% This file was mechanically generated
% from the master list in TarskiTheorems.php.
% Tarski-Szmielew's axiom system is used.
% T is Tarski's B,  non-strict betweenness.
% E is equidistance.
% Names for the axioms follow the book SST
% by Schwabhäuser, Szmielew, and Tarski.
% This file attempts to prove Satz10.6.

set(hyper_res).
set(para_into).
set(para_from).
set(binary_res).
set(ur_res).
set(order_history).
assign(max_seconds,120).
assign(max_mem,2000000).
clear(print_kept).
set(input_sos_first).
set(back_sub).
assign(bsub_hint_wt,-1).
set(keep_hint_subsumers).
assign(max_weight,20).
assign(max_distinct_vars,4).
assign(pick_given_ratio,4).
assign(max_proofs,1).

list(usable).
% Following is axiom A1
E(x,y,y,x).
% Following is axiom A2
-E(x,y,z,v) | -E(x,y,z2,v2) | E(z,v,z2,v2).
% Following is axiom A3
-E(x,y,z,z) | x=y.
% Following is axiom A4
T(x,y,ext(x,y,w,v)).
E(y,ext(x,y,w,v),w,v).
% Following is axiom A5
-E(x,y,x1,y1) | -E(y,z,y1,z1) | -E(x,v,x1,v1) | -E(y,v,y1,v1) | -T(x,y,z) 
|  -T(x1,y1,z1) | x=y | E(z,v,z1,v1).
% Following is axiom A6
 -T(x,y,x) | x=y.
% Following is axiom A7
-T(xa,xp,xc) | -T(xb,xq,xc) | T(xp,ip(xa,xp,xc,xb,xq),xb).
-T(xa,xp,xc) | -T(xb,xq,xc) | T(xq,ip(xa,xp,xc,xb,xq),xa).
% Following is axiom A8
-T(alpha,beta,gamma).
-T(beta,gamma,alpha).
-T(gamma,alpha,beta).

% Following is Satz2.1
E(xa,xb,xa,xb).
% Following is Satz2.2
-E(xa,xb,xc,xd) | E(xc,xd,xa,xb).
% Following is Satz2.3
-E(xa,xb,xc,xd) | -E(xc,xd,xe,xf) | E(xa,xb,xe,xf).
% Following is Satz2.4
-E(xa,xb,xc,xd) | E(xb,xa,xc,xd).
% Following is Satz2.5
-E(xa,xb,xc,xd) | E(xa,xb,xd,xc).
% Following is Satz2.8
E(xa,xa,xb,xb).
% Following is Satz2.11
-T(xa,xb,xc) | -T(xa1,xb1,xc1) | -E(xa,xb,xa1,xb1) | -E(xb,xc,xb1,xc1) 
|  E(xa,xc,xa1,xc1).
% Following is Satz2.12
xq = xa | -T(xq,xa,xd) | -E(xa,xd,xb,xc) | xd = ext(xq,xa,xb,xc).
% Following is Satz2.13
-E(xb,xc,xa,xa) | xb=xc.
% Following is Satz2.14
-E(xa,xb,xc,xd) | E(xb,xa,xd,xc).
% Following is Satz2.15
-T(xa,xb,xc) | -T(xA,xB,xC) | -E(xa,xb,xB,xC)| -E(xb,xc,xA,xB) 
|  E(xa,xc,xA,xC).
% Following is Satz3.1
T(xa,xb,xb).
% Following is Satz3.2
-T(xa,xb,xc) | T(xc,xb,xa).
% Following is Satz3.3
T(xa1,xa1,xb1).
% Following is Satz3.4
-T(xa,xb,xc) | -T(xb,xa,xc) | xa = xb.
% Following is Satz3.5a
-T(xa,xb,xd) | -T(xb,xc,xd) | T(xa,xb,xc).
% Following is Satz3.6a
-T(xa,xb,xc) | -T(xa,xc,xd) | T(xb,xc,xd).
% Following is Satz3.7a
-T(xa,xb,xc) | -T(xb,xc,xd) | xb = xc | T(xa,xc,xd).
% Following is Satz3.5b
-T(xa,xb,xd) | -T(xb,xc,xd) | T(xa,xc,xd).
% Following is Satz3.6b
-T(xa,xb,xc) | -T(xa,xc,xd) | T(xa,xb,xd).
% Following is Satz3.7b
-T(xa,xb,xc) | -T(xb,xc,xd) | xb = xc | T(xa,xb,xd).
% Following is Satz3.13a
alpha != beta.
% Following is Satz3.13b
beta != gamma.
% Following is Satz3.13a
alpha != gamma.
% Following is Satz3.14a
T(xa,xb,ext(xa,xb,alpha,gamma)).
% Following is Satz3.14b
xb != ext(xa,xb,alpha,gamma).
% Following is Satz3.17
-T(xa,xb,xc) | -T(xa1,xb1,xc) | -T(xa,xp,xa1) 
|  T(xp,crossbar(xa,xb,xc,xa1,xb1,xp),xc).
-T(xa,xb,xc) | -T(xa1,xb1,xc) | -T(xa,xp,xa1) 
|  T(xb,crossbar(xa,xb,xc,xa1,xb1,xp),xb1).
