Sindbad~EG File Manager

Length of proof is 65.  Level of proof is 21.
 
---------------- PROOF ----------------
 
7 [] -T(x,y,x)|x=y.
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
29 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
30 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xc,xd).
31 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xc,xd).
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).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
89 [] -sameside(xa,xp,xb)| -sameside(xb,xp,xc)|sameside(xa,xp,xc).
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).
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.
153 [] -perp(xa,xb,xp,xq)| -Col(xa,xb,xp)| -Col(xa,xb,xq).
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)).
187 [] -opposite(xa,xp,xq,xb)|opposite(xb,xp,xq,xa).
196 [] -opposite(xa,xp,xq,xc)| -Col(xp,xq,xr)| -sameside(xa,xr,xb)|opposite(xb,xp,xq,xc).
199 [] -opposite(xa,xp,xq,xc)|opposite(xb,xp,xq,xc)| -samesideline(xa,xb,xp,xq).
200 [] -opposite(xa,xp,xq,xb)| -samesideline(xa,xb,xp,xq).
222 [] Col(xa,xb,xc)| -T(xb,xc,xa).
233 [] -sameside(xa,xp,xb)|xb!=xp.
234 [] -sameside(xa,xp,xb)|T(xp,xa,xb)|T(xp,xb,xa).
235 [] -T(xp,xa,xb)|xa=xp|xb=xp|sameside(xa,xp,xb).
236 [] -T(xp,xb,xa)|xa=xp|xb=xp|sameside(xa,xp,xb).
259 [] xp=xq|Col(xp,xq,xa)|Col(xp,xq,xb)| -T(xa,xt,xb)| -Col(xp,xq,xt)|opposite(xa,xp,xq,xb).
260 [] -opposite(xa,xp,xq,xb)| -Col(xp,xq,xa).
262 [] -opposite(xa,xp,xq,xb)|T(xa,il(xa,xb,xp,xq),xb).
263 [] -opposite(xa,xp,xq,xb)|Col(xp,xq,il(xa,xb,xp,xq)).
264 [] -samesideline(xa,xb,xp,xq)|Col(xp,xq,ss1(xa,xb,xp,xq)).
265 [] -samesideline(xa,xb,xp,xq)|Col(xp,xq,ss2(xa,xb,xp,xq)).
266 [] -samesideline(xa,xb,xp,xq)|T(xa,ss1(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
267 [] -samesideline(xa,xb,xp,xq)|T(xb,ss2(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
268 [] -samesideline(xa,xb,xp,xq)|xa!=ss1(xa,xb,xp,xq).
270 [] -samesideline(xa,xb,xp,xq)|ss3(xa,xb,xp,xq)!=ss1(xa,xb,xp,xq).
273 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xa).
274 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xb).
275 [] -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).
276 [] s(xa,s(xa,xp))=xp.
277 [] p!=q.
278 [] samesideline(a,b,p,q).
279 [] samesideline(b,c,p,q).
280 [] -samesideline(a,c,p,q).
285 [] ss3(a,b,p,q)=t.
286 [] il(t,c,p,q)=r.
287 [] ss1(a,b,p,q)=cs.
288 [] ss2(a,b,p,q)=k.
360 [binary,277.1,172.1] T(x,erectAux(p,q,x),erect(p,q,x)).
361 [binary,277.1,171.1] Col(p,q,erectAux(p,q,x)).
362 [binary,277.1,170.1] perp(p,q,erect(p,q,x),p).
368 [binary,277.1,115.2] s(x,p)!=s(x,q).
410 [binary,278.1,274.1] -Col(p,q,b).
