Sindbad~EG File Manager

Length of proof is 26.  Level of proof is 10.
 
---------------- PROOF ----------------
 
1 [] E(x,y,y,x).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
22 [] -E(xa,xb,xc,xd)|E(xb,xa,xd,xc).
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).
47 [] -Col(xa,xb,xc)|Col(xc,xa,xb).
48 [] -Col(xa,xb,xc)|Col(xc,xb,xa).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
50 [] -Col(xa,xb,xc)|Col(xa,xc,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)).
55 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|xa=xb|E(xc,xd,xc1,xd1).
98 [] xp=xq|xp=xr| -T(xq,xp,xr)|xa!=xp|Col(xa,xp,xq).
104 [] xa=xb|xp=xq| -Col(xa,xb,xc)| -Col(xp,xq,xc)| -Col(xa,xb,xd)| -Col(xp,xq,xd)|xc=xd| -Col(xa,xb,xe)|Col(xp,xq,xe).
107 [] -M(xa,xm,xb)|M(xb,xm,xa).
126 [] -Col(xa,xm,xb)| -E(xm,xa,xm,xb)|xa=xb|M(xa,xm,xb).
145 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
154 [] -Col(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)| -E(xa,xd,xa1,xd1)| -E(xb,xd,xb1,xd1)|FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1).
174 [] -Col(a,b,c).
175 [] b!=d.
176 [] E(a,b,c,d).
177 [] E(b,c,d,a).
178 [] Col(a,p,c).
179 [] Col(b,p,d).
180 [] -M(a,p,c).
181 [] p1=insert5(b,d,p,d,b).
218 [binary,174.1,98.5] b=c|b=x| -T(c,b,x)|a!=b.
224 [binary,174.1,46.2] -Col(c,a,b).
257 [binary,176.1,22.1] E(b,a,d,c).
274 [binary,177.1,14.1] E(d,a,b,c).
290 [binary,178.1,48.1] Col(c,p,a).
291 [binary,178.1,47.1] Col(c,a,p).
297 [binary,179.1,50.1] Col(b,d,p).
307 [binary,180.1,107.2] -M(c,p,a).
313 [para_from,181.1.2,54.3.6,unit_del,297,1] E3(b,d,p,d,b,p1).
336 [binary,218.3,37.1,unit_del,38] b=c|a!=b.
366 [binary,257.1,14.1] E(d,c,b,a).
438 [binary,313.1,53.2,unit_del,297] Col(d,b,p1).
440 [hyper,154,297,313,257,274] FS(b,d,p,a,d,b,p1,c).
455 [para_from,336.1.1,224.1.3,unit_del,52] a!=b.
456 [hyper,154,297,313,177,366] FS(b,d,p,c,d,b,p1,a).
475 [binary,438.1,49.1] Col(b,d,p1).
482 [binary,440.1,55.1,unit_del,175] E(p,a,p1,c).
497 [ur,98,455,38,37,224] c!=a.
515 [binary,456.1,55.1,unit_del,175] E(p,c,p1,a).
543 [binary,482.1,22.1] E(a,p,c,p1).
566 [ur,126,290,497,307] -E(p,c,p,a).
618 [hyper,145,543,1,515] E3(a,p,c,c,p1,a).
642 [binary,618.1,53.2,unit_del,178] Col(c,p1,a).
656 [binary,642.1,50.1] Col(c,a,p1).
669 [hyper,104,297,291,475,656,52,unit_del,175,497,224] p=p1.
693 [para_from,669.1.1,566.1.3] -E(p,c,p1,a).
694 [binary,693.1,515.1] $F.