Sindbad~EG File Manager

Length of proof is 78.  Level of proof is 12.
 
---------------- PROOF ----------------
 
1 [] E(x,y,y,x).
2 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
4 [] T(x,y,ext(x,y,w,v)).
5 [] E(y,ext(x,y,w,v),w,v).
17 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
19 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
26 [] T(xa1,xa1,xb1).
28 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
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).
46 [] -Col(xa,xb,xc)|Col(xb,xc,xa).
48 [] -Col(xa,xb,xc)|Col(xc,xb,xa).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
52 [] Col(xa,xb,xa).
61 [] -T(xa,xb,xd)| -T(xa,xc,xd)|T(xa,xb,xc)|T(xa,xc,xb).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
87 [] xa=xp|sameside(xa,xp,xa).
98 [] xp=xq|xp=xr| -T(xq,xp,xr)|xa!=xp|Col(xa,xp,xq).
202 [] -samesideline(xp,xq,xa,xb)|samesideline(xp,xq,xb,xa).
204 [] xd=xe| -T(xe,xd,xd1)| -samesideline(xa,xb,xd1,xe)|samesideline(xa,xb,xd,xe).
232 [] xa=xb|Col(xa,xb,xc)|Col(xa1,xb1,xp)| -E(xa,xb,xa1,xb1)|E3(xa,xb,xc,xa1,xb1,triangle(xa,xb,xc,xa1,xb1,xp)).
233 [] xa=xb|Col(xa,xb,xc)|Col(xa1,xb1,xp)| -E(xa,xb,xa1,xb1)|samesideline(triangle(xa,xb,xc,xa1,xb1,xp),xp,xa1,xb1).
240 [] -sameside(xa1,xb,xa)| -sameside(xc1,xb,xc)| -sameside(xd1,xe,xd)| -sameside(xf1,xe,xf)| -E3(xa1,xb,xc1,xd1,xe,xf1)|congruent(xa,xb,xc,xd,xe,xf).
270 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa1,xa3,xb1,xb3).
271 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa2,xa3,xb2,xb3).
272 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
273 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
275 [] Col(xa,xb,xc)| -T(xb,xc,xa).
276 [] Col(xa,xb,xc)| -T(xc,xa,xb).
286 [] -sameside(xa,xp,xb)|xb!=xp.
326 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xa).
336 [] -Col(a,b,c).
337 [] -Col(d,e,p).
338 [] -congruent(a,b,c,d,e,x)| -samesideline(x,p,d,e).
339 [] a1=ext(b,a,e,d).
340 [] c1=ext(b,c,e,f).
341 [] d1=ext(e,d,b,a).
346 [] triangle(b,a1,c1,e,d1,p)=f1.
426 [binary,336.1,276.1] -T(c,a,b).
427 [binary,336.1,275.1] -T(b,c,a).
433 [binary,336.1,50.2] -Col(a,c,b).
443 [binary,337.1,276.1] -T(p,d,e).
444 [binary,337.1,275.1] -T(e,p,d).
450 [binary,337.1,50.2] -Col(d,p,e).
452 [binary,337.1,48.2] -Col(p,e,d).
470 [para_from,339.1.2,5.1.2] E(a,a1,e,d).
471 [para_from,339.1.2,4.1.3] T(b,a,a1).
485 [para_from,340.1.2,4.1.3] T(b,c,c1).
498 [para_from,341.1.2,5.1.2] E(d,d1,b,a).
499 [para_from,341.1.2,4.1.3] T(e,d,d1).
522 [binary,426.1,25.2] -T(b,a,c).
529 [ur,31,24,426] -T(b,a,b).
551 [ur,32,26,427] -T(b,c,b).
561 [binary,433.1,275.1] -T(c,b,a).
