Sindbad~EG File Manager

Length of proof is 163.  Level of proof is 48.

---------------- PROOF ----------------

1 [] x=x.
2 [] E(x,y,y,x).
3 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
5 [] T(x,y,ext(x,y,w,v)).
6 [] E(y,ext(x,y,w,v),w,v).
9 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xp,ip(xa,xp,xc,xb,xq),xb).
10 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xq,ip(xa,xp,xc,xb,xq),xa).
14 [] E(x,y,x,y).
15 [] -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(xc,xd,xe,xf)|E(xa,xb,xe,xf).
18 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
20 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
22 [] T(x,y,y).
23 [] -T(xa,xb,xc)|T(xc,xb,xa).
24 [] T(xa,xa,xb).
25 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
26 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
27 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xc,xd).
28 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
31 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
32 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xc,xd).
34 [] -IFS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xb,xd,xb1,xd1).
49 [] -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).
59 [] Col(xa,xb,xc)| -T(xa,xb,xc).
60 [] Col(xa,xb,xc)| -T(xb,xc,xa).
61 [] Col(xa,xb,xc)| -T(xc,xa,xb).
62 [] -Col(x,y,z)|Col(y,z,x).
63 [] -Col(x,y,z)|Col(z,x,y).
64 [] -Col(x,y,z)|Col(z,y,x).
65 [] -Col(x,y,z)|Col(y,x,z).
66 [] -Col(x,y,z)|Col(x,z,y).
76 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xp,xa,xq)| -E(xb,xp,xb,xq)|E(xc,xp,xc,xq).
79 [] xa=xb| -T(xa,xb,xc)| -T(xa,xb,xd)|T(xa,xc,xd)|T(xa,xd,xc).
81 [] -T(xa,xb,xd)| -T(xa,xc,xd)|T(xa,xb,xc)|T(xa,xc,xb).
83 [] -le(xa,xb,xc,xd)|T(xc,insert(xa,xb,xc,xd),xd).
84 [] -le(xa,xb,xc,xd)|E(xa,xb,xc,insert(xa,xb,xc,xd)).
104 [] -sameside(xa,xp,xb)|xa!=xp.
105 [] -sameside(xa,xp,xb)|xb!=xp.
109 [] -sameside(xa,xp,xb)|Col(xa,xp,xb).
111 [] -Col(xa,xp,xb)|T(xa,xp,xb)|sameside(xa,xp,xb).
112 [] xa=xp|sameside(xa,xp,xa).
115 [] xr=xa|xb=xc|sameside(insert(xb,xc,xa,xr),xa,xr).
123 [] -M(xa,xm,xb)|T(xa,xm,xb).
124 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
125 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
126 [] -M(xa,xm,xb)|M(xb,xm,xa).
127 [] M(xa,xa,xa).
129 [] -M(x,xa,z)| -M(x,xa,y)|z=y.
130 [] M(x,xa,s(xa,x)).
131 [] -M(x,y,z)|z=s(y,x).
132 [] s(x,s(x,y))=y.
133 [] s(xa,xp)!=xr|s(xa,xq)!=xr|xp=xq.
136 [] xp!=xa|s(xa,xp)=xp.
148 [] 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(xb,xp,xd).
149 [] -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).
157 [] -E(xc,xa,xc,xb)|M(xa,midpoint(xa,xb),xb).
158 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
159 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
160 [] -R(xa,xb,xc)|R(xc,xb,xa).
161 [] -R(xa,xb,xc)|xa=xb| -Col(xb,xa,xa1)|R(xa1,xb,xc).
164 [] -R(xa,xb,xc)| -R(xa1,xb,xc)| -T(xa,xc,xa1)|xb=xc.
165 [] -R(xa,xb,xc)| -R(xa,xc,xb)|xb=xc.
166 [] -R(xa,xb,xa)|xa=xb.
173 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
177 [] -perp(xp,xq,xp1,xq1)|perpAt(xp,xq,il(xp,xq,xp1,xq1),xp1,xq1).
181 [] -perp(x,y,u,v)|perp(u,v,x,y).
182 [] -perpAt(xa,xb,x,xp,xq)|xa!=xb.
183 [] -perpAt(xa,xb,x,xp,xq)|xp!=xq.
187 [] -perpAt(xa,xb,x,xp,xq)|R(xb,x,xp).
193 [] -perpAt(xa,xb,xc,xp,xq)|Col(xp,xq,xc).
