f(y,z,u)))=f(y,z,u).
f(f(x,y,z),f(x,y,u),f(w,u,f(x,y,u)))=f(x,y,u).
f(x,y,f(y,z,f(u,x,y)))=f(y,z,f(u,x,y)).
f(x,f(x,y,z),f(x,z,f(u,y,z)))=f(x,y,z).
f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,w))=f(y,z,f(x,z,u)).
f(x,y,f(z,u,f(u,x,y)))=f(u,x,y).
f(x,y,f(z,u,f(x,u,y)))=f(x,u,y).
f(x,f(y,z,f(x,z,u)),f(u,w,f(x,z,u)))=f(x,z,u).
f(x,y,f(z,u,y))=f(z,y,f(u,x,y)).
f(x,y,f(z,u,y))=f(z,y,f(x,u,y)).
f(x,f(x,y,f(z,y,u)),f(w,z,f(x,z,y)))=f(x,z,y).
f(x,f(y,z,f(y,x,u)),f(u,w,f(y,x,u)))=f(y,x,u).
f(x,f(x,y,f(y,z,u)),f(y,z,f(x,z,w)))=f(x,y,z).
f(x,f(x,y,f(y,z,u)),f(z,w,f(x,y,z)))=f(x,y,z).
f(x,f(x,y,f(y,z,u)),f(u,w,f(x,y,u)))=f(x,y,u).
f(f(x,y,z),f(x,y,f(y,z,u)),f(y,u,w))=f(x,y,f(y,z,u)).
f(x,y,f(f(x,z,u),f(y,u,w),f(z,u,f(x,y,u))))=f(x,y,u).
f(f(x,y,z),f(u,y,w),f(u,y,f(x,y,w)))=f(x,y,f(u,y,w)).
f(f(x,y,z),f(y,u,w),f(y,u,f(x,y,w)))=f(y,w,f(x,y,u)).
f(f(x,y,z),f(y,z,u),f(u,f(y,z,u),f(u,w,w5)))=f(y,z,u).
f(x,f(y,z,u),f(x,z,u))=f(x,z,u).
f(x,f(x,y,z),f(x,f(y,z,u),f(y,z,w)))=f(x,y,z).
f(f(x,y,z),f(x,y,f(y,u,z)),f(y,u,w))=f(x,y,f(y,u,z)).
f(f(x,y,z),f(x,u,w),f(x,u,f(x,z,w)))=f(x,w,f(x,z,u)).
f(f(x,y,z),f(y,u,w),f(y,u,f(y,z,w)))=f(y,w,f(y,z,u)).
f(x,f(x,y,z),f(f(x,y,z),f(x,u,w),f(y,z,w5)))=f(x,y,z).
f(f(x,y,z),f(x,f(x,y,z),f(x,u,w)),f(y,z,w5))=f(x,y,z).
f(x,f(y,z,x),f(f(u,y,z),f(y,z,x),f(x,w,w5)))=f(y,z,x).
f(x,f(y,z,u),f(y,z,f(z,x,u)))=f(y,z,f(z,x,u)).
f(f(x,y,z),f(x,y,u),f(x,y,w))=f(w,f(x,y,z),f(x,y,u)).
f(f(x,y,z),f(y,z,u),f(y,z,w))=f(w,f(x,y,z),f(y,z,u)).
f(f(x,y,z),f(x,z,u),f(x,z,w))=f(w,f(x,y,z),f(x,z,u)).
f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,y,f(x,z,u)).
f(f(x,y,z),f(x,y,u),f(x,y,w))=f(z,f(x,y,u),f(x,y,w)).
f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,z,f(x,y,u)).
f(f(x,y,z),f(x,z,u),f(y,z,u))=f(x,z,f(y,z,u)).
f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,u,f(x,y,z)).
f(f(x,y,z),f(x,z,u),f(y,z,u))=f(z,u,f(x,y,z)).
f(x,y,f(f(x,y,z),f(x,y,u),f(y,z,u)))=f(x,y,f(y,z,u)).
f(f(x,y,z),f(y,z,u),f(y,z,w))=f(u,f(x,y,z),f(y,z,w)).
f(x,f(y,z,x),f(z,x,u))=f(x,u,f(y,z,x)).
f(f(x,y,z),f(y,z,u),f(y,z,f(x,z,u)))=f(z,u,f(x,y,z)).
f(f(x,y,z),f(x,z,u),f(x,z,w))=f(u,f(x,y,z),f(x,z,w)).
f(x,f(y,z,x),f(y,x,u))=f(x,u,f(y,z,x)).
f(f(x,y,z),f(x,z,u),f(x,z,w))=f(y,f(x,z,u),f(x,z,w)).
f(x,f(y,z,u),f(w,z,u))=f(y,f(w,z,u),f(z,u,x)).
f(x,f(y,x,z),f(x,u,z))=f(y,x,f(x,u,z)).
f(f(x,y,z),f(u,y,z),f(y,z,f(x,u,z)))=f(x,z,f(u,y,z)).
f(f(x,y,f(x,z,u)),f(x,z,u),f(y,z,f(x,z,u)))=f(x,z,u).
f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,f(x,y,z),f(x,z,u)).
f(x,f(y,z,u),f(z,u,f(x,y,u)))=f(u,f(x,z,u),f(y,z,u)).
f(x,f(y,z,x),f(y,x,f(y,u,z)))=f(y,z,x).
f(x,f(y,x,z),f(y,u,z))=f(y,x,z).
f(f(x,y,z),f(x,y,u),f(w,u,f(y,u,f(x,u,w5))))=f(x,y,u).
f(f(x,y,z),f(y,z,u),f(u,w,f(z,u,f(y,u,w5))))=f(y,z,u).
f(f(x,y,z),f(x,z,f(x,y,u)),f(w,y,z))=f(x,y,z).
f(x,y,f(z,y,f(u,x,y)))=f(z,y,f(u,x,y)).
f(f(x,y,z),f(x,u,f(y,z,u)),f(y,z,u))=f(y,z,u).
f(x,y,f(y,z,f(u,x,y)))=f(u,y,f(x,y,z)).
f(f(x,y,f(y,z,u)),f(x,z,u),f(y,z,u))=f(y,z,u).
f(x,f(x,y,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(x,y,z).
f(f(x,y,z),f(x,z,u),f(y,z,u))=f(y,z,f(z,u,f(x,y,z))).
f(x,f(x,y,z),f(f(y,u,w),f(y,u,z),f(y,w,z)))=f(x,y,z).
f(x,f(y,z,u),f(y,x,u))=f(y,x,u).
f(x,y,f(f(x,z,u),f(z,y,w),f(z,y,f(x,z,w))))=f(x,z,y).
f(x,y,f(f(z,x,u),f(z,y,w),f(z,y,f(z,x,w))))=f(z,x,y).
f(x,f(y,z,u),f(x,w,f(z,w,f(y,u,w5))))=f(x,w,f(y,z,u)).
f(x,f(y,z,u),f(w,f(x,z,w),f(y,u,w5)))=f(x,w,f(y,z,u)).
f(x,y,f(x,f(z,y,u),f(y,u,f(x,z,u))))=f(x,y,u).
f(x,f(y,z,u),f(u,x,w))=f(x,w,f(y,u,f(z,u,x))).
f(x,f(y,z,u),f(z,f(y,w,f(y,w5,u)),f(y,z,u)))=f(y,z,u).
f(f(x,y,z),f(y,z,u),f(u,f(y,z,u),f(w,w5,w6)))=f(y,z,u).
f(f(x,y,z),f(x,f(x,y,z),f(u,w,w5)),f(y,z,w6))=f(x,y,z).
f(x,f(x,y,z),f(z,f(x,y,z),f(u,w,w5)))=f(x,y,z).
f(x,y,f(z,f(x,y,z),f(u,w,w5)))=f(x,y,z).
f(x,y,f(f(x,y,z),f(u,z,f(x,y,z)),f(w,w5,w6)))=f(x,y,z).
f(x,y,f(f(x,y,z),f(x,z,f(y,z,u)),f(w,w5,w6)))=f(x,y,z).
f(x,y,f(x,z,f(f(y,u,z),f(y,u,w),f(y,z,w))))=f(x,y,z).
f(x,f(y,z,u),f(z,x,u))=f(z,x,u).
f(x,f(y,z,u),f(z,u,w))=f(y,f(z,x,u),f(z,u,w)).
f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,f(x,y,u),f(x,z,u)).
f(x,y,f(z,y,f(f(x,u,z),f(x,u,y),f(x,z,y))))=f(x,z,y).
f(x,f(y,z,f(y,u,w)),f(y,u,x))=f(y,u,x).
f(x,y,f(z,u,f(f(x,y,u),f(x,z,u),f(y,z,u))))=f(x,y,u).
f(f(x,y,f(y,z,f(x,y,u))),f(x,z,u),f(y,z,u))=f(y,z,u).
f(f(x,y,f(y,z,f(x,y,u))),f(x,u,z),f(y,u,z))=f(y,u,z).
f(x,f(y,z,u),f(y,z,f(y,x,u)))=f(y,f(y,x,z),f(y,x,u)).
f(x,f(y,z,u),f(y,u,f(y,x,z)))=f(y,z,f(y,x,u)).
f(x,f(y,z,f(u,z,x)),f(y,x,f(u,y,z)))=f(y,z,x).
f(x,y,f(f(z,x,u),f(z,y,u),f(x,y,u)))=f(x,y,u).
f(x,y,f(f(x,y,z),f(x,z,u),f(y,z,w)))=f(x,y,z).
f(x,y,f(f(z,x,y),f(z,x,u),f(z,y,w)))=f(z,x,y).
f(x,f(x,y,f(z,y,u)),f(x,u,f(z,y,u)))=f(x,y,u).
f(f(x,y,z),f(x,u,z),f(y,z,f(x,u,z)))=f(y,z,f(x,u,z)).
f(f(x,y,f(z,u,y)),f(z,u,w),f(z,u,y))=f(z,u,y).
f(f(x,y,f(z,u,y)),f(z,w,u),f(z,u,y))=f(z,u,y).
f(x,y,f(f(x,z,u),f(x,z,f(z,u,y)),f(z,u,y)))=f(x,z,y).
f(x,y,f(z,u,f(f(x,z,u),f(x,u,y),f(z,u,y))))=f(x,u,y).
f(x,y,f(z,u,f(f(z,u,x),f(z,u,y),f(u,x,y))))=f(u,x,y).
f(x,y,f(z,u,f(f(x,z,u),f(x,z,y),f(z,u,y))))=f(x,z,y).
f(x,y,f(x,z,f(f(z,u,y),f(z,u,w),f(z,y,w))))=f(x,z,y).
f(x,f(y,x,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(y,x,z).
f(x,f(x,y,z),f(f(x,y,z),f(y,u,w),f(y,w,z)))=f(x,y,z).
f(x,f(y,x,z),f(f(y,u,w),f(y,w,z),f(y,x,z)))=f(y,x,z).
f(x,f(y,z,x),f(f(y,u,z),f(y,u,w),f(y,z,x)))=f(y,z,x).
f(x,f(x,y,z),f(f(x,y,z),f(y,u,w),f(y,u,z)))=f(x,y,z).
f(x,f(y,x,z),f(f(y,u,w),f(y,u,z),f(y,x,z)))=f(y,x,z).
f(f(x,y,z),f(x,u,z),f(y,u,f(x,y,z)))=f(x,y,z).
f(f(x,y,z),f(x,u,f(y,u,z)),f(y,u,z))=f(y,u,z).
f(x,f(y,x,z),f(u,w,f(y,u,x)))=f(x,f(y,u,x),f(y,x,z)).
f(x,f(y,x,z),f(f(y,u,z),f(y,x,z),f(u,x,z)))=f(y,x,z).
f(x,f(y,z,x),f(x,f(u,y,z),f(y,z,w)))=f(y,z,x).
f(x,f(x,y,z),f(x,f(u,y,z),f(y,z,w)))=f(x,y,z).
f(x,f(y,z,u),f(z,u,w))=f(w,f(y,z,u),f(z,u,x)).
f(B,f(A,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
f(A,f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
f(x,f(y,z,u),f(y,u,w))=f(z,f(y,u,x),f(y,u,w)).
f(x,f(x,y,z),f(u,f(w,y,z),f(y,z,w5)))=f(x,y,z).
f(x,f(y,z,f(x,z,u)),f(y,u,w))=f(x,z,f(y,u,w)).
f(x,f(y,z,u),f(u,w,f(x,y,w)))=f(x,w,f(y,z,u)).
f(x,f(y,x,f(y,z,u)),f(x,u,f(y,z,u)))=f(y,x,u).
f(x,y,f(z,u,f(f(z,x,u),f(z,x,y),f(z,u,y))))=f(z,x,y).
f(x,f(y,z,f(y,u,x)),f(u,w,z))=f(y,x,f(u,w,z)).
f(x,f(y,x,z),f(u,w,f(y,u,x)))=f(x,z,f(y,u,x)).
f(x,f(y,x,f(z,y,u)),f(u,w,f(y,x,u)))=f(y,x,u).
f(x,f(y,z,u),f(z,u,f(y,x,w)))=f(z,u,f(y,x,w)).
f(f(x,y,z),f(x,u,z),f(u,z,f(x,u,w)))=f(x,u,z).
f(f(x,y,z),f(x,u,w),f(y,u,w))=f(u,w,f(x,y,z)).
f(f(x,y,z),f(x,u,w),f(z,u,w))=f(u,w,f(x,y,z)).
f(f(x,y,z),f(x,u,w),f(u,w,f(y,z,w5)))=f(u,w,f(x,y,z)).
f(f(x,y,z),f(x,u,w),f(y,z,w))=f(y,z,f(x,u,w)).
f(f(x,y,z),f(x,z,u),f(y,w,u))=f(x,z,f(y,w,u)).
f(f(x,y,z),f(x,u,w),f(z,u,f(y,u,w)))=f(u,w,f(x,y,z)).
f(f(A,C,f(B,D,E)),f(A,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
f(D,E,f(A,C,f(B,D,E)))!=f(D,E,f(A,B,C)).
f(D,E,f(f(A,B,C),f(A,C,E),f(B,D,E)))!=f(D,E,f(A,B,C)).
f(D,E,f(A,B,C))!=f(D,E,f(A,B,C)).



f(f(x,v,w),f(y,v,w),f(z,v,w)) = f(v,w,f(x,y,z))   # label("original").
f(f(x,f(x,v,w),f(x,v,w)),f(y,v,w),f(z,v,w)) = f(v,w,f(x,y,z)).
f(f(x,f(x,v,f(y,v,w)),f(x,v,w)),f(y,v,w),f(z,v,w)) = f(v,w,f(x,y,z)).
f(y,f(x,v,w),f(z,v,w)) = f(v,w,f(x,y,z)).
f(x,f(y,v,w),f(z,v,w)) = f(v,w,f(x,y,z)).
f(f(x,z,f(y,v,w)),f(x,v,w),f(z,v,w)) = f(v,w,f(x,y,z)).
f(v,w,f(x,z,f(y,v,w))) = f(v,w,f(x,y,z)).
f(v,w,f(f(x,y,z),f(x,z,w),f(y,v,w))) = f(v,w,f(x,y,z)).
f(v,w,f(x,y,z)) = f(v,w,f(x,y,z)).


end_of_list.

% Length of proof is 183.  Level of proof is 32.
% 
% ---------------- PROOF ----------------
% 
% 1 [] f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
% 2 [] f(x,y,z)=f(y,x,z).
% 5 [] f(x,x,y)=x.
% 6 [] f(x,y,x)=x.
% 7 [] f(y,x,x)=x.
% 8 [] f(x,y,z)=f(y,x,z).
% 9 [] f(x,y,z)=f(x,z,y).
% 10 [] f(x,y,z)=f(z,y,x).
% 11 [] f(x,y,f(x,y,z))=f(x,y,z).
% 12 [] f(x,y,f(x,z,y))=f(x,y,z).
% 15 [] f(x,y,f(z,x,y))=f(x,y,z).
% 17 [] f(x,y,f(x,z,f(y,z,u)))=f(x,y,z).
% 19 [] f(x,y,f(x,z,f(z,y,u)))=f(x,y,z).
% 29 [] f(y,x,f(x,z,f(y,z,u)))=f(x,y,z).
% 39 [] f(y,x,f(z,x,f(u,y,z)))=f(x,y,z).
% 41 [] f(x,x,y)=x.
% 42 [] f(x,y,z)=f(y,x,z).
% 43 [] f(x,y,z)=f(x,z,y).
% 44 [] f(x,y,z)=f(z,y,x).
% 45 [] f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
% 774 [] f(D,E,f(f(A,B,C),f(A,C,E),f(B,D,E)))!=f(D,E,f(A,B,C)).
% 862 [para_into,2.1.1,2.1.2] f(x,y,z)=f(x,y,z).
% 863 (heat=1) [para_into,862.1.1,1.1.2,demod,10,8,8] f(x,y,f(z,x,u))=f(z,x,f(x,u,y)).
% 864 (heat=1) [para_into,862.1.1,1.1.1,demod,8,10,8] f(x,y,f(y,z,u))=f(y,u,f(x,y,z)).
% 865 [para_into,41.1.1,41.1.1] x=x.
% 866 [para_into,45.1.1.1,45.1.2,demod,10,8,10,8,8,10,8] f(x,y,f(x,z,f(u,x,v)))=f(u,x,f(x,y,f(x,v,z))).
% 867 [para_into,45.1.1.1,45.1.1,demod,8,10,8,8,8] f(x,y,f(z,x,f(x,u,v)))=f(x,f(z,x,u),f(x,v,y)).
% 868 [para_into,45.1.1.1,44.1.2,demod,10,8,8] f(x,y,f(z,x,u))=f(x,u,f(z,x,y)).
% 869 [para_into,45.1.1.1,43.1.2,demod,10,8] f(x,y,f(z,u,x))=f(z,x,f(u,x,y)).
% 870 [para_into,45.1.1.1,42.1.2,demod,10,8,8,8] f(x,y,f(x,z,u))=f(x,z,f(x,u,y)).
% 873 [para_into,45.1.2.3,45.1.2,demod,8,8,8,10,8] f(x,f(y,x,z),f(x,u,v))=f(y,x,f(x,v,f(x,z,u))).
% 883,882 (heat=1) [para_into,866.1.2.3,1.1.2,demod,10,8,6,8] f(x,y,f(x,z,f(x,y,u)))=f(x,u,f(x,y,z)).
% 909 (heat=1) [para_from,868.1.1,1.1.2.3,demod,8,8,10] f(x,f(y,x,z),f(z,u,v))=f(y,x,f(z,v,f(x,z,u))).
% 953,952 (heat=1) [para_into,873.1.2.3,1.1.2,demod,8,9,6,8] f(x,f(x,y,z),f(x,z,u))=f(x,y,f(x,z,u)).
% 975 [para_from,45.1.2,43.1.2,demod,9,9,10,8] f(x,y,f(z,y,u))=f(y,u,f(x,z,y)).
% 980 (heat=1) [para_into,975.1.2.3,1.1.1,demod,8,8] f(x,f(y,z,u),f(z,x,v))=f(x,v,f(y,z,f(z,u,x))).
% 989 [para_into,863.1.1.3,863.1.1,demod,10,9,9,8] f(x,y,f(z,u,f(x,u,v)))=f(x,u,f(x,y,f(z,u,v))).
% 991 [para_into,863.1.1.3,45.1.1,demod,8,8,8,9,10,8,flip.1] f(x,f(x,y,z),f(x,u,v))=f(x,y,f(x,u,f(x,v,z))).
% 992 [para_into,863.1.2.3,863.1.2,demod,10,8,9,8] f(x,f(x,y,z),f(y,u,v))=f(x,z,f(y,v,f(x,y,u))).
% 999,998 (heat=1) [para_into,989.1.1,1.1.2,demod,8,8,11] f(x,f(y,x,z),f(y,x,u))=f(y,x,f(x,z,u)).
% 1006,1005 (heat=1) [para_into,989.1.2,1.1.2,demod,8,6,8] f(x,y,f(y,z,f(x,y,u)))=f(x,y,f(y,z,u)).
