Sindbad~EG File Manager

Length of proof is 56.  Level of proof is 14.
 
---------------- PROOF ----------------
 
2 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
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).
18 [] E(xa,xa,xb,xb).
28 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
48 [] -Col(xa,xb,xc)|Col(xc,xb,xa).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
51 [] Col(xa,xa,xb).
52 [] Col(xa,xb,xa).
53 [] -Col(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|Col(xa1,xb1,xc1).
56 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xp,xa,xq)| -E(xb,xp,xb,xq)|E(xc,xp,xc,xq).
58 [] -T(xa,xc,xb)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
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).
112 [] -M(xp,xa,xq)|xq=s(xa,xp).
113 [] s(xa,s(xa,xp))=xp.
114 [] s(xa,xp)!=xr|s(xa,xq)!=xr|xp=xq.
115 [] s(xa,xp)!=s(xa,xq)|xp=xq.
117 [] s(xa,xp)=xp|xp!=xa.
123 [] -M(xp,xa,xq)| -M(xp,xb,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).
174 [] M(xa,midpoint(xa,xb),xb).
199 [] -opposite(xa,xp,xq,xc)|opposite(xb,xp,xq,xc)| -samesideline(xa,xb,xp,xq).
201 [] xp=xq| -samesideline(xa,xb,xp,xq)| -samesideline(xb,xc,xp,xq)|samesideline(xa,xc,xp,xq).
205 [] xa=xb| -samesideline(xp,xq,xa,xb)|samesideline(xq,xp,xa,xb).
215 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))| -perp(xa,xb,xp,xp1)|xp1=reflect(xa,xb,xp).
216 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))|xp!=xp1|xp1=reflect(xa,xb,xp).
220 [] xa=xb|reflect(xa,xb,xp)!=reflect(xa,xb,xq)|xp=xq.
222 [] xa=xb| -Col(xa,xb,xp)|reflect(xa,xb,xp)=xp.
224 [] xa=xb|E(xp,xq,reflect(xa,xb,xp),reflect(xa,xb,xq)).
229 [] xa=xb|reflect(xa,xb,xp)!=xp1|Col(xa,xb,xp)|opposite(xp,xa,xb,xp1).
250 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa1,xa3,xb1,xb3).
251 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa2,xa3,xb2,xb3).
252 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
256 [] Col(xa,xb,xc)| -T(xc,xa,xb).
265 [] -sameside(xa,xp,xb)|xa!=xp.
272 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
281 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
291 [] perp(xp,xq,xp1,xq1)| -perpAt(xp,xq,x,xp1,xq1).
295 [] -opposite(xa,xp,xq,xb)|T(xa,il(xa,xb,xp,xq),xb).
296 [] -opposite(xa,xp,xq,xb)|Col(xp,xq,il(xa,xb,xp,xq)).
305 [] -samesideline(xa,xb,xp,xq)|xp!=xq.
306 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xa).
309 [] s(xa,s(xa,xp))=xp.
310 [] a!=b.
311 [] -Col(a,b,c).
313 [] E(a,b,a1,b1).
314 [] E3(a,b,c,a1,b1,c1).
315 [] samesideline(c1,p,a1,b1).
316 [] E3(a,b,c,a1,b1,c2).
317 [] samesideline(c2,p,a1,b1).
318 [] c1!=c2.
319 [] cstar=reflect(a1,b1,c2).
322 [] reflect(a1,b1,c2)=cstar.
323 [] il(c1,cstar,a1,b1)=t.
396 [binary,310.1,115.2] s(x,a)!=s(x,b).
