Sindbad~EG File Manager

Length of proof is 40.  Level of proof is 9.
 
---------------- PROOF ----------------
 
7 [] -T(x,y,x)|x=y.
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
46 [] -Col(xa,xb,xc)|Col(xb,xc,xa).
48 [] -Col(xa,xb,xc)|Col(xc,xb,xa).
52 [] Col(xa,xb,xa).
77 [] xa=xp|xb=xp|xc=xp| -T(xa,xp,xc)|T(xb,xp,xc)| -sameside(xa,xp,xb).
84 [] -sameside(xa,xp,xb)|Col(xa,xp,xb).
85 [] -sameside(xa,xp,xb)| -T(xa,xp,xb).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
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).
107 [] -M(xa,xm,xb)|M(xb,xm,xa).
109 [] M(xa,xm,xa)|xm!=xa.
110 [] M(xp,xa,s(xa,xp)).
111 [] -M(xp,xa,xr)| -M(xp,xa,xq)|xr=xq.
112 [] -M(xp,xa,xq)|xq=s(xa,xp).
142 [] -perp(xa,xb,xp,xq)|perp(xp,xq,xa,xb).
156 [] xa=xb| -Col(xa,xb,xd)| -perp(xa,xb,xc,xd)|perpAt(xa,xb,xd,xc,xd).
176 [] -perp(xp,xa,xa,xb)| -perp(xq,xb,xa,xb)| -Col(xa,xb,xt)| -T(xp,xt,xq)| -T(xb,xr,xq)| -E(xa,xp,xb,xr)|xcx!=ip(xp,xt,xq,xb,xr)|M(xp,xcx,xr).
182 [] -perp(xa,xb,xp,xq)|perp(xa,xb,xq,xp).
183 [] -Col(xa,xb,xp)| -Col(xa,xb,xq)|xp=xq|xa=xb|perp(xp,xq,xc,xd)| -perp(xa,xb,xc,xd).
190 [] -sameside(xa,xb,xc)|sameside(s(xm,xa),s(xm,xb),s(xm,xc)).
213 [] Col(xa,xb,xc)| -T(xc,xa,xb).
219 [] -le(xa,xb,xc,xd)|T(xc,insert(xa,xb,xc,xd),xd).
220 [] -le(xa,xb,xc,xd)|E(xa,xb,xc,insert(xa,xb,xc,xd)).
222 [] -sameside(xa,xp,xb)|xa!=xp.
223 [] -sameside(xa,xp,xb)|xb!=xp.
227 [] -M(xa,xm,xb)|T(xa,xm,xb).
242 [] -perpAt(y,z,x,y1,z1)|y1!=z1.
252 [] -opposite(xa,xp,xq,xb)|T(xa,il(xa,xb,xp,xq),xb).
253 [] -opposite(xa,xp,xq,xb)|Col(xp,xq,il(xa,xb,xp,xq)).
267 [] opposite(a,p,q,c).
268 [] p!=q.
269 [] Col(p,q,cs).
270 [] Col(p,q,r).
271 [] perp(p,q,a,r).
272 [] perp(p,q,c,cs).
273 [] M(r,m,cs).
274 [] sameside(cu,r,a).
275 [] le(cs,c,r,a).
276 [] r!=cs.
277 [] -sameside(s(m,cu),cs,c).
280 [] m=ip(c,t,a,r,b).
281 [] il(a,c,p,q)=t.
282 [] insert(cs,c,r,a)=b.
329 [binary,267.1,253.1,demod,281] Col(p,q,t).
330 [binary,267.1,252.1,demod,281] T(a,t,c).
457 [hyper,183,270,269,271,unit_del,276,268] perp(r,cs,a,r).
469 [binary,272.1,156.3,unit_del,268,269] perpAt(p,q,cs,c,cs).
471 [hyper,183,270,269,272,unit_del,276,268] perp(r,cs,c,cs).
485 [binary,273.1,112.1] cs=s(m,r).
496 [binary,274.1,223.1] a!=r.
497 [binary,274.1,222.1] cu!=r.
504 [binary,274.1,84.1] Col(cu,r,a).
517 [binary,275.1,220.1,demod,282] E(cs,c,r,b).
518 [binary,275.1,219.1,demod,282] T(r,b,a).
650 [hyper,103,270,269,329,unit_del,276,268] Col(r,cs,t).
694 [binary,330.1,25.1] T(c,t,a).
732 [binary,457.1,142.1] perp(a,r,r,cs).
736 [binary,469.1,242.1] c!=cs.
759 [binary,471.1,142.1] perp(c,cs,r,cs).
839 [binary,496.1,7.2] -T(a,r,a).
952 [binary,504.1,46.1] Col(r,a,cu).
1024 [binary,518.1,213.2] Col(b,a,r).
1082 [binary,650.1,102.2,unit_del,276] Col(cs,r,t).
1157 [binary,732.1,182.1] perp(a,r,cs,r).
1175 [binary,736.1,7.2] -T(c,cs,c).
1225 [binary,759.1,182.1] perp(c,cs,cs,r).
1252 [binary,839.1,227.2] -M(a,r,a).
1294 [binary,1024.1,48.1] Col(r,a,b).
1347 [binary,1175.1,227.2] -M(c,cs,c).
1364 [hyper,176,1225,1157,1082,694,518,517,280] M(c,m,b).
1371 [binary,1252.1,109.1] r!=a.
1395 [hyper,103,952,52,1294,unit_del,497,1371] Col(cu,r,b).
1410 [binary,1347.1,109.1] cs!=c.
1431 [binary,1364.1,107.1] M(b,m,c).
1594 [ur,90,496,1410,demod,282] sameside(b,r,a).
1652 [hyper,111,110,1431] s(m,b)=c.
1656 [binary,1594.1,222.1] b!=r.
1660 [binary,1594.1,85.1] -T(b,r,a).
1711 [para_from,1652.1.2,277.1.3] -sameside(s(m,cu),cs,s(m,b)).
1808 [binary,1660.1,25.2] -T(a,r,b).
1823 [para_into,1711.1.2,485.1.1] -sameside(s(m,cu),s(m,r),s(m,b)).
1834 [ur,77,497,496,1656,1808,274] -T(cu,r,b).
1847 [binary,1823.1,190.2] -sameside(cu,r,b).
1863 [binary,1834.1,86.3,unit_del,1847,1395] $F.