% 1007 (heat=1) [para_into,989.1.2,1.1.1,demod,10,8,8,8,8,8,8] f(x,f(y,z,u),f(z,v,f(z,w,f(y,z,u))))=f(y,z,f(z,u,f(x,f(y,z,u),f(z,v,w)))).
% 1026,1025 (heat=1) [para_into,991.1.2,1.1.2,demod,6,9] f(x,f(x,y,z),f(x,y,u))=f(x,y,f(x,z,u)).
% 1036,1035 (heat=1) [para_into,992.1.1,1.1.2,demod,9,11,5,11,flip.1] f(x,y,f(z,u,f(x,z,y)))=f(x,z,y).
% 1040 (heat=1) [para_into,992.1.2,1.1.2,demod,9,9,8] f(x,f(x,y,z),f(y,z,u))=f(z,f(x,y,z),f(x,y,u)).
% 1064 [para_into,864.1.1.3,864.1.1,demod,9,9] f(x,y,f(z,u,f(y,z,v)))=f(y,f(x,y,z),f(z,u,v)).
% 1066 [para_into,864.1.1.3,45.1.1,demod,8,9,10,8] f(x,f(y,z,u),f(y,z,f(z,u,v)))=f(v,f(x,z,f(y,z,u)),f(y,z,u)).
% 1067 [para_into,864.1.2.3,864.1.2,demod,8,9,9,8] f(x,y,f(y,z,f(x,u,v)))=f(y,z,f(x,u,f(x,y,v))).
% 1090 (heat=1) [para_into,1064.1.2.3,1.1.2,demod,8,10,8] f(x,y,f(z,u,f(y,z,f(u,v,w))))=f(y,f(x,y,z),f(u,w,f(z,u,v))).
% 1095 (heat=1) [para_from,1064.1.1,1.1.1.1,demod,8,10,8,10,8,8] f(x,y,f(x,f(x,z,u),f(u,v,w)))=f(x,z,f(x,y,f(u,v,f(x,u,w)))).
% 1115 (heat=1) [para_into,1066.1.2.2,1.1.2,demod,9,10,8,9] f(x,f(y,z,u),f(y,z,f(z,u,v)))=f(v,f(y,z,u),f(z,u,f(x,y,z))).
% 1133,1132 (heat=1) [para_into,1067.1.2,1.1.2,demod,29,8,10,9,8,flip.1] f(x,f(y,z,x),f(y,z,u))=f(y,z,x).
% 1140,1139 (heat=1) [para_from,1067.1.2,1.1.2,demod,8,8,8,8,19,9] f(x,f(y,x,z),f(y,z,u))=f(y,x,z).
% 1149,1148 [back_demod,1040,demod,1133] f(x,f(x,y,z),f(y,z,u))=f(x,y,z).
% 1166 [para_into,1139.1.1.2,864.1.2,demod,10,9,9,8] f(x,f(y,z,f(x,z,u)),f(z,v,f(y,z,u)))=f(x,z,f(y,z,u)).
% 1175,1174 [para_into,1139.1.1.3,1139.1.1,demod,8,8,8,8,8] f(x,f(x,y,f(y,z,u)),f(y,z,u))=f(x,y,f(y,z,u)).
% 1176 [para_into,1139.1.1.3,864.1.2,demod,8,9,8,8] f(x,f(x,y,z),f(y,u,f(y,z,v)))=f(x,y,z).
% 1179,1178 [para_into,1139.1.1,44.1.2,demod,9,10,9,9] f(x,f(y,z,u),f(y,z,x))=f(y,z,x).
% 1205 (heat=1) [para_from,1166.1.1,1.1.2.3,demod,8,9,8,8,8] f(f(x,y,f(z,u,f(u,y,v))),f(z,u,f(u,y,v)),f(u,w,f(z,u,v)))=f(x,f(z,u,f(u,y,v)),f(u,y,f(z,u,v))).
% 1299 (heat=1) [para_into,1176.1.1.3.3,1.1.2,demod,10,8] f(x,f(x,y,z),f(y,u,f(z,v,f(y,z,w))))=f(x,y,z).
% 1320,1319 (heat=1) [para_into,1178.1.2,1.1.1,demod,10,8,10,9,10] f(x,f(x,y,f(z,y,u)),f(y,v,f(z,y,u)))=f(z,y,f(x,y,u)).
% 1327 (heat=1) [para_from,1178.1.2,1.1.1.1,demod,10,9,9,1149,10,8] f(x,y,f(z,u,x))=f(u,x,f(z,x,y)).
% 1362 [para_from,1139.1.1,45.1.2.3,demod,9,7] f(f(x,y,f(z,y,u)),f(z,y,u),f(z,u,v))=f(z,y,u).
% 1364 [para_from,1139.1.2,864.1.2,demod,9,flip.1] f(x,f(y,x,f(z,y,u)),f(y,v,f(z,y,u)))=f(z,y,f(y,u,x)).
% 1515 (heat=1) [para_from,1364.1.2,1.1.2.3,demod,8,8,8,flip.1] f(x,y,f(z,f(y,z,f(y,u,v)),f(y,w,f(y,u,v))))=f(y,f(x,y,u),f(y,v,z)).
% 1713 [para_into,1362.1.1.1.3,864.1.2,demod,10,9,8,9,8] f(f(x,y,f(z,u,f(y,u,v))),f(y,u,f(z,u,v)),f(u,w,f(z,u,v)))=f(y,u,f(z,u,v)).
% 1750,1749 (heat=1) [para_into,1713.1.1.2,1.1.2,demod,9,10,8] f(f(x,y,f(z,u,f(y,u,v))),f(u,v,f(y,z,u)),f(u,w,f(z,u,v)))=f(y,u,f(z,u,v)).
% 1929 [para_from,1362.1.2,864.1.2,demod,8,9,10,8,flip.1] f(f(x,y,f(z,x,u)),f(x,v,f(z,x,u)),f(y,w,f(x,y,f(z,x,u))))=f(z,x,f(x,u,y)).
% 2039,2038 (heat=1) [para_into,1929.1.1.3,1.1.2,demod,8,8,5,8,5,10,9,9,8] f(x,f(y,x,f(y,z,u)),f(y,v,f(y,z,u)))=f(y,z,f(y,x,u)).
% 2227 [back_demod,1515,demod,2039,9] f(x,y,f(y,z,f(y,u,v)))=f(y,f(x,y,z),f(y,u,v)).
% 2231,2230 (heat=1) [para_into,2227.1.1.3,1.1.2,demod,6,flip.1] f(x,f(y,x,z),f(x,z,u))=f(y,x,f(x,z,u)).
% 2421 [para_into,869.1.1.3,1148.1.1,demod,10,8,8,10,8,10,flip.1] f(x,f(y,z,u),f(v,f(y,z,u),f(y,z,x)))=f(v,f(y,z,u),f(y,z,x)).
% 2478 (heat=1) [para_into,2421.1.1,1.1.2,demod,9,10,9,10,9,10,9,9] f(f(x,y,z),f(x,u,f(y,z,v)),f(y,z,v))=f(u,f(x,y,z),f(y,z,v)).
% 2612 [para_from,869.1.2,1362.1.1.1,demod,10,9,10,8,8,8,10,8] f(f(x,y,z),f(x,y,f(x,u,z)),f(y,z,v))=f(x,y,z).
% 2650 (heat=1) [para_from,2612.1.2,1.1.1.1,demod,9,10,8,8] f(x,y,f(f(z,x,u),f(z,x,f(z,u,v)),f(x,u,w)))=f(z,x,f(x,u,y)).
% 2656 [para_into,866.1.1.3.3,866.1.1,demod,8,9,8] f(x,y,f(x,z,f(u,v,f(x,v,f(v,w,v6)))))=f(x,v,f(x,y,f(x,z,f(v,v6,f(u,v,w))))).
% 2670 [para_into,866.1.2,869.1.1,demod,9,10,8,12,9,11,9,9,10,9,9,flip.1] f(x,f(x,y,f(x,z,u)),f(x,z,u))=f(x,y,f(x,z,u)).
% 2706,2705 (heat=1) [para_into,2656.1.1.3.3.3,1.1.2,demod,7,5,7,7,6,flip.1] f(x,y,f(x,z,f(x,u,y)))=f(x,z,f(x,u,y)).
% 2847 (heat=1) [para_into,2670.1.1.2.3,1.1.2,demod,10,8,8,8] f(x,f(x,y,f(z,u,f(x,z,v))),f(x,z,f(z,v,u)))=f(x,y,f(x,z,f(z,v,u))).
% 3276 [para_into,1327.1.1.3,1362.1.1,demod,9,8,9,9,8,10,8,flip.1] f(f(x,y,z),f(x,y,u),f(v,f(x,y,z),f(u,w,f(x,y,u))))=f(v,f(x,y,z),f(x,y,u)).
% 3278 [para_into,1327.1.1.3,1327.1.2,demod,9,8,10,9] f(x,f(y,z,u),f(z,u,f(y,z,v)))=f(z,f(y,z,u),f(x,v,f(y,z,u))).
% 3281,3280 [para_into,1327.1.1.3,1148.1.1,demod,10,8,8,10,8,10,9,8,flip.1] f(f(x,y,z),f(x,y,u),f(v,u,f(x,y,z)))=f(v,f(x,y,z),f(x,y,u)).
% 3301 (heat=1) [para_into,3276.1.1.3,1.1.2,demod,10,9,10,8,11] f(f(x,y,z),f(x,y,u),f(u,v,f(x,y,z)))=f(v,f(x,y,z),f(x,y,u)).
% 3324 (heat=1) [para_into,3278.1.2.3,1.1.2,demod,7,6,9,9,10,8,2231,flip.1] f(x,y,f(y,z,f(u,x,y)))=f(u,y,f(x,y,z)).
% 3532 [back_demod,2650,demod,8,8,9,8] f(x,y,f(f(x,z,u),f(x,z,f(z,u,v)),f(x,u,w)))=f(x,z,f(x,y,u)).
% 3560 (heat=1) [para_into,3532.1.1,1.1.2,demod,9,1026,17,9,19,9,11] f(f(x,y,z),f(x,y,f(y,z,u)),f(x,z,v))=f(x,y,z).
% 3572 [para_into,3560.1.1.1,1327.1.2,demod,10,9,10,8,9,8,10,8,9,10,8,8] f(f(x,y,f(x,z,u)),f(x,u,f(x,v,f(x,y,z))),f(u,w,f(x,y,z)))=f(x,u,f(x,y,z)).
% 3620 [para_into,3560.1.1,44.1.2,demod,8,9,9,9] f(f(x,y,z),f(x,y,u),f(x,u,f(y,u,v)))=f(x,y,u).
% 3634 (heat=1) [para_into,3572.1.1.1,1.1.2,demod,6,7,9,7,10,9,7,9] f(f(x,y,z),f(x,z,f(x,y,u)),f(y,z,v))=f(x,y,z).
% 4918,4917 [para_from,3634.1.1,864.1.1.3,demod,7,10,9,flip.1] f(f(x,f(y,z,u),f(y,u,f(y,z,v))),f(y,z,u),f(z,u,w))=f(y,z,u).
% 5202 [para_into,3324.1.1.3,1362.1.2,demod,10,8,10,8,10,8,9,10,8,8] f(x,y,f(f(y,z,f(x,y,u)),f(y,v,f(x,y,u)),f(w,z,f(y,z,f(x,y,u)))))=f(y,u,f(x,y,z)).
% 5227,5226 [para_into,3324.1.2.3,1327.1.1,demod,10,9,10,8,9,10,8,8,8] f(x,y,f(y,f(x,y,z),f(x,u,v)))=f(y,z,f(x,v,f(x,y,u))).
% 5229 [para_into,3324.1.2.3,866.1.1,demod,8,10,8,9,5227,9,9,8,8] f(x,y,f(z,f(z,x,u),f(z,v,w)))=f(x,y,f(z,v,f(z,x,f(z,u,w)))).
% 5348 (heat=1) [para_into,5202.1.1.3,1.1.2,demod,9,12,9,5,9,12,9,5,1006,1006,flip.1] f(x,y,f(z,x,f(x,u,y)))=f(z,x,f(x,u,y)).
% 5569,5568 (heat=1) [para_into,5229.1.2,1.1.2,demod,8,8,8,8,1140] f(x,y,f(z,f(x,z,u),f(y,z,v)))=f(x,y,z).
% 5721 [para_from,3324.1.1,1148.1.1.2,demod,8,9,8] f(x,f(y,z,f(x,z,u)),f(z,v,f(z,u,f(x,y,z))))=f(x,z,f(z,u,f(x,y,z))).
% 5723 [para_from,3324.1.1,864.1.1.3,demod,8,9,flip.1] f(x,f(y,x,z),f(z,u,f(x,v,z)))=f(y,x,f(v,z,f(x,z,u))).
% 5844 (heat=1) [para_into,5721.1.1.3,1.1.2,demod,6] f(x,f(y,z,f(x,z,u)),f(z,u,f(x,y,z)))=f(x,z,f(z,u,f(x,y,z))).
% 5872,5871 (heat=1) [para_into,5723.1.2.3,1.1.2,demod,8,9,10,10,8,8] f(x,f(x,y,z),f(z,u,f(x,z,v)))=f(x,y,f(z,u,f(x,z,v))).
% 6001 [back_demod,2847,demod,9,9] f(x,f(x,y,f(z,u,f(x,z,v))),f(x,z,f(z,u,v)))=f(x,y,f(x,z,f(z,u,v))).
% 6536 [para_into,867.1.1.3.3,3324.1.1,demod,8,8,8,9,9,flip.1] f(x,f(x,y,f(z,u,f(x,v,z))),f(x,w,z))=f(x,y,f(x,w,f(v,z,f(x,z,u)))).
% 6561 [para_into,867.1.2.2,866.1.1,demod,8,9,8,9,8,8,9,9,flip.1] f(x,f(x,y,z),f(u,v,f(x,u,f(u,w,v6))))=f(x,y,f(x,u,f(x,z,f(u,w,f(u,v,v6))))).
% 6592,6591 (heat=1) [para_into,6536.1.2.3.3,1.1.2,demod,9,9,10,10,8] f(x,f(x,y,f(z,u,f(x,z,v))),f(x,z,w))=f(x,y,f(x,w,f(z,u,f(x,z,v)))).
% 6809 (heat=1) [para_into,6561.1.2.3.3,1.1.2,demod,8,8] f(x,f(x,y,z),f(u,v,f(x,u,f(z,u,w))))=f(x,y,f(x,u,f(z,f(x,z,u),f(u,v,w)))).
% 6974 [back_demod,6001,demod,6592] f(x,y,f(x,f(z,u,v),f(z,u,f(x,z,v))))=f(x,y,f(x,z,f(z,u,v))).
% 7007 (heat=1) [para_into,6974.1.1,1.1.2,demod,6,9,1175] f(x,f(y,z,u),f(y,z,f(x,y,u)))=f(x,y,f(y,z,u)).
% 7160 [para_from,867.1.1,863.1.1.3,demod,8,10,9,9,8,9,8] f(x,y,f(z,f(x,z,u),f(z,v,w)))=f(x,z,f(x,y,f(z,v,f(z,w,u)))).
% 7502,7501 (heat=1) [para_into,7160.1.2.3,1.1.2,demod,8,5569,9,8,flip.1] f(x,y,f(z,f(x,z,y),f(y,u,v)))=f(x,z,y).
% 7771 [back_demod,6809,demod,7502] f(x,f(x,y,z),f(u,v,f(x,u,f(z,u,w))))=f(x,y,f(x,z,u)).
% 7840 (heat=1) [para_into,7771.1.2,1.1.2,demod,7,6] f(x,y,f(z,u,f(x,z,f(y,z,v))))=f(x,y,z).
% 8285,8284 [back_demod,1205,demod,8,8,8,8,9] f(f(x,y,f(z,u,f(y,u,v))),f(z,u,f(y,u,v)),f(u,w,f(z,u,v)))=f(x,f(y,u,f(z,u,v)),f(z,u,f(y,u,v))).
% 8393,8392 (heat=1) [para_into,8284.1.1.2,1.1.2,demod,10,9,10,8,1750,flip.1] f(x,f(y,z,f(u,z,v)),f(u,z,f(y,z,v)))=f(y,z,f(u,z,v)).
% 8403,8402 (heat=1) [para_into,8284.1.2.2,1.1.2,demod,8285,8393,9,10,8,9,flip.1] f(x,f(y,z,f(u,z,v)),f(z,v,f(u,y,z)))=f(u,z,f(y,z,v)).
% 8433,8432 [back_demod,5844,demod,8403,flip.1] f(x,y,f(y,z,f(x,u,y)))=f(x,y,f(u,y,z)).
% 8624,8623 [para_from,5348.1.1,869.1.2.3,demod,10,9,10,9,10,9,8] f(x,f(x,y,z),f(u,y,f(x,y,v)))=f(x,z,f(u,y,f(x,y,v))).
% 8647 [para_from,5348.1.2,869.1.1.3,demod,8,2706,8,9] f(x,f(y,z,u),f(y,v,f(y,z,u)))=f(v,f(y,z,u),f(y,x,f(y,z,u))).
% 8890,8889 (heat=1) [para_into,8647.1.1.3,1.1.2,demod,6,7,8,9,flip.1] f(x,f(y,z,f(z,x,u)),f(z,x,u))=f(z,x,u).
% 9165 [para_into,7840.1.1.3.3,1148.1.2,demod,9,1320] f(x,y,f(z,u,f(y,z,f(x,z,v))))=f(x,y,z).
% 9179 [para_into,7840.1.1.3,42.1.2] f(x,y,f(z,u,f(x,u,f(y,u,v))))=f(x,y,u).
% 9861 [para_from,7840.1.2,5348.1.2,demod,9,8,883,9,9,9,9,8,8,flip.1] f(x,y,f(z,f(x,u,v),f(y,f(x,u,v),f(x,w,f(x,u,v)))))=f(x,v,f(x,u,y)).
% 10172,10171 (heat=1) [para_from,9861.1.2,1.1.2,demod,6,7,7,7,9,8,8,flip.1] f(x,y,f(z,u,f(z,y,f(x,z,v))))=f(x,z,y).
% 11216,11215 [para_into,9179.1.1.3.3,9165.1.1,demod,9] f(x,y,f(z,u,f(x,y,u)))=f(x,y,u).
% 11246,11245 [para_into,9179.1.1,44.1.2,demod,8,8,10,10,9] f(x,y,f(z,u,f(u,x,f(u,y,v))))=f(u,x,y).
% 11962 [para_into,992.1.1.2,992.1.1,demod,9,10,8,9,9,9,9,8] f(x,f(x,y,f(z,u,f(x,z,v))),f(w,v6,f(x,y,z)))=f(x,f(z,u,v),f(v6,f(x,y,z),f(x,w,f(x,y,z)))).
% 11970,11969 [para_into,992.1.1.3,3634.1.1,demod,9,10,9,4918] f(x,f(x,y,f(z,u,v)),f(z,u,v))=f(x,y,f(z,u,v)).
% 11981,11980 [para_into,992.1.1,9179.1.2,demod,10,9,9] f(x,f(x,y,z),f(u,f(x,f(y,v,w),f(v6,f(x,y,z),f(y,v,w))),f(y,v,w)))=f(x,z,f(y,w,f(x,y,v))).
% 11984 [para_into,992.1.1,9165.1.1,demod,9,11,8,999,9,999,flip.1] f(x,y,f(x,z,f(z,u,f(z,y,v))))=f(x,z,y).
% 12003 [para_into,992.1.2.3.3,5348.1.1,demod,9,8,9,9,8] f(x,f(x,y,z),f(y,u,f(x,v,f(x,y,w))))=f(x,z,f(y,u,f(x,v,f(x,y,w)))).
% 12128,12127 (heat=1) [para_into,11962.1.1.2.3,1.1.2,demod,5,5,5,flip.1] f(x,y,f(z,f(x,u,y),f(x,v,f(x,u,y))))=f(x,f(x,u,y),f(v,z,f(x,u,y))).
% 12347,12346 (heat=1) [para_into,11984.1.2,1.1.2,demod,9,9,9,10,8] f(x,f(x,y,f(y,z,f(y,u,f(v,y,w)))),f(v,y,w))=f(y,w,f(x,v,y)).