% Following is Satz4.2
-IFS(xa,xb,xc,xd,xa1,xb1,xc1,xd1) | E(xb,xd,xb1,xd1).
% Following is Satz4.3
-T(xa,xb,xc) | -T(xa1,xb1,xc1) | -E(xa,xc,xa1,xc1) | -E(xb,xc,xb1,xc1) 
|  E(xa,xb,xa1,xb1).
% Following is Satz4.5
-T(xa,xb,xc) | -E(xa,xc,xa1,xc1) | T(xa1,insert(xa,xb,xa1,xc1),xc1).
-T(xa,xb,xc) | -E(xa,xc,xa1,xc1) | E3(xa,xb,xc,xa1,insert(xa,xb,xa1,xc1),xc1).
% Following is Satz4.6
-T(xa,xb,xc) | -E3(xa,xb,xc,xa1,xb1,xc1) | T(xa1,xb1,xc1).
% Following is Satz4.11a
-Col(xa,xb,xc) | Col(xb,xc,xa).
% Following is Satz4.11b
-Col(xa,xb,xc) | Col(xc,xa,xb).
% Following is Satz4.11c
-Col(xa,xb,xc) | Col(xc,xb,xa).
% Following is Satz4.11d
-Col(xa,xb,xc) | Col(xb,xa,xc).
% Following is Satz4.11e
-Col(xa,xb,xc) | Col(xa,xc,xb).
% Following is Satz4.12
Col(xa,xa,xb).
% Following is Satz4.12b
Col(xa,xb,xa).
% Following is Satz4.13
-Col(xa,xb,xc) | - E3(xa,xb,xc,xa1,xb1,xc1) | Col(xa1,xb1,xc1).
% Following is Satz4.14
-Col(xa,xb,xc) | -E(xa,xb,xa1,xb1) 
|  E3(xa,xb,xc,xa1,xb1,insert5(xa,xb,xc,xa1,xb1)).
% Following is Satz4.16
-FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1) | xa = xb | E(xc,xd,xc1,xd1).
% Following is Satz4.17
xa = xb | -Col(xa,xb,xc) | -E(xa,xp,xa,xq) | -E(xb,xp,xb,xq) |E(xc,xp,xc,xq).
% Following is Satz4.18
xa = xb | -Col(xa,xb,xc) | -E(xa,xc,xa,xc1) | -E(xb,xc,xb,xc1) | xc = xc1.
% Following is Satz4.19
-T(xa,xc,xb) | -E(xa,xc,xa,xc1) | -E(xb,xc,xb,xc1) | xc = xc1.
% Following is Satz5.1
xa = xb | -T(xa,xb,xc) | -T(xa,xb,xd) | T(xa,xc,xd) | T(xa,xd,xc).
% Following is Satz5.2
xa = xb | -T(xa,xb,xc) | -T(xa,xb,xd)| T(xb,xc,xd) | T(xb,xd,xc).
% Following is Satz5.3
-T(xa,xb,xd) | -T(xa,xc,xd) | T(xa,xb,xc) | T(xa,xc,xb).
% Following is Satz5.5a
-le(xa,xb,xc,xd) | T(xa,xb,ins(xc,xd,xa,xb)).
-le(xa,xb,xc,xd) | E(xa,ins(xc,xd,xa,xb),xc,xd).
-le(xa,xb,xc,xd) | ins(xc,xd,xa,xb) = ext(xa,xb,insert(xa,xb,xc,xd),xd).
% Following is Satz5.5b
 le(xa,xb,xc,xd) | -T(xa,xb,xe) | -E(xa,xe,xc,xd).
% Following is Satz5.6
-le(xa,xb,xc,xd) | -E(xa,xb,xa1,xb1) | - E(xc,xd,xc1,xd1) 
| le(xa1,xb1,xc1,xd1).
% Following is Satz5.7
le(xa,xb,xa,xb).
% Following is Satz5.8
-le(xa,xb,xc,xd) | - le(xc,xd,xe,xf) | le(xa,xb,xe,xf).
% Following is Satz5.9
-le(xa,xb,xc,xd) | -le(xc,xd,xa,xb) | E(xa,xb,xc,xd).
% Following is Satz5.10
le(xa,xb,xc,xd) | le(xc,xd,xa,xb).
% Following is Satz5.11
le(xa,xa,xc,xd).
% Following is Satz5.12a1
-Col(xa,xb,xc) | -T(xa,xb,xc) | le(xa,xb,xa,xc).
% Following is Satz5.12a2
-Col(xa,xb,xc) | -T(xa,xb,xc) | le(xb,xc,xa,xc).
% Following is NarbouxLemma1
-T(xa,xb,xc) | -E(xa,xc,xa,xb) | xc = xb.
% Following is Satz5.12b
-Col(xa,xb,xc) | T(xa,xb,xc) | -le(xa,xb,xa,xc) | -le(xb,xc,xa,xc).
% Following is Satz6.2a
xa = xp | xb = xp | xc = xp | -T(xa,xp,xc) | -T(xb,xp,xc) 
|  sameside(xa,xp,xb).
