Sindbad~EG File Manager

Length of proof is 209.  Level of proof is 31.
 
---------------- 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).
6 [] -E(x,y,x1,y1)| -E(y,z,y1,z1)| -E(x,v,x1,v1)| -E(y,v,y1,v1)| -T(x,y,z)| -T(x1,y1,z1)|x=y|E(z,v,z1,v1).
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).
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).
45 [] -T(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|T(xa1,xb1,xc1).
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).
51 [] Col(xa,xa,xb).
52 [] Col(xa,xb,xa).
59 [] xa=xb| -T(xa,xb,xc)| -T(xa,xb,xd)|T(xa,xc,xd)|T(xa,xd,xc).
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).
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).
89 [] -sameside(xa,xp,xb)| -sameside(xb,xp,xc)|sameside(xa,xp,xc).
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).
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).
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.
123 [] -M(xp,xa,xq)| -M(xp,xb,xq)|xa=xb.
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).
138 [] -R(xa,xb,xa)|xa=xb.
140 [] -R(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|R(xa1,xb1,xc1).
159 [] xa=xb| -Col(xa,xb,xp)| -Col(xa,xb,xq)|xq=xp|perp(xa,xb,xc,xp)|Col(xa,xb,xc)| -R(xc,xp,xq).
179 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
180 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
181 [] Col(xa,xb,xc)| -T(xa,xb,xc).
182 [] Col(xa,xb,xc)| -T(xb,xc,xa).
183 [] Col(xa,xb,xc)| -T(xc,xa,xb).
191 [] -T(xc,y,xd)| -E(xa,xb,xc,y)|le(xa,xb,xc,xd).
192 [] -sameside(xa,xp,xb)|xa!=xp.
193 [] -sameside(xa,xp,xb)|xb!=xp.
194 [] -sameside(xa,xp,xb)|T(xp,xa,xb)|T(xp,xb,xa).
195 [] -T(xp,xa,xb)|xa=xp|xb=xp|sameside(xa,xp,xb).
196 [] -T(xp,xb,xa)|xa=xp|xb=xp|sameside(xa,xp,xb).
197 [] -M(xa,xm,xb)|T(xa,xm,xb).
207 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
208 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
220 [] -Col(a,b,c).
221 [] -Col(a,b,x)| -perp(a,b,c,x).
222 [] cy=ext(b,a,a,c).
223 [] p=isomidpoint(cy,c,a).
224 [] cz=ext(a,cy,cy,p).
225 [] q=ext(p,cy,cy,a).
226 [] q1=s(cz,q).
227 [] c1=ext(q1,cy,cy,c).
228 [] cx=isomidpoint(c,c1,cy).
229 [] ext(b,a,a,c)=cy.
230 [] isomidpoint(cy,c,a)=p.
468 [binary,220.1,183.1] -T(c,a,b).
469 [binary,220.1,182.1] -T(b,c,a).
470 [binary,220.1,181.1] -T(a,b,c).
473 [binary,220.1,50.2] -Col(a,c,b).
475 [binary,220.1,48.2] -Col(c,b,a).
476 [binary,220.1,47.2] -Col(b,c,a).
487 [binary,222.1,109.2,demod,229,229] M(cy,cy,cy).
489 [para_from,222.1.2,5.1.2] E(a,cy,a,c).
490 [para_from,222.1.2,4.1.3] T(b,a,cy).
496 [binary,223.1,109.2,demod,230,230] M(p,p,p).
498 [para_from,223.1.2,131.2.2,unit_del,489] M(cy,p,c).
506 [para_from,224.1.2,5.1.2] E(cy,cz,cy,p).
507 [para_from,224.1.2,4.1.3] T(a,cy,cz).
515 [para_from,225.1.2,5.1.2] E(cy,q,cy,a).
516 [para_from,225.1.2,4.1.3] T(p,cy,q).
527 [para_from,226.1.2,207.2.4] -R(x,cz,q)|E(x,q,x,q1).
534 [para_from,226.1.2,116.1.1] q1!=q|q=cz.
536 [para_from,226.1.2,113.1.1.2] s(cz,q1)=q.
538 [para_from,226.1.2,110.1.3] M(q,cz,q1).
546 [para_from,227.1.2,5.1.2] E(cy,c1,cy,c).
547 [para_from,227.1.2,4.1.3] T(q1,cy,c1).
555 [para_from,228.1.2,131.2.2] -E(cy,c,cy,c1)|M(c,cx,c1).
566 [binary,468.1,25.2] -T(b,a,c).
