Sindbad~EG File Manager

%  T is Tarski's B,  non-strict betweenness
%  E is equidistance
%  Names for the axioms as in SST.
% Proves Lemma 5B,  extensionality of Col, making use of Lemma 5A
% Lemma 5B says that if u and v both lie on Line(a,b), 
% then points on Line(u,v) are also on Line(a,b).  In the positive form:
% -Col(xa,xb,u) | -Col(xa,xb,v) | xa=xb | u=v | -Col(u,v,z) | -Col(u,v,z) | Col(xa,xb,z).


set(hyper_res).
clear(order_hyper).
set(para_into).
set(para_from).
set(binary_res).
%set(neg_hyper_res).
set(ur_res).
set(para_from).
set(para_into).
%  set(unit_deletion).
set(order_history).
assign(report,5400).
%  assign(max_seconds, 36000).
assign(max_mem,840000).
%clear(print_kept).
% set(very_verbose).
set(input_sos_first).
%  set(ancestor_subsume).
set(back_sub).
% set(sos_queue).



assign(max_weight,25).
assign(max_distinct_vars,1).
assign(pick_given_ratio,2).
assign(max_proofs,1).

assign(bsub_hint_wt,-1).
%assign(fsub_hint_wt,-1).
set(keep_hint_subsumers).


weight_list(pick_and_purge).
end_of_list.

list(hot).    
-T(xa,xb,xc) | T(xc,xb,xa).  % Satz 3.2.   
end_of_list.
 

list(usable).      

x=x.
T(x,y,y).    % Satz 3.1
-T(xa,xb,xc) | T(xc,xb,xa).  % Satz 3.2.
T(xa,xa,xb).  % Satz 3.3
-T(xa,xb,xc) | -T(xb,xa,xc) | xa = xb.  % Satz 3.4.
-T(xa,xb,xd) | -T(xb,xc,xd) | T(xa,xb,xc). % Satz 3.51.
-T(xa,xb,xd) | -T(xb,xc,xd) | T(xa,xc,xd). % Satz 3.52.
-T(xa,xb,xc) | -T(xa,xc,xd) | T(xb,xc,xd). % Satz 3.61.
-T(xa,xb,xc) | -T(xa,xc,xd) | T(xa,xb,xd). % Satz 3.61.
-T(xa,xb,xc) | -T(xb,xc,xd) | xb = xc | T(xa,xc,xd).  % Satz 3.71
-T(xa,xb,xc) | -T(xa,xc,xd) | T(xa,xb,xd). % Satz 3.62.
-T(xa,xb,xc) | -T(xb,xc,xd) | xb = xc | T(xa,xc,xd).  % Satz 3.71
-T(xa,xb,xc) | -T(xb,xc,xd) | xb = xc | T(xa,xb,xd).  % Satz 3.72
 

 
 % following is Definition 4.10
-Col(xa,xb,xc) | T(xa,xb,xc) | T(xb,xc,xa) | T(xc,xa,xb).
Col(xa,xb,xc) | -T(xa,xb,xc).
Col(xa,xb,xc) | -T(xb,xc,xa).
Col(xa,xb,xc) | -T(xc,xa,xb).

% Following are Satz 4.11
-Col(x,y,z) | Col(y,z,x).
 
% following is Satz 4.12
Col(x,x,y).
 
 
% Following is Satz 5.1
xa = xb | -T(xa,xb,xc) | -T(xa,xb,xd) | T(xa,xc,xd) | T(xa,xd,xc).
% Following is Satz 5.2
xa = xb | -T(xa,xb,xc) | -T(xa,xb,xd)| T(xb,xc,xd) | T(xb,xd,xc).
% Following is Satz 5.3
-T(xa,xb,xd) | -T(xa,xc,xd) | T(xa,xb,xc) | T(xa,xc,xb).

% Following is Lemma 5A

 -Col(xa,xb,v) | xa=xb |  -Col(xa,v,z) | xa=v | Col(xa,xb,z).

end_of_list.  


list(hints2).    
Col(c,b,p).
Col(b,c,p).
Col(b,a,p).
Col(a,b,p).
end_of_list.

list(passive).
-Col(c,b,p) | $ANS(1).
-Col(b,c,p) | $ANS(2).
-Col(b,a,p) | $ANS(3).
-Col(a,b,p) | $ANS(4).
end_of_list | $ANS(5).  
 

list(sos). 
a != b.
c != d.
Col(a,b,c).
Col(a,b,d).
Col(c,d,p).
-Col(a,b,p).
 

 
end_of_list.