Sindbad~EG File Manager

Length of proof is 182.  Level of proof is 44.
 
---------------- 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).
18 [] E(xa,xa,xb,xb).
19 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
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).
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).
48 [] -Col(xa,xb,xc)|Col(xc,xb,xa).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
51 [] Col(xa,xa,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).
59 [] xa=xb| -T(xa,xb,xc)| -T(xa,xb,xd)|T(xa,xc,xd)|T(xa,xd,xc).
61 [] -T(xa,xb,xd)| -T(xa,xc,xd)|T(xa,xb,xc)|T(xa,xc,xb).
66 [] -le(xa,xb,xc,xd)| -E(xa,xb,xa1,xb1)| -E(xc,xd,xc1,xd1)|le(xa1,xb1,xc1,xd1).
67 [] le(xa,xb,xa,xb).
69 [] -le(xa,xb,xc,xd)| -le(xc,xd,xa,xb)|E(xa,xb,xc,xd).
74 [] -T(xa,xb,xc)| -E(xa,xc,xa,xb)|xc=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).
95 [] xp=xq|xp=xr| -T(xq,xp,xr)| -Col(xa,xp,xq)|xa=xp|sameside(xa,xp,xq)|sameside(xa,xp,xr).
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).
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).
108 [] -M(xa,xm,xa)|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).
113 [] s(xa,s(xa,xp))=xp.
116 [] s(xa,xp)!=xp|xp=xa.
117 [] s(xa,xp)=xp|xp!=xa.
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).
187 [] -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).
193 [] Col(xa,xb,xc)| -T(xa,xb,xc).
194 [] Col(xa,xb,xc)| -T(xb,xc,xa).
195 [] Col(xa,xb,xc)| -T(xc,xa,xb).
201 [] -le(xa,xb,xc,xd)|T(xc,insert(xa,xb,xc,xd),xd).
202 [] -le(xa,xb,xc,xd)|E(xa,xb,xc,insert(xa,xb,xc,xd)).
203 [] -T(xc,y,xd)| -E(xa,xb,xc,y)|le(xa,xb,xc,xd).
204 [] -sameside(xa,xp,xb)|xa!=xp.
205 [] -sameside(xa,xp,xb)|xb!=xp.
206 [] -sameside(xa,xp,xb)|T(xp,xa,xb)|T(xp,xb,xa).
209 [] -M(xa,xm,xb)|T(xa,xm,xb).
210 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
211 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
219 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
220 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
222 [] -perpAt(y,z,x,y1,z1)|Col(y1,z1,x).
223 [] -perpAt(y,z,x,y1,z1)|y!=z.
224 [] -perpAt(y,z,x,y1,z1)|y1!=z1.
225 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
229 [] -perp(xp,xq,xp1,xq1)|perpAt(xp,xq,il(xp,xq,xp1,xq1),xp1,xq1).
232 [] le(a,p,b,q).
233 [] perp(a,b,a,p).
234 [] perp(a,b,b,q).
235 [] T(p,t,q).
236 [] Col(a,b,t).
237 [] -M(a,x,b).
238 [] r=insert(a,p,b,q).
239 [] cx=ip(p,t,q,b,r).
240 [] p1=s(a,p).
241 [] r1=ext(p1,cx,cx,r).
242 [] m=isomidpoint(r,r1,cx).
243 [] insert(a,p,b,q)=r.
245 [] s(a,p)=p1.
430 [binary,232.1,202.1,demod,243] E(a,p,b,r).
431 [binary,232.1,201.1,demod,243] T(b,r,q).
435 [binary,233.1,229.1] perpAt(a,b,il(a,b,a,p),a,p).
436 [binary,233.1,165.1] perp(b,a,a,p).
437 [binary,233.1,153.1,unit_del,52] -Col(a,b,p).
441 [binary,234.1,229.1] perpAt(a,b,il(a,b,b,q),b,q).
443 [binary,234.1,142.1] perp(b,q,a,b).
461 [binary,236.1,49.1] Col(b,a,t).
477 [para_from,238.1.2,90.3.1] q=b|a=p|sameside(r,b,q).
