Sindbad~EG File Manager

Length of proof is 30.  Level of proof is 11.

---------------- PROOF ----------------

1 [] E(x,y,y,x).
13 [] E(xa,xb,xa,xb).
18 [] E(xa,xa,xb,xb).
24 [] T(xa,xb,xb).
26 [] T(xa1,xa1,xb1).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
51 [] Col(xa,xa,xb).
83 [] -sameside(xa,xp,xb)|Col(xa,xp,xb).
86 [] xa=xp|sameside(xa,xp,xa).
87 [] -sameside(xa,xp,xb)|sameside(xb,xp,xa).
91 [] xr=xa|xb=xc| -sameside(xp,xa,xr)| -E(xa,xp,xb,xc)| -sameside(xq,xa,xr)| -E(xa,xq,xb,xc)|xp=xq.
107 [] M(xa,xm,xa)|xm!=xa.
128 [] -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).
159 [] Col(xa,xb,xc)|Col(xa,xb,foot(xa,xb,xc)).
160 [] Col(xa,xb,xc)|perp(xa,xb,xc,foot(xa,xb,xc)).
164 [] xa=xb|xp=xq| -Col(xa,xb,xp)| -Col(xa,xb,xq)| -Col(xa,xb,xt)|Col(xp,xq,xt).
165 [] xa=xb|xc=xd| -Col(xa,xb,xc)| -Col(xa,xb,xd)| -Col(xc,xd,xp)|Col(xa,xb,xp).
173 [] M(xa,midpoint(xa,xb),xb).
185 [] -opposite(xa,xp,xq,xb)|opposite(xb,xp,xq,xa).
192 [] -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).
193 [] -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).
214 [] Col(xa,xb,xc)| -T(xa,xb,xc).
216 [] Col(xa,xb,xc)| -T(xc,xa,xb).
225 [] -sameside(xa,xp,xb)|xa!=xp.
226 [] -sameside(xa,xp,xb)|xb!=xp.
252 [] xp=xq|Col(xp,xq,xa)|Col(xp,xq,xb)| -T(xa,xt,xb)| -Col(xp,xq,xt)|opposite(xa,xp,xq,xb).
253 [] -opposite(xa,xp,xq,xb)| -Col(xp,xq,xa).
254 [] -opposite(xa,xp,xq,xb)| -Col(xp,xq,xb).
270 [] opposite(a,p,q,c).
271 [] Col(p,q,r).
272 [] sameside(a,r,b).
273 [] -opposite(b,p,q,c).
277 [] m=midpoint(cx,cz).
279 [] foot(p,q,a)=cx.
281 [] foot(p,q,c)=cz.
286 [binary,270.1,254.1] -Col(p,q,c).
287 [binary,270.1,253.1] -Col(p,q,a).
288 [binary,270.1,185.1] opposite(c,p,q,a).
289 [hyper,254,270,160,demod,281] perp(p,q,c,cz).
290 [hyper,254,270,159,demod,281] Col(p,q,cz).
291 [hyper,253,270,160,demod,279] perp(p,q,a,cx).
292 [hyper,253,270,159,demod,279] Col(p,q,cx).
344 [binary,272.1,226.1] b!=r.
345 [binary,272.1,225.1] a!=r.
353 [binary,272.1,87.1] sameside(b,r,a).
390 [hyper,91,272,1,272,1,unit_del,344,345] a=a.
441 [para_from,277.1.2,173.1.2] M(cx,m,cz).
690 [binary,390.1,107.2] M(a,a,a).
774 [binary,287.1,216.1] -T(a,p,q).
776 [binary,287.1,214.1] -T(p,q,a).
788 [binary,287.1,49.2] -Col(q,p,a).
1200 [binary,353.1,83.1] Col(b,r,a).
2295 [ur,128,24,24,13,18,690,774] -M(p,q,p).
2365 [ur,128,26,26,18,13,690,776] -M(q,p,q).
5335 [binary,2295.1,107.1] q!=p.
5403 [ur,164,5335,51,51,51,788] x=x.
5489 [binary,5403.1,107.2] M(x,x,x).
6168 [binary,2365.1,107.1] p!=q.
6237 [ur,165,6168,344,271,1200,287] -Col(p,q,b).
12285 [ur,252,6168,6237,286,290,273] -T(b,cz,c).
23138 [ur,128,24,24,13,18,5489,12285] -M(cz,c,cz).
32315 [binary,23138.1,107.1] c!=cz.
32365 [binary,32315.1,86.1] sameside(c,cz,c).
42446 [hyper,192,288,292,290,289,291,173,32365,unit_del,6168] sameside(s(midpoint(cz,cx),c),cx,a).
42465 [ur,193,270,6168,290,292,291,289,441,32365] -sameside(x,cx,a).
42466 [binary,42465.1,42446.1] $F.