195 [] xa=xb| -Col(xa,xb,x)| -perp(xa,xb,xc,x)|perpAt(xa,xb,x,xc,x).
205 [] -perp(xa,xb,xc,xd)|perp(xb,xa,xc,xd).
210 [] -Col(xa,xb,xc)| -Col(xa,xb,xd)|xa=xb|Col(xa,xc,xd).
211 [] le(a,p,b,q).
212 [] perp(a,b,a,p).
213 [] perp(a,b,b,q).
214 [] T(p,t,q).
215 [] Col(a,b,t).
216 [] r=insert(a,p,b,q).
217 [] cx=ip(p,t,q,b,r).
218 [] p1=s(a,p).
219 [] r1=ext(p1,cx,cx,r).
220 [] m=midpoint(r,r1).
221 [] -M(a,x,b).
412 [binary,212.1,205.1] perp(b,a,a,p).
416 [binary,212.1,177.1] perpAt(a,b,il(a,b,a,p),a,p).
425 [binary,213.1,181.1] perp(b,q,a,b).
426 [binary,213.1,177.1] perpAt(a,b,il(a,b,b,q),b,q).
575 [binary,215.1,65.1] Col(b,a,t).
578 [binary,215.1,62.1] Col(b,t,a).
598 [para_from,216.1.2,115.3.1] q=b|a=p|sameside(r,b,q).
601 [para_from,216.1.2,84.2.4,unit_del,211] E(a,p,b,r).
602 [para_from,216.1.2,83.2.2,unit_del,211] T(b,r,q).
610 [para_from,217.1.2,10.3.2,unit_del,214,602] T(r,cx,p).
611 [para_from,217.1.2,9.3.2,unit_del,214,602] T(t,cx,b).
624 [para_from,218.1.2,158.2.4] -R(x,a,p)|E(x,p,x,p1).
652 [para_from,218.1.2,132.1.1.2] s(a,p1)=p.
664 [para_from,219.1.2,6.1.2] E(cx,r1,cx,r).
665 [para_from,219.1.2,5.1.3] T(p1,cx,r1).
674 [para_from,220.1.2,157.2.2] -E(x,r,x,r1)|M(r,m,r1).
679 [binary,412.1,181.1] perp(a,p,b,a).
692 [binary,416.1,183.1] a!=p.
693 [binary,416.1,182.1] a!=b.
711 [hyper,182,416,112] sameside(a,b,a).
741 [binary,426.1,183.1] b!=q.
751 [hyper,183,426,112] sameside(b,q,b).
839 [hyper,183,416,598] q=b|sameside(r,b,q).
849 [binary,601.1,18.1] E(a,p,r,b).
853 [binary,601.1,15.1] E(b,r,a,p).
904 [binary,602.1,61.2] Col(r,q,b).
1048 [binary,610.1,60.2] Col(p,r,cx).
1067 [binary,610.1,23.1] T(p,cx,r).
1179 [binary,611.1,60.2] Col(b,t,cx).
1350 [hyper,133,132,652] s(a,p)=p1.
1395 [para_from,652.1.1,130.1.3] M(p1,a,p).
1430 [binary,664.1,18.1] E(cx,r1,r,cx).
1434 [binary,664.1,15.1] E(cx,r,cx,r1).
1527 [binary,665.1,23.1] T(r1,cx,p1).
1642 [binary,679.1,205.1] perp(p,a,b,a).
1730 [binary,693.1,195.1] -Col(a,b,x)| -perp(a,b,y,x)|perpAt(a,b,x,y,x).
1789 [ur,25,22,693] -T(b,a,b).
1804 [binary,711.1,109.1] Col(a,b,a).
1909 [binary,751.1,109.1] Col(b,q,b).
1918 [para_from,839.1.1,741.1.2,unit_del,1] sameside(r,b,q).
1930 [binary,849.1,16.1] E(p,a,r,b).
2028 [binary,904.1,64.1] Col(b,q,r).
2077 [binary,1048.1,66.1] Col(p,cx,r).
2289 [binary,1395.1,124.1] E(a,p1,a,p).
2290 [binary,1395.1,123.1] T(p1,a,p).
2441 [hyper,3,1430,2] E(r,cx,r1,cx).
2446 [binary,1434.1,674.1] M(r,m,r1).
2638 [binary,1642.1,181.1] perp(b,a,p,a).