485 [para_from,239.1.2,9.3.2,unit_del,235,431] T(r,cx,p).
486 [para_from,239.1.2,8.3.2,unit_del,235,431] T(t,cx,b).
494 [para_into,240.1.2,117.1.1] p1=p|p!=a.
496 [para_from,240.1.2,219.2.4] -R(x,a,p)|E(x,p,x,p1).
500 [para_from,240.1.2,113.1.1.2] s(a,p1)=p.
502 [para_from,240.1.2,110.1.3] M(p,a,p1).
510 [para_from,241.1.2,5.1.2] E(cx,r1,cx,r).
511 [para_from,241.1.2,4.1.3] T(p1,cx,r1).
519 [para_from,242.1.2,131.2.2] -E(cx,r,cx,r1)|M(r,m,r1).
521 [binary,430.1,17.1] E(a,p,r,b).
523 [binary,430.1,14.1] E(b,r,a,p).
545 [binary,435.1,224.1] a!=p.
546 [binary,435.1,223.1] a!=b.
551 [binary,436.1,142.1] perp(a,p,b,a).
568 [binary,441.1,224.1] b!=q.
572 [binary,443.1,156.3,unit_del,568,52] perpAt(b,q,b,a,b).
573 [binary,443.1,153.1,unit_del,52] -Col(b,q,a).
584 [hyper,224,435,477] q=b|sameside(r,b,q).
585 [binary,485.1,195.2] Col(cx,p,r).
586 [binary,485.1,194.2] Col(p,r,cx).
587 [binary,485.1,193.2] Col(r,cx,p).
593 [binary,485.1,25.1] T(p,cx,r).
600 [binary,486.1,194.2] Col(b,t,cx).
607 [binary,486.1,25.1] T(b,cx,t).
637 [para_from,500.1.1,110.1.3] M(p1,a,p).
648 [binary,502.1,210.1] E(a,p,a,p1).
649 [binary,502.1,209.1] T(p,a,p1).
659 [binary,510.1,17.1] E(cx,r1,r,cx).
661 [binary,510.1,14.1] E(cx,r,cx,r1).
662 [hyper,203,24,510] le(cx,r1,cx,r).
666 [hyper,66,67,510,13] le(cx,r,cx,r1).
674 [binary,511.1,194.2] Col(r1,p1,cx).
681 [binary,511.1,25.1] T(r1,cx,p1).
688 [binary,519.1,69.3,unit_del,666,662] M(r,m,r1).
690 [binary,519.2,209.1,unit_del,661] T(r,m,r1).
693 [binary,519.2,112.1,unit_del,661] r1=s(m,r).
696 [binary,519.2,107.1,unit_del,661] M(r1,m,r).
707 [hyper,2,521,1] E(r,b,p,a).
717 [binary,545.1,108.2] -M(p,a,p).
732 [binary,546.1,137.3] -R(x,a,b)| -R(x,b,a).
743 [ur,103,546,51,51,51,437] x=x.
744 [ur,102,546,52] Col(b,a,a).
745 [ur,27,24,546] -T(b,a,b).
748 [binary,551.1,165.1] perp(p,a,b,a).
771 [binary,572.1,222.1] Col(a,b,b).
794 [para_from,584.1.1,573.1.2,unit_del,51] sameside(r,b,q).
797 [binary,585.1,49.1] Col(p,cx,r).
823 [binary,593.1,85.2] -sameside(p,cx,r).
837 [binary,600.1,49.1] Col(t,b,cx).
865 [binary,637.1,210.1] E(a,p1,a,p).
866 [binary,637.1,209.1] T(p1,a,p).
874 [para_into,637.1.1,494.1.1,unit_del,717] p!=a.
878 [binary,648.1,17.1] E(a,p,p1,a).
933 [hyper,2,659,1] E(r,cx,r1,cx).
968 [binary,690.1,194.2] Col(r1,r,m).
975 [binary,690.1,25.1] T(r1,m,r).
992 [para_from,693.1.1,661.1.4] E(cx,r,cx,s(m,r)).
1024 [binary,743.1,109.2] M(x,x,x).
1043 [binary,745.1,86.3,unit_del,52] sameside(b,a,b).