411 [binary,278.1,273.1] -Col(p,q,a).
413 [binary,278.1,270.1,demod,285,287] t!=cs.
415 [binary,278.1,268.1,demod,287] a!=cs.
416 [binary,278.1,267.1,demod,288,285] T(b,k,t).
417 [binary,278.1,266.1,demod,287,285] T(a,cs,t).
418 [binary,278.1,265.1,demod,288] Col(p,q,k).
419 [binary,278.1,264.1,demod,287] Col(p,q,cs).
438 [binary,279.1,274.1] -Col(p,q,c).
443 [binary,279.1,200.2] -opposite(b,p,q,c).
501 [binary,362.1,153.1,unit_del,52] -Col(p,q,erect(p,q,x)).
505 [ur,114,113,368,demod,276] q!=p.
558 [binary,413.1,7.2] -T(t,cs,t).
675 [binary,416.1,25.1] T(t,k,b).
743 [binary,417.1,25.1] T(t,cs,a).
832 [binary,419.1,260.2] -opposite(cs,p,q,x).
883 [binary,438.1,48.2] -Col(c,q,p).
884 [binary,438.1,47.2] -Col(q,c,p).
885 [binary,438.1,46.2] -Col(c,p,q).
891 [binary,443.1,187.2] -opposite(c,p,q,b).
909 [ur,259,277,411,501,360,361] opposite(a,p,q,erect(p,q,a)).
932 [ur,102,505,52] Col(p,q,q).
982 [ur,29,417,558] -T(a,t,cs).
1055 [binary,743.1,222.2] Col(a,t,cs).
1133 [ur,98,505,38,37,883] c!=q.
1153 [ur,98,277,38,37,885] c!=p.
1232 [binary,982.1,86.3,unit_del,1055] sameside(a,t,cs).
1359 [ur,98,1153,38,37,884] q!=c.
1424 [ur,196,909,1232,832] -Col(p,q,t).
1497 [binary,1424.1,48.2] -Col(t,q,p).
1502 [ur,259,277,410,1424,416,418] opposite(b,p,q,t).
1505 [ur,259,277,1424,410,675,418] opposite(t,p,q,b).
1520 [ur,98,505,38,37,1497] t!=q.
1574 [hyper,199,1502,279] opposite(c,p,q,t).
1583 [ur,196,1505,932,891] -sameside(t,q,c).
1608 [ur,275,417,419,932,277,413,1520,415,1133,411,438,280] -T(c,q,t).
1759 [binary,1574.1,187.1] opposite(t,p,q,c).
1764 [binary,1583.1,236.4,unit_del,1520,1133] -T(q,c,t).
1765 [binary,1583.1,235.4,unit_del,1520,1133] -T(q,t,c).
1877 [binary,1759.1,263.1,demod,286] Col(p,q,r).
1878 [binary,1759.1,262.1,demod,286] T(t,r,c).
1896 [binary,1764.1,25.2] -T(t,c,q).
1922 [binary,1765.1,25.2] -T(c,t,q).
1947 [binary,1877.1,260.2] -opposite(r,p,q,x).
2005 [ur,259,277,410,438,1877,443] -T(b,r,c).
2052 [binary,1878.1,25.1] T(c,r,t).
2128 [binary,1922.1,234.2,unit_del,1608] -sameside(t,c,q).
2228 [ur,31,24,2005] -T(c,r,c).
2238 [binary,2052.1,222.2] Col(t,c,r).
2353 [ur,29,1878,2228] -T(t,c,r).
2365 [binary,2238.1,86.2,unit_del,2353] sameside(t,c,r).
2405 [binary,2365.1,233.1] r!=c.
2421 [ur,89,2365,2128] -sameside(r,c,q).
2497 [ur,30,1878,2405,1896] -T(r,c,q).
2511 [binary,2421.1,86.1,unit_del,2497] -Col(r,c,q).
2549 [binary,2511.1,50.2] -Col(r,q,c).
2550 [binary,2511.1,49.2] -Col(c,r,q).
2570 [ur,98,1359,38,37,2549] r!=q.
2628 [ur,98,2570,38,37,2550] c!=r.
2711 [ur,275,417,2052,419,1877,277,413,415,2628,411,438,280] t=r.
2804 [para_from,2711.1.1,1759.1.1] opposite(r,p,q,c).
2805 [binary,2804.1,1947.1] $F.