% Following is Satz6.2b
xa = xp | xb = xp | xc = xp | -T(xa,xp,xc) | T(xb,xp,xc) 
|  -sameside(xa,xp,xb).
% Following is Satz6.3a
-sameside(xa,xp,xb) | xa != xp.
-sameside(xa,xp,xb) | xb != xp.
-sameside(xa,xp,xb) | c63(xa,xp,xb) != xp.
-sameside(xa,xp,xb) | T(xa,xp,c63(xa,xp,xb)).
-sameside(xa,xp,xb) | T(xb,xp,c63(xa,xp,xb)).
% Following is Satz6.3b
sameside(xa,xp,xb) | xa=xp | xb = xp | xc = xp | -T(xa,xp,xc) | -T(xb,xp,xc).
% Following is Satz6.4a
-sameside(xa,xp,xb) | Col(xa,xp,xb).
-sameside(xa,xp,xb) | -T(xa,xp,xb).
% Following is Satz6.4b
 sameside(xa,xp,xb) | -Col(xa,xp,xb) | T(xa,xp,xb).
% Following is Satz6.5
xa = xp | sameside(xa,xp,xa).
% Following is Satz6.6
-sameside(xa,xp,xb) | sameside(xb,xp,xa).
% Following is Satz6.7
-sameside(xa,xp,xb) | -sameside(xb,xp,xc) | sameside(xa,xp,xc).
% Following is Satz6.11a
xr = xa | xb = xc | sameside(insert(xb,xc,xa,xr),xa,xr).
xr = xa | xb = xc | E(xa,insert(xb,xc,xa,xr),xb,xc).
% Following is Satz6.11b
xr = xa | xb = xc | -sameside(xp,xa,xr) | -E(xa,xp,xb,xc) 
|  -sameside(xq,xa,xr) |  -E(xa,xq,xb,xc) | xp=xq.
% Following is Satz6.13a
-sameside(xa,xp,xb) | -le(xp,xa,xp,xb) | T(xp,xa,xb).
% Following is Satz6.13b
-sameside(xa,xp,xb) | le(xp,xa,xp,xb) | -T(xp,xa,xb).
% Following is Satz6.15a
xp = xq | xp = xr | -T(xq,xp,xr) | -Col(xa,xp,xq) | xa = xp 
|  sameside(xa,xp,xq) | sameside(xa,xp,xr).
% Following is Satz6.15b
xp = xq | xp = xr | -T(xq,xp,xr) | -sameside(xa,xp,xq) | Col(xa,xp,xq).
% Following is Satz6.15c
xp = xq | xp = xr | -T(xq,xp,xr) | -sameside(xa,xp,xr) | Col(xa,xp,xq).
% Following is Satz6.15d
xp = xq | xp = xr | -T(xq,xp,xr) | xa != xp | Col(xa,xp,xq).
% Following is Satz6.16a
xa=xb | -T(xc,xa,xb) | -T(xd,xa,xb) | T(xd,xc,xb) | T(xc,xd,xb).
% Following is Satz6.16b
xp = xq  | xcs = xp | -Col(xp,xq,xcs) | -Col(xp,xq,xr) | Col(xp,xcs,xr).
% Following is Satz6.17a
xp = xq | Col(xp,xq,xp).
% Following is Satz6.17b
xp = xq | -Col(xp,xq,xr) | Col(xq,xp,xr).
% Following is Satz6.18
xa = xb | xp = xq | -Col(xp,xq,xa) | -Col(xp,xq,xb) | -Col(xp,xq,xr) 
|  Col(xa,xb,xr).
% Following is Satz6.21
xa = xb | xp = xq | -Col(xa,xb,xc) | -Col(xp,xq,xc) | -Col(xa,xb,xd) 
|  -Col(xp,xq,xd) | xc=xd | -Col(xa,xb,xe) | Col(xp,xq,xe).
% Following is Satz6.25
xa = xb | -Col(xa,xb,pointOffLine(xa,xb)).
% Following is Satz6.28
-sameside(xa,xb,xc)| -sameside(xa1,xb1,xc1) | -E(xb,xa,xb1,xa1) 
|  -E(xb,xc,xb1,xc1) | E(xa,xc,xa1,xc1).
% Following is Satz7.2
-M(xa,xm,xb) | M(xb,xm,xa).
% Following is Satz7.3a
-M(xa,xm,xa) | xm = xa.
% Following is Satz7.3b
M(xa,xm,xa) | xm != xa.
% Following is Satz7.4a
M(xp,xa,s(xa,xp)).
% Following is Satz7.4b
-M(xp,xa,xr) | -M(xp,xa,xq) | xr=xq.
% Following is Satz7.6
-M(xp,xa,xq) | xq = s(xa,xp).
% Following is Satz7.7
s(xa,s(xa,xp)) = xp.
% Following is Satz7.8
s(xa,xp) != xr | s(xa,xq) != xr | xp = xq.
% Following is Satz7.9
s(xa,xp) != s(xa,xq) | xp = xq.
% Following is Satz7.10a
s(xa,xp) != xp | xp = xa.
% Following is Satz7.10b
s(xa,xp)=xp | xp != xa.
% Following is Satz7.13
E(xp,xq,s(xa,xp),s(xa,xq)).
