Sindbad~EG File Manager

Length of proof is 43.  Level of proof is 5.
 
---------------- 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).
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).
27 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
52 [] Col(xa,xb,xa).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
222 [] xa=xb| -Col(xa,xb,xp)|reflect(xa,xb,xp)=xp.
253 [] -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(xb,xc,xa).
270 [] -T(xp,xb,xa)|xa=xp|xb=xp|sameside(xa,xp,xb).
310 [] -congruent(xa,xb,xc,xd,xe,xf)|E(ext(xb,xc,xe,xf),ext(xb,xa,xe,xd),ext(xe,xf,xb,xc),ext(xe,xd,xb,xa)).
311 [] -congruent(xa,xb,xc,xd,xe,xf)|xa!=xb.
312 [] -congruent(xa,xb,xc,xd,xe,xf)|xc!=xb.
313 [] -congruent(xa,xb,xc,xd,xe,xf)|xd!=xe.
314 [] -congruent(xa,xb,xc,xd,xe,xf)|xf!=xe.
317 [] congruent(a,b,c,d,e,f).
318 [] -sameside(ext(b,a,e,d),b,a)| -sameside(ext(b,c,e,f),b,c)| -sameside(ext(e,d,b,a),e,d)| -sameside(ext(e,f,b,c),e,f)| -E3(ext(b,a,e,d),b,ext(b,c,e,f),ext(e,d,b,a),e,ext(e,f,b,c)).
319 [] a1=ext(b,a,e,d).
320 [] c1=ext(b,c,e,f).
321 [] d1=ext(e,d,b,a).
322 [] f1=ext(e,f,b,c).
323 [] ext(b,a,e,d)=a1.
324 [] ext(b,c,e,f)=c1.
325 [] ext(e,d,b,a)=d1.
326 [] ext(e,f,b,c)=f1.
370 [binary,317.1,314.1] f!=e.
371 [binary,317.1,313.1] d!=e.
372 [binary,317.1,312.1] c!=b.
373 [binary,317.1,311.1] a!=b.
374 [binary,317.1,310.1,demod,324,323,326,325] E(c1,a1,f1,d1).
399 [para_from,319.1.2,5.1.2] E(a,a1,e,d).
400 [para_from,319.1.2,4.1.3] T(b,a,a1).
413 [para_from,320.1.2,5.1.2] E(c,c1,e,f).
414 [para_from,320.1.2,4.1.3] T(b,c,c1).
427 [para_from,321.1.2,5.1.2] E(d,d1,b,a).
428 [para_from,321.1.2,4.1.3] T(e,d,d1).
441 [para_from,322.1.2,5.1.2] E(f,f1,b,c).
442 [para_from,322.1.2,4.1.3] T(e,f,f1).
443 [binary,370.1,270.3] -T(e,f,x)|x=e|sameside(x,e,f).
463 [ur,222,370,52] reflect(f,e,f)=f.
482 [ur,27,24,370] -T(e,f,e).
642 [binary,374.1,22.1] E(a1,c1,d1,f1).
667 [hyper,2,399,1] E(e,d,a1,a).
671 [binary,400.1,256.2] Col(a1,b,a).
685 [binary,400.1,27.2,unit_del,373] -T(a,b,a1).
686 [binary,400.1,25.1] T(a1,a,b).
700 [binary,413.1,17.1] E(c,c1,f,e).
715 [binary,414.1,256.2] Col(c1,b,c).
729 [binary,414.1,27.2,unit_del,372] -T(c,b,c1).
755 [binary,427.1,17.1] E(d,d1,a,b).
771 [binary,428.1,256.2] Col(d1,e,d).
785 [binary,428.1,27.2,unit_del,371] -T(d,e,d1).
813 [hyper,2,441,1] E(b,c,f1,f).
832 [binary,442.1,25.1] T(f1,f,e).
869 [para_into,482.1.3,443.2.2,factor_simp] -T(e,f,x)|sameside(x,e,f).
926 [binary,685.1,25.2] -T(a1,b,a).
1025 [binary,729.1,25.2] -T(c1,b,c).
1053 [hyper,19,428,686,667,755] E(e,d1,a1,b).
1084 [binary,785.1,25.2] -T(d1,e,d).
1142 [hyper,19,414,832,813,700] E(b,c1,f1,e).
1155 [binary,869.1,442.1] sameside(f1,e,f).
1167 [binary,926.1,86.3,unit_del,671] sameside(a1,b,a).
1191 [binary,1025.1,86.3,unit_del,715] sameside(c1,b,c).
1225 [hyper,2,1053,1] E(a1,b,d1,e).
1241 [binary,1084.1,86.3,unit_del,771] sameside(d1,e,d).
1263 [binary,1142.1,17.1] E(b,c1,e,f1).
1332 [hyper,253,1225,642,1263] E3(a1,b,c1,d1,e,f1).
5012 [para_from,463.1.2,1155.1.3] sameside(f1,e,reflect(f,e,f)).
5044 [para_from,463.1.2,318.4.3,demod,323,324,325,326,323,324,325,326,unit_del,1167,1191,1241,5012,1332] $F.