Sindbad~EG File Manager

Length of proof is 74.  Level of proof is 18.
 
---------------- PROOF ----------------
 
4 [] T(x,y,ext(x,y,w,v)).
5 [] E(y,ext(x,y,w,v),w,v).
13 [] E(xa,xb,xa,xb).
18 [] E(xa,xa,xb,xb).
21 [] -E(xb,xc,xa,xa)|xb=xc.
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.
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
42 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xc,xa1,xc1)| -E(xb,xc,xb1,xc1)|E(xa,xb,xa1,xb1).
46 [] -Col(xa,xb,xc)|Col(xb,xc,xa).
47 [] -Col(xa,xb,xc)|Col(xc,xa,xb).
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).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
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.
111 [] -M(xp,xa,xr)| -M(xp,xa,xq)|xr=xq.
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.
123 [] -M(xp,xa,xq)| -M(xp,xb,xq)|xa=xb.
130 [] -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).
153 [] -perp(xa,xb,xp,xq)| -Col(xa,xb,xp)| -Col(xa,xb,xq).
166 [] xa=xb|xc=xd| -Col(xa,xb,xc)| -Col(xa,xb,xd)| -Col(xc,xd,xp)|Col(xa,xb,xp).
170 [] xa=xb|perp(xa,xb,erect(xa,xb,xc),xa).
171 [] xa=xb|Col(xa,xb,erectAux(xa,xb,xc)).
172 [] xa=xb|T(xc,erectAux(xa,xb,xc),erect(xa,xb,xc)).
174 [] M(xa,midpoint(xa,xb),xb).
178 [] -Col(xa,xb,xc)| -Col(xa,xb,xd)|xa=xb|Col(xa,xc,xd).
183 [] -Col(xa,xb,xp)| -Col(xa,xb,xq)|xp=xq|xa=xb|perp(xp,xq,xc,xd)| -perp(xa,xb,xc,xd).
203 [] xa=xb| -M(u,v,w)| -Col(xa,xb,u)| -Col(xa,xb,w)|Col(xa,xb,v).
213 [] xa=xb|Col(xa,xb,midpoint(xp,reflect(xa,xb,xp))).
221 [] xa=xb|reflect(xa,xb,xp)!=xp|Col(xa,xb,xp).
250 [] Col(xa,xb,xc)| -T(xa,xb,xc).
252 [] Col(xa,xb,xc)| -T(xc,xa,xb).
262 [] -sameside(xa,xp,xb)|xb!=xp.
266 [] -M(xa,xm,xb)|T(xa,xm,xb).
304 [] -T(xa,xu,xc)| -T(xb,xv,xc)| -Col(xp,xq,xu)| -Col(xp,xq,xv)|xp=xq|xc=xu|xc=xv|xa=xu|xb=xv|Col(xp,xq,xa)|Col(xp,xq,xb)|samesideline(xa,xb,xp,xq).
305 [] s(xa,s(xa,xp))=xp.
306 [] b!=c.
307 [] Col(b,c,a).
308 [] -Col(b,c,q).
309 [] -perp(b,c,x,a)| -samesideline(x,q,b,c).
310 [] e=ext(b,c,b,a).
311 [] p1=reflect(e,a,q).
312 [] p=erect(a,e,p1).
313 [] t=erectAux(a,e,p1).
314 [] m=midpoint(q,p1).
316 [] reflect(e,a,q)=p1.
318 [] erectAux(a,e,p1)=t.
319 [] midpoint(q,p1)=m.
405 [binary,306.1,115.2] s(x,b)!=s(x,c).
411 [binary,306.1,21.2] -E(b,c,x,x).
419 [ur,102,306,52] Col(c,b,b).
444 [binary,307.1,102.2,unit_del,306] Col(c,b,a).
473 [binary,308.1,49.2] -Col(c,b,q).
477 [ur,203,306,307,307,308] -M(a,q,a).
485 [ur,103,306,51,51,51,308] x=x.
496 [para_from,310.1.2,5.1.2] E(c,e,b,a).
497 [para_from,310.1.2,4.1.3] T(b,c,e).
505 [para_from,311.1.2,213.2.3.2,demod,319] e=a|Col(e,a,m).
513 [para_from,312.1.2,172.2.3,demod,318] a=e|T(p1,t,p).
514 [para_from,312.1.2,170.2.3] a=e|perp(a,e,p,a).