% Following is Satz7.15a
-T(xp,xq,xr) | T(s(xa,xp),s(xa,xq),s(xa,xr)).
% Following is Satz7.15b
T(xp,xq,xr) | -T(s(xa,xp),s(xa,xq),s(xa,xr)).
% Following is Satz7.16a
-E(xp,xq,xr,xcs) | E(s(xa,xp),s(xa,xq),s(xa,xr),s(xa,xcs)).
% Following is Satz7.16b
E(xp,xq,xr,xcs) | -E(s(xa,xp),s(xa,xq),s(xa,xr),s(xa,xcs)).
% Following is Satz7.17
-M(xp,xa,xq) | -M(xp,xb,xq) | xa = xb.
% Following is Satz7.18
s(xa,xp) != s(xb,xp) | xa = xb.
% Following is Satz7.19
s(xa,s(xb,xp)) != s(xb,s(xa,xp)) | xa = xb.
% Following is Satz7.20
-Col(xa,xm,xb) | -E(xm,xa,xm,xb) | xa = xb | M(xa,xm,xb).
% Following is Satz7.21
Col(xa,xb,xc) | xb = xd | -E(xa,xb,xc,xd) | -E(xb,xc,xd,xa) | -Col(xa,xp,xc) 
|  -Col(xb,xp,xd) | M(xa,xp,xc).
% Following is Satz7.22a
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) | T(xm1,xc,xm2) | -le(xc,xa1,xc,xa2) .
% Following is Satz7.22b
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) | T(xm1,xc,xm2).
% Following is Satz7.22
-T(xa1,xc,xa2) | -T(xb1,xc,xb2) | -E(xc,xa1,xc,xb1) | -E(xc,xa2,xc,xb2) 
|  -M(xa1,xm1,xb1) | -M(xa2,xm2,xb2) | T(xm1,xc,xm2).
% Following is Satz7.25
-E(xc,xa,xc,xb) | M(xa,isomidpoint(xa,xb,xc),xb).
% Following is Satz8.2
-R(xa,xb,xc) | R(xc,xb,xa).
% Following is Satz8.3
-R(xa,xb,xc) | xa = xb | -Col(xb,xa,xa1) | R(xa1,xb,xc).
% Following is Satz8.4
-R(xa,xb,xc) | R(xa,xb,s(xb,xc)).
% Following is Satz8.5
R(xa,xb,xb).
% Following is Satz8.6
-R(xa,xb,xc) | -R(xa1,xb,xc) | -T(xa,xc,xa1) | xb = xc.
% Following is Satz8.7
-R(xa,xb,xc) | -R(xa,xc,xb) | xb = xc.
% Following is Satz8.8
-R(xa,xb,xa) | xa = xb.
% Following is Satz8.9
-R(xa,xb,xc) | -Col(xa,xb,xc) | xa=xb | xc=xb.
% Following is Satz8.10
-R(xa,xb,xc) | -E3(xa,xb,xc,xa1,xb1,xc1) | R(xa1,xb1,xc1).
% Following is Satz8.12a
-perpAt(xa,xb,xc,xp,xq) | perpAt(xp,xq,xc,xa,xb).
% Following is Satz8.12b
-perp(xa,xb,xp,xq) | perp(xp,xq,xa,xb).
% Following is Satz8.13a
-perpAt(xa,xb,xc,xp,xq) | xa != xb.
-perpAt(xa,xb,xc,xp,xq) | xp != xq.
-perpAt(xa,xb,xc,xp,xq) | Col(xp,xq,xc).
-perpAt(xa,xb,xc,xp,xq) | Col(xa,xb,xc).
-perpAt(xa,xb,xc,xp,xq) | Col(xa,xb,f813(xa,xb,xp,xq,xc)).
-perpAt(xa,xb,xc,xp,xq) | Col(xp,xq,g813(xa,xb,xp,xq,xc)).
-perpAt(xa,xb,xc,xp,xq) | xc != f813(xa,xb,xp,xq,xc).
-perpAt(xa,xb,xc,xp,xq) | xc != g813(xa,xb,xp,xq,xc).
-perpAt(xa,xb,xc,xp,xq) | R(f813(xa,xb,xp,xq,xc),xc,g813(xa,xb,xp,xq,xc)).
% Following is Satz8.13b
xa=xb | xp=xq | -Col(xp,xq,xcx) | -Col(xa,xb,xcx) | -Col(xa,xb,u) 
|  -Col(xp,xq,v) | xcx = u | xcx=v | -R(u,xcx,v) | perpAt(xa,xb,xcx,xp,xq).
% Following is Satz8.14a
-perp(xa,xb,xp,xq) | -Col(xa,xb,xp) | -Col(xa,xb,xq).
% Following is Satz8.14b
-perp(xa,xb,xp,xq) | -Col(xa,xb,xc) | -Col(xp,xq,xc) | perpAt(xa,xb,xc,xp,xq).
% Following is Satz8.14c
-perpAt(xa,xb,xc,xp,xq) | xc = il(xa,xb,xp,xq).
% Following is Satz8.15
xa=xb | -Col(xa,xb,xd) | -perp(xa,xb,xc,xd) | perpAt(xa,xb,xd,xc,xd).