577 [binary,443.1,25.2] -T(e,d,p).
584 [ur,31,24,443] -T(e,d,e).
616 [binary,450.1,275.1] -T(p,e,d).
629 [binary,470.1,17.1] E(a,a1,d,e).
640 [hyper,2,470,1] E(e,d,a1,a).
642 [binary,471.1,275.2] Col(a1,b,a).
658 [binary,471.1,25.1] T(a1,a,b).
676 [binary,485.1,275.2] Col(c1,b,c).
692 [binary,485.1,25.1] T(c1,c,b).
712 [binary,498.1,17.1] E(d,d1,a,b).
724 [hyper,2,498,1] E(b,a,d1,d).
749 [binary,499.1,275.2] Col(d1,e,d).
765 [binary,499.1,25.1] T(d1,d,e).
792 [ur,61,471,427,522] -T(b,c,a1).
795 [ur,61,485,427,522] -T(b,a,c1).
804 [ur,32,471,522] -T(b,a1,c).
883 [ur,28,471,561] -T(c,b,a1).
896 [ur,61,499,444,577] -T(e,p,d1).
908 [ur,32,499,577] -T(e,d1,p).
920 [binary,584.1,86.3,unit_del,52] sameside(e,d,e).
960 [ur,28,499,616] -T(p,e,d1).
1050 [ur,29,658,529] -T(a1,b,a).
1110 [ur,29,692,551] -T(c1,b,c).
1123 [hyper,19,499,658,640,712] E(e,d1,a1,b).
1179 [hyper,19,471,765,724,629] E(b,a1,d1,e).
1196 [ur,29,765,584] -T(d1,e,d).
1212 [binary,792.1,25.2] -T(a1,c,b).
1257 [ur,32,471,795] -T(b,a1,c1).
1278 [binary,804.1,273.4,unit_del,1212,883] -Col(a1,c,b).
1280 [binary,804.1,273.2,unit_del,1212,883] -Col(b,a1,c).
1328 [ur,29,692,883] -T(c1,b,a1).
1348 [binary,896.1,25.2] -T(d1,p,e).
1369 [binary,908.1,273.4,unit_del,1348,960] -Col(d1,p,e).
1371 [binary,908.1,273.2,unit_del,1348,960] -Col(e,d1,p).
1405 [binary,920.1,286.1] e!=d.
1441 [binary,1050.1,86.3,unit_del,642] sameside(a1,b,a).
1465 [binary,1110.1,86.3,unit_del,676] sameside(c1,b,c).
1508 [hyper,2,1123,1] E(a1,b,d1,e).
1509 [binary,1179.1,17.1] E(b,a1,e,d1).
1522 [binary,1196.1,86.3,unit_del,749] sameside(d1,e,d).
1564 [ur,31,692,1212] -T(a1,c1,b).
1588 [binary,1257.1,273.2,unit_del,1564,1328] -Col(b,a1,c1).
1726 [ur,98,1405,38,37,452] p!=e.
1756 [binary,1465.1,286.1] c!=b.
1788 [binary,1522.1,286.1] d!=e.
1877 [ur,98,1726,38,37,1369] d1!=p.
1929 [ur,98,1756,38,37,1278] a1!=c.
2041 [ur,98,1877,38,37,1371] e!=d1.
2108 [ur,98,1929,38,37,1280] b!=a1.
2262 [ur,233,2108,1588,1371,1509,demod,346] samesideline(f1,p,e,d1).
2263 [ur,232,2108,1588,1371,1509,demod,346] E3(b,a1,c1,e,d1,f1).
2308 [binary,2262.1,326.1] -Col(e,d1,f1).
2314 [binary,2262.1,202.1] samesideline(f1,p,d1,e).
2321 [binary,2263.1,271.1] E(a1,c1,d1,f1).
2322 [binary,2263.1,270.1] E(b,c1,e,f1).
2340 [binary,2308.1,46.2] -Col(f1,e,d1).
2360 [hyper,204,499,2314,unit_del,1788] samesideline(f1,p,d,e).
2380 [hyper,272,1508,2321,2322] E3(a1,b,c1,d1,e,f1).
2409 [ur,98,2041,38,37,2340] f1!=e.
2416 [binary,2360.1,338.2] -congruent(a,b,c,d,e,f1).
2442 [binary,2409.1,87.1] sameside(f1,e,f1).
2521 [ur,240,1441,1465,1522,2380,2416] -sameside(f1,e,f1).
2522 [binary,2521.1,2442.1] $F.