Sindbad~EG File Manager

Length of proof is 91.  Level of proof is 18.
 
---------------- PROOF ----------------
 
13 [] E(xa,xb,xa,xb).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
15 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
16 [] -E(xa,xb,xc,xd)|E(xb,xa,xc,xd).
17 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
22 [] -E(xa,xb,xc,xd)|E(xb,xa,xd,xc).
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
26 [] T(xa1,xa1,xb1).
27 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
29 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
31 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xc,xd).
32 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
47 [] -Col(xa,xb,xc)|Col(xc,xa,xb).
48 [] -Col(xa,xb,xc)|Col(xc,xb,xa).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
51 [] Col(xa,xa,xb).
52 [] Col(xa,xb,xa).
56 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xp,xa,xq)| -E(xb,xp,xb,xq)|E(xc,xp,xc,xq).
84 [] -sameside(xa,xp,xb)|Col(xa,xp,xb).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
89 [] -sameside(xa,xp,xb)| -sameside(xb,xp,xc)|sameside(xa,xp,xc).
98 [] xp=xq|xp=xr| -T(xq,xp,xr)|xa!=xp|Col(xa,xp,xq).
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).
109 [] M(xa,xm,xa)|xm!=xa.
110 [] M(xp,xa,s(xa,xp)).
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.
123 [] -M(xp,xa,xq)| -M(xp,xb,xq)|xa=xb.
132 [] -R(xa,xb,xc)|R(xc,xb,xa).
133 [] -R(xa,xb,xc)|xa=xb| -Col(xb,xa,xa1)|R(xa1,xb,xc).
134 [] -R(xa,xb,xc)|R(xa,xb,s(xb,xc)).
138 [] -R(xa,xb,xa)|xa=xb.
142 [] -perp(xa,xb,xp,xq)|perp(xp,xq,xa,xb).
152 [] 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).
159 [] 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).
164 [] -R(xa,xb,xc)| -M(s(xa,xc),xp,s(xb,xc))|xb=xc|xa!=xp.
165 [] -perp(xa,xb,xp,xq)|perp(xb,xa,xp,xq).
174 [] M(xa,midpoint(xa,xb),xb).
183 [] -Col(xa,xb,xp)| -Col(xa,xb,xq)|xp=xq|xa=xb|perp(xp,xq,xc,xd)| -perp(xa,xb,xc,xd).
215 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))| -perp(xa,xb,xp,xp1)|xp1=reflect(xa,xb,xp).
224 [] xa=xb|E(xp,xq,reflect(xa,xb,xp),reflect(xa,xb,xq)).
245 [] Col(xa,xb,xc)| -T(xa,xb,xc).
246 [] Col(xa,xb,xc)| -T(xb,xc,xa).
247 [] Col(xa,xb,xc)| -T(xc,xa,xb).
257 [] -sameside(xa,xp,xb)|xb!=xp.
259 [] -T(xp,xa,xb)|xa=xp|xb=xp|sameside(xa,xp,xb).
261 [] -M(xa,xm,xb)|T(xa,xm,xb).
271 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
272 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
282 [] perp(xp,xq,xp1,xq1)| -perpAt(xp,xq,x,xp1,xq1).
301 [] R(a,b,c).
302 [] R(a1,b,c).
303 [] E(a,b,a1,b).
304 [] -E(a,c,a1,c).
305 [] cz=midpoint(a,a1).
306 [] cstar=s(b,c).
307 [] bstar=midpoint(c,cstar).
308 [] a1!=a|a1=a.
309 [] b=cz|b!=cz.
312 [] s(b,c)=cstar.
313 [] midpoint(c,cstar)=bstar.
406 [binary,301.1,271.1,demod,312] E(a,c,a,cstar).
409 [binary,301.1,134.1,demod,312] R(a,b,cstar).
410 [binary,301.1,132.1] R(c,b,a).
412 [hyper,133,301,52] a=b|R(b,b,c).
416 [binary,302.1,134.1,demod,312] R(a1,b,cstar).
420 [binary,303.1,22.1] E(b,a,b,a1).
439 [binary,304.1,16.2] -E(c,a,a1,c).
450 [para_from,305.1.2,174.1.2] M(a,cz,a1).
467 [para_from,306.1.2,116.1.1] cstar!=c|c=b.
470 [para_from,306.1.2,112.2.2] -M(c,b,x)|x=cstar.
471 [para_from,306.1.2,110.1.3] M(c,b,cstar).
480 [para_from,307.1.2,174.1.2] M(c,bstar,cstar).
484 [para_from,308.2.1,304.1.3,unit_del,13] a1!=a.
519 [ur,15,406,304] -E(a,cstar,a1,c).
520 [binary,409.1,271.1] E(a,cstar,a,s(b,cstar)).
527 [binary,410.1,271.1] E(c,a,c,s(b,a)).
540 [para_from,412.1.1,301.1.1,factor_simp] R(b,b,c).