% Following is Satz8.16a
xa = xb | -Col(xa,xb,xp) | -Col(xa,xb,xq) | xq = xp | -Col(xa,xb,xc) 
|  -perp(xa,xb,xc,xp) .
xa = xb | -Col(xa,xb,xp) | -Col(xa,xb,xq) | xq = xp |  R(xc,xp,xq) 
|  -perp(xa,xb,xc,xp).
% Following is Satz8.16b
xa = xb | -Col(xa,xb,xp) | -Col(xa,xb,xq) | xq = xp | perp(xa,xb,xc,xp) 
|  Col(xa,xb,xc) | -R(xc,xp,xq).
% Following is Satz8.18a
Col(xa,xb,xc) | -Col(xa,xb,xp) | -Col(xa,xb,xq) | -perp(xa,xb,xc,xp) 
|  -perp(xa,xb,xc,xq) | xp = xq.
% Following is Satz8.18
Col(xa,xb,xc) | Col(xa,xb,foot(xa,xb,xc)).
Col(xa,xb,xc) | perp(xa,xb,xc,foot(xa,xb,xc)).
% Following is Satz8.20a
-R(xa,xb,xc) | -M(s(xa,xc),xp,s(xb,xc)) | R(xb,xa,xp).
% Following is Satz8.20b
-R(xa,xb,xc) | -M(s(xa,xc),xp,s(xb,xc)) |   xb = xc | xa!=xp.
% Following is perp1
-perp(xa,xb,xp,xq) | perp(xb,xa,xp,xq).
% Following is ExtCol2
xa = xb | xc = xd | -Col(xa,xb,xc) | -Col(xa,xb,xd) | -Col(xc,xd,xp) 
|  Col(xa,xb,xp).
% Following is Satz8.21a
xa = xb |  perp(xa,xb,erect21a(xa,xb,xc),xa) | Col(xa,xb,xc).
xa = xb |  Col(xa,xb,erectAux21a(xa,xb,xc)) | Col(xa,xb,xc).
xa = xb | T(xc,erectAux21a(xa,xb,xc),erect21a(xa,xb,xc)) | Col(xa,xb,xc).
% Following is Satz8.21
xa = xb |  perp(xa,xb,erect(xa,xb,xc),xa).
xa = xb |  Col(xa,xb,erectAux(xa,xb,xc)).
xa = xb | T(xc,erectAux(xa,xb,xc),erect(xa,xb,xc)).
% Following is Satz8.22b
-le(xa,xp,xb,xq) | -perp(xa,xb,xa,xp) | -perp(xa,xb,xb,xq) |  -T(xp,xt,xq) 
|  -Col(xa,xb,xt) | M(xa,midpointAux(xa,xb,xp,xq,xt),xb).
% Following is Satz8.22
M(xa,midpoint(xa,xb),xb).
% Following is Satz8.24a
-perp(xp,xa,xa,xb) | -perp(xq,xb,xa,xb) | -Col(xa,xb,xt) | -T(xp,xt,xq) 
|  -T(xb,xr,xq) | -E(xa,xp,xb,xr) | xcx != ip(xp,xt,xq,xb,xr) | M(xa,xcx,xb).
% Following is Satz8.24b
-perp(xp,xa,xa,xb) | -perp(xq,xb,xa,xb) | -Col(xa,xb,xt) | -T(xp,xt,xq) 
|  -T(xb,xr,xq) | -E(xa,xp,xb,xr) | xcx != ip(xp,xt,xq,xb,xr) | M(xp,xcx,xr).
% Following is Satz8.24
-perp(xp,xa,xa,xb) | -perp(xq,xb,xa,xb) | -Col(xa,xb,xt) | -T(xp,xt,xq) 
|  -T(xb,xr,xq) | -E(xa,xp,xb,xr) | M(xp,midpoint(xa,xb),xr).
% Following is ext1
-Col(xa,xb,xc) | -Col(xa,xb,xd) |  xa =xb | Col(xa,xc,xd).
% Following is ExtPerp
-Col(xa,xb,xp) | -Col(xa,xb,xq) | xp=xq | xa = xb | -perpAt(xp,xq,xr,xc,xd) 
|  perpAt(xa,xb,xr,xc,xd).
% Following is ExtPerp2
-Col(xa,xb,xp) | -Col(xa,xb,xq) | xp=xq | xa = xb | -perp(xp,xq,xc,xd) 
|  perp(xa,xb,xc,xd).
% Following is ExtPerp3
xa = xb | xa = xc | xb = xc | xd = xc | xa = xd | -perp(xb,xa,xa,xc) 
|  -Col(xa,xc,xd) | perp(xb,xa,xa,xd).
% Following is ExtPerp4
-perp(xa,xb,xp,xq) | perp(xa,xb,xq,xp).
% Following is ExtPerp5
-Col(xa,xb,xp) | -Col(xa,xb,xq) | xp=xq | xa = xb | perp(xp,xq,xc,xd) 
|  -perp(xa,xb,xc,xd).
% Following is ExtPerp6
-Col(xa,xb,xp) | -Col(xa,xb,xq) | xp=xq  | xa=xb |  perp(xc,xd,xp,xq) 
|  -perp(xc,xd,xa,xb).
