Sindbad~EG File Manager

Length of proof is 154.  Level of proof is 38.
 
---------------- PROOF ----------------
 
1 [] E(x,y,y,x).
2 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
4 [] T(x,y,ext(x,y,w,v)).
5 [] E(y,ext(x,y,w,v),w,v).
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).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
16 [] -E(xa,xb,xc,xd)|E(xb,xa,xc,xd).
17 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
19 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
21 [] -E(xb,xc,xa,xa)|xb=xc.
22 [] -E(xa,xb,xc,xd)|E(xb,xa,xd,xc).
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
26 [] T(xa1,xa1,xb1).
27 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
28 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
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).
32 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
33 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xb,xd).
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
41 [] -IFS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xb,xd,xb1,xd1).
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).
52 [] Col(xa,xb,xa).
56 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xp,xa,xq)| -E(xb,xp,xb,xq)|E(xc,xp,xc,xq).
60 [] xa=xb| -T(xa,xb,xc)| -T(xa,xb,xd)|T(xb,xc,xd)|T(xb,xd,xc).
61 [] -T(xa,xb,xd)| -T(xa,xc,xd)|T(xa,xb,xc)|T(xa,xc,xb).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
98 [] xp=xq|xp=xr| -T(xq,xp,xr)|xa!=xp|Col(xa,xp,xq).
99 [] xa=xb| -T(xc,xa,xb)| -T(xd,xa,xb)|T(xd,xc,xb)|T(xc,xd,xb).
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).
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).
113 [] s(xa,s(xa,xp))=xp.
127 [] Col(xa,xb,xc)|xb=xd| -E(xa,xb,xc,xd)| -E(xb,xc,xd,xa)| -Col(xa,xp,xc)| -Col(xb,xp,xd)|M(xa,xp,xc).
130 [] -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).
131 [] -E(xc,xa,xc,xb)|M(xa,isomidpoint(xa,xb,xc),xb).
132 [] -R(xa,xb,xc)|R(xc,xb,xa).
133 [] -R(xa,xb,xc)|xa=xb| -Col(xb,xa,xa1)|R(xa1,xb,xc).
136 [] -R(xa,xb,xc)| -R(xa1,xb,xc)| -T(xa,xc,xa1)|xb=xc.
137 [] -R(xa,xb,xc)| -R(xa,xc,xb)|xb=xc.
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).
158 [] xa=xb| -Col(xa,xb,xp)| -Col(xa,xb,xq)|xq=xp|R(xc,xp,xq)| -perp(xa,xb,xc,xp).
165 [] -perp(xa,xb,xp,xq)|perp(xb,xa,xp,xq).
166 [] xa=xb|xc=xd| -Col(xa,xb,xc)| -Col(xa,xb,xd)| -Col(xc,xd,xp)|Col(xa,xb,xp).
175 [] -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(xa,xcx,xb).
190 [] -T(xa,xb,xc)| -T(za,zb,zc)| -E(xa,xc,za,zc)| -E(xb,xc,zb,zc)| -E(xa,xd,za,zd)| -E(xc,xd,zc,zd)|IFS(xa,xb,xc,xd,za,zb,zc,zd).
195 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
196 [] Col(xa,xb,xc)| -T(xa,xb,xc).
197 [] Col(xa,xb,xc)| -T(xb,xc,xa).
198 [] Col(xa,xb,xc)| -T(xc,xa,xb).
207 [] -sameside(xa,xp,xb)|xa!=xp.
208 [] -sameside(xa,xp,xb)|xb!=xp.
212 [] -M(xa,xm,xb)|T(xa,xm,xb).
213 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
214 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
222 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
223 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
226 [] -perpAt(y,z,x,y1,z1)|y!=z.
227 [] -perpAt(y,z,x,y1,z1)|y1!=z1.