574 [ur,31,24,468] -T(b,a,b).
591 [binary,469.1,25.2] -T(a,c,b).
608 [binary,470.1,194.2,unit_del,591] -sameside(b,a,c).
649 [binary,489.1,14.1] E(a,c,a,cy).
659 [binary,490.1,183.2] Col(a,cy,b).
660 [binary,490.1,182.2] Col(cy,b,a).
661 [binary,490.1,181.2] Col(b,a,cy).
662 [binary,490.1,85.2] -sameside(b,a,cy).
676 [binary,490.1,25.1] T(cy,a,b).
693 [binary,498.1,197.1] T(cy,p,c).
696 [binary,498.1,112.1] c=s(p,cy).
699 [binary,498.1,107.1] M(c,p,cy).
707 [binary,506.1,17.1] E(cy,cz,p,cy).
709 [binary,506.1,14.1] E(cy,p,cy,cz).
719 [binary,507.1,183.2] Col(cy,cz,a).
720 [binary,507.1,182.2] Col(cz,a,cy).
732 [binary,507.1,28.2] -T(x,a,cz)|T(x,a,cy).
736 [binary,507.1,25.1] T(cz,cy,a).
744 [hyper,30,490,507] a=cy|T(b,cy,cz).
772 [binary,515.1,17.1] E(cy,q,a,cy).
801 [binary,516.1,25.1] T(q,cy,p).
886 [para_from,536.1.1,110.1.3] M(q1,cz,q).
894 [binary,538.1,197.1] T(q,cz,q1).
909 [binary,546.1,14.1] E(cy,c,cy,c1).
910 [hyper,191,24,546] le(cy,c1,cy,c).
914 [hyper,66,67,546,13] le(cy,c,cy,c1).
936 [binary,547.1,25.1] T(c1,cy,q1).
954 [binary,555.1,69.3,unit_del,914,910] M(c,cx,c1).
956 [binary,555.2,197.1,unit_del,909] T(c,cx,c1).
959 [binary,555.2,112.1,unit_del,909] c1=s(cx,c).
962 [binary,555.2,107.1,unit_del,909] M(c1,cx,c).
971 [ur,61,490,469,566] -T(b,c,cy).
987 [ur,28,490,566] -T(a,c,cy).
994 [binary,574.1,86.3,unit_del,52] sameside(b,a,b).
1062 [binary,659.1,50.1] Col(a,b,cy).
1064 [binary,659.1,48.1] Col(b,cy,a).
1117 [ur,31,676,468] -T(c,cy,b).
1118 [ur,29,676,574] -T(cy,b,a).
1119 [ur,29,676,468] -T(cy,c,a).
1120 [ur,29,676,470] -T(cy,b,c).
1138 [binary,693.1,25.1] T(c,p,cy).
1172 [para_from,696.1.1,489.1.4] E(a,cy,a,s(p,cy)).
1175 [para_from,696.1.1,476.1.2] -Col(b,s(p,cy),a).
1219 [hyper,2,707,1] E(p,cy,cz,cy).
1336 [hyper,2,772,1] E(a,cy,q,cy).
1342 [binary,801.1,182.2] Col(p,q,cy).
1362 [hyper,33,801,693] cy=p|T(q,cy,c).
1382 [binary,886.1,197.1] T(q1,cz,q).
1624 [para_from,959.1.1,909.1.4] E(cy,c,cy,s(cx,c)).
1655 [binary,971.1,180.4,unit_del,1117,1120] -Col(c,cy,b).
1791 [binary,1118.1,86.3,unit_del,660] sameside(cy,b,a).
1863 [binary,1120.1,25.2] -T(c,b,cy).
1948 [binary,1172.1,208.2] R(a,p,cy).
1966 [para_into,1175.1.2,117.1.1,unit_del,1064] cy!=p.
1997 [hyper,19,516,736,1219,515] E(p,q,cz,a).
2000 [hyper,6,1219,515,1,506,516,736] p=cy|E(q,cz,a,p).
2017 [hyper,6,1336,506,1,515,507,801] a=cy|E(cz,q,p,a).
2065 [binary,1362.2,182.2,unit_del,1966] Col(c,q,cy).
2081 [binary,1362.2,25.1,unit_del,1966] T(c,cy,q).
2082 [para_into,1362.1.1,222.1.1,demod,229,unit_del,1966] T(q,cy,c).
2136 [binary,1624.1,208.2] R(cy,cx,c).
2172 [binary,1655.1,49.2] -Col(cy,c,b).