% Following is ExtSameSide1
-Col(xa,xb,xc) | xa = xb | xa = xc | -samesideline(xp,xq,xa,xb) 
|  samesideline(xp,xq,xa,xc).
% Following is ExtSameSide2
xa = xb  | -samesideline(xp,xq,xa,xb) | samesideline(xp,xq,xb,xa).
% Following is Satz9.2
-opposite(xa,xp,xq,xb) | opposite(xb,xp,xq,xa).
% Following is Satz9.3a
-opposite(xa,xp,xq,xc) | -Col(xp,xq,xm) | -M(xa,xm,xc) | -Col(xp,xq,xr) 
|  -sameside(xa,xr,xb) | opposite(xb,xp,xq,xc) | -T(xr,xb,xa).
% Following is Satz9.3
-opposite(xa,xp,xq,xc) | -Col(xp,xq,xm) | -M(xa,xm,xc) | -Col(xp,xq,xr) 
|  -sameside(xa,xr,xb) | opposite(xb,xp,xq,xc).
% Following is SideReflect
-sameside(xa,xb,xc) | sameside(s(xm,xa),s(xm,xb),s(xm,xc)).
% Following is Satz9.4a
-opposite(xa,xp,xq,xc) | xp = xq | -Col(xp,xq,xcs) | -Col(xp,xq,xr) 
|  -perp(xp,xq,xa,xr) | -perp(xp,xq,xc,xcs) | -M(xr,xm,xcs) 
|  -sameside(u,xr,xa) | -le(xcs,xc,xr,xa) | xr = xcs 
|  sameside(s(xm,u),xcs,xc).
% Following is Satz9.4a2
-opposite(xa,xp,xq,xc) | xp = xq | -Col(xp,xq,xcs) | -Col(xp,xq,xr) 
|  -perp(xp,xq,xa,xr) | -perp(xp,xq,xc,xcs) | -M(xr,xm,xcs) 
|  sameside(u,xr,xa) | -le(xcs,xc,xr,xa) | xr = xcs 
|  -sameside(s(xm,u),xcs,xc).
% Following is Satz9.4b
-opposite(xa,xp,xq,xc) | xp = xq | -Col(xp,xq,xcs) | -Col(xp,xq,xr) 
|  -perp(xp,xq,xa,xr) | -perp(xp,xq,xc,xcs) | -M(xr,xm,xcs) 
|  -sameside(u,xr,xa) | xr != xcs | sameside(s(xm,u),xcs,xc).
% Following is Satz9.4
-opposite(xa,xp,xq,xc) | xp = xq | -Col(xp,xq,xcs) | -Col(xp,xq,xr) 
|  -perp(xp,xq,xa,xr) | -perp(xp,xq,xc,xcs) | -M(xr,xm,xcs) 
|  -sameside(u,xr,xa) |  sameside(s(xm,u),xcs,xc).
% Following is Satz9.4c
-opposite(xa,xp,xq,xc) | xp = xq | -Col(xp,xq,xcs) | -Col(xp,xq,xr) 
|  -perp(xp,xq,xa,xr) | -perp(xp,xq,xc,xcs) | -M(xr,xm,xcs) 
|   -sameside(u,xr,xa) | -sameside(v,xcs,xc) | opposite(u,xp,xq,v).
% Following is Satz9.5
-opposite(xa,xp,xq,xc) | -Col(xp,xq,xr) | -sameside(xa,xr,xb) 
|  opposite(xb,xp,xq,xc).
% Following is Satz9.6
-T(xa,xc,xp) | -T(xb,xq,xc) | T(xa,op(xq,xb,xp,xc,xa),xb).
-T(xa,xc,xp) | -T(xb,xq,xc) | T(xp,xq,op(xq,xb,xp,xc,xa)).
% Following is Satz9.8
-opposite(xa,xp,xq,xc) | opposite(xb,xp,xq,xc) | -samesideline(xa,xb,xp,xq).
% Following is Satz9.9
-opposite(xa,xp,xq,xb) | -samesideline(xa,xb,xp,xq).
% Following is Satz9.13
xp=xq | -samesideline(xa,xb,xp,xq) | -samesideline(xb,xc,xp,xq) 
|  samesideline(xa,xc,xp,xq).
% Following is Lemma9.13a
-samesideline(xp,xq,xa,xb) | samesideline(xp,xq,xb,xa).
% Following is Lemma9.13b
xa = xb | -M(u,v,w) | -Col(xa,xb,u) | -Col(xa,xb,w) | Col(xa,xb,v).
% Following is Lemma9.13c
xd = xe | -T(xe,xd,xd1) | -samesideline(xa,xb,xd1,xe) 
|  samesideline(xa,xb,xd,xe).
% Following is Lemma9.13d
xa = xb | -samesideline(xp,xq,xa,xb) | samesideline(xq,xp,xa,xb).
% Following is Lemma9.13e
-opposite(xa,xp,xq,xb) | -samesideline(xb,xc,xp,xq) | opposite(xa,xp,xq,xc).
% Following is Lemma9.13g
xp=xq | -perpAt(xp,xq,xc,xa,xc) | -perpAt(xp,xq,xc,xb,xc) | xa = xc 
|  Col(xc,xa,xb).
