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Length of proof is 49.  Level of proof is 20.
 
---------------- PROOF ----------------
 
26 [] T(xa1,xa1,xb1).
52 [] Col(xa,xb,xa).
102 [] xp=xq| -Col(xp,xq,xr)|Col(xq,xp,xr).
103 [] xa=xb|xp=xq| -Col(xp,xq,xa)| -Col(xp,xq,xb)| -Col(xp,xq,xr)|Col(xa,xb,xr).
107 [] -M(xa,xm,xb)|M(xb,xm,xa).
108 [] -M(xa,xm,xa)|xm=xa.
109 [] M(xa,xm,xa)|xm!=xa.
111 [] -M(xp,xa,xr)| -M(xp,xa,xq)|xr=xq.
112 [] -M(xp,xa,xq)|xq=s(xa,xp).
116 [] s(xa,xp)!=xp|xp=xa.
117 [] s(xa,xp)=xp|xp!=xa.
132 [] -R(xa,xb,xc)|R(xc,xb,xa).
136 [] -R(xa,xb,xc)| -R(xa1,xb,xc)| -T(xa,xc,xa1)|xb=xc.
137 [] -R(xa,xb,xc)| -R(xa,xc,xb)|xb=xc.
142 [] -perp(xa,xb,xp,xq)|perp(xp,xq,xa,xb).
153 [] -perp(xa,xb,xp,xq)| -Col(xa,xb,xp)| -Col(xa,xb,xq).
154 [] -perp(xa,xb,xp,xq)| -Col(xa,xb,xc)| -Col(xp,xq,xc)|perpAt(xa,xb,xc,xp,xq).
166 [] xa=xb|xc=xd| -Col(xa,xb,xc)| -Col(xa,xb,xd)| -Col(xc,xd,xp)|Col(xa,xb,xp).
174 [] M(xa,midpoint(xa,xb),xb).
182 [] -perp(xa,xb,xp,xq)|perp(xa,xb,xq,xp).
213 [] xa=xb|Col(xa,xb,midpoint(xp,reflect(xa,xb,xp))).
214 [] xa=xb|xp=reflect(xa,xb,xp)|perp(xa,xb,xp,reflect(xa,xb,xp)).
235 [] Col(xa,xb,xc)| -T(xa,xb,xc).
236 [] Col(xa,xb,xc)| -T(xb,xc,xa).
251 [] -M(xa,xm,xb)|T(xa,xm,xb).
267 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
273 [] xp=xq|Col(xp,xq,xa)|Col(xp,xq,xb)| -T(xa,xt,xb)| -Col(xp,xq,xt)|opposite(xa,xp,xq,xb).
274 [] -opposite(xa,xp,xq,xb)| -Col(xp,xq,xa).
291 [] a!=b.
292 [] Col(a,b,midpoint(p,p1)).
293 [] perp(a,b,p,p1)|p=p1.
294 [] p1!=reflect(a,b,p).
295 [] q=reflect(a,b,p).
296 [] r=midpoint(p,q).
297 [] j=midpoint(p,p1).
298 [] p=p1|p!=p1.
300 [] reflect(a,b,p)=q.
301 [] midpoint(p,q)=r.
302 [] midpoint(p,p1)=j.
392 [binary,292.1,274.2,demod,302] -opposite(j,a,b,x).
395 [binary,292.1,166.3,demod,302,302,unit_del,291] j=x| -Col(a,b,x)| -Col(j,x,y)|Col(a,b,y).
396 [binary,292.1,153.2,demod,302] -perp(a,b,j,x)| -Col(a,b,x).
405 [hyper,273,26,292,demod,302,302,unit_del,291,392,factor_simp] Col(a,b,j).
471 [para_from,295.1.2,294.1.2] p1!=q.
472 [para_from,295.1.2,214.2.2,demod,300,unit_del,291] p=q|perp(a,b,p,q).
473 [para_from,295.1.2,213.2.3.2,demod,301,unit_del,291] Col(a,b,r).
482 [para_from,296.1.2,174.1.2] M(p,r,q).
490 [para_from,297.1.2,174.1.2] M(p,j,p1).
518 [para_into,472.1.1,298.1.1,unit_del,471] perp(a,b,p,q)|p!=p1.
558 [binary,482.1,251.1] T(p,r,q).
561 [binary,482.1,112.1] q=s(r,p).
564 [binary,482.1,107.1] M(q,r,p).
571 [binary,490.1,251.1] T(p,j,p1).
580 [ur,111,490,471] -M(p,j,q).
583 [para_into,490.1.3,298.1.2] M(p,j,p)|p!=p1.
597 [binary,558.1,236.2] Col(q,p,r).
598 [binary,558.1,235.2] Col(p,r,q).
646 [para_from,561.1.2,116.1.1] q!=p|p=r.
657 [hyper,111,564,564] p=p.
665 [binary,571.1,236.2] Col(p1,p,j).
698 [binary,580.1,107.2] -M(q,j,p).
702 [binary,583.1,108.1] p!=p1|j=p.
815 [para_from,702.2.2,598.1.1] Col(j,r,q)|p!=p1.
823 [para_from,702.2.2,518.1.3,factor_simp] perp(a,b,j,q)|p!=p1.
828 [binary,815.1,395.3,unit_del,473] p!=p1|j=r|Col(a,b,q).
841 [binary,823.1,396.1] p!=p1| -Col(a,b,q).
861 [para_from,828.2.1,698.1.2,unit_del,564] p!=p1|Col(a,b,q).
879 [binary,861.2,841.2,factor_simp] p!=p1.
880 [binary,879.1,293.2] perp(a,b,p,p1).
899 [ur,111,490,879] -M(p,j,p).
903 [ur,102,879,52] Col(p1,p,p).
930 [binary,880.1,182.1] perp(a,b,p1,p).
946 [binary,899.1,109.1] j!=p.
973 [hyper,154,930,405,665] perpAt(a,b,j,p1,p).
1029 [hyper,267,973,473,903] R(r,j,p).
1046 [binary,1029.1,132.1] R(p,j,r).
1049 [ur,136,1029,26,946] -R(p,j,p).
1053 [para_into,1029.1.1,646.2.2,unit_del,1049] q!=p.
1127 [para_into,1053.1.1,561.1.1] s(r,p)!=p.
1128 [para_into,1053.1.1,472.1.2,unit_del,657] perp(a,b,p,q).
1130 [binary,1127.1,117.1] p!=r.
1145 [binary,1128.1,182.1] perp(a,b,q,p).
1207 [ur,103,1053,1130,598,52,52] Col(q,p,p).
1237 [binary,1145.1,142.1] perp(q,p,a,b).
1304 [hyper,154,1237,597,473] perpAt(q,p,r,a,b).
1309 [hyper,267,1304,1207,405] R(p,r,j).
1322 [binary,1309.1,137.2,unit_del,1046] j=r.
1341 [para_from,1322.1.1,698.1.2] -M(q,r,p).
1342 [binary,1341.1,564.1] $F.