Sindbad~EG File Manager

Length of proof is 44.  Level of proof is 13.
 
---------------- PROOF ----------------
 
5 [] E(y,ext(x,y,w,v),w,v).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
18 [] E(xa,xa,xb,xb).
24 [] T(xa,xb,xb).
28 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
47 [] -Col(xa,xb,xc)|Col(xc,xa,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).
54 [] -Col(xa,xb,xc)| -E(xa,xb,xa1,xb1)|E3(xa,xb,xc,xa1,xb1,insert5(xa,xb,xc,xa1,xb1)).
84 [] -sameside(xa,xp,xb)|Col(xa,xp,xb).
88 [] -sameside(xa,xp,xb)|sameside(xb,xp,xa).
90 [] xr=xa|xb=xc|sameside(insert(xb,xc,xa,xr),xa,xr).
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).
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.
138 [] -R(xa,xb,xa)|xa=xb.
156 [] xa=xb| -Col(xa,xb,xd)| -perp(xa,xb,xc,xd)|perpAt(xa,xb,xd,xc,xd).
161 [] Col(xa,xb,xc)|Col(xa,xb,foot(xa,xb,xc)).
162 [] Col(xa,xb,xc)|perp(xa,xb,xc,foot(xa,xb,xc)).
201 [] xp=xq| -samesideline(xa,xb,xp,xq)| -samesideline(xb,xc,xp,xq)|samesideline(xa,xc,xp,xq).
212 [] xc=xd| -Col(xc,xd,xp)| -Col(xa,xb,xp)| -sameside(xa,xp,xb)|Col(xc,xd,xa)|samesideline(xa,xb,xc,xd).
228 [] -R(xa,xb,xc)| -R(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
230 [] xb=xc| -Col(xb,xc,xa)|Col(xb,xc,xq)|perp(xb,xc,erectsameside(xb,xc,xa,xq),xa).
231 [] xb=xc| -Col(xb,xc,xa)|Col(xb,xc,xq)|samesideline(erectsameside(xb,xc,xa,xq),xq,xb,xc).
232 [] insert(xa,xb,xa1,xc1)=ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
248 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa1,xa3,xb1,xb3).
249 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa2,xa3,xb2,xb3).
250 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
254 [] Col(xa,xb,xc)| -T(xc,xa,xb).
263 [] -sameside(xa,xp,xb)|xa!=xp.
284 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
303 [] -samesideline(xa,xb,xp,xq)|xp!=xq.
304 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xa).
307 [] s(xa,s(xa,xp))=xp.
308 [] a!=b.
309 [] -Col(a,b,c).
310 [] -Col(a1,b1,p).
311 [] E(a,b,a1,b1).
312 [] -E3(a,b,c,a1,b1,x)| -samesideline(x,p,a1,b1).
314 [] cx1=insert5(a,b,cx,a1,b1).
315 [] q=erectsameside(a1,b1,cx1,p).
316 [] c1=insert(cx,c,cx1,q).
317 [] foot(a,b,c)=cx.
319 [] erectsameside(a1,b1,cx1,p)=q.
377 [binary,308.1,115.2] s(x,a)!=s(x,b).
391 [ur,102,308,52] Col(b,a,a).
416 [binary,309.1,162.1,demod,317] perp(a,b,c,cx).
417 [binary,309.1,161.1,demod,317] Col(a,b,cx).
434 [binary,310.1,254.1] -T(p,a1,b1).
454 [hyper,250,311,311,18] E3(a,b,b,a1,b1,b1).
475 [para_from,314.1.2,54.3.6,unit_del,417,311] E3(a,b,cx,a1,b1,cx1).
483 [para_from,315.1.2,231.4.1,unit_del,310] a1=b1| -Col(a1,b1,cx1)|samesideline(q,p,a1,b1).
491 [para_into,316.1.2,232.1.1] c1=ext(ext(q,cx1,alpha,gamma),cx1,cx,c).
492 [para_from,316.1.2,90.3.1] q=cx1|cx=c|sameside(c1,cx1,q).
494 [ur,114,113,377,demod,307] b!=a.
532 [hyper,103,391,52,52,unit_del,308,494] Col(a,b,b).
540 [binary,416.1,156.3,unit_del,308,417] perpAt(a,b,cx,c,cx).
606 [ur,28,24,434] -T(a1,b1,a1).
608 [binary,454.1,53.2,unit_del,532] Col(a1,b1,b1).
609 [binary,475.1,249.1] E(b,cx,b1,cx1).
610 [binary,475.1,248.1] E(a,cx,a1,cx1).
612 [binary,475.1,53.2,unit_del,417] Col(a1,b1,cx1).
618 [para_into,483.2.1,483.1.1,unit_del,51,612,factor_simp] a1=b1|samesideline(q,p,a1,b1).
631 [para_from,491.1.2,5.1.2] E(cx1,c1,cx,c).
633 [para_from,492.2.1,417.1.3,unit_del,309] q=cx1|sameside(c1,cx1,q).
702 [hyper,284,540,532,52] R(b,cx,c).
705 [hyper,284,540,52,52] R(a,cx,c).
770 [binary,612.1,304.2] -samesideline(cx1,x,a1,b1).
788 [para_from,618.1.1,606.1.3,unit_del,24] samesideline(q,p,a1,b1).
795 [binary,631.1,14.1] E(cx,c,cx1,c1).
844 [binary,788.1,303.1] a1!=b1.
860 [para_into,788.1.1,633.1.1,unit_del,770] sameside(c1,cx1,q).
882 [ur,230,844,612,310,demod,319] perp(a1,b1,q,cx1).
932 [binary,860.1,263.1] c1!=cx1.
935 [binary,860.1,88.1] sameside(q,cx1,c1).
949 [binary,882.1,156.3,unit_del,844,612] perpAt(a1,b1,cx1,q,cx1).
957 [binary,932.1,138.2] -R(c1,cx1,c1).
1002 [binary,935.1,84.1] Col(q,cx1,c1).
1035 [binary,1002.1,47.1] Col(c1,q,cx1).
1038 [hyper,284,949,608,1002] R(b1,cx1,c1).
1039 [hyper,284,949,52,1002] R(a1,cx1,c1).
1050 [ur,284,949,1002,957] -Col(a1,b1,c1).
1086 [hyper,212,612,1035,860,unit_del,844,1050] samesideline(c1,q,a1,b1).
1098 [hyper,228,702,1038,609,795] E(b,c,b1,c1).
1106 [hyper,228,705,1039,610,795] E(a,c,a1,c1).
1170 [hyper,250,311,1106,1098] E3(a,b,c,a1,b1,c1).
1177 [binary,1170.1,312.1] -samesideline(c1,p,a1,b1).
1183 [ur,201,844,788,1177] -samesideline(c1,q,a1,b1).
1184 [binary,1183.1,1086.1] $F.