% 12498,12497 (heat=1) [para_from,12003.1.2,1.1.2,demod,8,9,8,1149] f(x,f(y,x,z),f(y,u,f(y,z,v)))=f(y,x,z).
% 13248 [para_from,992.1.1,1327.1.1.3,demod,10,8,8,8,10,9,8] f(x,f(y,z,u),f(v,w,f(y,u,f(y,z,v))))=f(f(y,z,u),f(y,v,w),f(x,v,f(y,z,u))).
% 13467,13466 (heat=1) [para_into,13248.1.2.3,1.1.2,demod,7,9,9,10,8,flip.1] f(f(x,y,z),f(x,y,u),f(y,z,f(v,x,y)))=f(v,f(x,y,z),f(y,u,f(x,y,z))).
% 15209 [para_from,1299.1.1,3324.1.1.3.3,demod,10,8,15,10,9,10,9,flip.1] f(x,f(y,z,f(u,v,f(y,u,w))),f(v6,f(x,y,u),f(y,z,f(u,v,f(y,u,w)))))=f(v6,f(x,y,u),f(y,z,f(u,v,f(y,u,w)))).
% 15258 [para_from,1299.1.2,774.1.1.3.2,demod,10,9,8,8,9] f(D,E,f(f(A,B,C),f(A,f(x,C,f(y,E,f(z,C,E))),f(A,C,E)),f(B,D,E)))!=f(D,E,f(A,B,C)).
% 15343,15342 (heat=1) [para_into,15209.1.1.2.3,1.1.2,demod,5,5,5,5] f(x,f(y,z,u),f(v,f(x,y,u),f(y,z,u)))=f(v,f(x,y,u),f(y,z,u)).
% 15873,15872 [para_into,7007.1.1,42.1.2,demod,10,8,8,8] f(x,f(y,z,u),f(y,z,f(y,u,x)))=f(y,x,f(y,z,u)).
% 16522 [para_from,7007.1.1,3324.1.2.3,demod,8,10,9,9] f(x,f(y,z,u),f(f(x,v,f(y,z,u)),f(y,z,u),f(y,z,f(x,y,u))))=f(v,f(x,y,f(y,z,u)),f(y,z,u)).
% 16800,16799 (heat=1) [para_into,16522.1.1.3.1,1.1.2,demod,9,10,8,10,8,13467,15343,15343,8890] f(x,f(y,z,u),f(z,x,u))=f(z,x,u).
% 17037 [para_into,16799.1.1,16799.1.2,demod,9,9,16800,9] f(x,f(y,z,u),f(z,u,x))=f(z,u,x).
% 17055 [para_into,16799.1.1,45.1.1,demod,9,9,9,9] f(x,f(y,z,u),f(v,f(y,z,u),f(z,u,f(x,v,f(y,z,u)))))=f(z,u,f(x,v,f(y,z,u))).
% 17742 (heat=1) [para_from,17055.1.2,1.1.2,demod,10,8,8,999,10,8,10,8,10,8,8,1006,999,12,9,flip.1] f(x,f(y,z,u),f(y,z,f(z,x,u)))=f(y,z,f(z,x,u)).
% 18122,18121 [para_from,16799.1.1,1148.1.1.3,demod,8] f(x,f(x,y,f(z,u,v)),f(y,u,v))=f(x,y,f(z,u,v)).
% 18129 [para_from,16799.1.1,45.1.1,demod,8,9,9,8,8,8,9,9,flip.1] f(x,f(y,z,u),f(v,f(y,z,u),f(y,u,f(x,v,f(y,z,u)))))=f(y,u,f(x,v,f(y,z,u))).
% 18153 [para_from,16799.1.2,3560.1.1.2.3,demod,8,9] f(f(x,y,z),f(x,y,f(z,f(y,z,u),f(y,v,u))),f(x,z,w))=f(x,y,z).
% 18155 [para_from,16799.1.2,864.1.1.3,demod,8,9] f(x,y,f(z,f(y,z,u),f(y,v,u)))=f(y,u,f(x,y,z)).
% 18679,18678 (heat=1) [para_into,18129.1.1.3.3.3,1.1.2,demod,9,10,8,39,10,8,7,7,flip.1] f(x,y,f(z,u,f(x,u,y)))=f(x,u,y).
% 18782 (heat=1) [para_into,18153.1.1.2.3.3,1.1.2,demod,9,10,8] f(f(x,y,z),f(x,y,f(z,f(y,z,f(u,v,w)),f(v,w,f(y,u,v)))),f(x,z,v6))=f(x,y,z).
% 18787,18786 (heat=1) [para_into,18155.1.1.3.3,1.1.2,demod,9,10,8,9] f(x,y,f(z,f(y,z,f(u,v,w)),f(v,w,f(y,u,v))))=f(y,f(x,y,z),f(u,v,w)).
% 18832 [back_demod,18782,demod,18787,9] f(f(x,y,z),f(x,z,u),f(y,f(x,y,z),f(v,w,v6)))=f(x,y,z).
% 19393 [para_into,17037.1.1.3,9179.1.1,demod,8,8,10,8,10,9,9,8,8,11246] f(f(x,y,f(y,z,f(y,u,v))),f(y,z,u),f(z,u,w))=f(y,z,u).
% 19397 [para_into,17037.1.1.3,7007.1.2,demod,10,9,10,8,15873,8] f(f(x,y,z),f(x,u,v),f(x,v,f(x,y,z)))=f(x,v,f(x,y,z)).
% 19431 [para_into,17037.1.1.3,866.1.1,demod,8,8,9,8,9,8] f(f(x,y,f(x,z,u)),f(x,z,f(x,v,f(x,y,u))),f(x,w,v))=f(x,v,f(x,y,f(x,z,u))).
% 19517 (heat=1) [para_into,19397.1.2,1.1.1,demod,10,8,10,10,8,8,10,8,10,8,8] f(f(x,y,f(z,x,u)),f(x,f(z,x,u),f(v,w,f(z,x,u))),f(v,w,f(z,x,u)))=f(z,x,f(x,u,f(v,w,f(z,x,u)))).
% 19870,19869 (heat=1) [para_into,19431.1.1.1,1.1.2,demod,6,883,9,11] f(f(x,y,z),f(x,z,f(x,y,u)),f(x,u,v))=f(x,u,f(x,y,z)).
% 20404 [para_into,18678.1.1.3.3,9165.1.1,demod,8,9,8,8,10172] f(x,f(y,z,f(y,u,f(x,y,v))),f(u,w,f(x,y,u)))=f(x,y,u).
% 20432 [para_into,18678.1.1,17037.1.2,demod,8,10,8,8,1179,8] f(x,y,f(z,u,f(u,x,y)))=f(u,x,y).
% 20503,20502 (heat=1) [para_into,20404.1.1.2.3.3,1.1.1,demod,8,10,8,10,8] f(f(x,y,z),f(y,u,f(y,v,f(x,y,f(y,z,w)))),f(v,v6,f(y,v,f(x,y,z))))=f(y,v,f(x,y,z)).
% 21482 [para_into,20432.1.1.3.3,9179.1.1,demod,8,10,8,8,8,8] f(x,f(y,z,f(z,u,f(x,z,v))),f(u,w,f(x,z,u)))=f(x,u,f(y,z,f(z,u,f(x,z,v)))).
% 21509,21508 [para_into,20432.1.2,9179.1.1,demod,8,8,8,8,1036,10,8] f(x,y,f(z,u,f(u,y,f(x,u,v))))=f(x,u,y).
% 21514 [para_into,20432.1.2,869.1.1,demod,8,8,1036,10,9] f(x,y,f(z,u,y))=f(z,y,f(x,u,y)).
% 21518,21517 (heat=1) [para_into,21482.1.1.2.3.3,1.1.1,demod,8,8,10,8,20503,10,8,8,8,flip.1] f(x,f(y,z,u),f(z,v,f(z,x,f(z,w,f(y,z,u)))))=f(z,x,f(y,z,u)).
% 23572 [para_into,21514.1.2.3,870.1.1] f(x,f(x,y,z),f(u,v,f(x,y,z)))=f(u,f(x,y,z),f(x,y,f(x,z,v))).
% 24235 [para_into,18832.1.1.1,16799.1.1,demod,9,10,8,10,8,9,1140,8,10,8,9,1140] f(f(x,y,z),f(y,u,f(x,y,z)),f(f(x,y,z),f(x,z,v),f(w,v6,v7)))=f(x,y,z).
% 24314,24313 [para_into,18832.1.1,20432.1.2,demod,9,9,9,9,8,18679,9] f(f(x,y,z),f(x,y,u),f(u,f(x,y,u),f(v,w,v6)))=f(x,y,u).
% 24325 [para_into,18832.1.1,864.1.2,demod,8,8,9,8] f(x,f(x,y,z),f(f(x,y,z),f(y,z,u),f(v,w,v6)))=f(x,y,z).
% 24454,24453 (heat=1) [para_into,24235.1.1.2,1.1.2,demod,5,5,8] f(x,f(y,x,z),f(f(y,x,z),f(y,z,u),f(v,w,v6)))=f(y,x,z).
% 25062,25061 (heat=1) [para_into,24325.1.2,1.1.2,demod,8,8,8,9,10,8] f(x,f(x,y,f(y,z,u)),f(f(x,y,f(y,z,u)),f(y,v,f(y,z,u)),f(w,v6,v7)))=f(y,u,f(x,y,z)).
% 25644 [para_into,24325.1.1.2,17037.1.2,demod,8,9,9,9,8,9] f(x,f(y,f(x,y,z),f(x,u,z)),f(f(x,y,z),f(y,z,v),f(w,v6,v7)))=f(x,y,z).
% 25797,25796 (heat=1) [para_from,25644.1.1,1.1.2.3,demod,8,9,1149,9,8,9,1149,8,8,9,1149,8,7] f(f(x,y,f(z,y,u)),f(z,y,u),f(f(z,y,u),f(z,u,v),f(w,v6,v7)))=f(z,y,u).
% 26362 [back_demod,19517,demod,8,8,8,8,8,8] f(f(x,y,f(x,z,u)),f(x,f(x,z,u),f(v,w,f(x,z,u))),f(v,w,f(x,z,u)))=f(x,z,f(x,u,f(v,w,f(x,z,u)))).
% 26365,26364 (heat=1) [para_into,26362.1.1.2.3,1.1.2,demod,10,10,8,1149,8,8,1036,11] f(f(x,y,f(x,z,u)),f(x,z,u),f(z,v,f(x,z,u)))=f(x,z,u).
% 26393 [para_from,24325.1.2,20432.1.2,demod,10,8,11216,10,8,10,8,flip.1] f(x,f(y,z,x),f(f(y,z,x),f(y,z,u),f(v,w,v6)))=f(y,z,x).
% 26918 [para_into,19393.1.1.1.3.3,26393.1.2,demod,9,9,24454] f(f(x,y,f(y,z,f(y,u,v))),f(y,z,v),f(z,v,w))=f(y,z,v).
% 26962 [para_into,19869.1.1.1,44.1.2,demod,8,8,10] f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,v))=f(z,u,f(x,y,z)).
% 27036 [para_into,26918.1.1.1.3,19869.1.2,demod,19870,9,8,9] f(f(x,y,f(y,z,f(y,u,v))),f(y,v,z),f(v,z,w))=f(y,v,z).
% 27085 [para_from,26962.1.2,24453.1.2,demod,10,9,8,10,9,8,10,9,9,25062,10,9,10,8,8,10,9,flip.1] f(f(x,y,z),f(y,u,v),f(y,u,f(x,y,v)))=f(y,v,f(x,y,u)).
% 27103 [para_into,27036.1.1,20432.1.1,demod,8,10,9,9,8624,10,9] f(x,y,f(z,u,f(x,u,f(u,v,y))))=f(x,u,y).
% 27113 [para_into,27085.1.1.1,20432.1.2,demod,10,8,11216,8,8] f(f(x,y,z),f(x,u,v),f(x,u,f(x,z,v)))=f(x,v,f(x,z,u)).
% 27178 [para_into,27113.1.1.3,21514.1.2,demod,7,12,9,8,12,9] f(x,f(y,z,u),f(y,u,x))=f(y,u,x).
% 27197 [para_into,27103.1.1,17037.1.2,demod,8,10,8,8,1179,8] f(x,y,f(z,u,f(u,x,f(u,v,y))))=f(u,x,y).
% 27259,27258 [para_into,17742.1.1.3,26393.1.1,demod,9,24314,8,flip.1] f(x,f(y,z,x),f(f(y,z,u),f(y,z,x),f(v,w,v6)))=f(y,z,x).
% 27303 [para_from,18121.1.2,27258.1.2,demod,27259,10,8,9,flip.1] f(x,f(y,z,u),f(x,u,f(v,y,z)))=f(x,u,f(v,y,z)).
% 27312 [para_from,18121.1.2,44.1.2,demod,10,8,8,10,8,9,flip.1] f(x,f(y,z,u),f(u,x,f(v,y,z)))=f(u,x,f(v,y,z)).
% 27404,27403 [para_into,27303.1.1,27197.1.2,demod,10,8,8,10,8,8,8,21518,10,8,8] f(x,f(y,z,u),f(u,x,f(y,z,v)))=f(u,x,f(y,z,v)).
% 27531 [para_into,3620.1.1.1,16799.1.1,demod,10,8,9,10,8,10,8,10,8,9] f(f(x,y,z),f(y,u,f(x,z,v)),f(y,u,f(u,w,f(x,z,v))))=f(y,u,f(x,z,v)).
% 27539 (heat=1) [para_into,27531.1.1.3,1.1.2,demod,7,5,10,9] f(x,f(y,z,u),f(z,x,f(y,u,v)))=f(z,x,f(y,u,v)).
% 27551 [para_into,27539.1.1,27103.1.2,demod,8,8,8,8,8,10,8,9,11981,9,8] f(x,f(y,z,f(x,y,u)),f(u,z,v))=f(x,y,f(u,z,v)).
% 27602 [para_into,27531.1.1.2,27036.1.1,demod,10,9,9,21509,8,10,9,8,8,8,8,5,10,9,8,10,8,flip.1] f(f(x,y,z),f(x,z,u),f(v,y,f(y,z,f(x,y,w))))=f(x,y,z).
% 28270,28269 [para_from,909.1.2,26962.1.2,demod,8,8,8,9,8624,18679,8,10,8,26365,8,10,11,9,9,flip.1] f(x,f(y,z,u),f(y,x,u))=f(y,x,u).
% 28988,28987 [para_from,980.1.1,27539.1.1,demod,10,8] f(x,f(y,z,u),f(y,v,f(x,z,v)))=f(x,v,f(y,z,u)).
% 29121 [para_from,27602.1.1,27531.1.1.2,demod,9,10,8,25797,10,9,flip.1] f(f(x,y,f(y,z,f(u,y,v))),f(u,y,z),f(u,z,w))=f(u,y,z).
% 29540 [para_into,29121.1.1.1,27303.1.2,demod,9,8,9,11970,10,9,8,10,9] f(f(x,y,f(z,y,f(u,y,v))),f(z,u,y),f(z,u,w))=f(z,u,y).
% 30301,30300 [para_from,1095.1.1,27303.1.1,demod,9,8,28988,10,8] f(x,y,f(x,z,f(u,v,f(x,y,z))))=f(x,f(x,y,z),f(u,v,z)).
% 30303,30302 [para_from,1095.1.1,1090.1.1,demod,10,8,8,11,11,30301,10,9,6,9,8,8,12128,flip.1] f(x,f(x,y,z),f(u,v,f(x,y,z)))=f(x,f(x,y,z),f(z,u,v)).
% 30315,30314 [back_demod,23572,demod,30303,flip.1] f(x,f(y,z,u),f(y,z,f(y,u,v)))=f(y,f(y,z,u),f(u,x,v)).
% 31169 [para_from,11984.1.2,29540.1.1.1,demod,8,8,9,9,12347,9,9,10,8,9] f(f(x,y,z),f(x,z,u),f(y,f(v,x,y),f(y,z,w)))=f(x,y,z).
% 32144,32143 [para_into,3301.1.1.3,2478.1.2,demod,10,8,8,10,9,3281,27404,10,8,10,8,flip.1] f(f(x,y,z),f(x,y,u),f(x,y,v))=f(u,f(x,y,z),f(x,y,v)).
% 32160 [para_into,32143.1.1,27303.1.2,demod,9,32144,16800] f(x,f(y,z,u),f(y,z,v))=f(v,f(y,z,u),f(y,z,x)).
% 32309 [para_into,32160.1.2,1115.1.1,demod,10,8,8,10,8,10,30315,8] f(f(x,y,z),f(x,y,u),f(x,u,v))=f(x,f(x,y,u),f(z,u,v)).
% 32606,32605 [para_from,32309.1.2,27178.1.2,demod,10,9,10,9,9,28270,10,9,10,9,10,8,9,flip.1] f(f(x,y,z),f(u,v,y),f(u,y,z))=f(y,f(x,u,v),f(u,y,z)).
% 35265 [para_into,27312.1.2,31169.1.1,demod,8,8,9,10,9,9,8,8,8,9,18122,9] f(f(x,y,z),f(x,y,u),f(u,f(x,v,u),f(y,u,w)))=f(x,y,u).
% 35313,35312 [para_from,35265.1.1,1007.1.1.3.3,demod,10,9,8,953,10,9,10,9,6,9,30315,8,9,10,9,10,9,8,10,9,8,953,10,9,10,9,6,9,30315,8,9,8433,32606,5872,flip.1] f(x,y,f(z,f(u,x,y),f(x,z,v)))=f(x,f(u,z,v),f(x,y,z)).
% 35470 [para_from,27551.1.2,15258.1.1.3,demod,10,9,12498,10,8,9,35313,12498,12,9] f(D,E,f(A,B,C))!=f(D,E,f(A,B,C)).
% 35471 [binary,35470.1,865.1] $F.