1060 [binary,748.1,142.1] perp(b,a,p,a).
1074 [binary,794.1,204.1] r!=b.
1077 [binary,794.1,84.1] Col(r,b,q).
1139 [binary,874.1,116.2,demod,245] p1!=p.
1162 [hyper,2,521,878] E(r,b,p1,a).
1197 [binary,992.1,220.2] R(cx,m,r).
1231 [binary,1043.1,205.1] b!=a.
1240 [hyper,158,744,52,1060,unit_del,1231,1231] R(p,a,b).
1263 [binary,1077.1,46.1] Col(b,q,r).
1314 [binary,1240.1,732.1] -R(p,b,a).
1317 [binary,1240.1,132.1] R(b,a,p).
1325 [hyper,225,572,1263,52] R(r,b,a).
1327 [hyper,158,52,1263,443,unit_del,568,1074] R(a,b,r).
1330 [ur,166,568,1074,1263,52,573] -Col(r,b,a).
1359 [hyper,133,1317,236,unit_del,1231] R(t,a,p).
1365 [binary,1325.1,732.2] -R(r,a,b).
1373 [ur,133,1325,1074,1314] -Col(b,r,p).
1377 [hyper,133,1327,461,unit_del,546] R(t,b,r).
1390 [binary,1330.1,46.2] -Col(a,r,b).
1418 [ur,136,1317,1359,545] -T(b,p,t).
1438 [ur,133,1240,874,1365] -Col(a,p,r).
1451 [binary,1373.1,195.1] -T(p,b,r).
1532 [ur,32,607,1418] -T(b,p,cx).
1553 [binary,1438.1,195.1] -T(r,a,p).
1554 [binary,1438.1,194.1] -T(p,r,a).
1604 [ur,32,593,1451] -T(p,b,cx).
1628 [ur,28,24,1532] -T(p,cx,p).
1631 [binary,1553.1,25.2] -T(p,a,r).
1649 [ur,32,485,1553] -T(r,a,cx).
1650 [ur,31,866,1553] -T(r,p1,p).
1709 [ur,31,24,1604] -T(cx,b,cx).
1713 [binary,1628.1,86.3,unit_del,52] sameside(p,cx,p).
1731 [ur,28,593,1628] -T(cx,p,r).
1735 [ur,61,649,1554,1631] -T(p,r,p1).
1752 [ur,32,649,1631] -T(p,p1,r).
1790 [ur,28,24,1649] -T(a,cx,a).
1807 [ur,32,485,1650] -T(r,p1,cx).
1809 [ur,31,485,1650] -T(cx,p1,p).
1829 [ur,29,486,1709] -T(t,b,cx).
1831 [binary,1713.1,205.1] p!=cx.
1839 [binary,1731.1,86.3,unit_del,585] sameside(cx,p,r).
1895 [ur,31,593,1752] -T(cx,p1,r).
1898 [ur,130,26,26,18,13,1024,1790] -M(cx,a,cx).
1932 [ur,31,24,1807] -T(cx,p1,cx).
1954 [binary,1829.1,86.3,unit_del,837] sameside(t,b,cx).
2000 [binary,1839.1,205.1] r!=p.
2027 [ur,29,681,1895] -T(r1,p1,r).
2028 [binary,1898.1,109.1] a!=cx.
2046 [ur,29,681,1932] -T(r1,p1,cx).
2066 [binary,1954.1,204.1] t!=b.
2090 [ur,98,2000,38,37,1373] b!=r.
2134 [binary,2046.1,86.3,unit_del,674] sameside(r1,p1,cx).
2159 [ur,166,1231,2066,461,52,837] Col(b,a,cx).
2160 [ur,166,546,2066,236,771,837] Col(a,b,cx).
2164 [ur,133,1377,2066,600] R(cx,b,r).
2195 [binary,2134.1,205.1] cx!=p1.
2211 [binary,2159.1,46.1] Col(a,cx,b).
2242 [hyper,133,1317,2160,unit_del,1231] R(cx,a,p).
2267 [ur,136,2164,2164,2090] -T(cx,r,cx).
2339 [ur,127,1390,2000,707,2211,587,237] -E(a,r,b,p).