228 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
232 [] -perp(xp,xq,xp1,xq1)|perpAt(xp,xq,il(xp,xq,xp1,xq1),xp1,xq1).
235 [] perp(p,a,a,b).
236 [] perp(q,b,a,b).
237 [] Col(a,b,t).
238 [] T(p,t,q).
239 [] T(b,r,q).
240 [] E(a,p,b,r).
241 [] cx=ip(p,t,q,b,r).
242 [] -M(p,cx,r).
243 [] p1=s(a,p).
244 [] m=isomidpoint(r,r1,cx).
245 [] r1=ext(p1,cx,cx,r).
412 [binary,235.1,232.1] perpAt(p,a,il(p,a,a,b),a,b).
415 [binary,235.1,142.1] perp(a,b,p,a).
417 [binary,236.1,165.1] perp(b,q,a,b).
423 [binary,237.1,49.1] Col(b,a,t).
462 [binary,239.1,198.2] Col(r,q,b).
477 [binary,239.1,27.2] -T(r,b,q)|r=b.
493 [binary,240.1,22.1] E(p,a,r,b).
494 [binary,240.1,17.1] E(a,p,r,b).
495 [binary,240.1,16.1] E(p,a,b,r).
496 [binary,240.1,14.1] E(b,r,a,p).
509 [hyper,175,235,236,237,238,239,240,241] M(a,cx,b).
511 [para_from,241.1.2,9.3.2,unit_del,238,239] T(r,cx,p).
512 [para_from,241.1.2,8.3.2,unit_del,238,239] T(t,cx,b).
525 [para_from,243.1.2,222.2.4] -R(x,a,p)|E(x,p,x,p1).
534 [para_from,243.1.2,113.1.1.2] s(a,p1)=p.
536 [para_from,243.1.2,110.1.3] M(p,a,p1).
544 [para_from,244.1.2,131.2.2] -E(cx,r,cx,r1)|M(r,m,r1).
552 [para_from,245.1.2,5.1.2] E(cx,r1,cx,r).
553 [para_from,245.1.2,4.1.3] T(p1,cx,r1).
554 [binary,412.1,227.1] a!=b.
555 [binary,412.1,226.1] p!=a.
582 [binary,417.1,142.1] perp(a,b,b,q).
600 [binary,462.1,48.1] Col(b,q,r).
647 [binary,511.1,198.2] Col(cx,p,r).
648 [binary,511.1,197.2] Col(p,r,cx).
664 [binary,511.1,25.1] T(p,cx,r).
678 [binary,512.1,197.2] Col(b,t,cx).
694 [binary,512.1,25.1] T(b,cx,t).
737 [para_from,534.1.1,110.1.3] M(p1,a,p).
749 [binary,536.1,213.1] E(a,p,a,p1).
750 [binary,536.1,212.1] T(p,a,p1).
759 [binary,544.1,14.2,unit_del,552] M(r,m,r1).
766 [binary,552.1,17.1] E(cx,r1,r,cx).
768 [binary,552.1,14.1] E(cx,r,cx,r1).
797 [binary,553.1,25.1] T(r1,cx,p1).
811 [binary,554.1,137.3] -R(x,a,b)| -R(x,b,a).
839 [ur,27,24,554] -T(b,a,b).
853 [binary,555.1,21.2] -E(p,a,x,x).
885 [binary,582.1,232.1] perpAt(a,b,il(a,b,b,q),b,q).
895 [binary,647.1,49.1] Col(p,cx,r).
943 [binary,678.1,49.1] Col(t,b,cx).
974 [binary,737.1,213.1] E(a,p1,a,p).
975 [binary,737.1,212.1] T(p1,a,p).
995 [binary,749.1,17.1] E(a,p,p1,a).
1054 [binary,759.1,212.1] T(r,m,r1).
1057 [binary,759.1,112.1] r1=s(m,r).
1060 [binary,759.1,107.1] M(r1,m,r).