522 [para_from,313.1.2,171.2.3] a=e|Col(a,e,t).
530 [para_from,314.1.2,174.1.2] M(q,m,p1).
532 [ur,114,113,405,demod,305] c!=b.
625 [binary,477.1,109.1] q!=a.
632 [binary,485.1,109.2] M(x,x,x).
656 [binary,497.1,252.2] Col(c,e,b).
658 [binary,497.1,250.2] Col(b,c,e).
673 [binary,497.1,27.2,unit_del,532] -T(c,b,e).
692 [ur,42,497,26,13,411] -E(c,e,b,e).
715 [para_from,505.1.2,496.1.4,unit_del,692] Col(e,a,m).
724 [para_from,513.1.1,496.1.4,unit_del,692] T(p1,t,p).
729 [para_from,514.1.1,496.1.4,unit_del,692] perp(a,e,p,a).
742 [para_from,522.1.1,496.1.4,unit_del,692] Col(a,e,t).
746 [binary,530.1,266.1] T(q,m,p1).
752 [binary,530.1,107.1] M(p1,m,q).
851 [ur,123,632,625] -M(q,a,q).
875 [binary,656.1,50.1] Col(c,b,e).
903 [hyper,178,658,658,unit_del,306] Col(b,e,e).
905 [hyper,178,307,658,unit_del,306] Col(b,a,e).
907 [hyper,178,658,307,unit_del,306] Col(b,e,a).
938 [binary,673.1,86.3,unit_del,875] sameside(c,b,e).
975 [binary,715.1,49.1] Col(a,e,m).
1003 [binary,724.1,25.1] T(p,t,p1).
1022 [binary,729.1,153.1,unit_del,52] -Col(a,e,p).
1059 [binary,746.1,252.2] Col(m,p1,q).
1107 [binary,851.1,109.1] a!=q.
1127 [hyper,178,444,875,unit_del,532] Col(c,a,e).
1170 [binary,905.1,46.1] Col(a,e,b).
1188 [binary,938.1,262.1] e!=b.
1252 [binary,1022.1,252.1] -T(p,a,e).
1260 [binary,1022.1,47.2] -Col(e,p,a).
1261 [binary,1022.1,46.2] -Col(p,a,e).
1350 [binary,1127.1,46.1] Col(a,e,c).
1424 [ur,166,532,1188,875,419,473] -Col(e,b,q).
1430 [ur,123,632,1188] -M(e,b,e).
1471 [ur,130,26,26,18,13,632,1252] -M(a,p,a).
1588 [binary,1424.1,49.2] -Col(b,e,q).
1617 [binary,1430.1,109.1] b!=e.
1636 [binary,1471.1,109.1] p!=a.
1744 [ur,103,1636,306,307,658,1261] -Col(b,c,p).
1746 [ur,98,1636,38,37,1260] e!=p.
1903 [ur,98,1746,38,37,1022] a!=e.
1970 [ur,203,1903,742,742,1022] -M(t,p,t).
2006 [ur,183,1170,1350,306,1903,729] perp(b,c,p,a).
2026 [ur,166,1617,1903,907,903,1588] -Col(a,e,q).
2034 [ur,166,306,1903,307,658,975] Col(b,c,m).
2035 [ur,166,306,1903,307,658,742] Col(b,c,t).
2082 [binary,1970.1,109.1] p!=t.
2130 [binary,2006.1,309.1] -samesideline(p,q,b,c).
2154 [binary,2026.1,49.2] -Col(e,a,q).
2165 [ur,203,1903,975,975,2026] -M(m,q,m).
2489 [ur,98,1107,38,37,2154] e!=a.
2516 [binary,2165.1,109.1] q!=m.
2532 [ur,221,2489,2154,demod,316] p1!=q.
2674 [ur,111,752,2532] -M(p1,m,p1).
2720 [binary,2674.1,109.1] m!=p1.
2745 [ur,166,1903,2720,975,1059,2026] -Col(a,e,p1).
2749 [ur,123,632,2720] -M(m,p1,m).
2840 [ur,203,1903,742,742,2745] -M(t,p1,t).
2879 [binary,2749.1,109.1] p1!=m.
2883 [binary,2840.1,109.1] p1!=t.
2895 [ur,304,1003,746,2035,2034,306,2879,2082,2516,1744,308,2130] p1=t.
2896 [binary,2895.1,2883.1] $F.