Sindbad~EG File Manager

Length of proof is 177.  Level of proof is 42.
 
---------------- 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).
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.
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).
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).
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).
104 [] 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,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).
153 [] -perp(xa,xb,xp,xq)| -Col(xa,xb,xp)| -Col(xa,xb,xq).
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).
189 [] -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).
194 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
195 [] Col(xa,xb,xc)| -T(xa,xb,xc).
196 [] Col(xa,xb,xc)| -T(xb,xc,xa).
197 [] Col(xa,xb,xc)| -T(xc,xa,xb).
206 [] -sameside(xa,xp,xb)|xa!=xp.
207 [] -sameside(xa,xp,xb)|xb!=xp.
211 [] -M(xa,xm,xb)|T(xa,xm,xb).
212 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
213 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
221 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
222 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
225 [] -perpAt(y,z,x,y1,z1)|y!=z.
226 [] -perpAt(y,z,x,y1,z1)|y1!=z1.
227 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
231 [] -perp(xp,xq,xp1,xq1)|perpAt(xp,xq,il(xp,xq,xp1,xq1),xp1,xq1).
234 [] perp(p,a,a,b).
235 [] perp(q,b,a,b).
236 [] Col(a,b,t).
237 [] T(p,t,q).
238 [] T(b,r,q).
239 [] E(a,p,b,r).
240 [] cx=ip(p,t,q,b,r).
241 [] -M(a,cx,b).
242 [] p1=s(a,p).
243 [] m=isomidpoint(r,r1,cx).
244 [] r1=ext(p1,cx,cx,r).
419 [binary,234.1,231.1] perpAt(p,a,il(p,a,a,b),a,b).
420 [binary,234.1,165.1] perp(a,p,a,b).
422 [binary,234.1,142.1] perp(a,b,p,a).
424 [binary,235.1,165.1] perp(b,q,a,b).
430 [binary,236.1,49.1] Col(b,a,t).
469 [binary,238.1,197.2] Col(r,q,b).
484 [binary,238.1,27.2] -T(r,b,q)|r=b.
501 [binary,239.1,17.1] E(a,p,r,b).
503 [binary,239.1,14.1] E(b,r,a,p).
517 [para_from,240.1.2,9.3.2,unit_del,237,238] T(r,cx,p).
518 [para_from,240.1.2,8.3.2,unit_del,237,238] T(t,cx,b).
531 [para_from,242.1.2,221.2.4] -R(x,a,p)|E(x,p,x,p1).
540 [para_from,242.1.2,113.1.1.2] s(a,p1)=p.
542 [para_from,242.1.2,110.1.3] M(p,a,p1).
550 [para_from,243.1.2,131.2.2] -E(cx,r,cx,r1)|M(r,m,r1).
558 [para_from,244.1.2,5.1.2] E(cx,r1,cx,r).
559 [para_from,244.1.2,4.1.3] T(p1,cx,r1).
560 [binary,419.1,226.1] a!=b.
561 [binary,419.1,225.1] p!=a.
573 [binary,422.1,156.3,unit_del,560,52] perpAt(a,b,a,p,a).
587 [binary,424.1,153.1,unit_del,52] -Col(b,q,a).
588 [binary,424.1,142.1] perp(a,b,b,q).
592 [binary,420.1,153.1,unit_del,52] -Col(a,p,b).
604 [binary,469.1,50.1] Col(r,b,q).
606 [binary,469.1,48.1] Col(b,q,r).
621 [hyper,2,501,1] E(r,b,p,a).
644 [binary,517.1,197.2] Col(cx,p,r).
645 [binary,517.1,196.2] Col(p,r,cx).
646 [binary,517.1,195.2] Col(r,cx,p).
661 [binary,517.1,25.1] T(p,cx,r).
675 [binary,518.1,196.2] Col(b,t,cx).
691 [binary,518.1,25.1] T(b,cx,t).
734 [para_from,540.1.1,110.1.3] M(p1,a,p).
744 [binary,542.1,212.1] E(a,p,a,p1).
745 [binary,542.1,211.1] T(p,a,p1).
754 [binary,550.1,14.2,unit_del,558] M(r,m,r1).
759 [binary,558.1,17.1] E(cx,r1,r,cx).
761 [binary,558.1,14.1] E(cx,r,cx,r1).
792 [binary,559.1,25.1] T(r1,cx,p1).
806 [binary,560.1,137.3] -R(x,a,b)| -R(x,b,a).
834 [ur,27,24,560] -T(b,a,b).
848 [binary,561.1,21.2] -E(p,a,x,x).
875 [binary,588.1,231.1] perpAt(a,b,il(a,b,b,q),b,q).
948 [binary,675.1,49.1] Col(t,b,cx).