1078 [hyper,2,766,1] E(r,cx,r1,cx).
1130 [binary,839.1,86.3,unit_del,52] sameside(b,a,b).
1177 [binary,885.1,227.1] b!=q.
1263 [hyper,2,494,995] E(r,b,p1,a).
1268 [binary,1054.1,197.2] Col(r1,r,m).
1284 [binary,1054.1,25.1] T(r1,m,r).
1310 [para_from,1057.1.1,768.1.4] E(cx,r,cx,s(m,r)).
1344 [binary,1130.1,208.1] b!=a.
1364 [ur,156,1177,52,417] perpAt(b,q,b,a,b).
1440 [binary,1310.1,223.2] R(cx,m,r).
1458 [ur,102,1344,52] Col(a,b,b).
1478 [hyper,228,1364,600,52] R(r,b,a).
1498 [hyper,158,52,1458,415,unit_del,554,1344] R(p,a,b).
1512 [binary,1478.1,811.2] -R(r,a,b).
1518 [binary,1478.1,132.1] R(a,b,r).
1522 [binary,1498.1,811.1] -R(p,b,a).
1528 [binary,1498.1,132.1] R(b,a,p).
1574 [ur,133,1498,555,1512] -Col(a,p,r).
1586 [hyper,133,1518,423,unit_del,554] R(t,b,r).
1587 [hyper,133,1518,52,unit_del,554] R(b,b,r).
1603 [ur,228,1364,52,1522] -Col(b,q,p).
1628 [binary,1574.1,198.1] -T(r,a,p).
1629 [binary,1574.1,197.1] -T(p,r,a).
1630 [binary,1574.1,196.1] -T(a,p,r).
1633 [binary,1574.1,102.3,unit_del,555] -Col(p,a,r).
1677 [binary,1603.1,198.1] -T(p,b,q).
1723 [binary,1628.1,25.2] -T(p,a,r).
1739 [ur,32,511,1628] -T(r,a,cx).
1820 [ur,29,975,1630] -T(p1,p,r).
1903 [ur,61,750,1629,1723] -T(p,r,p1).
1921 [ur,32,750,1723] -T(p,p1,r).
2077 [ur,31,664,1921] -T(cx,p1,r).
2114 [ur,29,797,2077] -T(r1,p1,r).
2150 [ur,31,1284,2114] -T(m,p1,r).
2406 [binary,509.1,212.1] T(a,cx,b).
5208 [para_from,477.2.1,495.1.4,unit_del,853] -T(r,b,q).
7246 [binary,2406.1,197.2] Col(b,a,cx).
7247 [binary,2406.1,196.2] Col(a,cx,b).
7347 [binary,7246.1,102.2,unit_del,1344] Col(a,b,cx).
7450 [ur,127,1633,554,493,895,7247,242] -E(a,r,b,p).
7476 [hyper,133,1528,7347,unit_del,1344] R(cx,a,p).
7525 [binary,7476.1,525.1] E(cx,p,cx,p1).
7562 [binary,7525.1,14.1] E(cx,p1,cx,p).
7572 [hyper,130,511,797,768,7525,759,536] T(m,cx,a).
7576 [hyper,130,664,553,7525,768,536,759] T(a,cx,m).
7585 [hyper,19,511,797,1078,7525] E(r,p,r1,p1).
7719 [binary,7576.1,198.2] Col(cx,m,a).
7721 [binary,7576.1,196.2] Col(a,cx,m).
7830 [hyper,2,7585,1] E(r1,p1,p,r).
11782 [ur,29,26,5208] -T(b,r,b).
11802 [binary,11782.1,86.3,unit_del,52] sameside(b,r,b).
11946 [binary,11802.1,208.1] b!=r.
11972 [ur,136,1587,1586,11946] -T(b,r,t).
12043 [ur,33,239,11946,1677] -T(p,b,r).
12084 [ur,32,694,11972] -T(b,r,cx).
