Sindbad~EG File Manager

Length of proof is 63.  Level of proof is 15.

---------------- PROOF ----------------

7 [] -T(x,y,x)|x=y.
8 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xp,ip(xa,xp,xc,xb,xq),xb).
9 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xq,ip(xa,xp,xc,xb,xq),xa).
13 [] E(xa,xb,xa,xb).
18 [] E(xa,xa,xb,xb).
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
26 [] T(xa1,xa1,xb1).
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).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
51 [] Col(xa,xa,xb).
82 [] sameside(xa,xp,xb)|xa=xp|xb=xp|xc=xp| -T(xa,xp,xc)| -T(xb,xp,xc).
97 [] xp=xq|xp=xr| -T(xq,xp,xr)|xa!=xp|Col(xa,xp,xq).
100 [] xp=xq|Col(xp,xq,xp).
101 [] xp=xq| -Col(xp,xq,xr)|Col(xq,xp,xr).
103 [] 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,xa)|xm!=xa.
128 [] -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).
164 [] xa=xb|xp=xq| -Col(xa,xb,xp)| -Col(xa,xb,xq)| -Col(xa,xb,xt)|Col(xp,xq,xt).
165 [] xa=xb|xc=xd| -Col(xa,xb,xc)| -Col(xa,xb,xd)| -Col(xc,xd,xp)|Col(xa,xb,xp).
184 [] xa=xb| -samesideline(xp,xq,xa,xb)|samesideline(xp,xq,xb,xa).
194 [] -opposite(xa,xp,xq,xc)| -Col(xp,xq,xr)| -sameside(xa,xr,xb)|opposite(xb,xp,xq,xc).
219 [] Col(xa,xb,xc)| -T(xc,xa,xb).
231 [] -T(xp,xa,xb)|xb=xp|xp=xa|sameside(xa,xp,xb).
232 [] -T(xp,xb,xa)|xb=xp|xp=xa|sameside(xa,xp,xb).
233 [] -M(xa,xm,xb)|T(xa,xm,xb).
255 [] xp=xq|Col(xp,xq,xa)|Col(xp,xq,xb)| -T(xa,xt,xb)| -Col(xp,xq,xt)|opposite(xa,xp,xq,xb).
257 [] -opposite(xa,xp,xq,xb)| -Col(xp,xq,xb).
260 [] -samesideline(xa,xb,xp,xq)|Col(xp,xq,ss1(xa,xb,xp,xq)).
261 [] -samesideline(xa,xb,xp,xq)|Col(xp,xq,ss2(xa,xb,xp,xq)).
262 [] -samesideline(xa,xb,xp,xq)|T(xa,ss1(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
263 [] -samesideline(xa,xb,xp,xq)|T(xb,ss2(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
264 [] -samesideline(xa,xb,xp,xq)|xa!=ss1(xa,xb,xp,xq).
266 [] -samesideline(xa,xb,xp,xq)|ss3(xa,xb,xp,xq)!=ss1(xa,xb,xp,xq).
267 [] -samesideline(xa,xb,xp,xq)|ss3(xa,xb,xp,xq)!=ss2(xa,xb,xp,xq).
268 [] -samesideline(xa,xb,xp,xq)|xp!=xq.
270 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xb).
273 [] opposite(a,p,q,c).
274 [] -opposite(b,p,q,c).
275 [] samesideline(a,b,p,q).
279 [] cz=ip(a,cx,d,b,cy).
280 [] ss1(a,b,p,q)=cx.
281 [] ss2(a,b,p,q)=cy.
282 [] ss3(a,b,p,q)=d.
286 [binary,273.1,257.1] -Col(p,q,c).
288 [binary,273.1,194.1] -Col(p,q,x)| -sameside(a,x,y)|opposite(y,p,q,c).
295 [binary,274.1,194.4] -opposite(x,p,q,c)| -Col(p,q,y)| -sameside(x,y,b).
297 [binary,275.1,270.1] -Col(p,q,b).
298 [binary,275.1,268.1] p!=q.
299 [binary,275.1,267.1,demod,282,281] d!=cy.