984 [binary,734.1,212.1] E(a,p1,a,p).
985 [binary,734.1,211.1] T(p1,a,p).
1000 [binary,744.1,17.1] E(a,p,p1,a).
1060 [binary,754.1,211.1] T(r,m,r1).
1063 [binary,754.1,112.1] r1=s(m,r).
1066 [binary,754.1,107.1] M(r1,m,r).
1089 [hyper,2,759,1] E(r,cx,r1,cx).
1146 [binary,834.1,86.3,unit_del,52] sameside(b,a,b).
1172 [binary,848.1,14.2] -E(x,x,p,a).
1182 [binary,875.1,226.1] b!=q.
1264 [hyper,2,501,1000] E(r,b,p1,a).
1269 [binary,1060.1,196.2] Col(r1,r,m).
1285 [binary,1060.1,25.1] T(r1,m,r).
1311 [para_from,1063.1.1,761.1.4] E(cx,r,cx,s(m,r)).
1345 [binary,1146.1,207.1] b!=a.
1365 [ur,156,1182,52,424] perpAt(b,q,b,a,b).
1441 [binary,1311.1,222.2] R(cx,m,r).
1459 [ur,102,1345,52] Col(a,b,b).
1479 [hyper,227,1365,606,52] R(r,b,a).
1499 [hyper,158,52,1459,422,unit_del,560,1345] R(p,a,b).
1513 [binary,1479.1,806.2] -R(r,a,b).
1519 [binary,1479.1,132.1] R(a,b,r).
1523 [binary,1499.1,806.1] -R(p,b,a).
1529 [binary,1499.1,132.1] R(b,a,p).
1569 [ur,133,1499,561,1513] -Col(a,p,r).
1581 [hyper,133,1519,430,unit_del,560] R(t,b,r).
1582 [hyper,133,1519,52,unit_del,560] R(b,b,r).
1602 [ur,227,1365,52,1523] -Col(b,q,p).
1620 [hyper,133,1529,236,unit_del,1345] R(t,a,p).
1627 [binary,1569.1,197.1] -T(r,a,p).
1628 [binary,1569.1,196.1] -T(p,r,a).
1629 [binary,1569.1,195.1] -T(a,p,r).
1634 [binary,1569.1,50.2] -Col(a,r,p).
1635 [binary,1569.1,48.2] -Col(r,p,a).
1637 [binary,1569.1,46.2] -Col(r,a,p).
1676 [binary,1602.1,197.1] -T(p,b,q).
1688 [binary,1602.1,46.2] -Col(p,b,q).
1722 [binary,1627.1,25.2] -T(p,a,r).
1738 [ur,32,517,1627] -T(r,a,cx).
1819 [ur,29,985,1629] -T(p1,p,r).
1869 [ur,61,745,1628,1722] -T(p,r,p1).
1890 [ur,32,745,1722] -T(p,p1,r).
2047 [ur,31,661,1890] -T(cx,p1,r).
2089 [ur,29,792,2047] -T(r1,p1,r).
2125 [ur,31,1285,2089] -T(m,p1,r).
4171 [ur,98,561,38,37,1635] r!=p.
4252 [ur,98,4171,38,37,1634] a!=r.
4844 [ur,98,1182,38,37,1688] p!=b.
4894 [ur,98,4844,38,37,592] a!=p.
4959 [ur,136,1529,1620,4894] -T(b,p,t).
4960 [ur,98,4894,38,37,1637] r!=a.
5063 [ur,102,4960,52] Col(a,r,r).
5191 [para_from,484.2.1,621.1.1,unit_del,1172] -T(r,b,q).
10314 [ur,32,691,4959] -T(b,p,cx).
10359 [ur,28,24,10314] -T(p,cx,p).
10395 [ur,28,661,10359] -T(cx,p,r).
10404 [binary,10395.1,86.3,unit_del,644] sameside(cx,p,r).
10441 [binary,10404.1,206.1] cx!=p.
10930 [binary,5191.1,86.3,unit_del,604] sameside(r,b,q).
10958 [ur,29,26,5191] -T(b,r,b).
10963 [binary,10930.1,206.1] r!=b.
10978 [binary,10958.1,86.3,unit_del,52] sameside(b,r,b).
11046 [ur,104,4252,1182,5063,606,52,10963,52,587] -Col(a,r,b).
11118 [binary,10978.1,207.1] b!=r.
11297 [ur,136,1582,1581,11118] -T(b,r,t).
11367 [ur,33,238,11118,1676] -T(p,b,r).
11405 [ur,32,691,11297] -T(b,r,cx).
11445 [ur,32,661,11367] -T(p,b,cx).
11495 [ur,31,24,11405] -T(cx,r,cx).
11553 [ur,31,24,11445] -T(cx,b,cx).