12127 [ur,32,664,12043] -T(p,b,cx).
12198 [ur,31,24,12084] -T(cx,r,cx).
12243 [ur,31,24,12127] -T(cx,b,cx).
12282 [ur,29,664,12198] -T(p,r,cx).
12321 [ur,29,512,12243] -T(t,b,cx).
12334 [binary,12282.1,86.3,unit_del,648] sameside(p,r,cx).
12371 [binary,12321.1,86.3,unit_del,943] sameside(t,b,cx).
12403 [binary,12334.1,208.1] cx!=r.
12414 [binary,12371.1,208.1] cx!=b.
12465 [ur,99,12403,664,1921,1820] -T(p1,cx,r).
12466 [ur,99,12403,664,1723,1630] -T(a,cx,r).
12532 [ur,30,664,12403,1903] -T(cx,r,p1).
12533 [ur,30,664,12403,1629] -T(cx,r,a).
12806 [binary,12466.1,195.2,unit_del,12533,1739] -Col(a,cx,r).
12812 [binary,12466.1,25.2] -T(r,cx,a).
12860 [binary,12532.1,25.2] -T(p1,r,cx).
12942 [ur,98,12403,38,37,12806] a!=cx.
13022 [ur,29,7572,12812] -T(m,r,cx).
13044 [ur,61,553,12465,12860] -T(p1,r,r1).
13087 [ur,166,554,12942,52,7347,7721] Col(a,b,m).
13187 [ur,56,12942,7247,974,7562] E(b,p1,b,p).
13235 [ur,29,26,13022] -T(r,m,r).
13259 [binary,13044.1,25.2] -T(r1,r,p1).
13300 [hyper,228,1364,600,13087] R(r,b,m).
13329 [hyper,103,7347,1458,13087,unit_del,12414,554] Col(cx,b,m).
13434 [ur,2,13187,7450] -E(b,p1,a,r).
13467 [ur,29,1284,13235] -T(r1,r,m).
13563 [binary,13329.1,47.1] Col(m,cx,b).
13608 [binary,13434.1,41.2] -IFS(x,b,y,p1,z,a,u,r).
13618 [binary,13467.1,86.3,unit_del,1268] sameside(r1,r,m).
13777 [binary,13618.1,208.1] m!=r.
13778 [binary,13618.1,207.1] r1!=r.
13889 [ur,30,1284,13777,13259] -T(m,r,p1).
13909 [ur,111,1060,13778] -M(r1,m,r1).
14045 [binary,13909.1,214.3,unit_del,13] -T(r1,m,r1).
14055 [binary,14045.1,86.3,unit_del,52] sameside(r1,m,r1).
14203 [binary,14055.1,208.1] r1!=m.
14293 [ur,60,14203,1284,2150,13889] -T(r1,m,p1).
14347 [ur,32,797,14293] -T(r1,m,cx).
14399 [ur,28,24,14347] -T(m,cx,m).
14446 [ur,28,7572,14399] -T(cx,m,a).
14453 [binary,14446.1,86.3,unit_del,7719] sameside(cx,m,a).
14490 [binary,14453.1,207.1] cx!=m.
14524 [ur,133,1440,14490,13563] R(b,m,r).
14636 [binary,14524.1,132.1] R(r,m,b).
14669 [binary,14636.1,137.1,unit_del,13300] m=b.
14741 [para_from,14669.1.1,1054.1.2] T(r,b,r1).
14742 [para_from,14669.1.1,759.1.2] M(r,b,r1).
15211 [binary,14742.1,213.1] E(b,r,b,r1).
15271 [hyper,2,15211,496] E(b,r1,a,p).
15285 [hyper,19,14741,975,1263,15271] E(r,r1,p1,p).
15290 [ur,190,14741,975,15271,1,7830,13608] -E(r,r1,p1,p).
15291 [binary,15290.1,15285.1] $F.