2173 [binary,1655.1,48.2] -Col(b,cy,c).
2184 [binary,1791.1,193.1] a!=b.
2185 [binary,1791.1,192.1] cy!=b.
2197 [binary,1948.1,132.1] R(cy,p,a).
2203 [binary,1966.1,138.2] -R(cy,p,cy).
2219 [ur,123,487,1966] -M(cy,p,cy).
2242 [ur,27,516,1966] -T(cy,p,q).
2277 [binary,2000.1,109.2,unit_del,2219] E(q,cz,a,p).
2285 [para_from,2017.1.1,1948.1.1,unit_del,2203] E(cz,q,p,a).
2307 [hyper,32,1138,2081] T(c,p,q).
2366 [binary,2136.1,132.1] R(c,cx,cy).
2395 [ur,103,2184,51,51,51,220] x=x.
2435 [ur,102,2185,52] Col(b,cy,cy).
2436 [ur,98,2185,38,37,1655] c!=cy.
2466 [para_into,2197.1.3,744.1.1,unit_del,2203] T(b,cy,cz).
2503 [binary,2219.1,109.1] p!=cy.
2554 [binary,2277.1,14.1] E(a,p,q,cz).
2579 [hyper,179,2285,18,2277] E3(cz,q,cz,p,a,p).
2594 [binary,2307.1,183.2] Col(p,q,c).
2747 [ur,111,699,2436] -M(c,p,c).
2765 [ur,74,649,2436] -T(a,cy,c).
2846 [binary,2466.1,25.1] T(cz,cy,b).
2923 [hyper,179,2554,1336,1219] E3(a,p,cy,q,cz,cy).
2969 [binary,2765.1,25.2] -T(c,cy,a).
2970 [ur,61,507,987,2765] -T(a,c,cz).
2995 [ur,33,693,1966,2765] -T(a,cy,p).
3058 [hyper,31,2846,676] T(cz,a,b).
3087 [binary,2923.1,140.2,unit_del,1948] R(q,cz,cy).
3131 [ur,31,736,2969] -T(c,cz,a).
3132 [ur,30,1138,2503,2969] -T(p,cy,a).
3199 [ur,130,801,801,13,13,496,2995] -M(q,a,q).
3200 [ur,130,26,26,18,13,496,2995] -M(cy,a,cy).
3226 [ur,31,801,2995] -T(a,q,p).
3288 [binary,3058.1,85.2] -sameside(cz,a,b).
3345 [binary,3087.1,132.1] R(cy,cz,q).
3438 [ur,29,736,3132] -T(cz,p,cy).
3496 [binary,3345.1,527.1] E(cy,q,cy,q1).
3573 [hyper,130,2081,936,909,3496,954,538] T(cx,cy,cz).
3599 [binary,3573.1,183.2] Col(cy,cz,cx).
3790 [binary,2395.1,109.2] M(x,x,x).
4431 [binary,994.1,193.1] b!=a.
4443 [ur,98,4431,38,37,475] c!=b.
4478 [ur,98,4443,38,37,473] a!=c.
5586 [ur,98,4443,38,37,2172] cy!=c.
5668 [ur,98,5586,38,37,2173] b!=cy.
5927 [ur,28,693,2242] -T(p,q,c).
6758 [binary,2594.1,86.2,unit_del,5927] sameside(p,q,c).
6780 [binary,6758.1,193.1] c!=q.
6781 [binary,6758.1,192.1] p!=q.
7280 [binary,2747.1,109.1] p!=c.
8897 [binary,3199.1,109.1] a!=q.
8919 [ur,111,3790,8897] -M(q,q,a).
8975 [binary,8919.1,107.2] -M(a,q,q).
8992 [binary,3200.1,109.1] a!=cy.
9016 [ur,104,6780,5668,1064,2065,2435,8992,52,2173] -Col(c,q,a).
9023 [ur,99,8992,490,971,1863] -T(c,a,cy).
9024 [ur,95,8992,4478,661,4431,662,608] -T(cy,a,c).
9095 [binary,9016.1,47.2] -Col(q,a,c).
9158 [ur,99,2503,1138,987,9023] -T(a,p,cy).
9161 [ur,61,2081,2969,9023] -T(c,a,q).
9194 [ur,31,1138,9023] -T(p,a,cy).
9218 [ur,59,1966,693,1119,9024] -T(cy,p,a).
9250 [ur,29,736,9024] -T(cz,a,c).
9399 [ur,98,4478,38,37,9095] q!=a.
9474 [binary,9158.1,194.2,unit_del,2995] -sameside(p,a,cy).