% 
% ------------ end of proof / derivation -------------

list(hints2).
 f(f(x,w,y),w,z)=f(x,w,f(y,w,z))  # label("Hint 1(1)").
 f(x,y,z)=f(y,x,z)  # label("Hint 2(2)").
 f(x,x,y)=x  # label("Hint 3(5)").
 f(x,y,x)=x  # label("Hint 4(6)").
 f(y,x,x)=x  # label("Hint 5(7)").
 f(x,y,z)=f(y,x,z)  # label("Hint 6(8)").
 f(x,y,z)=f(x,z,y)  # label("Hint 7(9)").
 f(x,y,z)=f(z,y,x)  # label("Hint 8(10)").
 f(x,y,f(x,y,z))=f(x,y,z)  # label("Hint 9(11)").
 f(x,y,f(x,z,y))=f(x,y,z)  # label("Hint 10(12)").
 f(x,y,f(z,x,y))=f(x,y,z)  # label("Hint 11(15)").
 f(x,y,f(x,z,f(y,z,u)))=f(x,y,z)  # label("Hint 12(17)").
 f(x,y,f(x,z,f(z,y,u)))=f(x,y,z)  # label("Hint 13(19)").
 f(y,x,f(x,z,f(y,z,u)))=f(x,y,z)  # label("Hint 14(29)").
 f(y,x,f(z,x,f(u,y,z)))=f(x,y,z)  # label("Hint 15(39)").
 f(x,x,y)=x  # label("Hint 16(41)").
 f(x,y,z)=f(y,x,z)  # label("Hint 17(42)").
 f(x,y,z)=f(x,z,y)  # label("Hint 18(43)").
 f(x,y,z)=f(z,y,x)  # label("Hint 19(44)").
 f(f(x,w,y),w,z)=f(x,w,f(y,w,z))  # label("Hint 20(45)").
 f(D,E,f(f(A,B,C),f(A,C,E),f(B,D,E)))!=f(D,E,f(A,B,C))  # label("Hint 21(774)").
 f(x,y,z)=f(x,y,z)  # label("Hint 22(862)").
 f(x,y,f(z,x,u))=f(z,x,f(x,u,y))  # label("Hint 23(863)").
 f(x,y,f(y,z,u))=f(y,u,f(x,y,z))  # label("Hint 24(864)").
 x=x  # label("Hint 25(865)").
 f(x,y,f(x,z,f(u,x,v)))=f(u,x,f(x,y,f(x,v,z)))  # label("Hint 26(866)").
 f(x,y,f(z,x,f(x,u,v)))=f(x,f(z,x,u),f(x,v,y))  # label("Hint 27(867)").
 f(x,y,f(z,x,u))=f(x,u,f(z,x,y))  # label("Hint 28(868)").
 f(x,y,f(z,u,x))=f(z,x,f(u,x,y))  # label("Hint 29(869)").
 f(x,y,f(x,z,u))=f(x,z,f(x,u,y))  # label("Hint 30(870)").
 f(x,f(y,x,z),f(x,u,v))=f(y,x,f(x,v,f(x,z,u)))  # label("Hint 31(873)").
 f(x,y,f(x,z,f(x,y,u)))=f(x,u,f(x,y,z))  # label("Hint 32(882)").
 f(x,f(y,x,z),f(z,u,v))=f(y,x,f(z,v,f(x,z,u)))  # label("Hint 33(909)").
 f(x,f(x,y,z),f(x,z,u))=f(x,y,f(x,z,u))  # label("Hint 34(952)").
 f(x,y,f(z,y,u))=f(y,u,f(x,z,y))  # label("Hint 35(975)").
 f(x,f(y,z,u),f(z,x,v))=f(x,v,f(y,z,f(z,u,x)))  # label("Hint 36(980)").
 f(x,y,f(z,u,f(x,u,v)))=f(x,u,f(x,y,f(z,u,v)))  # label("Hint 37(989)").
 f(x,f(x,y,z),f(x,u,v))=f(x,y,f(x,u,f(x,v,z)))  # label("Hint 38(991)").
 f(x,f(x,y,z),f(y,u,v))=f(x,z,f(y,v,f(x,y,u)))  # label("Hint 39(992)").
 f(x,f(y,x,z),f(y,x,u))=f(y,x,f(x,z,u))  # label("Hint 40(998)").
 f(x,y,f(y,z,f(x,y,u)))=f(x,y,f(y,z,u))  # label("Hint 41(1005)").
 f(x,f(y,z,u),f(z,v,f(z,w,f(y,z,u))))=f(y,z,f(z,u,f(x,f(y,z,u),f(z,v,w))))  # label("Hint 42(1007)").
 f(x,f(x,y,z),f(x,y,u))=f(x,y,f(x,z,u))  # label("Hint 43(1025)").
 f(x,y,f(z,u,f(x,z,y)))=f(x,z,y)  # label("Hint 44(1035)").
 f(x,f(x,y,z),f(y,z,u))=f(z,f(x,y,z),f(x,y,u))  # label("Hint 45(1040)").
 f(x,y,f(z,u,f(y,z,v)))=f(y,f(x,y,z),f(z,u,v))  # label("Hint 46(1064)").
 f(x,f(y,z,u),f(y,z,f(z,u,v)))=f(v,f(x,z,f(y,z,u)),f(y,z,u))  # label("Hint 47(1066)").
 f(x,y,f(y,z,f(x,u,v)))=f(y,z,f(x,u,f(x,y,v)))  # label("Hint 48(1067)").
 f(x,y,f(z,u,f(y,z,f(u,v,w))))=f(y,f(x,y,z),f(u,w,f(z,u,v)))  # label("Hint 49(1090)").
 f(x,y,f(x,f(x,z,u),f(u,v,w)))=f(x,z,f(x,y,f(u,v,f(x,u,w))))  # label("Hint 50(1095)").
 f(x,f(y,z,u),f(y,z,f(z,u,v)))=f(v,f(y,z,u),f(z,u,f(x,y,z)))  # label("Hint 51(1115)").
 f(x,f(y,z,x),f(y,z,u))=f(y,z,x)  # label("Hint 52(1132)").
 f(x,f(y,x,z),f(y,z,u))=f(y,x,z)  # label("Hint 53(1139)").
 f(x,f(x,y,z),f(y,z,u))=f(x,y,z)  # label("Hint 54(1148)").
 f(x,f(y,z,f(x,z,u)),f(z,v,f(y,z,u)))=f(x,z,f(y,z,u))  # label("Hint 55(1166)").
 f(x,f(x,y,f(y,z,u)),f(y,z,u))=f(x,y,f(y,z,u))  # label("Hint 56(1174)").
 f(x,f(x,y,z),f(y,u,f(y,z,v)))=f(x,y,z)  # label("Hint 57(1176)").
 f(x,f(y,z,u),f(y,z,x))=f(y,z,x)  # label("Hint 58(1178)").
 f(f(x,y,f(z,u,f(u,y,v))),f(z,u,f(u,y,v)),f(u,w,f(z,u,v)))=f(x,f(z,u,f(u,y,v)),f(u,y,f(z,u,v)))  # label("Hint 59(1205)").
 f(x,f(x,y,z),f(y,u,f(z,v,f(y,z,w))))=f(x,y,z)  # label("Hint 60(1299)").
 f(x,f(x,y,f(z,y,u)),f(y,v,f(z,y,u)))=f(z,y,f(x,y,u))  # label("Hint 61(1319)").
 f(x,y,f(z,u,x))=f(u,x,f(z,x,y))  # label("Hint 62(1327)").
 f(f(x,y,f(z,y,u)),f(z,y,u),f(z,u,v))=f(z,y,u)  # label("Hint 63(1362)").
 f(x,f(y,x,f(z,y,u)),f(y,v,f(z,y,u)))=f(z,y,f(y,u,x))  # label("Hint 64(1364)").
 f(x,y,f(z,f(y,z,f(y,u,v)),f(y,w,f(y,u,v))))=f(y,f(x,y,u),f(y,v,z))  # label("Hint 65(1515)").
 f(f(x,y,f(z,u,f(y,u,v))),f(y,u,f(z,u,v)),f(u,w,f(z,u,v)))=f(y,u,f(z,u,v))  # label("Hint 66(1713)").
 f(f(x,y,f(z,u,f(y,u,v))),f(u,v,f(y,z,u)),f(u,w,f(z,u,v)))=f(y,u,f(z,u,v))  # label("Hint 67(1749)").
 f(f(x,y,f(z,x,u)),f(x,v,f(z,x,u)),f(y,w,f(x,y,f(z,x,u))))=f(z,x,f(x,u,y))  # label("Hint 68(1929)").
 f(x,f(y,x,f(y,z,u)),f(y,v,f(y,z,u)))=f(y,z,f(y,x,u))  # label("Hint 69(2038)").
 f(x,y,f(y,z,f(y,u,v)))=f(y,f(x,y,z),f(y,u,v))  # label("Hint 70(2227)").
 f(x,f(y,x,z),f(x,z,u))=f(y,x,f(x,z,u))  # label("Hint 71(2230)").
 f(x,f(y,z,u),f(v,f(y,z,u),f(y,z,x)))=f(v,f(y,z,u),f(y,z,x))  # label("Hint 72(2421)").
 f(f(x,y,z),f(x,u,f(y,z,v)),f(y,z,v))=f(u,f(x,y,z),f(y,z,v))  # label("Hint 73(2478)").
 f(f(x,y,z),f(x,y,f(x,u,z)),f(y,z,v))=f(x,y,z)  # label("Hint 74(2612)").
 f(x,y,f(f(z,x,u),f(z,x,f(z,u,v)),f(x,u,w)))=f(z,x,f(x,u,y))  # label("Hint 75(2650)").
 f(x,y,f(x,z,f(u,v,f(x,v,f(v,w,v6)))))=f(x,v,f(x,y,f(x,z,f(v,v6,f(u,v,w)))))  # label("Hint 76(2656)").
 f(x,f(x,y,f(x,z,u)),f(x,z,u))=f(x,y,f(x,z,u))  # label("Hint 77(2670)").
 f(x,y,f(x,z,f(x,u,y)))=f(x,z,f(x,u,y))  # label("Hint 78(2705)").
 f(x,f(x,y,f(z,u,f(x,z,v))),f(x,z,f(z,v,u)))=f(x,y,f(x,z,f(z,v,u)))  # label("Hint 79(2847)").
 f(f(x,y,z),f(x,y,u),f(v,f(x,y,z),f(u,w,f(x,y,u))))=f(v,f(x,y,z),f(x,y,u))  # label("Hint 80(3276)").
 f(x,f(y,z,u),f(z,u,f(y,z,v)))=f(z,f(y,z,u),f(x,v,f(y,z,u)))  # label("Hint 81(3278)").
 f(f(x,y,z),f(x,y,u),f(v,u,f(x,y,z)))=f(v,f(x,y,z),f(x,y,u))  # label("Hint 82(3280)").
 f(f(x,y,z),f(x,y,u),f(u,v,f(x,y,z)))=f(v,f(x,y,z),f(x,y,u))  # label("Hint 83(3301)").
 f(x,y,f(y,z,f(u,x,y)))=f(u,y,f(x,y,z))  # label("Hint 84(3324)").
 f(x,y,f(f(x,z,u),f(x,z,f(z,u,v)),f(x,u,w)))=f(x,z,f(x,y,u))  # label("Hint 85(3532)").
 f(f(x,y,z),f(x,y,f(y,z,u)),f(x,z,v))=f(x,y,z)  # label("Hint 86(3560)").
 f(f(x,y,f(x,z,u)),f(x,u,f(x,v,f(x,y,z))),f(u,w,f(x,y,z)))=f(x,u,f(x,y,z))  # label("Hint 87(3572)").
 f(f(x,y,z),f(x,y,u),f(x,u,f(y,u,v)))=f(x,y,u)  # label("Hint 88(3620)").
 f(f(x,y,z),f(x,z,f(x,y,u)),f(y,z,v))=f(x,y,z)  # label("Hint 89(3634)").
 f(f(x,f(y,z,u),f(y,u,f(y,z,v))),f(y,z,u),f(z,u,w))=f(y,z,u)  # label("Hint 90(4917)").
 f(x,y,f(f(y,z,f(x,y,u)),f(y,v,f(x,y,u)),f(w,z,f(y,z,f(x,y,u)))))=f(y,u,f(x,y,z))  # label("Hint 91(5202)").
 f(x,y,f(y,f(x,y,z),f(x,u,v)))=f(y,z,f(x,v,f(x,y,u)))  # label("Hint 92(5226)").
 f(x,y,f(z,f(z,x,u),f(z,v,w)))=f(x,y,f(z,v,f(z,x,f(z,u,w))))  # label("Hint 93(5229)").
 f(x,y,f(z,x,f(x,u,y)))=f(z,x,f(x,u,y))  # label("Hint 94(5348)").
 f(x,y,f(z,f(x,z,u),f(y,z,v)))=f(x,y,z)  # label("Hint 95(5568)").
 f(x,f(y,z,f(x,z,u)),f(z,v,f(z,u,f(x,y,z))))=f(x,z,f(z,u,f(x,y,z)))  # label("Hint 96(5721)").
 f(x,f(y,x,z),f(z,u,f(x,v,z)))=f(y,x,f(v,z,f(x,z,u)))  # label("Hint 97(5723)").
 f(x,f(y,z,f(x,z,u)),f(z,u,f(x,y,z)))=f(x,z,f(z,u,f(x,y,z)))  # label("Hint 98(5844)").
 f(x,f(x,y,z),f(z,u,f(x,z,v)))=f(x,y,f(z,u,f(x,z,v)))  # label("Hint 99(5871)").
 f(x,f(x,y,f(z,u,f(x,z,v))),f(x,z,f(z,u,v)))=f(x,y,f(x,z,f(z,u,v)))  # label("Hint 100(6001)").
 f(x,f(x,y,f(z,u,f(x,v,z))),f(x,w,z))=f(x,y,f(x,w,f(v,z,f(x,z,u))))  # label("Hint 101(6536)").
 f(x,f(x,y,z),f(u,v,f(x,u,f(u,w,v6))))=f(x,y,f(x,u,f(x,z,f(u,w,f(u,v,v6)))))  # label("Hint 102(6561)").
 f(x,f(x,y,f(z,u,f(x,z,v))),f(x,z,w))=f(x,y,f(x,w,f(z,u,f(x,z,v))))  # label("Hint 103(6591)").
 f(x,f(x,y,z),f(u,v,f(x,u,f(z,u,w))))=f(x,y,f(x,u,f(z,f(x,z,u),f(u,v,w))))  # label("Hint 104(6809)").
 f(x,y,f(x,f(z,u,v),f(z,u,f(x,z,v))))=f(x,y,f(x,z,f(z,u,v)))  # label("Hint 105(6974)").
 f(x,f(y,z,u),f(y,z,f(x,y,u)))=f(x,y,f(y,z,u))  # label("Hint 106(7007)").
 f(x,y,f(z,f(x,z,u),f(z,v,w)))=f(x,z,f(x,y,f(z,v,f(z,w,u))))  # label("Hint 107(7160)").
 f(x,y,f(z,f(x,z,y),f(y,u,v)))=f(x,z,y)  # label("Hint 108(7501)").
 f(x,f(x,y,z),f(u,v,f(x,u,f(z,u,w))))=f(x,y,f(x,z,u))  # label("Hint 109(7771)").
 f(x,y,f(z,u,f(x,z,f(y,z,v))))=f(x,y,z)  # label("Hint 110(7840)").
 f(f(x,y,f(z,u,f(y,u,v))),f(z,u,f(y,u,v)),f(u,w,f(z,u,v)))=f(x,f(y,u,f(z,u,v)),f(z,u,f(y,u,v)))  # label("Hint 111(8284)").
 f(x,f(y,z,f(u,z,v)),f(u,z,f(y,z,v)))=f(y,z,f(u,z,v))  # label("Hint 112(8392)").
 f(x,f(y,z,f(u,z,v)),f(z,v,f(u,y,z)))=f(u,z,f(y,z,v))  # label("Hint 113(8402)").
 f(x,y,f(y,z,f(x,u,y)))=f(x,y,f(u,y,z))  # label("Hint 114(8432)").
 f(x,f(x,y,z),f(u,y,f(x,y,v)))=f(x,z,f(u,y,f(x,y,v)))  # label("Hint 115(8623)").
 f(x,f(y,z,u),f(y,v,f(y,z,u)))=f(v,f(y,z,u),f(y,x,f(y,z,u)))  # label("Hint 116(8647)").
 f(x,f(y,z,f(z,x,u)),f(z,x,u))=f(z,x,u)  # label("Hint 117(8889)").
 f(x,y,f(z,u,f(y,z,f(x,z,v))))=f(x,y,z)  # label("Hint 118(9165)").
 f(x,y,f(z,u,f(x,u,f(y,u,v))))=f(x,y,u)  # label("Hint 119(9179)").
 f(x,y,f(z,f(x,u,v),f(y,f(x,u,v),f(x,w,f(x,u,v)))))=f(x,v,f(x,u,y))  # label("Hint 120(9861)").
 f(x,y,f(z,u,f(z,y,f(x,z,v))))=f(x,z,y)  # label("Hint 121(10171)").
 f(x,y,f(z,u,f(x,y,u)))=f(x,y,u)  # label("Hint 122(11215)").
 f(x,y,f(z,u,f(u,x,f(u,y,v))))=f(u,x,y)  # label("Hint 123(11245)").
 f(x,f(x,y,f(z,u,f(x,z,v))),f(w,v6,f(x,y,z)))=f(x,f(z,u,v),f(v6,f(x,y,z),f(x,w,f(x,y,z))))  # label("Hint 124(11962)").
 f(x,f(x,y,f(z,u,v)),f(z,u,v))=f(x,y,f(z,u,v))  # label("Hint 125(11969)").
 f(x,f(x,y,z),f(u,f(x,f(y,v,w),f(v6,f(x,y,z),f(y,v,w))),f(y,v,w)))=f(x,z,f(y,w,f(x,y,v)))  # label("Hint 126(11980)").
 f(x,y,f(x,z,f(z,u,f(z,y,v))))=f(x,z,y)  # label("Hint 127(11984)").
 f(x,f(x,y,z),f(y,u,f(x,v,f(x,y,w))))=f(x,z,f(y,u,f(x,v,f(x,y,w))))  # label("Hint 128(12003)").
 f(x,y,f(z,f(x,u,y),f(x,v,f(x,u,y))))=f(x,f(x,u,y),f(v,z,f(x,u,y)))  # label("Hint 129(12127)").
 f(x,f(x,y,f(y,z,f(y,u,f(v,y,w)))),f(v,y,w))=f(y,w,f(x,v,y))  # label("Hint 130(12346)").
 f(x,f(y,x,z),f(y,u,f(y,z,v)))=f(y,x,z)  # label("Hint 131(12497)").
 f(x,f(y,z,u),f(v,w,f(y,u,f(y,z,v))))=f(f(y,z,u),f(y,v,w),f(x,v,f(y,z,u)))  # label("Hint 132(13248)").
 f(f(x,y,z),f(x,y,u),f(y,z,f(v,x,y)))=f(v,f(x,y,z),f(y,u,f(x,y,z)))  # label("Hint 133(13466)").
 f(x,f(y,z,f(u,v,f(y,u,w))),f(v6,f(x,y,u),f(y,z,f(u,v,f(y,u,w)))))=f(v6,f(x,y,u),f(y,z,f(u,v,f(y,u,w))))  # label("Hint 134(15209)").
 f(D,E,f(f(A,B,C),f(A,f(x,C,f(y,E,f(z,C,E))),f(A,C,E)),f(B,D,E)))!=f(D,E,f(A,B,C))  # label("Hint 135(15258)").
 f(x,f(y,z,u),f(v,f(x,y,u),f(y,z,u)))=f(v,f(x,y,u),f(y,z,u))  # label("Hint 136(15342)").
 f(x,f(y,z,u),f(y,z,f(y,u,x)))=f(y,x,f(y,z,u))  # label("Hint 137(15872)").
 f(x,f(y,z,u),f(f(x,v,f(y,z,u)),f(y,z,u),f(y,z,f(x,y,u))))=f(v,f(x,y,f(y,z,u)),f(y,z,u))  # label("Hint 138(16522)").
 f(x,f(y,z,u),f(z,x,u))=f(z,x,u)  # label("Hint 139(16799)").
 f(x,f(y,z,u),f(z,u,x))=f(z,u,x)  # label("Hint 140(17037)").
 f(x,f(y,z,u),f(v,f(y,z,u),f(z,u,f(x,v,f(y,z,u)))))=f(z,u,f(x,v,f(y,z,u)))  # label("Hint 141(17055)").
 f(x,f(y,z,u),f(y,z,f(z,x,u)))=f(y,z,f(z,x,u))  # label("Hint 142(17742)").
 f(x,f(x,y,f(z,u,v)),f(y,u,v))=f(x,y,f(z,u,v))  # label("Hint 143(18121)").
 f(x,f(y,z,u),f(v,f(y,z,u),f(y,u,f(x,v,f(y,z,u)))))=f(y,u,f(x,v,f(y,z,u)))  # label("Hint 144(18129)").
 f(f(x,y,z),f(x,y,f(z,f(y,z,u),f(y,v,u))),f(x,z,w))=f(x,y,z)  # label("Hint 145(18153)").
 f(x,y,f(z,f(y,z,u),f(y,v,u)))=f(y,u,f(x,y,z))  # label("Hint 146(18155)").
 f(x,y,f(z,u,f(x,u,y)))=f(x,u,y)  # label("Hint 147(18678)").
 f(f(x,y,z),f(x,y,f(z,f(y,z,f(u,v,w)),f(v,w,f(y,u,v)))),f(x,z,v6))=f(x,y,z)  # label("Hint 148(18782)").
 f(x,y,f(z,f(y,z,f(u,v,w)),f(v,w,f(y,u,v))))=f(y,f(x,y,z),f(u,v,w))  # label("Hint 149(18786)").
 f(f(x,y,z),f(x,z,u),f(y,f(x,y,z),f(v,w,v6)))=f(x,y,z)  # label("Hint 150(18832)").
 f(f(x,y,f(y,z,f(y,u,v))),f(y,z,u),f(z,u,w))=f(y,z,u)  # label("Hint 151(19393)").