% Following is Lemma9.13f-case1
xp = xq | Col(xp,xq,xr) | Col(xp,xq,xcs) | samesideline(xr,xcs,xp,xq) 
|  opposite(xr,xp,xq,xcs)| xp != foot(xp,xq,xr).
% Following is Lemma9.13f-case2
xp = xq | Col(xp,xq,xr) | Col(xp,xq,xcs) | samesideline(xr,xcs,xp,xq) 
|  opposite(xr,xp,xq,xcs) | xp = foot(xp,xq,xr).
% Following is Lemma9.13f
xp = xq | Col(xp,xq,xr) | Col(xp,xq,xcs) | samesideline(xr,xcs,xp,xq) 
|  opposite(xr,xp,xq,xcs).
% Following is Satz9.16
-samesideline(xa,xb,xp,xq) | -sameside(xa,xq,xr) | samesideline(xr,xb,xp,xq).
% Following is Satz9.19b
xc = xd | -Col(xc,xd,xp) | -Col(xa,xb,xp) | -sameside(xa,xp,xb) 
|  Col(xc,xd,xa) |  samesideline(xa,xb,xc,xd).
% Following is Satz10.2a
xa = xb | Col(xa,xb,midpoint(xp,reflect(xa,xb,xp))).
xa = xb | xp = reflect(xa,xb,xp) | perp(xa,xb,xp,reflect(xa,xb,xp)).
% Following is Satz10.2b
xa = xb | -Col(xa,xb,midpoint(xp,xp1)) | -perp(xa,xb,xp,xp1) 
|  xp1 = reflect(xa,xb,xp).
xa = xb | -Col(xa,xb,midpoint(xp,xp1)) | xp != xp1  | xp1 = reflect(xa,xb,xp).
% Following is Satz10.4
xa = xb | reflect(xa,xb,xp) != xp1 | reflect(xa,xb,xp1) = xp.
% Following is Satz10.5
xa = xb | reflect(xa,xb,reflect(xa,xb,xp)) = xp.
% Following defines the function insert
insert(xa,xb,xa1,xc1) = ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
% Following is Defn2.10
-AFS(xa,xb,xc,xd,za,zb,zc,zd) | T(xa,xb,xc).
-AFS(xa,xb,xc,xd,za,zb,zc,zd) | T(za,zb,zc).
-AFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xa,xb,za,zb).
-AFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xb,xc,zb,zc).
-AFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xa,xd,za,zd).
-AFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xb,xd,zb,zd).
-T(xa,xb,xc) | -T(za,zb,zc) | -E(xa,xb,za,zb) | -E(xb,xc,zb,zc) 
|  -E(xa,xd,za,zd) | -E(xb,xd,zb,zd)| AFS(xa,xb,xc,xd,za,zb,zc,zd).
% Following is Defn4.1
-IFS(xa,xb,xc,xd,za,zb,zc,zd) | T(xa,xb,xc).
-IFS(xa,xb,xc,xd,za,zb,zc,zd) | T(za,zb,zc).
-IFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xa,xc,za,zc).
-IFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xb,xc,zb,zc).
-IFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xa,xd,za,zd).
-IFS(xa,xb,xc,xd,za,zb,zc,zd) | E(xc,xd,zc,zd).
 -T(xa,xb,xc) | -T(za,zb,zc) | -E(xa,xc,za,zc) | -E(xb,xc,zb,zc) 
|  -E(xa,xd,za,zd) | -E(xc,xd,zc,zd)| IFS(xa,xb,xc,xd,za,zb,zc,zd).
% Following is Defn4.4
-E3(xa1,xa2,xa3,xb1,xb2,xb3) | E(xa1,xa2,xb1,xb2).
-E3(xa1,xa2,xa3,xb1,xb2,xb3) | E(xa1,xa3,xb1,xb3).
-E3(xa1,xa2,xa3,xb1,xb2,xb3) | E(xa2,xa3,xb2,xb3).
-E(xa1,xa2,xb1,xb2) | -E(xa1,xa3,xb1,xb3) | -E(xa2,xa3,xb2,xb3) 
|  E3(xa1,xa2,xa3,xb1,xb2,xb3).
% Following is Defn4.10
-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 is Defn4.15
-FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1) | Col(xa,xb,xc).
-FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1) | E3(xa,xb,xc,xa1,xb1,xc1).
-FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1) | E(xa,xd,xa1,xd1).
-FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1) | E(xb,xd,xb1,xd1).
-Col(xa,xb,xc) | -E3(xa,xb,xc,xa1,xb1,xc1) | -E(xa,xd,xa1,xd1) 
|  -E(xb,xd,xb1,xd1) | FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1).
% Following is Defn5.4
-le(xa,xb,xc,xd) | T(xc,insert(xa,xb,xc,xd),xd).
-le(xa,xb,xc,xd) | E(xa,xb,xc,insert(xa,xb,xc,xd)).
-T(xc,y,xd) | -E(xa,xb,xc,y) | le(xa,xb,xc,xd).
% Following is Defn6.1
-sameside(xa,xp,xb) | xa != xp.
-sameside(xa,xp,xb) | xb != xp.