9521 [ur,29,26,9158] -T(p,a,p).
9572 [ur,31,2307,9161] -T(p,a,q).
9580 [binary,9194.1,732.2] -T(p,a,cz).
9587 [binary,9194.1,180.2,unit_del,2995,9218] -Col(p,a,cy).
9677 [ur,29,801,9218] -T(q,p,a).
9689 [binary,9250.1,180.2,unit_del,2970,3131] -Col(cz,a,c).
9813 [ur,102,9399,52] Col(a,q,q).
9881 [ur,45,2579,9521] -T(cz,q,cz).
9921 [binary,9572.1,180.3,unit_del,9677,3226] -Col(q,p,a).
10023 [ur,98,8992,2184,676,9587] p!=a.
10130 [ur,98,4478,38,37,9689] cz!=a.
10187 [binary,9881.1,86.3,unit_del,52] sameside(cz,q,cz).
10230 [para_into,9881.1.1,534.2.2,unit_del,26] q1!=q.
10235 [binary,9921.1,48.2] -Col(a,p,q).
10311 [ur,104,6781,10023,52,52,2594,7280,1342,9587] -Col(p,a,c).
10385 [ur,95,8992,2184,676,720,10130,3288] sameside(cz,a,cy).
10615 [binary,10311.1,46.2] -Col(c,p,a).
10765 [ur,89,10385,9474] -sameside(p,a,cz).
10859 [ur,98,10023,38,37,10615] c!=p.
10931 [binary,10765.1,86.1,unit_del,9580] -Col(p,a,cz).
11017 [binary,10931.1,50.2] -Col(p,cz,a).
11019 [binary,10931.1,46.2] -Col(cz,p,a).
11064 [ur,98,10130,38,37,11017] p!=cz.
11135 [ur,98,10023,38,37,11019] cz!=p.
11216 [ur,127,10235,11064,2554,1997,9813,8975] -Col(p,q,cz).
11286 [ur,74,709,11064] -T(cy,cz,p).
11374 [binary,11216.1,182.1] -T(q,cz,p).
11375 [binary,11216.1,181.1] -T(p,q,cz).
11377 [binary,11216.1,84.2] -sameside(p,q,cz).
11521 [binary,11374.1,25.2] -T(p,cz,q).
11585 [ur,28,894,11375] -T(p,q,q1).
11611 [ur,59,2503,516,11375,11521] -T(p,cy,cz).
11641 [ur,31,1382,11521] -T(p,q1,q).
11707 [binary,11611.1,180.4,unit_del,11286,3438] -Col(cy,cz,p).
11777 [ur,60,10859,2307,11585,11641] -T(c,p,q1).
11826 [ur,98,11135,38,37,11707] cy!=cz.
11879 [binary,11777.1,25.2] -T(q1,p,c).
11965 [ur,104,11826,2184,719,52,52,1062,8992,3599] Col(a,b,cx).
12103 [ur,31,693,11879] -T(q1,cy,c).
12165 [binary,11965.1,221.1] -perp(a,b,c,cx).
12173 [hyper,159,11965,1062,2366,unit_del,2184,12165,220] cy=cx.
12362 [para_from,12173.1.1,5586.1.1] cx!=c.
12576 [para_from,12173.1.1,547.1.2] T(q1,cx,c1).
13236 [ur,111,3790,12362] -M(cx,cx,c).
25826 [binary,10187.1,193.1] cz!=q.
25836 [ur,196,894,10230,25826] sameside(q1,q,cz).
25988 [ur,89,25836,11377] -sameside(p,q,q1).
26050 [binary,25988.1,195.4,unit_del,6781,10230] -T(q,p,q1).
26054 [ur,89,6758,25988] -sameside(c,q,q1).
26083 [binary,26050.1,25.2] -T(q1,p,q).
26128 [binary,26054.1,196.4,unit_del,6780,10230] -T(q,q1,c).
26176 [ur,33,516,2503,26083] -T(q1,p,cy).
26303 [ur,31,2082,26128] -T(cy,q1,c).
26414 [ur,31,1138,26176] -T(q1,c,cy).
26596 [ur,29,936,26303] -T(c1,q1,c).
26764 [ur,61,547,12103,26414] -T(q1,c,c1).
26819 [binary,26596.1,25.2] -T(c,q1,c1).
27134 [ur,99,956,12576,26764,26819] cx=c1.
27339 [para_from,27134.1.2,962.1.1] M(cx,cx,c).
27340 [binary,27339.1,13236.1] $F.