 f(f(x,y,z),f(x,u,v),f(x,v,f(x,y,z)))=f(x,v,f(x,y,z))  # label("Hint 152(19397)").
 f(f(x,y,f(x,z,u)),f(x,z,f(x,v,f(x,y,u))),f(x,w,v))=f(x,v,f(x,y,f(x,z,u)))  # label("Hint 153(19431)").
 f(f(x,y,f(z,x,u)),f(x,f(z,x,u),f(v,w,f(z,x,u))),f(v,w,f(z,x,u)))=f(z,x,f(x,u,f(v,w,f(z,x,u))))  # label("Hint 154(19517)").
 f(f(x,y,z),f(x,z,f(x,y,u)),f(x,u,v))=f(x,u,f(x,y,z))  # label("Hint 155(19869)").
 f(x,f(y,z,f(y,u,f(x,y,v))),f(u,w,f(x,y,u)))=f(x,y,u)  # label("Hint 156(20404)").
 f(x,y,f(z,u,f(u,x,y)))=f(u,x,y)  # label("Hint 157(20432)").
 f(f(x,y,z),f(y,u,f(y,v,f(x,y,f(y,z,w)))),f(v,v6,f(y,v,f(x,y,z))))=f(y,v,f(x,y,z))  # label("Hint 158(20502)").
 f(x,f(y,z,f(z,u,f(x,z,v))),f(u,w,f(x,z,u)))=f(x,u,f(y,z,f(z,u,f(x,z,v))))  # label("Hint 159(21482)").
 f(x,y,f(z,u,f(u,y,f(x,u,v))))=f(x,u,y)  # label("Hint 160(21508)").
 f(x,y,f(z,u,y))=f(z,y,f(x,u,y))  # label("Hint 161(21514)").
 f(x,f(y,z,u),f(z,v,f(z,x,f(z,w,f(y,z,u)))))=f(z,x,f(y,z,u))  # label("Hint 162(21517)").
 f(x,f(x,y,z),f(u,v,f(x,y,z)))=f(u,f(x,y,z),f(x,y,f(x,z,v)))  # label("Hint 163(23572)").
 f(f(x,y,z),f(y,u,f(x,y,z)),f(f(x,y,z),f(x,z,v),f(w,v6,v7)))=f(x,y,z)  # label("Hint 164(24235)").
 f(f(x,y,z),f(x,y,u),f(u,f(x,y,u),f(v,w,v6)))=f(x,y,u)  # label("Hint 165(24313)").
 f(x,f(x,y,z),f(f(x,y,z),f(y,z,u),f(v,w,v6)))=f(x,y,z)  # label("Hint 166(24325)").
 f(x,f(y,x,z),f(f(y,x,z),f(y,z,u),f(v,w,v6)))=f(y,x,z)  # label("Hint 167(24453)").
 f(x,f(x,y,f(y,z,u)),f(f(x,y,f(y,z,u)),f(y,v,f(y,z,u)),f(w,v6,v7)))=f(y,u,f(x,y,z))  # label("Hint 168(25061)").
 f(x,f(y,f(x,y,z),f(x,u,z)),f(f(x,y,z),f(y,z,v),f(w,v6,v7)))=f(x,y,z)  # label("Hint 169(25644)").
 f(f(x,y,f(z,y,u)),f(z,y,u),f(f(z,y,u),f(z,u,v),f(w,v6,v7)))=f(z,y,u)  # label("Hint 170(25796)").
 f(f(x,y,f(x,z,u)),f(x,f(x,z,u),f(v,w,f(x,z,u))),f(v,w,f(x,z,u)))=f(x,z,f(x,u,f(v,w,f(x,z,u))))  # label("Hint 171(26362)").
 f(f(x,y,f(x,z,u)),f(x,z,u),f(z,v,f(x,z,u)))=f(x,z,u)  # label("Hint 172(26364)").
 f(x,f(y,z,x),f(f(y,z,x),f(y,z,u),f(v,w,v6)))=f(y,z,x)  # label("Hint 173(26393)").
 f(f(x,y,f(y,z,f(y,u,v))),f(y,z,v),f(z,v,w))=f(y,z,v)  # label("Hint 174(26918)").
 f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,v))=f(z,u,f(x,y,z))  # label("Hint 175(26962)").
 f(f(x,y,f(y,z,f(y,u,v))),f(y,v,z),f(v,z,w))=f(y,v,z)  # label("Hint 176(27036)").
 f(f(x,y,z),f(y,u,v),f(y,u,f(x,y,v)))=f(y,v,f(x,y,u))  # label("Hint 177(27085)").
 f(x,y,f(z,u,f(x,u,f(u,v,y))))=f(x,u,y)  # label("Hint 178(27103)").
 f(f(x,y,z),f(x,u,v),f(x,u,f(x,z,v)))=f(x,v,f(x,z,u))  # label("Hint 179(27113)").
 f(x,f(y,z,u),f(y,u,x))=f(y,u,x)  # label("Hint 180(27178)").
 f(x,y,f(z,u,f(u,x,f(u,v,y))))=f(u,x,y)  # label("Hint 181(27197)").
 f(x,f(y,z,x),f(f(y,z,u),f(y,z,x),f(v,w,v6)))=f(y,z,x)  # label("Hint 182(27258)").
 f(x,f(y,z,u),f(x,u,f(v,y,z)))=f(x,u,f(v,y,z))  # label("Hint 183(27303)").
 f(x,f(y,z,u),f(u,x,f(v,y,z)))=f(u,x,f(v,y,z))  # label("Hint 184(27312)").
 f(x,f(y,z,u),f(u,x,f(y,z,v)))=f(u,x,f(y,z,v))  # label("Hint 185(27403)").
 f(f(x,y,z),f(y,u,f(x,z,v)),f(y,u,f(u,w,f(x,z,v))))=f(y,u,f(x,z,v))  # label("Hint 186(27531)").
 f(x,f(y,z,u),f(z,x,f(y,u,v)))=f(z,x,f(y,u,v))  # label("Hint 187(27539)").
 f(x,f(y,z,f(x,y,u)),f(u,z,v))=f(x,y,f(u,z,v))  # label("Hint 188(27551)").
 f(f(x,y,z),f(x,z,u),f(v,y,f(y,z,f(x,y,w))))=f(x,y,z)  # label("Hint 189(27602)").
 f(x,f(y,z,u),f(y,x,u))=f(y,x,u)  # label("Hint 190(28269)").
 f(x,f(y,z,u),f(y,v,f(x,z,v)))=f(x,v,f(y,z,u))  # label("Hint 191(28987)").
 f(f(x,y,f(y,z,f(u,y,v))),f(u,y,z),f(u,z,w))=f(u,y,z)  # label("Hint 192(29121)").
 f(f(x,y,f(z,y,f(u,y,v))),f(z,u,y),f(z,u,w))=f(z,u,y)  # label("Hint 193(29540)").
 f(x,y,f(x,z,f(u,v,f(x,y,z))))=f(x,f(x,y,z),f(u,v,z))  # label("Hint 194(30300)").
 f(x,f(x,y,z),f(u,v,f(x,y,z)))=f(x,f(x,y,z),f(z,u,v))  # label("Hint 195(30302)").
 f(x,f(y,z,u),f(y,z,f(y,u,v)))=f(y,f(y,z,u),f(u,x,v))  # label("Hint 196(30314)").
 f(f(x,y,z),f(x,z,u),f(y,f(v,x,y),f(y,z,w)))=f(x,y,z)  # label("Hint 197(31169)").
 f(f(x,y,z),f(x,y,u),f(x,y,v))=f(u,f(x,y,z),f(x,y,v))  # label("Hint 198(32143)").
 f(x,f(y,z,u),f(y,z,v))=f(v,f(y,z,u),f(y,z,x))  # label("Hint 199(32160)").
 f(f(x,y,z),f(x,y,u),f(x,u,v))=f(x,f(x,y,u),f(z,u,v))  # label("Hint 200(32309)").
 f(f(x,y,z),f(u,v,y),f(u,y,z))=f(y,f(x,u,v),f(u,y,z))  # label("Hint 201(32605)").
 f(f(x,y,z),f(x,y,u),f(u,f(x,v,u),f(y,u,w)))=f(x,y,u)  # label("Hint 202(35265)").
 f(x,y,f(z,f(u,x,y),f(x,z,v)))=f(x,f(u,z,v),f(x,y,z))  # label("Hint 203(35312)").
 f(D,E,f(A,B,C))!=f(D,E,f(A,B,C))  # label("Hint 204(35470)").



 f(v,w,f(f(x,y,z),f(x,z,w),f(y,v,w))) = f(v,w,f(x,y,z))  # label("Hint 21(774)").
 f(v,w,f(f(x,y,z),f(x,f(x,z,f(y,w,f(z,z,w))),f(x,z,w)),f(y,v,w))) = f(v,w,f(x,y,z))  # label("Hint 135(15258)").
 f(v,w,f(x,y,z)) = f(v,w,f(x,y,z))  # label("Hint 204(35470)").

end_of_list.

% Length of proof is 212.  Level of proof is 37.
% 
% ---------------- PROOF ----------------
% 
% 1 [] f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
% 2 [] f(x,y,z)=f(y,x,z).
% 5 [] f(x,x,y)=x.
% 6 [] f(x,y,x)=x.
% 7 [] f(y,x,x)=x.
% 8 [] f(x,y,z)=f(y,x,z).
% 9 [] f(x,y,z)=f(x,z,y).
% 10 [] f(x,y,z)=f(z,y,x).
% 41 [] f(x,x,y)=x.
% 42 [] f(x,y,z)=f(y,x,z).
% 43 [] f(x,y,z)=f(x,z,y).
% 44 [] f(x,y,z)=f(z,y,x).
% 45 [] f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
% 48 [] f(f(A,D,E),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C))   # label("original").
% 849 [para_into,2.1.1,2.1.2] f(x,y,z)=f(x,y,z)   # label("Hint 204(35470)").
% 850 (heat=1) [para_into,849.1.1,1.1.2,demod,10,8,8] f(x,y,f(z,x,u))=f(z,x,f(x,u,y))   # label("Hint 24(864)").
% 852 [para_into,45.1.1.1,45.1.2,demod,10,8,10,8,8,10,8] f(x,y,f(x,z,f(u,x,w)))=f(u,x,f(x,y,f(x,w,z))).
% 853 [para_into,45.1.1.1,45.1.1,demod,8,10,8,8,8,flip.1] f(x,f(y,x,z),f(x,u,w))=f(x,w,f(y,x,f(x,z,u)))   # label("Hint 27(867)").
% 854 [para_into,45.1.1.1,44.1.2,demod,10,8,8] f(x,y,f(z,x,u))=f(x,u,f(z,x,y))   # label("Hint 28(868)").
% 855 [para_into,45.1.1.1,43.1.2,demod,10,8] f(x,y,f(z,u,x))=f(z,x,f(u,x,y))   # label("Hint 35(975)").
% 856 [para_into,45.1.1.1,42.1.2,demod,10,8,8,8] f(x,y,f(x,z,u))=f(x,z,f(x,u,y)).
% 858 [para_into,45.1.1,44.1.2,demod,8,10,8,flip.1] f(x,y,f(z,x,u))=f(z,x,f(x,y,u)).
% 859 [para_into,45.1.2.3,45.1.2,demod,8,8,8,10,8] f(x,f(y,x,z),f(x,u,w))=f(y,x,f(x,w,f(x,z,u))).
% 871 (heat=1) [para_from,852.1.1,1.1.2.3,demod,8,8,9,8,8] f(x,f(y,x,z),f(z,u,f(z,w,w5)))=f(y,x,f(z,w,f(x,z,f(z,u,w5)))).
% 878 (heat=1) [para_into,853.1.1.3,1.1.2,demod,8,10,8,8,8,9,flip.1] f(x,f(x,y,f(x,z,u)),f(u,w,w5))=f(x,f(x,y,z),f(u,w5,f(x,u,w))).
% 887 (heat=1) [para_from,853.1.2,1.1.2.3,demod,8,8,8,10,9,9] f(x,f(y,x,z),f(z,u,f(z,w,w5)))=f(y,x,f(z,f(x,z,w5),f(z,u,w))).
% 891 (heat=1) [para_into,854.1.1,1.1.1,demod,9,8,10,9,8,flip.1] f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(w,x,f(y,z,u)))).
% 894 (heat=1) [para_into,854.1.2,1.1.1,demod,10,9,8,10,9,8] f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(x,w,f(y,z,u)))).
% 896 (heat=1) [para_from,854.1.1,1.1.1.1,demod,8,10,8,10,8,10,8] f(x,y,f(z,u,f(z,w,x)))=f(z,x,f(x,y,f(z,u,w))).
% 897 (heat=1) [para_into,855.1.1.3,1.1.2,demod,10,10,8,8,9,flip.1] f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(w,f(y,z,u),f(z,u,f(y,z,x))).
% 900,899 (heat=1) [para_into,855.1.1,1.1.2,demod,10,6,10,8] f(x,y,f(x,y,z))=f(x,y,z)   # label("Hint 9(11)").
% 903 (heat=1) [para_from,855.1.1,1.1.2.3,demod,10,9,8,10,8] f(x,f(y,x,z),f(z,u,w))=f(y,x,f(z,u,f(x,z,w)))   # label("Hint 46(1064)").
% 960 [para_into,899.1.2,45.1.1,demod,10,8,8,8] f(x,f(y,x,z),f(x,u,f(y,x,z)))=f(y,x,f(x,z,u)).
% 1008 (heat=1) [para_into,960.1.2,1.1.1,demod,8,10,8,8,10,8,8,8] f(x,f(x,y,f(x,z,u)),f(x,w,f(x,y,f(x,z,u))))=f(x,z,f(x,u,f(x,y,w))).
% 1017,1016 [para_from,899.1.2,44.1.2,demod,10,8,flip.1] f(x,y,f(z,x,y))=f(z,x,y).
% 1019,1018 [para_from,899.1.2,43.1.2,demod,9,flip.1] f(x,y,f(x,z,y))=f(x,z,y).
% 1046 (heat=1) [para_from,1016.1.1,1.1.1.1,demod,10,8,10,8,flip.1] f(x,y,f(y,z,f(u,x,y)))=f(y,z,f(u,x,y)).
% 1049 [back_demod,1008,demod,1019] f(x,y,f(x,z,f(x,u,w)))=f(x,u,f(x,w,f(x,z,y))).
% 1074 (heat=1) [para_into,1049.1.1.3.3,1.1.1,demod,8,8,8,10,8,8] f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,f(z,u,w5))))=f(z,f(y,z,u),f(w5,f(y,z,u),f(x,w,f(y,z,u)))).
% 1075 (heat=1) [para_into,1049.1.1.3,1.1.2,demod,6,9,flip.1] f(x,y,f(x,z,f(x,u,y)))=f(x,u,f(x,y,z)).
% 1089 [para_into,850.1.1.3,850.1.1,demod,10,9,9,8,flip.1] f(x,y,f(x,z,f(u,y,w)))=f(x,z,f(u,y,f(x,y,w)))   # label("Hint 37(989)").
% 1091 [para_into,850.1.2.3,850.1.2,demod,10,8,9,8] f(x,f(x,y,z),f(y,u,w))=f(x,z,f(y,w,f(x,y,u)))   # label("Hint 39(992)").
% 1106 (heat=1) [para_into,1089.1.2,1.1.2,demod,8,900,8,flip.1] f(x,f(y,x,z),f(y,x,u))=f(y,x,f(x,z,u))   # label("Hint 40(998)").
% 1127,1126 (heat=1) [para_into,1091.1.1,1.1.2,demod,9,900,5,900,flip.1] f(x,y,f(z,u,f(x,z,y)))=f(x,z,y)   # label("Hint 44(1035)").
% 1136 (heat=1) [para_from,1091.1.2,1.1.2,demod,8,9,10,9] f(x,f(y,x,z),f(y,z,u))=f(y,f(y,x,z),f(x,z,u)).
% 1181 [para_from,854.1.1,850.1.1.3,demod,10,10,8,9,8,flip.1] f(x,y,f(x,z,f(y,u,w)))=f(x,z,f(y,u,f(x,y,w))).
% 1186 (heat=1) [para_into,1181.1.2,1.1.2,demod,9,8,flip.1] f(x,f(y,z,x),f(y,z,u))=f(y,z,f(y,x,f(z,x,u))).
% 1482 [para_into,855.1.2,852.1.1,demod,5,9,10,9,8,900,flip.1] f(x,y,f(z,y,u))=f(z,y,f(x,y,u)).
% 1594,1593 [para_into,1126.1.1.3.3,899.1.2,demod,9,1019,9] f(x,y,f(z,u,f(x,y,z)))=f(x,y,z)   # label(bd).
% 1603,1602 [para_into,1126.1.1.3,854.1.2,demod,8,9] f(x,y,f(y,z,f(x,z,u)))=f(x,y,z).
% 1605 [para_into,1126.1.1.3,850.1.1,demod,8,9] f(x,y,f(x,z,f(y,z,u)))=f(x,y,z)   # label("Hint 12(17)").
% 1609,1608 [para_into,1126.1.1.3,42.1.2,demod,9,9] f(x,y,f(z,u,f(x,y,u)))=f(x,y,u)   # label("Hint 122(11215)").
% 1611 [para_into,1126.1.1,44.1.2,demod,8,10,8] f(x,y,f(z,u,f(z,x,y)))=f(z,x,y).
% 1747 [back_demod,1186,demod,10,9,8,8,flip.1] f(x,y,f(z,x,f(z,y,u)))=f(z,f(z,x,y),f(x,y,u)).
% 1796 (heat=1) [para_into,1747.1.1.3.3,1.1.2,demod,8,10,8,8,10,8,8,flip.1] f(x,f(y,z,x),f(y,z,f(z,u,w)))=f(y,z,f(y,x,f(z,w,f(z,x,u)))).
% 2171 [para_into,853.1.2.3.3,1482.1.2,demod,8,8,9,8,8] f(x,f(x,y,z),f(x,u,f(z,w,w5)))=f(x,u,f(x,y,f(z,w,f(x,z,w5)))).
% 2424 (heat=1) [para_into,2171.1.2.3,1.1.2,demod,8,8] f(x,f(x,y,z),f(x,u,f(y,z,w)))=f(x,u,f(y,f(x,y,z),f(x,z,w))).
% 2914 [para_into,1605.1.1,853.1.1,demod,8,10,8,8,9,8,9] f(x,f(x,y,f(x,z,u)),f(u,w,f(x,y,z)))=f(x,u,f(x,y,z)).
% 2924 [back_demod,1796,demod,10,9,8,8,flip.1] f(x,y,f(z,x,f(y,u,f(z,y,w))))=f(z,f(z,x,y),f(x,y,f(y,w,u))).
% 3044,3043 (heat=1) [para_into,2914.1.1.2,1.1.2,demod,6,7,10,9,7,9] f(x,f(x,y,z),f(y,z,u))=f(x,y,z)   # label("Hint 54(1148)").
% 3159 (heat=1) [para_into,2924.1.1.3,1.1.2,demod,10,8,8,8,3044,900,10,8,10,9,900,flip.1] f(x,f(y,z,x),f(y,z,u))=f(y,z,x)   # label("Hint 52(1132)").
% 3177,3176 [back_demod,1136,demod,8,3044,8,flip.1] f(x,f(y,x,z),f(y,z,u))=f(y,x,z)   # label("Hint 53(1139)").
% 3255 [back_demod,2424,demod,3177] f(x,f(x,y,z),f(x,u,f(y,z,w)))=f(x,u,f(x,y,z)).
% 3266 (heat=1) [para_from,3176.1.1,1.1.2.3,demod,9,7] f(f(x,y,f(z,y,u)),f(z,y,u),f(z,u,w))=f(z,y,u)   # label("Hint 63(1362)").
% 3863,3862 [para_into,3266.1.1.1.3,1605.1.2,demod,8,1603,8,8] f(f(x,y,f(y,z,u)),f(y,z,u),f(z,u,w))=f(y,z,u).
% 3884,3883 [para_into,3266.1.1.1,1482.1.2,demod,8,8] f(f(x,y,z),f(x,y,f(y,u,z)),f(x,z,w))=f(x,y,z).
