Sindbad~EG File Manager

Length of proof is 40.  Level of proof is 12.
 
---------------- PROOF ----------------
 
25 [] T(xa,xb,xb).
26 [] -T(xa,xb,xc)|T(xc,xb,xa).
27 [] T(xa1,xa1,xb1).
28 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
30 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
32 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xc,xd).
47 [] -Col(xa,xb,xc)|Col(xb,xc,xa).
52 [] Col(xa,xa,xb).
53 [] Col(xa,xb,xa).
87 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
103 [] xp=xq| -Col(xp,xq,xr)|Col(xq,xp,xr).
104 [] xa=xb|xp=xq| -Col(xp,xq,xa)| -Col(xp,xq,xb)| -Col(xp,xq,xr)|Col(xa,xb,xr).
118 [] s(xa,xp)=xp|xp!=xa.
125 [] s(xa,xp)!=s(xb,xp)|xa=xb.
137 [] -R(xa,xb,xc)| -R(xa1,xb,xc)| -T(xa,xc,xa1)|xb=xc.
157 [] xa=xb| -Col(xa,xb,xd)| -perp(xa,xb,xc,xd)|perpAt(xa,xb,xd,xc,xd).
162 [] Col(xa,xb,xc)|Col(xa,xb,foot(xa,xb,xc)).
163 [] Col(xa,xb,xc)|perp(xa,xb,xc,foot(xa,xb,xc)).
167 [] xa=xb|xc=xd| -Col(xa,xb,xc)| -Col(xa,xb,xd)| -Col(xc,xd,xp)|Col(xa,xb,xp).
171 [] xa=xb|perp(xa,xb,erect(xa,xb,xc),xa).
172 [] xa=xb|Col(xa,xb,erectAux(xa,xb,xc)).
173 [] xa=xb|T(xc,erectAux(xa,xb,xc),erect(xa,xb,xc)).
180 [] -Col(xa,xb,xp)| -Col(xa,xb,xq)|xp=xq|xa=xb| -perpAt(xp,xq,xr,xc,xd)|perpAt(xa,xb,xr,xc,xd).
197 [] -opposite(xa,xp,xq,xc)| -Col(xp,xq,xr)| -sameside(xa,xr,xb)|opposite(xb,xp,xq,xc).
208 [] xp=xq| -perpAt(xp,xq,xc,xa,xc)| -perpAt(xp,xq,xc,xb,xc)|xa=xc|Col(xc,xa,xb).
228 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
241 [] -sameside(xa,xp,xb)|xb!=xp.
243 [] -T(xp,xa,xb)|xa=xp|xb=xp|sameside(xa,xp,xb).
244 [] -T(xp,xb,xa)|xa=xp|xb=xp|sameside(xa,xp,xb).
260 [] -perpAt(y,z,x,y1,z1)|y1!=z1.
261 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
267 [] xp=xq|Col(xp,xq,xa)|Col(xp,xq,xb)| -T(xa,xt,xb)| -Col(xp,xq,xt)|opposite(xa,xp,xq,xb).
283 [] -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).
285 [] p!=q.
286 [] -Col(p,q,r).
287 [] -Col(p,q,cs).
288 [] -samesideline(r,cs,p,q).
289 [] -opposite(r,p,q,cs).
290 [] p=foot(p,q,r).
292 [] r1=erect(e,q,cs).
293 [] f=erectAux(e,q,cs).
294 [] foot(p,q,r)=e.
296 [] erectAux(e,q,cs)=f.
362 [binary,285.1,125.2] s(p,x)!=s(q,x).
415 [binary,286.1,163.1,demod,294] perp(p,q,r,e).
416 [binary,286.1,162.1,demod,294] Col(p,q,e).
428 [ur,104,285,52,52,52,286] x=x.
473 [para_from,290.1.1,285.1.1,demod,294] e!=q.
492 [para_from,292.1.2,173.2.3,demod,296,unit_del,473] T(cs,f,r1).
493 [para_from,292.1.2,171.2.3,unit_del,473] perp(e,q,r1,e).
501 [para_from,293.1.2,172.2.3,unit_del,473] Col(e,q,f).
536 [binary,415.1,157.3,unit_del,285,416] perpAt(p,q,e,r,e).
587 [binary,428.1,118.2] s(x,x)=x.
680 [binary,492.1,26.1] T(r1,f,cs).
724 [binary,493.1,157.3,unit_del,473,53] perpAt(e,q,e,r1,e).
768 [binary,536.1,260.1] r!=e.
811 [para_from,587.1.1,362.1.2] s(p,q)!=q.
902 [binary,724.1,260.1] r1!=e.
910 [hyper,261,724,501,53] R(f,e,r1).
976 [binary,811.1,118.1] q!=p.
1086 [ur,28,25,902] -T(e,r1,e).
1147 [ur,103,976,53] Col(p,q,q).
1186 [binary,1086.1,87.3,unit_del,53] sameside(e,r1,e).
1218 [hyper,180,416,1147,724,unit_del,473,285] perpAt(p,q,e,r1,e).
1219 [hyper,167,416,1147,501,unit_del,285,473] Col(p,q,f).
1252 [binary,1186.1,241.1] e!=r1.
1276 [hyper,208,1218,536,unit_del,285,902] Col(e,r1,r).
1327 [ur,267,285,286,287,1219,289] -T(r,f,cs).
1372 [ur,137,910,910,1252] -T(f,r1,f).
1431 [binary,1276.1,47.1] Col(r1,r,e).
1439 [ur,167,285,1252,416,1276,286] -Col(p,q,r1).
1472 [ur,32,25,1327] -T(cs,f,cs).
1495 [ur,30,27,1372] -T(r1,f,r1).
1535 [ur,267,285,1439,287,680,1219] opposite(r1,p,q,cs).
1577 [binary,1472.1,87.3,unit_del,53] sameside(cs,f,cs).
1599 [binary,1495.1,87.3,unit_del,53] sameside(r1,f,r1).
1638 [ur,197,1535,416,289] -sameside(r1,e,r).
1696 [binary,1577.1,241.1] cs!=f.
1721 [binary,1599.1,241.1] r1!=f.
1743 [binary,1638.1,244.4,unit_del,902,768] -T(e,r,r1).
1744 [binary,1638.1,243.4,unit_del,902,768] -T(e,r1,r).
1846 [ur,283,492,416,1219,285,902,1721,768,1696,286,287,288] -T(r,e,r1).
2085 [binary,1743.1,26.2] -T(r1,r,e).
2102 [binary,1744.1,228.4,unit_del,1431,2085,1846] $F.