541 [binary,416.1,271.1] E(a1,cstar,a1,s(b,cstar)).
590 [binary,450.1,261.1] T(a,cz,a1).
593 [binary,450.1,112.1] a1=s(cz,a).
596 [binary,450.1,107.1] M(a1,cz,a).
651 [hyper,123,471,174,demod,313] b=bstar.
661 [binary,480.1,261.1] T(c,bstar,cstar).
696 [ur,111,450,484] -M(a,cz,a).
739 [binary,527.1,17.1] E(c,a,s(b,a),c).
795 [binary,590.1,246.2] Col(a1,a,cz).
811 [binary,590.1,25.1] T(a1,cz,a).
834 [para_into,593.1.2,117.1.1,unit_del,484] a!=cz.
838 [para_from,593.1.1,439.1.3] -E(c,a,s(cz,a),c).
839 [para_from,593.1.1,420.1.4] E(b,a,b,s(cz,a)).
862 [hyper,123,596,174] cz=midpoint(a1,a).
921 [binary,651.1,257.2] -sameside(x,bstar,b).
928 [binary,661.1,247.2] Col(bstar,cstar,c).
967 [binary,696.1,109.1] cz!=a.
982 [para_into,739.1.3.1,309.1.1,unit_del,838] b!=cz.
991 [binary,795.1,102.2,unit_del,484] Col(a,a1,cz).
1000 [hyper,56,795,541,520,unit_del,484] E(cz,cstar,cz,s(b,cstar)).
1041 [binary,834.1,138.2] -R(a,cz,a).
1096 [binary,838.1,17.2] -E(c,a,c,s(cz,a)).
1099 [binary,839.1,272.2] R(b,cz,a).
1131 [ur,86,921,52] T(b,bstar,b).
1147 [binary,928.1,48.1] Col(c,cstar,bstar).
1170 [ur,259,590,967,484] sameside(cz,a,a1).
1234 [para_into,982.1.1,651.1.1] bstar!=cz.
1259 [binary,1000.1,272.2] R(cz,b,cstar).
1288 [binary,1096.1,271.2] -R(c,cz,a).
1306 [ur,133,1099,982,1041] -Col(cz,b,a).
1309 [para_into,1099.1.1,467.2.2,unit_del,1288] cstar!=c.
1330 [binary,1131.1,32.1,unit_del,26] T(b,bstar,x).
1331 [binary,1131.1,31.2,unit_del,24] T(x,bstar,b).
1418 [para_into,1259.1.2,651.1.1] R(cz,bstar,cstar).
1446 [binary,1306.1,50.2] -Col(cz,a,b).
1448 [binary,1306.1,47.2] -Col(b,a,cz).
1481 [ur,102,1309,52] Col(c,cstar,cstar).
1503 [ur,27,24,1309] -T(c,cstar,c).
1513 [binary,1330.1,247.2] Col(bstar,x,b).
1514 [binary,1330.1,246.2] Col(x,b,bstar).
1546 [binary,1331.1,246.2] Col(b,x,bstar).
1590 [binary,1446.1,245.1] -T(cz,a,b).
1596 [binary,1446.1,84.2] -sameside(cz,a,b).
1598 [ur,103,967,51,51,51,1446] x=x.
1615 [ur,98,834,38,37,1448] b!=a.
1643 [binary,1503.1,86.3,unit_del,52] sameside(c,cstar,c).
1699 [para_into,1514.1.3,651.1.2] Col(x,b,b).
1743 [ur,29,811,1590] -T(a1,a,b).
1751 [ur,89,1170,1596] -sameside(a1,a,b).
1764 [binary,1598.1,109.2] M(x,x,x).
1819 [ur,98,1615,38,37,1306] cz!=b.
1847 [binary,1643.1,257.1] c!=cstar.
1876 [binary,1743.1,86.3,unit_del,1751] -Col(a1,a,b).
2011 [ur,103,1234,1819,1514,52,52] Col(bstar,cz,cz).
2012 [ur,103,982,1819,1699,52,52] Col(b,cz,cz).
2104 [binary,1876.1,50.2] -Col(a1,b,a).
2105 [binary,1876.1,49.2] -Col(a,a1,b).
2166 [para_into,2012.1.3,862.1.1] Col(b,cz,midpoint(a1,a)).
2182 [ur,98,1615,38,37,2104] a1!=b.
2290 [ur,98,2182,38,37,2105] a!=a1.
2356 [ur,159,2290,991,52,834,2105,1099] perp(a,a1,b,cz).
2396 [binary,2356.1,165.1] perp(a1,a,b,cz).
2410 [binary,2396.1,142.1] perp(b,cz,a1,a).
2420 [binary,2410.1,215.3,unit_del,982,2166] a=reflect(b,cz,a1).
2499 [para_from,2420.1.2,224.2.3,unit_del,982] E(a1,x,a,reflect(b,cz,x)).
2503 [binary,2499.1,14.1] E(a,reflect(b,cz,x),a1,x).
4323 [binary,470.1,109.1,unit_del,1847] b!=c.
4351 [ur,164,540,1764,4323,demod,312] b!=cstar.
4537 [para_into,4351.1.1,651.1.1] bstar!=cstar.
4572 [ur,152,1234,1847,1147,52,2011,1481,1234,4537,1418] perpAt(bstar,cz,bstar,c,cstar).
4643 [binary,4572.1,282.2] perp(bstar,cz,c,cstar).
4676 [hyper,183,1513,2011,4643,unit_del,982,1234] perp(b,cz,c,cstar).
4683 [binary,4676.1,215.3,demod,313,unit_del,982,1546] cstar=reflect(b,cz,c).
4736 [para_from,4683.1.1,519.1.2] -E(a,reflect(b,cz,c),a1,c).
4737 [binary,4736.1,2503.1] $F.