% 3885 [para_into,3266.1.1.1,855.1.2,demod,10,9,10,8,8,8,10,8] f(f(x,y,z),f(x,y,f(x,u,z)),f(y,z,w))=f(x,y,z)   # label("Hint 74(2612)").
% 3889 [para_into,3266.1.1.1,45.1.2,demod,10,8,8,8,8] f(f(x,y,z),f(x,z,f(u,x,y)),f(y,z,w))=f(x,y,z).
% 3893 [para_into,3266.1.1.1,44.1.2,demod,10,8,10,8] f(f(x,y,z),f(x,z,u),f(y,w,f(x,y,z)))=f(x,y,z).
% 3895 [para_into,3266.1.1.1,42.1.2,demod,8,8,8] f(f(x,y,f(x,z,u)),f(x,z,u),f(z,u,w))=f(x,z,u).
% 3922 [para_into,3266.1.1,44.1.2,demod,9,9,8,9] f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,u)))=f(x,y,u).
% 4374 (heat=1) [para_into,3922.1.1.1,1.1.2,demod,10,8,8] f(f(x,y,z),f(y,u,f(x,y,w)),f(z,w5,f(x,y,z)))=f(x,y,z).
% 5165 [para_into,3885.1.1,44.1.2,demod,10,9,8,10,8,9,10,8] f(f(x,y,z),f(x,y,u),f(x,u,f(y,u,w)))=f(x,y,u)   # label("Hint 88(3620)").
% 5591,5590 (heat=1) [para_into,5165.1.1.3.3,1.1.2,demod,10,8] f(f(x,y,z),f(x,y,u),f(x,u,f(u,w,f(y,u,w5))))=f(x,y,u).
% 5922,5921 [para_into,3889.1.1.1,44.1.2,demod,10,8,8,9,10] f(f(x,y,z),f(x,y,u),f(x,z,f(y,z,w)))=f(x,y,z).
% 5960,5959 [para_into,3889.1.1,44.1.2,demod,10,8,10,8,9,10,8] f(f(x,y,z),f(x,y,u),f(y,u,f(x,u,w)))=f(x,y,u).
% 6510 [para_into,3893.1.1.2,856.1.2] f(f(x,y,z),f(x,u,f(x,z,w)),f(y,w5,f(x,y,z)))=f(x,y,z).
% 6543,6542 [para_into,3893.1.1,855.1.2,demod,9,9,10,8,1017,9] f(x,f(y,z,u),f(y,z,x))=f(y,z,x)   # label("Hint 58(1178)").
% 6665 (heat=1) [para_into,6510.1.1.3,1.1.2,demod,5,5,10,9] f(x,f(y,x,z),f(y,u,f(y,z,w)))=f(y,x,z)   # label("Hint 131(12497)").
% 6847 (heat=1) [para_into,6542.1.1,1.1.1,demod,9,9] f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,f(x,w,f(y,z,u)))))=f(y,z,f(x,w,f(y,z,u))).
% 6852 (heat=1) [para_from,6542.1.2,1.1.1.1,demod,10,9,9,3044,10,8] f(x,y,f(z,u,x))=f(u,x,f(z,x,y)).
% 7034,7033 [para_into,3895.1.1.1.3,899.1.1,demod,900,9,900] f(f(x,y,f(x,z,u)),f(x,z,u),f(z,w,f(x,z,u)))=f(x,z,u)   # label("Hint 172(26364)").
% 7438 [para_into,3922.1.1.1,1126.1.2,demod,9,1594] f(f(x,y,z),f(x,z,u),f(u,w,f(x,z,u)))=f(x,z,u).
% 7452,7451 [para_into,3922.1.1.1,44.1.2,demod,8,8,8] f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u)))=f(y,z,u).
% 7875 [para_from,3922.1.1,852.1.1.3,demod,8,7,8,flip.1] f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,x)))=f(w,f(y,z,u),f(y,z,x))   # label("Hint 72(2421)").
% 7943 (heat=1) [para_into,7875.1.1,1.1.2,demod,9,10,9,10,9,10,9,9] f(f(x,y,z),f(x,u,f(y,z,w)),f(y,z,w))=f(u,f(x,y,z),f(y,z,w))   # label("Hint 73(2478)").
% 11202 [para_into,5165.1.1.1,1126.1.2,demod,9,1594] f(f(x,y,z),f(x,z,u),f(x,u,f(z,u,w)))=f(x,z,u).
% 11221 [para_into,5165.1.1.1,44.1.2,demod,8,8] f(f(x,y,z),f(y,z,u),f(z,u,f(y,u,w)))=f(y,z,u).
% 11436,11435 (heat=1) [para_into,11221.1.1.3.3,1.1.2,demod,10,8] f(f(x,y,z),f(y,z,u),f(z,u,f(u,w,f(y,u,w5))))=f(y,z,u).
% 12000,11999 [para_into,5959.1.1.1,44.1.2,demod,8,8] f(f(x,y,z),f(y,z,u),f(y,u,f(z,u,w)))=f(y,z,u).
% 12424,12423 [para_into,7438.1.1,858.1.1,demod,10,9,10,9,7,9,10,9] f(x,f(x,y,z),f(y,u,z))=f(x,y,z).
% 12716 (heat=1) [para_into,12423.1.1.2,1.1.1,demod,8,9,10,8] f(f(x,y,z),f(x,y,f(y,z,u)),f(y,u,w))=f(y,u,f(x,y,z)).
% 13798 [para_from,859.1.1,3895.1.1.1,demod,9,8,9] f(f(x,y,f(y,z,f(y,u,w))),f(y,z,w),f(z,w,w5))=f(y,z,w)   # label("Hint 174(26918)").
% 14993,14992 [para_into,7451.1.1.3,41.1.1,demod,10,9] f(x,f(y,z,u),f(z,u,x))=f(z,u,x)   # label("Hint 140(17037)").
% 15007,15006 [para_into,7451.1.1,858.1.1,demod,10,9,10,9,7,9,10,9] f(x,f(x,y,z),f(u,y,z))=f(x,y,z).
% 15650 [para_into,11202.1.1.1,1126.1.1,demod,9,10,8,9] f(f(x,y,z),f(x,u,f(y,w,f(x,y,z))),f(x,u,f(u,w5,f(y,w,f(x,y,z)))))=f(x,u,f(y,w,f(x,y,z))).
% 15761,15760 (heat=1) [para_into,15650.1.1.2,1.1.2,demod,9,10,8,6543,5591,flip.1] f(x,y,f(z,y,f(x,z,u)))=f(x,z,y).
% 18493 [para_into,11999.1.1.1,1126.1.1,demod,9,10,8,9] f(f(x,y,z),f(z,u,f(y,w,f(x,y,z))),f(z,u,f(u,w5,f(y,w,f(x,y,z)))))=f(z,u,f(y,w,f(x,y,z))).
% 18635,18634 (heat=1) [para_into,18493.1.1.2,1.1.2,demod,10,9,10,8,14993,11436,flip.1] f(x,y,f(z,y,f(u,z,x)))=f(z,x,y).
% 19102 [para_into,3043.1.1.2,858.1.2,demod,9] f(x,f(y,z,f(x,y,u)),f(y,w,f(y,z,u)))=f(x,y,f(y,z,u)).
% 19220 (heat=1) [para_into,19102.1.1.3,1.1.2,demod,6,9] f(x,f(y,z,u),f(y,z,f(x,y,u)))=f(x,y,f(y,z,u))   # label("Hint 106(7007)").
% 19440 [para_from,3043.1.2,48.1.1.3,demod,10,9,9] f(f(A,D,E),f(B,D,E),f(C,f(x,D,E),f(C,D,E)))!=f(D,E,f(A,B,C)).
% 19738 (heat=1) [para_into,19440.1.1,1.1.2,demod,10,9,10,8] f(f(B,D,E),f(C,D,E),f(C,f(A,D,E),f(B,D,E)))!=f(D,E,f(A,B,C)).
% 19763 [para_into,3159.1.1.2,856.1.2,demod,9] f(f(x,y,z),f(x,z,f(x,y,u)),f(x,u,w))=f(x,u,f(x,y,z))   # label("Hint 155(19869)").
% 19764 [para_into,3159.1.1.2,855.1.1] f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,w))=f(z,u,f(x,y,z))   # label("Hint 175(26962)").
% 19964 [para_from,3159.1.1,45.1.2.3,demod,9,7] f(f(x,y,f(z,u,y)),f(z,u,y),f(z,u,w))=f(z,u,y).
% 20672 [para_from,3176.1.1,11202.1.1.1,demod,9,10,8,9] f(f(x,y,z),f(y,u,f(x,z,w)),f(y,u,f(u,w5,f(x,z,w))))=f(y,u,f(x,z,w))   # label("Hint 186(27531)").
% 20674 (heat=1) [para_into,20672.1.1.3,1.1.2,demod,7,5,10,9] f(x,f(y,z,u),f(z,x,f(y,u,w)))=f(z,x,f(y,u,w))   # label("Hint 187(27539)").
% 20678,20677 [para_into,6542.1.1.2,1482.1.2,demod,8,10,9,10] f(x,f(x,y,z),f(u,y,f(y,z,w)))=f(x,y,z).
% 20682,20681 [para_into,6542.1.1.2,856.1.1,demod,10,9,9,10,9] f(x,f(x,y,z),f(y,u,f(y,w,z)))=f(x,y,z).
% 20729 [para_from,14992.1.1,3176.1.1.3,demod,8,10,9,8] f(x,f(x,y,f(z,u,w)),f(y,u,w))=f(x,y,f(z,u,w))   # label("Hint 143(18121)").
% 20761 [para_into,1608.1.1,14992.1.2,demod,10,9,10,8,10,9,6543,10,9] f(x,y,f(z,u,f(u,x,y)))=f(u,x,y)   # label("Hint 157(20432)").
% 20764,20763 [para_into,1608.1.1,1126.1.2,demod,9,9,1127,9] f(x,y,f(z,u,f(x,u,y)))=f(x,u,y)   # label("Hint 147(18678)").
% 20803 [para_into,1611.1.2,855.1.1,demod,8,1127,10,9,flip.1] f(x,y,f(z,u,y))=f(z,y,f(x,u,y))   # label("Hint 161(21514)").
% 20866,20865 [para_into,20803.1.1.3,899.1.1,demod,7,9,flip.1] f(x,f(y,z,f(x,z,u)),f(x,z,u))=f(x,z,u).
% 20905,20904 [para_into,4374.1.1,855.1.2,demod,8,8,8,8,10,8,1017,8] f(x,f(y,z,f(y,u,w)),f(y,u,x))=f(y,u,x).
% 20912 [para_into,12716.1.1.1,19964.1.2,demod,10,9,10,9,3863,8,10,9] f(f(x,y,z),f(y,z,f(x,z,u)),f(z,u,w))=f(z,u,f(x,y,z)).
% 20918 [para_from,12716.1.2,20761.1.2,demod,8,8,1127,10,9,8,10,9,flip.1] f(f(x,y,z),f(u,y,w),f(u,y,f(x,y,w)))=f(x,y,f(u,y,w)).
% 20923 (heat=1) [para_into,20918.1.2,1.1.2,demod,8,8,10,8] f(f(x,y,z),f(y,u,w),f(y,u,f(x,y,w)))=f(y,w,f(x,y,u))   # label("Hint 177(27085)").
% 20940,20939 [para_into,13798.1.1.1.3.3,20763.1.2,demod,9,1609] f(f(x,y,f(y,z,f(y,u,w))),f(y,z,u),f(z,u,w5))=f(y,z,u)   # label("Hint 151(19393)").
% 20941 [para_into,13798.1.1.1.3,20763.1.2,demod,20764,9,8,9] f(f(x,y,f(y,z,f(y,u,w))),f(y,w,z),f(w,z,w5))=f(y,w,z)   # label("Hint 176(27036)").
% 20946,20945 [para_into,13798.1.1.1,3176.1.2,demod,8,9,12424] f(f(x,y,f(x,z,f(x,u,w))),f(x,z,w),f(z,w,w5))=f(x,z,w).
% 20954,20953 [para_into,13798.1.1,14992.1.1,demod,10,9,8,10,8] f(x,y,f(z,u,f(x,u,f(y,u,w))))=f(x,y,u)   # label("Hint 119(9179)").
% 20958,20957 [para_into,13798.1.1,1593.1.1,demod,10,9] f(x,f(y,z,f(z,x,f(z,u,w))),f(z,x,w))=f(z,x,w).
% 20979,20978 [para_from,13798.1.1,14992.1.1,demod,9,8,flip.1] f(x,y,f(z,u,f(z,x,f(z,y,w))))=f(z,x,y).
% 20980 [para_from,13798.1.2,20761.1.2,demod,10,8,1609,10,9,8,8,10,8,10,8,flip.1] f(f(x,y,z),f(x,y,u),f(z,w,f(x,z,f(y,z,w5))))=f(x,y,z).
% 21006 [para_from,19764.1.2,858.1.1.3,demod,10,9,8,10,9,8] f(x,y,f(f(x,z,u),f(w,w5,z),f(w,z,f(x,w5,z))))=f(x,z,f(x,y,f(w,w5,z))).
% 21007 (heat=1) [para_into,21006.1.2.3,1.1.2,demod,10,8,8,10,8,15761] f(x,y,f(f(x,z,u),f(y,z,w),f(z,w,f(x,y,z))))=f(x,y,z).
% 21078 [para_from,20918.1.2,1482.1.2,demod,8,8,8,10,8,flip.1] f(f(x,y,z),f(x,y,f(y,u,z)),f(y,u,w))=f(x,y,f(y,u,z)).
% 21083 [para_into,20923.1.1.1,20761.1.2,demod,10,8,1609,8,8] f(f(x,y,z),f(x,u,w),f(x,u,f(x,z,w)))=f(x,w,f(x,z,u))   # label("Hint 179(27113)").
% 21086 [para_into,20923.1.1.1,44.1.2,demod,8,8] f(f(x,y,z),f(y,u,w),f(y,u,f(y,z,w)))=f(y,w,f(y,z,u)).
% 21139 [para_into,21007.1.1.3.1,20941.1.2,demod,8,9,8,20946] f(x,y,f(f(x,z,u),f(y,u,w),f(u,w,f(x,y,u))))=f(x,y,u).
% 21148,21147 (heat=1) [para_into,21139.1.1.3.3,1.1.2,demod,6,10,10,8,1017,10,8] f(x,y,f(y,f(x,y,z),f(x,u,z)))=f(x,y,z).
% 21151 [para_from,21007.1.2,19964.1.2,demod,10,9,10,9,3863,8,8,10,9,flip.1] f(x,y,f(f(z,x,u),f(z,y,w),f(z,w,f(z,x,y))))=f(z,x,y).
% 21161 [para_from,21078.1.1,20763.1.1,demod,8,flip.1] f(x,f(y,z,u),f(y,z,f(z,x,u)))=f(y,z,f(z,x,u))   # label("Hint 142(17742)").
% 21235,21234 [para_from,871.1.2,20923.1.2,demod,8,9,8,9,3177,9,5960,10,9,flip.1] f(x,f(y,z,x),f(y,u,f(y,z,w)))=f(y,z,x).
% 21571 [para_into,20677.1.1,44.1.2,demod,10,8,10,9,10,8] f(x,f(y,z,f(z,u,w)),f(z,u,x))=f(z,u,x).
% 21668 [para_from,1046.1.2,20761.1.2,demod,8,8,1127,8,flip.1] f(x,y,f(z,y,f(u,x,y)))=f(z,y,f(u,x,y)).
% 21669 [para_from,1046.1.2,6665.1.2,demod,10,9,8,10,9,9,20682,10,9,8,8,flip.1] f(x,y,f(z,x,f(x,u,y)))=f(z,x,f(x,u,y))   # label("Hint 94(5348)").
% 22017 [para_from,21669.1.1,854.1.1,demod,9,flip.1] f(x,f(y,x,z),f(x,u,z))=f(y,x,f(x,u,z)).
% 22193 [para_into,7943.1.1.2,855.1.2,demod,9,14993,flip.1] f(x,f(y,z,x),f(z,x,u))=f(x,u,f(y,z,x)).
% 22197,22196 [para_into,7943.1.2,20912.1.2,demod,18635,9,5] f(f(x,y,z),f(x,u,f(y,z,u)),f(y,z,u))=f(y,z,u).
% 22204,22203 [para_from,7943.1.2,1046.1.2,demod,10,9,10,8,9,21148,10,9,10,8,8,10,8,10,9,flip.1] f(f(x,y,z),f(x,u,z),f(y,u,f(x,y,z)))=f(x,y,z).
% 22205 [para_from,7943.1.2,1046.1.1.3,demod,10,9,10,8,8,10,8,10,9,22204,900,10,9,10,8,9,flip.1] f(x,f(y,x,z),f(y,u,z))=f(y,x,z).
% 22227 [para_from,878.1.1,7451.1.1.3,demod,10,8,1019,9] f(f(x,y,z),f(y,z,u),f(u,f(y,z,u),f(u,w,w5)))=f(y,z,u).
% 22236,22235 [para_from,878.1.2,21668.1.2,demod,8,9,20866,7,9,900,10,9,9,flip.1] f(x,f(y,z,u),f(x,z,u))=f(x,z,u).
% 22256,22255 [para_from,22203.1.1,1046.1.1.3,demod,7,8,8,10,8,flip.1] f(f(x,y,z),f(x,u,f(y,u,z)),f(y,u,z))=f(y,u,z).
% 22311,22310 [para_from,22235.1.1,19763.1.1.2,demod,8,8,3884,8,flip.1] f(x,y,f(x,z,f(z,u,y)))=f(x,z,y).
% 22335 [para_into,22227.1.1,1482.1.2,demod,10,9,10,8,10,9,10,8,10,9] f(x,f(x,y,z),f(f(x,y,z),f(x,u,w),f(y,z,w5)))=f(x,y,z).
% 22388 [para_into,22193.1.2,20941.1.1,demod,8,9,20958,9,14993,9] f(x,y,f(z,u,f(u,x,f(u,w,y))))=f(u,x,y)   # label("Hint 181(27197)").
% 22406 [para_into,22388.1.1,22255.1.2,demod,8,8,8,22256,8] f(x,y,f(z,u,f(x,u,f(u,w,y))))=f(x,u,y)   # label("Hint 178(27103)").
% 22510,22509 [para_from,903.1.2,20912.1.2,demod,8,8,8,9,900,7,8,10,8,7034,8,10,900,9,flip.1] f(x,f(y,z,u),f(y,x,u))=f(y,x,u)   # label("Hint 190(28269)").
% 22631 [para_into,3255.1.2,22235.1.1,demod,10,8] f(x,f(x,y,z),f(x,f(y,z,u),f(y,z,w)))=f(x,y,z).
% 22649 [para_from,3255.1.1,1611.1.1.3,demod,10,8,8,9,8] f(x,f(x,y,f(z,u,y)),f(z,u,w))=f(x,y,f(z,u,w)).
% 22670 [para_from,22631.1.1,21151.1.1.3.3,demod,9,10,8,6543,10,8,7] f(f(x,y,z),f(x,y,u),f(x,y,w))=f(w,f(x,y,z),f(x,y,u)).
% 22675 [para_into,22670.1.1.1,22406.1.2,demod,10,9,20954,9] f(f(x,y,z),f(x,z,u),f(x,z,w))=f(w,f(x,y,z),f(x,z,u)).
% 22676 [para_into,22670.1.1.1,22388.1.1,demod,9,8,20979] f(f(x,y,z),f(y,z,u),f(y,z,w))=f(w,f(x,y,z),f(y,z,u)).
% 22678 [para_into,22670.1.1,21083.1.1,demod,9,9,9,9,flip.1] f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,y,f(x,z,u)).
% 22686 [para_into,22678.1.1.1,22388.1.2,demod,10,9,8,20954,8,8,8,8] f(f(x,y,z),f(x,z,u),f(y,z,u))=f(x,z,f(y,z,u)).
% 22695 [para_into,22678.1.1,14992.1.2,demod,9,9,9,9,10,9,22236] f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,u,f(x,y,z)).