-sameside(xa,xp,xb) | T(xp,xa,xb) | T(xp,xb,xa).
-T(xp,xa,xb) | xa=xp |xb=xp | sameside(xa,xp,xb).
-T(xp,xb,xa) | xa=xp | xb=xp | sameside(xa,xp,xb).
% Following is Defn7.1
-M(xa,xm,xb) | T(xa,xm,xb).
-M(xa,xm,xb) | E(xm,xa,xm,xb).
-T(xa,xm,xb) | -E(xm,xa,xm,xb) | M(xa,xm,xb).
% Following is Defn7.23
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) | T(xa1,xc,xa2).
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) |  T(xb1,xc,xb2).
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) | E(xc,xa1,xc,xb1).
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) | E(xc,xa2,xc,xb2).
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) | M(xa1,xm1,xb1).
-KF(xa1,xm1,xb1,xc,xb2,xm2,xa2) |  M(xa2,xm2,xb2).
 -T(xa1,xc,xa2) | -T(xb1,xc,xb2) | -E(xc,xa1,xc,xb1) | -E(xc,xa2,xc,xb2) 
|  -M(xa1,xm1,xb1) | -M(xa2,xm2,xb2) | KF(xa1,xm1,xb1,xc,xb2,xm2,xa2).
% Following is Defn8.1
-R(xa,xb,xc) | E(xa,xc,xa,s(xb,xc)).
R(xa,xb,xc) | -E(xa,xc,xa,s(xb,xc)).
% Following is Defn8.11a
-perpAt(y,z,x,y1,z1) | Col(y,z,x).
-perpAt(y,z,x,y1,z1) | Col(y1,z1,x).
-perpAt(y,z,x,y1,z1) |y != z.
-perpAt(y,z,x,y1,z1) |y1 != z1.
-perpAt(y,z,x,y1,z1) | -Col(y,z,u) | -Col(y1,z1,v) | R(u,x,v).
perpAt(y,z,x,y1,z1) | y = z | y1 = z1 | -Col(y,z,x) | -Col(y1,z1,x) 
|   Col(y,z,f811(y,z,y1,z1,x)).
perpAt(y,z,x,y1,z1) | y = z | y1 = z1 | -Col(y,z,x) | -Col(y1,z1,x) 
|   Col(y1,z1,g811(y,z,y1,z1,x)).
perpAt(y,z,x,y1,z1) | y = z | y1 = z1 | -Col(y,z,x) | -Col(y1,z1,x) 
|   -R(f811(y,z,y1,z1,x),x,g811(y,z,y1,z1,x)).
% Following is Defn8.11b
-perp(xp,xq,xp1,xq1) | perpAt(xp,xq,il(xp,xq,xp1,xq1),xp1,xq1).
perp(xp,xq,xp1,xq1) | -perpAt(xp,xq,x,xp1,xq1).
% Following is Defn9.1
xp = xq | Col(xp,xq,xa) | Col(xp,xq,xb) | -T(xa,xt,xb) | -Col(xp,xq,xt) 
|  opposite(xa,xp,xq,xb).
-opposite(xa,xp,xq,xb) | -Col(xp,xq,xa).
-opposite(xa,xp,xq,xb) | -Col(xp,xq,xb).
-opposite(xa,xp,xq,xb) | T(xa,il(xa,xb,xp,xq),xb).
-opposite(xa,xp,xq,xb) | Col(xp,xq,il(xa,xb,xp,xq)).
% Following is Defn9.7
-samesideline(xa,xb,xp,xq) | Col(xp,xq,ss1(xa,xb,xp,xq)).
-samesideline(xa,xb,xp,xq) | Col(xp,xq,ss2(xa,xb,xp,xq)).
-samesideline(xa,xb,xp,xq) | T(xa,ss1(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
-samesideline(xa,xb,xp,xq) | T(xb,ss2(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
-samesideline(xa,xb,xp,xq) | xa != ss1(xa,xb,xp,xq).
-samesideline(xa,xb,xp,xq) | xb != ss2(xa,xb,xp,xq).
-samesideline(xa,xb,xp,xq) | ss3(xa,xb,xp,xq) != ss1(xa,xb,xp,xq).
-samesideline(xa,xb,xp,xq) | ss3(xa,xb,xp,xq) != ss2(xa,xb,xp,xq).
-samesideline(xa,xb,xp,xq) | xp != xq.
-samesideline(xa,xb,xp,xq) | -Col(xp,xq,xa).
-samesideline(xa,xb,xp,xq) | -Col(xp,xq,xb).
-T(xa,xu,xc) | -T(xb,xv,xc) | -Col(xp,xq,xu) | -Col(xp,xq,xv) |xp=xq 
|  xc = xu | xc = xv | xa = xu | xb = xv | Col(xp,xq,xa) | Col(xp,xq,xb)  
|  samesideline(xa,xb,xp,xq).
end_of_list.

list(demodulators).
% Following is Satz 7.7, the only theorem in SST that is an equality.
s(xa,s(xa,xp)) = xp.
end_of_list.

list(sos).
% Following is the negated form of Satz10.6
a != b.
reflect(a,b,p) = p1.
p != reflect(a,b,p1).
end_of_list.