11589 [ur,29,661,11495] -T(p,r,cx).
11624 [ur,29,518,11553] -T(t,b,cx).
11635 [binary,11589.1,86.3,unit_del,645] sameside(p,r,cx).
11671 [binary,11624.1,86.3,unit_del,948] sameside(t,b,cx).
11700 [binary,11635.1,207.1] cx!=r.
11712 [binary,11671.1,207.1] cx!=b.
11713 [binary,11671.1,206.1] t!=b.
11754 [ur,99,11700,661,1890,1819] -T(p1,cx,r).
11755 [ur,99,11700,661,1722,1629] -T(a,cx,r).
11823 [ur,30,661,11700,1869] -T(cx,r,p1).
11824 [ur,30,661,11700,1628] -T(cx,r,a).
11945 [ur,166,1345,11713,430,52,948] Col(b,a,cx).
11946 [ur,166,560,11713,236,1459,948] Col(a,b,cx).
12089 [binary,11755.1,194.2,unit_del,11824,1738] -Col(a,cx,r).
12095 [binary,11755.1,25.2] -T(r,cx,a).
12133 [binary,11823.1,25.2] -T(p1,r,cx).
12210 [binary,11945.1,46.1] Col(a,cx,b).
12316 [hyper,227,573,11946,52] R(cx,a,p).
12396 [ur,98,11700,10441,517,12089] a!=cx.
12492 [ur,61,559,11754,12133] -T(p1,r,r1).
12610 [ur,127,11046,4171,621,12210,646,241] -E(a,r,b,p).
12648 [binary,12316.1,531.1] E(cx,p,cx,p1).
12818 [binary,12492.1,25.2] -T(r1,r,p1).
12870 [binary,12648.1,14.1] E(cx,p1,cx,p).
12880 [hyper,130,517,792,761,12648,754,542] T(m,cx,a).
12884 [hyper,130,661,559,12648,761,542,754] T(a,cx,m).
12897 [hyper,19,517,792,1089,12648] E(r,p,r1,p1).
12980 [hyper,56,12210,984,12870,unit_del,12396] E(b,p1,b,p).
13134 [ur,29,12880,12095] -T(m,r,cx).
13139 [binary,12884.1,197.2] Col(cx,m,a).
13141 [binary,12884.1,195.2] Col(a,cx,m).
13313 [hyper,2,12897,1] E(r1,p1,p,r).
13349 [ur,2,12980,12610] -E(b,p1,a,r).
13385 [ur,29,26,13134] -T(r,m,r).
13523 [hyper,166,52,11946,13141,unit_del,560,12396] Col(a,b,m).
13560 [binary,13349.1,41.2] -IFS(x,b,y,p1,z,a,u,r).
13598 [ur,29,1285,13385] -T(r1,r,m).
13612 [hyper,227,1365,606,13523] R(r,b,m).
13639 [hyper,103,11946,1459,13523,unit_del,11712,560] Col(cx,b,m).
13710 [binary,13598.1,86.3,unit_del,1269] sameside(r1,r,m).
13785 [binary,13639.1,47.1] Col(m,cx,b).
13829 [binary,13710.1,207.1] m!=r.
13830 [binary,13710.1,206.1] r1!=r.
14067 [ur,30,1285,13829,12818] -T(m,r,p1).
14087 [ur,111,1066,13830] -M(r1,m,r1).
14222 [binary,14087.1,213.3,unit_del,13] -T(r1,m,r1).
14231 [binary,14222.1,86.3,unit_del,52] sameside(r1,m,r1).
14378 [binary,14231.1,207.1] r1!=m.
14468 [ur,60,14378,1285,2125,14067] -T(r1,m,p1).
14516 [ur,32,792,14468] -T(r1,m,cx).
14567 [ur,28,24,14516] -T(m,cx,m).
14613 [ur,28,12880,14567] -T(cx,m,a).
14620 [binary,14613.1,86.3,unit_del,13139] sameside(cx,m,a).
14660 [binary,14620.1,206.1] cx!=m.
14694 [ur,133,1441,14660,13785] R(b,m,r).
14804 [binary,14694.1,132.1] R(r,m,b).
14837 [binary,14804.1,137.1,unit_del,13612] m=b.
14914 [para_from,14837.1.1,1060.1.2] T(r,b,r1).
14915 [para_from,14837.1.1,754.1.2] M(r,b,r1).
15391 [binary,14915.1,212.1] E(b,r,b,r1).
15451 [hyper,2,15391,503] E(b,r1,a,p).
15465 [hyper,19,14914,985,1264,15451] E(r,r1,p1,p).
15470 [ur,189,14914,985,15451,1,13313,13560] -E(r,r1,p1,p).
15471 [binary,15470.1,15465.1] $F.