% 22722,22721 [para_from,22678.1.2,20904.1.1.2,demod,10,9,9,10,9] f(x,f(x,y,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(x,y,z).
% 22726,22725 [para_from,22678.1.2,6665.1.1.3,demod,8,9,9,8] f(x,f(x,y,z),f(f(y,z,u),f(y,z,w),f(y,u,w)))=f(x,y,z).
% 22775 [para_from,22686.1.2,899.1.1.3,demod,9,8,8] f(x,y,f(f(x,y,z),f(x,y,u),f(y,z,u)))=f(x,y,f(y,z,u)).
% 22785,22784 [para_from,22695.1.2,6542.1.1.2,demod,10,9,9,10,9] f(x,f(x,y,z),f(f(y,u,w),f(y,u,z),f(y,w,z)))=f(x,y,z).
% 22807 [para_into,22675.1.1,22255.1.2,demod,9,9,22197] f(f(x,y,z),f(x,z,u),f(x,z,w))=f(u,f(x,y,z),f(x,z,w)).
% 22810 [para_into,22675.1.2,20923.1.2,demod,7,10,9,1019,7] f(x,f(y,z,x),f(y,x,u))=f(x,u,f(y,z,x)).
% 22876 [para_from,22775.1.2,20761.1.1.3,demod,10,9,10,9,10,8,10,9,10,8] f(x,y,f(z,u,f(f(x,y,u),f(x,z,u),f(y,z,u))))=f(x,y,u).
% 22913 [para_into,22876.1.1,21571.1.2,demod,10,9,10,8,10,8,10,8,8,10,9,10,8,10,8,10,8,9,21235,10,9] f(x,y,f(z,u,f(f(z,u,x),f(z,u,y),f(u,x,y))))=f(u,x,y).
% 22956 [para_into,891.1.2.3.3,854.1.2,demod,5,9,10,9,900,flip.1] f(x,y,f(y,z,f(u,x,y)))=f(u,y,f(x,y,z))   # label("Hint 84(3324)").
% 23085 [para_from,22810.1.2,22807.1.2,demod,7,flip.1] f(x,f(y,z,x),f(y,x,f(y,u,z)))=f(y,z,x).
% 23118 [para_into,22956.1.1.3,22203.1.1,demod,7,8,9,12424,9,flip.1] f(x,f(y,z,u),f(z,x,u))=f(z,x,u)   # label("Hint 139(16799)").
% 23145 [para_from,22956.1.1,891.1.2.3,demod,1017,7,10,9,flip.1] f(x,y,f(x,z,f(u,y,z)))=f(x,y,z).
% 23196,23195 [para_from,23145.1.1,1075.1.1.3,demod,9,15007,9,flip.1] f(x,y,f(x,z,f(u,z,y)))=f(x,z,y).
% 23417 [para_from,19220.1.2,1106.1.2,demod,8,8,8,flip.1] f(x,f(y,z,u),f(y,z,f(y,x,u)))=f(y,f(y,x,z),f(y,x,u)).
% 23432 [para_into,896.1.2.3,20918.1.2,demod,10,9,8,1603,8,8,8,flip.1] f(x,y,f(f(x,z,u),f(z,y,w),f(z,y,f(x,z,w))))=f(x,z,y).
% 23485 [para_from,23432.1.2,23118.1.2,demod,8,9,15007,8,8,flip.1] f(x,y,f(f(z,x,u),f(z,y,w),f(z,y,f(z,x,w))))=f(z,x,y).
% 23593 [para_into,897.1.2.3,894.1.2,demod,6,6,6,9,8,6,6,6,10,8,8] f(x,f(y,z,u),f(u,x,w))=f(x,w,f(y,u,f(z,u,x))).
% 23595 [para_into,897.1.2.3,887.1.2,demod,8,9,900,8,8,9,900,6,7,8,9,900,8,10,900,9,flip.1] f(x,f(y,z,u),f(z,f(y,w,f(y,w5,u)),f(y,z,u)))=f(y,z,u).
% 23621 [para_into,20674.1.1.3,22913.1.1,demod,10,9,15007,9,10,9,10,10,8,8,flip.1] f(x,y,f(z,u,f(f(x,z,u),f(x,y,u),f(z,y,u))))=f(x,y,u).
% 23639 [para_from,20674.1.1,23485.1.1.3.3.3,demod,9,8,8,7,8,10,9] f(x,f(y,z,u),f(x,w,f(z,w,f(y,u,w5))))=f(x,w,f(y,z,u)).
% 23791 [para_from,20729.1.2,23085.1.2,demod,9,21235,10,8,9,flip.1] f(x,f(y,z,u),f(x,u,f(w,y,z)))=f(x,u,f(w,y,z))   # label("Hint 183(27303)").
% 24332 [para_into,23593.1.2,22017.1.2,demod,10,8,9,12424,10,9,10,9,flip.1] f(x,f(y,x,f(y,z,u)),f(x,u,f(y,z,u)))=f(y,x,u).
% 24485 [para_into,23791.1.1.3,22721.1.1,demod,9,10,9,9,9,8,22785] f(x,f(x,y,z),f(f(x,y,z),f(y,u,w),f(y,w,z)))=f(x,y,z).
% 24523 [para_from,23791.1.2,22649.1.1.2,demod,7,10,8,900,8,8] f(x,f(x,y,f(z,y,u)),f(z,u,w))=f(x,y,f(z,u,w)).
% 24530 (heat=1) [para_into,24523.1.1.2,1.1.2,demod,10,8] f(x,f(y,z,f(x,y,u)),f(u,z,w))=f(x,y,f(u,z,w))   # label("Hint 188(27551)").
% 24537 [para_from,24485.1.1,21161.1.1.3,demod,8,9,22510,8,7,8,8,10,8,flip.1] f(x,f(y,x,z),f(f(y,u,w),f(y,w,z),f(y,x,z)))=f(y,x,z).
% 24549 [para_from,24537.1.1,21668.1.1.3,demod,9,9,7,9,9,9,8,flip.1] f(x,f(y,z,x),f(f(y,u,z),f(y,u,w),f(y,z,x)))=f(y,z,x).
% 24947 [para_into,24530.1.1,44.1.2,demod,10,8,10,9,8] f(x,f(y,z,u),f(z,w,f(y,w,x)))=f(w,x,f(y,z,u)).
% 25143 [para_from,23417.1.2,21086.1.2,demod,900,7,9,flip.1] f(x,f(y,z,u),f(y,u,f(y,x,z)))=f(y,z,f(y,x,u)).
% 25194 [para_from,23595.1.1,5165.1.1.3.3,demod,7] f(f(x,y,z),f(x,y,f(u,w,w5)),f(u,w,w5))=f(x,y,f(u,w,w5)).
% 25201,25200 [para_from,23595.1.1,22335.1.1.3.2,demod,9] f(x,f(x,y,z),f(f(x,y,z),f(y,z,u),f(w,w5,w6)))=f(x,y,z)   # label("Hint 166(24325)").
% 25211 (heat=1) [para_into,25194.1.2,1.1.1,demod,10,8,8,8] f(f(x,y,f(z,x,u)),f(x,f(z,x,u),f(w,w5,w6)),f(w,w5,w6))=f(z,x,f(x,u,f(w,w5,w6)))   # label("Hint 154(19517)").
% 25855 [para_into,23639.1.1.3.3,22695.1.2,demod,5,9,8,5,9] f(x,y,f(x,z,f(f(y,u,z),f(y,u,w),f(y,z,w))))=f(x,y,z).
% 25922 [para_from,25855.1.1,1075.1.1.3,demod,9,22722,9,flip.1] f(x,y,f(x,z,f(f(z,u,y),f(z,u,w),f(z,y,w))))=f(x,z,y).
% 25942 [para_from,25922.1.1,25143.1.1.3,demod,9,8,9,3044,8,9,flip.1] f(x,f(y,x,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(y,x,z).
% 26078 [para_into,25211.1.1.1.3,25942.1.2,demod,8,9,9,22726,8,8] f(f(x,y,f(x,z,u)),f(x,f(x,z,u),f(w,w5,w6)),f(w,w5,w6))=f(x,z,f(x,u,f(w,w5,w6)))   # label("Hint 171(26362)").
% 26176 [para_into,26078.1.2,24332.1.1,demod,8,9,22311,8,9,22311,12424,8] f(f(x,y,f(x,z,u)),f(x,z,u),f(z,w,u))=f(x,z,u).
% 26344 [para_from,6847.1.2,7943.1.1.2,demod,9,12000,flip.1] f(x,f(y,z,u),f(z,u,f(y,x,w)))=f(z,u,f(y,x,w)).
% 26350 [para_into,26344.1.1.3.3,23118.1.1,demod,9,9,14993] f(f(x,y,z),f(u,w,w5),f(w,w5,f(y,z,u)))=f(w,w5,f(y,z,u)).
% 26403 [para_into,26344.1.1.3,11999.1.1,demod,8,10,9,9,10,9,9,20682,8,10,9,8,8,10,8,flip.1] f(f(x,y,z),f(x,y,f(x,z,u)),f(y,w,z))=f(x,y,z).
% 26416 [para_into,26344.1.1,24947.1.2,demod,18635,9] f(f(x,y,z),f(y,z,u),f(y,z,f(x,u,w)))=f(y,z,f(x,u,w)).
% 26890,26889 [para_from,26403.1.1,26344.1.1.3,demod,8,8,20678,8,7,8,8,8,10,9,flip.1] f(f(x,y,z),f(y,u,z),f(y,u,f(u,z,w)))=f(y,u,z).
% 28343,28342 [para_into,1074.1.2.3.3,22205.1.1,demod,8,26890,7,8,9,flip.1] f(x,f(y,x,z),f(u,f(w,y,z),f(y,x,z)))=f(y,x,z).
% 28447 [para_into,26350.1.1,24549.1.2,demod,10,8,10,8,10,8,10,8,10,8,10,8,10,8,10,8,10,8,10,8,10,8,8,28343] f(f(x,y,z),f(x,y,f(u,w,z)),f(u,w,w5))=f(x,y,f(u,w,z)).
% 28479 [para_from,28447.1.1,23621.1.1,demod,10,9,flip.1] f(x,f(y,z,u),f(y,z,f(w,x,u)))=f(y,z,f(w,x,u))   # label("Hint 142(17742)").
% 28481 [para_from,28447.1.1,1593.1.1.3] f(x,y,f(z,u,f(x,y,w)))=f(x,y,f(z,u,w))   # label("Hint 41(1005)").
% 28703 [para_into,28479.1.1.3,26176.1.1,demod,10,9,20905,7,8,10,9,flip.1] f(f(x,y,z),f(u,w,f(u,y,z)),f(u,y,z))=f(u,y,z).
% 28709 [para_into,28479.1.1.3,25942.1.1,demod,9,9,22510,7,9,8,flip.1] f(x,f(y,x,z),f(f(y,u,w),f(y,u,z),f(y,w,z)))=f(y,x,z).
% 28753 [para_into,28479.1.1.3,20980.1.1,demod,5922,7,8,10,9,flip.1] f(f(x,y,f(z,y,f(u,y,w))),f(z,u,y),f(z,u,w5))=f(z,u,y)   # label("Hint 193(29540)").
% 28962 [para_into,26416.1.1,22676.1.1,demod,10,9] f(f(x,y,z),f(x,u,w),f(y,u,w))=f(u,w,f(x,y,z)).
% 28974 [para_into,28962.1.1.1,28753.1.2,demod,8,8,10,9,20940,10,9] f(f(x,y,z),f(y,u,w),f(z,u,w))=f(u,w,f(x,y,z)).
% 28975 [para_into,28962.1.1.1,28703.1.2,demod,10,8,10,8,9,7452,9,10,8] f(f(x,y,z),f(x,u,w),f(z,u,w))=f(u,w,f(x,y,z)).
% 28977 [para_into,28962.1.1.1,22235.1.1,demod,10,8,10,8,10,8,9,3044] f(f(x,y,z),f(x,u,w),f(u,w,f(y,z,w5)))=f(u,w,f(x,y,z)).
% 28982 [para_into,28962.1.2,28481.1.2,demod,10,9] f(f(x,y,z),f(x,u,w),f(y,u,w))=f(u,w,f(x,y,f(z,u,w))).
% 29016,29015 [para_from,28962.1.2,6542.1.1.2,demod,10,9,9,10,9] f(x,f(x,y,z),f(f(u,w,w5),f(u,y,z),f(w,y,z)))=f(x,y,z).
% 29021 [para_into,28975.1.1,28709.1.2,demod,10,8,8,10,8,10,8,8,10,8,8,29016] f(f(x,y,z),f(x,u,w),f(y,z,w))=f(y,z,f(x,u,w)).
% 29038,29037 [para_from,28975.1.2,6542.1.1.2,demod,10,9,9,10,9] f(x,f(x,y,z),f(f(u,w,w5),f(u,y,z),f(w5,y,z)))=f(x,y,z).
% 29079 [para_from,29021.1.2,6542.1.1.2,demod,10,9,9,10,9] f(x,f(x,y,z),f(f(u,y,z),f(u,w,w5),f(y,z,w5)))=f(x,y,z).
% 29108 [para_into,28977.1.1.3,6852.1.1] f(f(x,y,z),f(x,u,w),f(z,u,f(y,u,w)))=f(u,w,f(x,y,z)).
% 29170 [para_from,29108.1.2,19738.1.1.3,demod,8,8,23196,8,1017] f(f(B,C,f(A,D,E)),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
% 29172 [para_into,29170.1.1,28962.1.1] f(D,E,f(B,C,f(A,D,E)))!=f(D,E,f(A,B,C)).
% 29277 [para_from,28974.1.2,29172.1.2,flip.1] f(f(A,B,C),f(B,D,E),f(C,D,E))!=f(D,E,f(B,C,f(A,D,E))).
% 29788 [para_into,29079.1.1,23791.1.2,demod,10,9,10,9,10,9,8,29038,9] f(x,f(x,y,z),f(f(x,y,z),f(u,w,w5),f(w5,y,z)))=f(x,y,z).
% 29808 [para_from,29788.1.1,28479.1.1.3,demod,9,22236,7,10,8,flip.1] f(x,f(x,y,z),f(f(u,w,w5),f(w5,y,z),f(x,y,z)))=f(x,y,z).
% 29821 [para_from,29808.1.1,28479.1.1.3,demod,10,8,10,8,7,10,8,7,10,8,10,9,10,8,8,flip.1] f(x,f(y,z,x),f(f(u,y,z),f(u,w,w5),f(y,z,x)))=f(y,z,x).
% 30676 [para_into,28982.1.1.1,29821.1.2,demod,10,9,10,8,10,9,10,9,25201] f(f(x,y,z),f(y,u,w),f(z,u,w))=f(u,w,f(y,z,f(x,u,w))).
% 30677 [binary,30676.1,29277.1] $F.
% 
% ------------ end of proof -------------

list(hints2).

f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
f(x,y,z)=f(y,x,z).
f(x,x,y)=x.
f(x,y,x)=x.
f(y,x,x)=x.
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(z,y,x).
f(x,x,y)=x.
f(x,y,z)=f(y,x,z).
f(x,y,z)=f(x,z,y).
f(x,y,z)=f(z,y,x).
f(f(x,w,y),w,z)=f(x,w,f(y,w,z)).
f(f(A,D,E),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C))   # label("original").
f(x,y,z)=f(x,y,z)   # label("Hint 204(35470)").
f(x,y,f(z,x,u))=f(z,x,f(x,u,y))   # label("Hint 24(864)").
f(x,y,f(x,z,f(u,x,w)))=f(u,x,f(x,y,f(x,w,z))).
f(x,f(y,x,z),f(x,u,w))=f(x,w,f(y,x,f(x,z,u)))   # label("Hint 27(867)").
f(x,y,f(z,x,u))=f(x,u,f(z,x,y))   # label("Hint 28(868)").
f(x,y,f(z,u,x))=f(z,x,f(u,x,y))   # label("Hint 35(975)").
f(x,y,f(x,z,u))=f(x,z,f(x,u,y)).
f(x,y,f(z,x,u))=f(z,x,f(x,y,u)).
f(x,f(y,x,z),f(x,u,w))=f(y,x,f(x,w,f(x,z,u))).
f(x,f(y,x,z),f(z,u,f(z,w,w5)))=f(y,x,f(z,w,f(x,z,f(z,u,w5)))).
f(x,f(x,y,f(x,z,u)),f(u,w,w5))=f(x,f(x,y,z),f(u,w5,f(x,u,w))).
f(x,f(y,x,z),f(z,u,f(z,w,w5)))=f(y,x,f(z,f(x,z,w5),f(z,u,w))).
f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(w,x,f(y,z,u)))).
f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(y,z,f(z,u,f(x,w,f(y,z,u)))).
f(x,y,f(z,u,f(z,w,x)))=f(z,x,f(x,y,f(z,u,w))).
f(x,f(y,z,u),f(z,w,f(y,z,u)))=f(w,f(y,z,u),f(z,u,f(y,z,x))).
f(x,y,f(x,y,z))=f(x,y,z)   # label("Hint 9(11)").
f(x,f(y,x,z),f(z,u,w))=f(y,x,f(z,u,f(x,z,w)))   # label("Hint 46(1064)").
f(x,f(y,x,z),f(x,u,f(y,x,z)))=f(y,x,f(x,z,u)).
f(x,f(x,y,f(x,z,u)),f(x,w,f(x,y,f(x,z,u))))=f(x,z,f(x,u,f(x,y,w))).
f(x,y,f(z,x,y))=f(z,x,y).
f(x,y,f(x,z,y))=f(x,z,y).
f(x,y,f(y,z,f(u,x,y)))=f(y,z,f(u,x,y)).
f(x,y,f(x,z,f(x,u,w)))=f(x,u,f(x,w,f(x,z,y))).
f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,f(z,u,w5))))=f(z,f(y,z,u),f(w5,f(y,z,u),f(x,w,f(y,z,u)))).
f(x,y,f(x,z,f(x,u,y)))=f(x,u,f(x,y,z)).
f(x,y,f(x,z,f(u,y,w)))=f(x,z,f(u,y,f(x,y,w)))   # label("Hint 37(989)").
f(x,f(x,y,z),f(y,u,w))=f(x,z,f(y,w,f(x,y,u)))   # label("Hint 39(992)").
f(x,f(y,x,z),f(y,x,u))=f(y,x,f(x,z,u))   # label("Hint 40(998)").
f(x,y,f(z,u,f(x,z,y)))=f(x,z,y)   # label("Hint 44(1035)").
f(x,f(y,x,z),f(y,z,u))=f(y,f(y,x,z),f(x,z,u)).
f(x,y,f(x,z,f(y,u,w)))=f(x,z,f(y,u,f(x,y,w))).
f(x,f(y,z,x),f(y,z,u))=f(y,z,f(y,x,f(z,x,u))).
f(x,y,f(z,y,u))=f(z,y,f(x,y,u)).
f(x,y,f(z,u,f(x,y,z)))=f(x,y,z)   # label(bd).
f(x,y,f(y,z,f(x,z,u)))=f(x,y,z).
f(x,y,f(x,z,f(y,z,u)))=f(x,y,z)   # label("Hint 12(17)").
f(x,y,f(z,u,f(x,y,u)))=f(x,y,u)   # label("Hint 122(11215)").
f(x,y,f(z,u,f(z,x,y)))=f(z,x,y).
f(x,y,f(z,x,f(z,y,u)))=f(z,f(z,x,y),f(x,y,u)).
f(x,f(y,z,x),f(y,z,f(z,u,w)))=f(y,z,f(y,x,f(z,w,f(z,x,u)))).
f(x,f(x,y,z),f(x,u,f(z,w,w5)))=f(x,u,f(x,y,f(z,w,f(x,z,w5)))).
f(x,f(x,y,z),f(x,u,f(y,z,w)))=f(x,u,f(y,f(x,y,z),f(x,z,w))).
f(x,f(x,y,f(x,z,u)),f(u,w,f(x,y,z)))=f(x,u,f(x,y,z)).
f(x,y,f(z,x,f(y,u,f(z,y,w))))=f(z,f(z,x,y),f(x,y,f(y,w,u))).
f(x,f(x,y,z),f(y,z,u))=f(x,y,z)   # label("Hint 54(1148)").