410 [ur,102,310,52] Col(b,a,a).
448 [ur,103,310,51,51,51,311] x=x.
473 [hyper,252,313,313,18] E3(a,b,b,a1,b1,b1).
480 [binary,314.1,251.1] E(b,c,b1,c1).
481 [binary,314.1,250.1] E(a,c,a1,c1).
484 [binary,315.1,305.1] a1!=b1.
489 [binary,315.1,205.2,unit_del,484] samesideline(p,c1,a1,b1).
499 [binary,316.1,251.1] E(b,c,b1,c2).
500 [binary,316.1,250.1] E(a,c,a1,c2).
502 [binary,317.1,306.1] -Col(a1,b1,c2).
561 [para_from,319.1.2,224.2.4,unit_del,484] E(x,c2,reflect(a1,b1,x),cstar).
581 [ur,114,113,396,demod,309] b!=a.
594 [hyper,103,410,52,52,unit_del,310,581] Col(a,b,b).
605 [binary,448.1,117.2] s(x,x)=x.
629 [binary,473.1,53.2,unit_del,594] Col(a1,b1,b1).
646 [binary,481.1,14.1] E(a1,c1,a,c).
716 [hyper,201,317,489,unit_del,484] samesideline(c2,c1,a1,b1).
734 [hyper,2,480,499] E(b1,c1,b1,c2).
751 [hyper,2,481,500] E(a1,c1,a1,c2).
769 [ur,229,484,448,502,demod,322] opposite(c2,a1,b1,cstar).
790 [hyper,15,500,561] E(a,c,reflect(a1,b1,a1),cstar).
867 [ur,114,605,318] s(c1,c2)!=c1.
889 [binary,629.1,222.2,unit_del,484] reflect(a1,b1,b1)=b1.
948 [hyper,15,734,561] E(b1,c1,reflect(a1,b1,b1),cstar).
983 [hyper,199,769,716] opposite(c1,a1,b1,cstar).
998 [para_into,790.1.3,222.3.1,unit_del,484,52] E(a,c,a1,cstar).
1010 [ur,114,605,867,demod,309] c2!=c1.
1052 [para_into,948.1.3,889.1.1] E(b1,c1,b1,cstar).
1053 [binary,983.1,296.1,demod,323] Col(a1,b1,t).
1054 [binary,983.1,295.1,demod,323] T(c1,t,cstar).
1090 [hyper,15,646,998] E(a1,c1,a1,cstar).
1108 [ur,220,484,1010,demod,322] cstar!=reflect(a1,b1,c1).
1182 [hyper,56,1053,751,734,unit_del,484] E(t,c1,t,c2).
1208 [binary,1054.1,256.2] Col(t,cstar,c1).
1253 [hyper,56,1053,1090,1052,unit_del,484] E(t,c1,t,cstar).
1309 [ur,58,1182,1182,318] -T(t,c1,t).
1323 [binary,1208.1,50.1] Col(t,c1,cstar).
1325 [binary,1208.1,48.1] Col(c1,cstar,t).
1387 [binary,1253.1,272.2,unit_del,1054] M(c1,t,cstar).
1499 [ur,28,1054,1309] -T(t,c1,cstar).
1512 [binary,1323.1,86.2,unit_del,1499] sameside(t,c1,cstar).
1539 [binary,1387.1,112.1] cstar=s(t,c1).
1547 [hyper,123,174,1387] midpoint(c1,cstar)=t.
1603 [binary,1512.1,265.1] t!=c1.
1636 [para_from,1539.1.1,1090.1.4] E(a1,c1,a1,s(t,c1)).
1638 [para_from,1539.1.1,1052.1.4] E(b1,c1,b1,s(t,c1)).
1677 [para_from,1547.1.2,1053.1.3] Col(a1,b1,midpoint(c1,cstar)).
1770 [binary,1636.1,281.2] R(a1,t,c1).
1791 [binary,1638.1,281.2] R(b1,t,c1).
1825 [binary,1677.1,216.2,unit_del,484,1108] c1!=cstar.
1826 [binary,1677.1,215.2,unit_del,484,1108] -perp(a1,b1,c1,cstar).
2003 [binary,1826.1,291.1] -perpAt(a1,b1,x,c1,cstar).
2011 [ur,152,484,1825,1325,1053,629,52,1603,1791,2003] t=b1.
2012 [ur,152,484,1825,1325,1053,52,52,1603,1770,2003] t=a1.
2122 [para_from,2012.1.1,2011.1.1] a1=b1.
2123 [binary,2122.1,484.1] $F.