300 [binary,275.1,266.1,demod,282,280] d!=cx.
302 [binary,275.1,264.1,demod,280] a!=cx.
303 [binary,275.1,263.1,demod,281,282] T(b,cy,d).
304 [binary,275.1,262.1,demod,280,282] T(a,cx,d).
305 [binary,275.1,261.1,demod,281] Col(p,q,cy).
306 [binary,275.1,260.1,demod,280] Col(p,q,cx).
307 [binary,275.1,184.2,unit_del,298] samesideline(a,b,q,p).
350 [hyper,264,275,100,demod,280] Col(a,cx,a).
394 [para_from,279.1.2,9.3.2,unit_del,304,303] T(cy,cz,a).
395 [para_from,279.1.2,8.3.2,unit_del,304,303] T(cx,cz,b).
516 [binary,299.1,7.2] -T(d,cy,d).
814 [binary,302.1,7.2] -T(a,cx,a).
951 [ur,164,298,51,51,51,286] x=x.
962 [binary,951.1,107.2] M(x,x,x).
1014 [binary,297.1,49.2] -Col(q,p,b).
1025 [binary,303.1,219.2] Col(cy,d,b).
1185 [binary,304.1,219.2] Col(cx,d,a).
1384 [binary,305.1,101.2,unit_del,298] Col(q,p,cy).
1482 [binary,306.1,101.2,unit_del,298] Col(q,p,cx).
1547 [ur,288,306,274] -sameside(a,cx,b).
1548 [ur,255,298,297,286,306,274] -T(b,cx,c).
1856 [binary,350.1,101.2,unit_del,302] Col(cx,a,a).
1887 [binary,394.1,219.2] Col(cz,a,cy).
2153 [binary,395.1,25.1] T(b,cz,cx).
2356 [binary,516.1,233.2] -M(d,cy,d).
2685 [binary,814.1,233.2] -M(a,cx,a).
2845 [binary,307.1,268.1] q!=p.
6277 [binary,1185.1,50.1] Col(cx,a,d).
7935 [ur,128,26,26,18,13,962,1548] -M(cx,b,cx).
9396 [binary,2356.1,107.1] cy!=d.
9450 [ur,165,2845,9396,1384,1025,1014] -Col(q,p,d).
10285 [binary,2685.1,107.1] cx!=a.
10383 [binary,10285.1,100.1] Col(cx,a,cx).
22034 [binary,7935.1,107.1] b!=cx.
22105 [ur,231,22034,10285,1547] -T(cx,a,b).
22246 [ur,82,1547,302,22034,300,304] -T(b,cx,d).
38131 [ur,32,395,22105] -T(cx,a,cz).
38502 [ur,32,303,22246] -T(b,cx,cy).
38506 [ur,31,303,22246] -T(cy,cx,d).
46807 [ur,128,24,24,13,18,962,38131] -M(a,cz,a).
47850 [ur,128,24,24,13,18,962,38502] -M(cx,cy,cx).
48010 [ur,128,304,304,13,13,962,38506] -M(a,cy,a).
55390 [binary,46807.1,107.1] cz!=a.
56604 [binary,47850.1,107.1] cy!=cx.
56731 [ur,165,2845,56604,1384,1482,1014] -Col(cy,cx,b).
56754 [ur,103,10285,2845,1384,10383,1482,56604,6277,9450] -Col(cx,a,cy).
57247 [binary,48010.1,107.1] cy!=a.
64942 [binary,56731.1,219.1] -T(b,cy,cx).
67945 [ur,165,10285,55390,1856,1887,56754] -Col(cx,a,cz).
76340 [ur,32,2153,64942] -T(b,cy,cz).
83265 [binary,67945.1,50.2] -Col(cx,cz,a).
86887 [ur,128,24,24,13,18,962,76340] -M(cy,cz,cy).
91494 [ur,97,55390,38,37,83265] cx!=cz.
91747 [ur,231,395,22034,91494] sameside(cz,cx,b).
95160 [binary,86887.1,107.1] cz!=cy.
95238 [ur,232,394,95160,57247] sameside(a,cy,cz).
99829 [binary,91747.1,295.3,unit_del,306] -opposite(cz,p,q,c).
104941 [binary,95238.1,288.2,unit_del,305,99829] $F.