2348 [binary,2242.1,496.1] E(cx,p,cx,p1).
2377 [ur,29,593,2267] -T(p,r,cx).
2412 [binary,2348.1,14.1] E(cx,p1,cx,p).
2418 [hyper,130,485,681,661,2348,688,502] T(m,cx,a).
2419 [hyper,130,593,511,2348,661,502,688] T(a,cx,m).
2425 [hyper,19,485,681,933,2348] E(r,p,r1,p1).
2434 [binary,2377.1,86.3,unit_del,586] sameside(p,r,cx).
2454 [binary,2412.1,74.2,unit_del,1139] -T(cx,p,p1).
2467 [hyper,56,2211,865,2412,unit_del,2028] E(b,p1,b,p).
2475 [binary,2418.1,193.2] Col(m,cx,a).
2516 [binary,2419.1,195.2] Col(cx,m,a).
2518 [binary,2419.1,193.2] Col(a,cx,m).
2575 [hyper,2,2425,1] E(r1,p1,p,r).
2578 [binary,2434.1,205.1] cx!=r.
2590 [binary,2454.1,206.2,unit_del,1809] -sameside(p,cx,p1).
2656 [ur,2,2467,2339] -E(b,p1,a,r).
2688 [hyper,166,744,2159,2518,unit_del,1231,2028] Col(b,a,m).
2691 [hyper,166,52,2160,2518,unit_del,546,2028] Col(a,b,m).
2749 [ur,30,593,2578,1735] -T(cx,r,p1).
2752 [ur,95,2578,2195,797,1831,823,2590] -T(r,cx,p1).
2757 [binary,2656.1,41.2] -IFS(x,b,y,p1,z,a,u,r).
2766 [binary,2688.1,48.1] Col(m,a,b).
2770 [hyper,133,1327,2688,unit_del,546] R(m,b,r).
2814 [hyper,225,572,1263,2691] R(r,b,m).
2837 [binary,2749.1,25.2] -T(p1,r,cx).
2861 [binary,2752.1,25.2] -T(p1,cx,r).
2905 [ur,136,2770,2164,2090] -T(m,r,cx).
2939 [ur,61,511,2837,2861] -T(p1,r,r1).
2979 [ur,29,26,2905] -T(r,m,r).
2987 [binary,2939.1,25.2] -T(r1,r,p1).
3029 [ur,29,975,2979] -T(r1,r,m).
3056 [binary,3029.1,86.3,unit_del,968] sameside(r1,r,m).
3076 [binary,3056.1,204.1] r1!=r.
3096 [ur,111,696,3076] -M(r1,m,r1).
3104 [binary,3096.1,211.3,unit_del,13] -T(r1,m,r1).
3108 [binary,3104.1,86.3,unit_del,52] sameside(r1,m,r1).
3132 [binary,3108.1,205.1] r1!=m.
3155 [ur,59,3132,975,2027,2987] -T(r1,m,p1).
3183 [ur,32,681,3155] -T(r1,m,cx).
3210 [ur,28,24,3183] -T(m,cx,m).
3236 [ur,28,2418,3210] -T(cx,m,a).
3240 [binary,3236.1,86.3,unit_del,2516] sameside(cx,m,a).
3258 [binary,3240.1,205.1] a!=m.
3259 [binary,3240.1,204.1] cx!=m.
3297 [ur,133,1197,3259,2475] R(a,m,r).
3318 [hyper,133,3297,2766,unit_del,3258] R(b,m,r).
3325 [binary,3318.1,132.1] R(r,m,b).
3330 [binary,3325.1,137.1,unit_del,2814] m=b.
3363 [para_from,3330.1.1,690.1.2] T(r,b,r1).
3364 [para_from,3330.1.1,688.1.2] M(r,b,r1).
3515 [binary,3364.1,210.1] E(b,r,b,r1).
3557 [hyper,2,3515,523] E(b,r1,a,p).
3568 [hyper,19,3363,866,1162,3557] E(r,r1,p1,p).
3573 [ur,187,3363,866,3557,1,2575,2757] -E(r,r1,p1,p).
3574 [binary,3573.1,3568.1] $F.