f(x,f(y,z,x),f(y,z,u))=f(y,z,x)   # label("Hint 52(1132)").
f(x,f(y,x,z),f(y,z,u))=f(y,x,z)   # label("Hint 53(1139)").
f(x,f(x,y,z),f(x,u,f(y,z,w)))=f(x,u,f(x,y,z)).
f(f(x,y,f(z,y,u)),f(z,y,u),f(z,u,w))=f(z,y,u)   # label("Hint 63(1362)").
f(f(x,y,f(y,z,u)),f(y,z,u),f(z,u,w))=f(y,z,u).
f(f(x,y,z),f(x,y,f(y,u,z)),f(x,z,w))=f(x,y,z).
f(f(x,y,z),f(x,y,f(x,u,z)),f(y,z,w))=f(x,y,z)   # label("Hint 74(2612)").
f(f(x,y,z),f(x,z,f(u,x,y)),f(y,z,w))=f(x,y,z).
f(f(x,y,z),f(x,z,u),f(y,w,f(x,y,z)))=f(x,y,z).
f(f(x,y,f(x,z,u)),f(x,z,u),f(z,u,w))=f(x,z,u).
f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,u)))=f(x,y,u).
f(f(x,y,z),f(y,u,f(x,y,w)),f(z,w5,f(x,y,z)))=f(x,y,z).
f(f(x,y,z),f(x,y,u),f(x,u,f(y,u,w)))=f(x,y,u)   # label("Hint 88(3620)").
f(f(x,y,z),f(x,y,u),f(x,u,f(u,w,f(y,u,w5))))=f(x,y,u).
f(f(x,y,z),f(x,y,u),f(x,z,f(y,z,w)))=f(x,y,z).
f(f(x,y,z),f(x,y,u),f(y,u,f(x,u,w)))=f(x,y,u).
f(f(x,y,z),f(x,u,f(x,z,w)),f(y,w5,f(x,y,z)))=f(x,y,z).
f(x,f(y,z,u),f(y,z,x))=f(y,z,x)   # label("Hint 58(1178)").
f(x,f(y,x,z),f(y,u,f(y,z,w)))=f(y,x,z)   # label("Hint 131(12497)").
f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,f(x,w,f(y,z,u)))))=f(y,z,f(x,w,f(y,z,u))).
f(x,y,f(z,u,x))=f(u,x,f(z,x,y)).
f(f(x,y,f(x,z,u)),f(x,z,u),f(z,w,f(x,z,u)))=f(x,z,u)   # label("Hint 172(26364)").
f(f(x,y,z),f(x,z,u),f(u,w,f(x,z,u)))=f(x,z,u).
f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u)))=f(y,z,u).
f(x,f(y,z,u),f(w,f(y,z,u),f(y,z,x)))=f(w,f(y,z,u),f(y,z,x))   # label("Hint 72(2421)").
f(f(x,y,z),f(x,u,f(y,z,w)),f(y,z,w))=f(u,f(x,y,z),f(y,z,w))   # label("Hint 73(2478)").
f(f(x,y,z),f(x,z,u),f(x,u,f(z,u,w)))=f(x,z,u).
f(f(x,y,z),f(y,z,u),f(z,u,f(y,u,w)))=f(y,z,u).
f(f(x,y,z),f(y,z,u),f(z,u,f(u,w,f(y,u,w5))))=f(y,z,u).
f(f(x,y,z),f(y,z,u),f(y,u,f(z,u,w)))=f(y,z,u).
f(x,f(x,y,z),f(y,u,z))=f(x,y,z).
f(f(x,y,z),f(x,y,f(y,z,u)),f(y,u,w))=f(y,u,f(x,y,z)).
f(f(x,y,f(y,z,f(y,u,w))),f(y,z,w),f(z,w,w5))=f(y,z,w)   # label("Hint 174(26918)").
f(x,f(y,z,u),f(z,u,x))=f(z,u,x)   # label("Hint 140(17037)").
f(x,f(x,y,z),f(u,y,z))=f(x,y,z).
f(f(x,y,z),f(x,u,f(y,w,f(x,y,z))),f(x,u,f(u,w5,f(y,w,f(x,y,z)))))=f(x,u,f(y,w,f(x,y,z))).
f(x,y,f(z,y,f(x,z,u)))=f(x,z,y).
f(f(x,y,z),f(z,u,f(y,w,f(x,y,z))),f(z,u,f(u,w5,f(y,w,f(x,y,z)))))=f(z,u,f(y,w,f(x,y,z))).
f(x,y,f(z,y,f(u,z,x)))=f(z,x,y).
f(x,f(y,z,f(x,y,u)),f(y,w,f(y,z,u)))=f(x,y,f(y,z,u)).
f(x,f(y,z,u),f(y,z,f(x,y,u)))=f(x,y,f(y,z,u))   # label("Hint 106(7007)").
f(f(A,D,E),f(B,D,E),f(C,f(x,D,E),f(C,D,E)))!=f(D,E,f(A,B,C)).
f(f(B,D,E),f(C,D,E),f(C,f(A,D,E),f(B,D,E)))!=f(D,E,f(A,B,C)).
f(f(x,y,z),f(x,z,f(x,y,u)),f(x,u,w))=f(x,u,f(x,y,z))   # label("Hint 155(19869)").
f(f(x,y,z),f(x,z,f(y,z,u)),f(z,u,w))=f(z,u,f(x,y,z))   # label("Hint 175(26962)").
f(f(x,y,f(z,u,y)),f(z,u,y),f(z,u,w))=f(z,u,y).
f(f(x,y,z),f(y,u,f(x,z,w)),f(y,u,f(u,w5,f(x,z,w))))=f(y,u,f(x,z,w))   # label("Hint 186(27531)").
f(x,f(y,z,u),f(z,x,f(y,u,w)))=f(z,x,f(y,u,w))   # label("Hint 187(27539)").
f(x,f(x,y,z),f(u,y,f(y,z,w)))=f(x,y,z).
f(x,f(x,y,z),f(y,u,f(y,w,z)))=f(x,y,z).
f(x,f(x,y,f(z,u,w)),f(y,u,w))=f(x,y,f(z,u,w))   # label("Hint 143(18121)").
f(x,y,f(z,u,f(u,x,y)))=f(u,x,y)   # label("Hint 157(20432)").
f(x,y,f(z,u,f(x,u,y)))=f(x,u,y)   # label("Hint 147(18678)").
f(x,y,f(z,u,y))=f(z,y,f(x,u,y))   # label("Hint 161(21514)").
f(x,f(y,z,f(x,z,u)),f(x,z,u))=f(x,z,u).
f(x,f(y,z,f(y,u,w)),f(y,u,x))=f(y,u,x).
f(f(x,y,z),f(y,z,f(x,z,u)),f(z,u,w))=f(z,u,f(x,y,z)).
f(f(x,y,z),f(u,y,w),f(u,y,f(x,y,w)))=f(x,y,f(u,y,w)).
f(f(x,y,z),f(y,u,w),f(y,u,f(x,y,w)))=f(y,w,f(x,y,u))   # label("Hint 177(27085)").
f(f(x,y,f(y,z,f(y,u,w))),f(y,z,u),f(z,u,w5))=f(y,z,u)   # label("Hint 151(19393)").
f(f(x,y,f(y,z,f(y,u,w))),f(y,w,z),f(w,z,w5))=f(y,w,z)   # label("Hint 176(27036)").
f(f(x,y,f(x,z,f(x,u,w))),f(x,z,w),f(z,w,w5))=f(x,z,w).
f(x,y,f(z,u,f(x,u,f(y,u,w))))=f(x,y,u)   # label("Hint 119(9179)").
f(x,f(y,z,f(z,x,f(z,u,w))),f(z,x,w))=f(z,x,w).
f(x,y,f(z,u,f(z,x,f(z,y,w))))=f(z,x,y).
f(f(x,y,z),f(x,y,u),f(z,w,f(x,z,f(y,z,w5))))=f(x,y,z).
f(x,y,f(f(x,z,u),f(w,w5,z),f(w,z,f(x,w5,z))))=f(x,z,f(x,y,f(w,w5,z))).
f(x,y,f(f(x,z,u),f(y,z,w),f(z,w,f(x,y,z))))=f(x,y,z).
f(f(x,y,z),f(x,y,f(y,u,z)),f(y,u,w))=f(x,y,f(y,u,z)).
f(f(x,y,z),f(x,u,w),f(x,u,f(x,z,w)))=f(x,w,f(x,z,u))   # label("Hint 179(27113)").
f(f(x,y,z),f(y,u,w),f(y,u,f(y,z,w)))=f(y,w,f(y,z,u)).
f(x,y,f(f(x,z,u),f(y,u,w),f(u,w,f(x,y,u))))=f(x,y,u).
f(x,y,f(y,f(x,y,z),f(x,u,z)))=f(x,y,z).
f(x,y,f(f(z,x,u),f(z,y,w),f(z,w,f(z,x,y))))=f(z,x,y).
f(x,f(y,z,u),f(y,z,f(z,x,u)))=f(y,z,f(z,x,u))   # label("Hint 142(17742)").
f(x,f(y,z,x),f(y,u,f(y,z,w)))=f(y,z,x).
f(x,f(y,z,f(z,u,w)),f(z,u,x))=f(z,u,x).
f(x,y,f(z,y,f(u,x,y)))=f(z,y,f(u,x,y)).
f(x,y,f(z,x,f(x,u,y)))=f(z,x,f(x,u,y))   # label("Hint 94(5348)").
f(x,f(y,x,z),f(x,u,z))=f(y,x,f(x,u,z)).
f(x,f(y,z,x),f(z,x,u))=f(x,u,f(y,z,x)).
f(f(x,y,z),f(x,u,f(y,z,u)),f(y,z,u))=f(y,z,u).
f(f(x,y,z),f(x,u,z),f(y,u,f(x,y,z)))=f(x,y,z).
f(x,f(y,x,z),f(y,u,z))=f(y,x,z).
f(f(x,y,z),f(y,z,u),f(u,f(y,z,u),f(u,w,w5)))=f(y,z,u).
f(x,f(y,z,u),f(x,z,u))=f(x,z,u).
f(f(x,y,z),f(x,u,f(y,u,z)),f(y,u,z))=f(y,u,z).
f(x,y,f(x,z,f(z,u,y)))=f(x,z,y).
f(x,f(x,y,z),f(f(x,y,z),f(x,u,w),f(y,z,w5)))=f(x,y,z).
f(x,y,f(z,u,f(u,x,f(u,w,y))))=f(u,x,y)   # label("Hint 181(27197)").
f(x,y,f(z,u,f(x,u,f(u,w,y))))=f(x,u,y)   # label("Hint 178(27103)").
f(x,f(y,z,u),f(y,x,u))=f(y,x,u)   # label("Hint 190(28269)").
f(x,f(x,y,z),f(x,f(y,z,u),f(y,z,w)))=f(x,y,z).
f(x,f(x,y,f(z,u,y)),f(z,u,w))=f(x,y,f(z,u,w)).
f(f(x,y,z),f(x,y,u),f(x,y,w))=f(w,f(x,y,z),f(x,y,u)).
f(f(x,y,z),f(x,z,u),f(x,z,w))=f(w,f(x,y,z),f(x,z,u)).
f(f(x,y,z),f(y,z,u),f(y,z,w))=f(w,f(x,y,z),f(y,z,u)).
f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,y,f(x,z,u)).
f(f(x,y,z),f(x,z,u),f(y,z,u))=f(x,z,f(y,z,u)).
f(f(x,y,z),f(x,y,u),f(x,z,u))=f(x,u,f(x,y,z)).
f(x,f(x,y,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(x,y,z).
f(x,f(x,y,z),f(f(y,z,u),f(y,z,w),f(y,u,w)))=f(x,y,z).
f(x,y,f(f(x,y,z),f(x,y,u),f(y,z,u)))=f(x,y,f(y,z,u)).
f(x,f(x,y,z),f(f(y,u,w),f(y,u,z),f(y,w,z)))=f(x,y,z).
f(f(x,y,z),f(x,z,u),f(x,z,w))=f(u,f(x,y,z),f(x,z,w)).
f(x,f(y,z,x),f(y,x,u))=f(x,u,f(y,z,x)).
f(x,y,f(z,u,f(f(x,y,u),f(x,z,u),f(y,z,u))))=f(x,y,u).
f(x,y,f(z,u,f(f(z,u,x),f(z,u,y),f(u,x,y))))=f(u,x,y).
f(x,y,f(y,z,f(u,x,y)))=f(u,y,f(x,y,z))   # label("Hint 84(3324)").
f(x,f(y,z,x),f(y,x,f(y,u,z)))=f(y,z,x).
f(x,f(y,z,u),f(z,x,u))=f(z,x,u)   # label("Hint 139(16799)").
f(x,y,f(x,z,f(u,y,z)))=f(x,y,z).
f(x,y,f(x,z,f(u,z,y)))=f(x,z,y).
f(x,f(y,z,u),f(y,z,f(y,x,u)))=f(y,f(y,x,z),f(y,x,u)).
f(x,y,f(f(x,z,u),f(z,y,w),f(z,y,f(x,z,w))))=f(x,z,y).
f(x,y,f(f(z,x,u),f(z,y,w),f(z,y,f(z,x,w))))=f(z,x,y).
f(x,f(y,z,u),f(u,x,w))=f(x,w,f(y,u,f(z,u,x))).
f(x,f(y,z,u),f(z,f(y,w,f(y,w5,u)),f(y,z,u)))=f(y,z,u).
f(x,y,f(z,u,f(f(x,z,u),f(x,y,u),f(z,y,u))))=f(x,y,u).
f(x,f(y,z,u),f(x,w,f(z,w,f(y,u,w5))))=f(x,w,f(y,z,u)).
f(x,f(y,z,u),f(x,u,f(w,y,z)))=f(x,u,f(w,y,z))   # label("Hint 183(27303)").
f(x,f(y,x,f(y,z,u)),f(x,u,f(y,z,u)))=f(y,x,u).
f(x,f(x,y,z),f(f(x,y,z),f(y,u,w),f(y,w,z)))=f(x,y,z).
f(x,f(x,y,f(z,y,u)),f(z,u,w))=f(x,y,f(z,u,w)).
f(x,f(y,z,f(x,y,u)),f(u,z,w))=f(x,y,f(u,z,w))   # label("Hint 188(27551)").
f(x,f(y,x,z),f(f(y,u,w),f(y,w,z),f(y,x,z)))=f(y,x,z).
f(x,f(y,z,x),f(f(y,u,z),f(y,u,w),f(y,z,x)))=f(y,z,x).
f(x,f(y,z,u),f(z,w,f(y,w,x)))=f(w,x,f(y,z,u)).
f(x,f(y,z,u),f(y,u,f(y,x,z)))=f(y,z,f(y,x,u)).
f(f(x,y,z),f(x,y,f(u,w,w5)),f(u,w,w5))=f(x,y,f(u,w,w5)).
f(x,f(x,y,z),f(f(x,y,z),f(y,z,u),f(w,w5,w6)))=f(x,y,z)   # label("Hint 166(24325)").
f(f(x,y,f(z,x,u)),f(x,f(z,x,u),f(w,w5,w6)),f(w,w5,w6))=f(z,x,f(x,u,f(w,w5,w6)))   # label("Hint 154(19517)").
f(x,y,f(x,z,f(f(y,u,z),f(y,u,w),f(y,z,w))))=f(x,y,z).
f(x,y,f(x,z,f(f(z,u,y),f(z,u,w),f(z,y,w))))=f(x,z,y).
f(x,f(y,x,z),f(f(y,u,z),f(y,u,w),f(y,z,w)))=f(y,x,z).
f(f(x,y,f(x,z,u)),f(x,f(x,z,u),f(w,w5,w6)),f(w,w5,w6))=f(x,z,f(x,u,f(w,w5,w6)))   # label("Hint 171(26362)").
f(f(x,y,f(x,z,u)),f(x,z,u),f(z,w,u))=f(x,z,u).
f(x,f(y,z,u),f(z,u,f(y,x,w)))=f(z,u,f(y,x,w)).
f(f(x,y,z),f(u,w,w5),f(w,w5,f(y,z,u)))=f(w,w5,f(y,z,u)).
f(f(x,y,z),f(x,y,f(x,z,u)),f(y,w,z))=f(x,y,z).
f(f(x,y,z),f(y,z,u),f(y,z,f(x,u,w)))=f(y,z,f(x,u,w)).
f(f(x,y,z),f(y,u,z),f(y,u,f(u,z,w)))=f(y,u,z).
f(x,f(y,x,z),f(u,f(w,y,z),f(y,x,z)))=f(y,x,z).
f(f(x,y,z),f(x,y,f(u,w,z)),f(u,w,w5))=f(x,y,f(u,w,z)).
f(x,f(y,z,u),f(y,z,f(w,x,u)))=f(y,z,f(w,x,u))   # label("Hint 142(17742)").
f(x,y,f(z,u,f(x,y,w)))=f(x,y,f(z,u,w))   # label("Hint 41(1005)").
f(f(x,y,z),f(u,w,f(u,y,z)),f(u,y,z))=f(u,y,z).
f(x,f(y,x,z),f(f(y,u,w),f(y,u,z),f(y,w,z)))=f(y,x,z).
f(f(x,y,f(z,y,f(u,y,w))),f(z,u,y),f(z,u,w5))=f(z,u,y)   # label("Hint 193(29540)").
f(f(x,y,z),f(x,u,w),f(y,u,w))=f(u,w,f(x,y,z)).
f(f(x,y,z),f(y,u,w),f(z,u,w))=f(u,w,f(x,y,z)).
f(f(x,y,z),f(x,u,w),f(z,u,w))=f(u,w,f(x,y,z)).
f(f(x,y,z),f(x,u,w),f(u,w,f(y,z,w5)))=f(u,w,f(x,y,z)).
f(f(x,y,z),f(x,u,w),f(y,u,w))=f(u,w,f(x,y,f(z,u,w))).
f(x,f(x,y,z),f(f(u,w,w5),f(u,y,z),f(w,y,z)))=f(x,y,z).
f(f(x,y,z),f(x,u,w),f(y,z,w))=f(y,z,f(x,u,w)).
f(x,f(x,y,z),f(f(u,w,w5),f(u,y,z),f(w5,y,z)))=f(x,y,z).
f(x,f(x,y,z),f(f(u,y,z),f(u,w,w5),f(y,z,w5)))=f(x,y,z).
f(f(x,y,z),f(x,u,w),f(z,u,f(y,u,w)))=f(u,w,f(x,y,z)).
f(f(B,C,f(A,D,E)),f(B,D,E),f(C,D,E))!=f(D,E,f(A,B,C)).
f(D,E,f(B,C,f(A,D,E)))!=f(D,E,f(A,B,C)).
f(f(A,B,C),f(B,D,E),f(C,D,E))!=f(D,E,f(B,C,f(A,D,E))).
f(x,f(x,y,z),f(f(x,y,z),f(u,w,w5),f(w5,y,z)))=f(x,y,z).
f(x,f(x,y,z),f(f(u,w,w5),f(w5,y,z),f(x,y,z)))=f(x,y,z).
f(x,f(y,z,x),f(f(u,y,z),f(u,w,w5),f(y,z,x)))=f(y,z,x).
f(f(x,y,z),f(y,u,w),f(z,u,w))=f(u,w,f(y,z,f(x,u,w))).


f(f(x,v,w),f(y,v,w),f(z,v,w)) = f(v,w,f(x,y,z))   # label("original").
f(f(x,v,w),f(y,v,w),f(z,f(x,v,w),f(z,v,w))) = f(v,w,f(x,y,z)).
f(f(y,v,w),f(z,v,w),f(z,f(x,v,w),f(y,v,w))) = f(v,w,f(x,y,z)).
f(f(y,z,f(x,v,w)),f(y,v,w),f(z,v,w)) = f(v,w,f(x,y,z)).
f(v,w,f(y,z,f(x,v,w))) = f(v,w,f(x,y,z)).
f(f(x,y,z),f(y,v,w),f(z,v,w)) = f(v,w,f(y,z,f(x,v,w))).

end_of_list.