2695 [binary,1730.3,187.1] -Col(a,b,x)| -perp(a,b,y,x)|R(b,x,y).
2856 [hyper,195,1909,425,unit_del,741] perpAt(b,q,b,a,b).
2878 [binary,1918.1,104.1] r!=b.
2985 [hyper,210,2028,1909,unit_del,741] Col(b,r,b).
3121 [hyper,17,2289,849] E(a,p1,r,b).
3147 [binary,2290.1,61.2] Col(a,p,p1).
3167 [binary,2290.1,23.1] T(p,a,p1).
3588 [binary,2446.1,131.1] r1=s(m,r).
3591 [binary,2446.1,126.1] M(r1,m,r).
3593 [binary,2446.1,123.1] T(r,m,r1).
3601 [binary,2638.1,205.1] perp(a,b,p,a).
3712 [binary,2856.1,193.1] Col(a,b,b).
3718 [hyper,173,2856,2028,1804] R(r,b,a).
3737 [binary,2878.1,166.2] -R(r,b,r).
3805 [ur,25,22,2878] -T(b,r,b).
3828 [binary,2985.1,111.1,unit_del,3805] sameside(b,r,b).
3895 [hyper,3,3121,2] E(r,b,p1,a).
3930 [binary,3167.1,25.2,unit_del,692] -T(a,p,p1).
4197 [para_from,3588.1.1,1434.1.4] E(cx,r,cx,s(m,r)).
4242 [binary,3591.1,123.1] T(r1,m,r).
4268 [binary,3593.1,60.2] Col(r1,r,m).
4464 [binary,3828.1,105.1] b!=r.
4553 [binary,4197.1,159.2] R(cx,m,r).
7276 [binary,3147.1,111.1,unit_del,3930] sameside(a,p,p1).
7560 [binary,3712.1,65.1] Col(b,a,b).
7622 [binary,7560.1,111.1,unit_del,1789] sameside(b,a,b).
7673 [binary,7622.1,105.1] b!=a.
7876 [ur,210,575,7560,7673] Col(b,t,b).
8074 [binary,3718.1,165.2,unit_del,693] -R(r,a,b).
8590 [ur,173,2856,2028,3737] -Col(a,b,r).
11651 [binary,7276.1,105.1] p1!=p.
29934 [para_from,1350.1.1,136.2.1,unit_del,11651] p!=a.
35245 [binary,3601.1,2695.2,unit_del,1804] R(b,a,p).
35263 [binary,35245.1,160.1] R(p,a,b).
35440 [binary,35263.1,165.1,unit_del,693] -R(p,b,a).
35546 [ur,161,35263,29934,8074] -Col(a,p,r).
35600 [ur,173,2856,1804,35440] -Col(b,q,p).
35935 [binary,35546.1,65.2] -Col(p,a,r).
35939 [binary,35546.1,61.1] -T(r,a,p).
35940 [binary,35546.1,60.1] -T(p,r,a).
36053 [binary,35600.1,61.1] -T(p,b,q).
36131 [binary,35939.1,23.2] -T(p,a,r).
36194 [ur,31,610,35939] -T(r,a,cx).
36199 [ur,27,2290,35939] -T(r,p1,p).
36422 [ur,27,214,36053] -T(t,b,q).
36448 [ur,81,3167,35940,36131] -T(p,r,p1).
36789 [ur,26,22,36194] -T(a,cx,a).
36878 [ur,31,610,36199] -T(r,p1,cx).
37006 [ur,28,24,36422] -T(b,t,b).
37292 [ur,26,665,36878] -T(r,p1,r1).
37630 [binary,37006.1,111.2,unit_del,7876] sameside(b,t,b).
37731 [binary,37292.1,23.2] -T(r1,p1,r).
37812 [binary,37630.1,105.1] b!=t.
37964 [ur,210,1179,578,37812] Col(b,cx,a).
38142 [binary,37964.1,64.1] Col(a,cx,b).
38143 [binary,37964.1,63.1] Col(a,b,cx).
38788 [hyper,210,38143,1804,unit_del,693] Col(a,cx,a).
38819 [hyper,161,35245,38143,unit_del,7673] R(cx,a,p).
38871 [binary,38788.1,111.1,unit_del,36789] sameside(a,cx,a).
39039 [binary,38819.1,624.1] E(cx,p,cx,p1).
39159 [binary,38871.1,105.1] a!=cx.
39192 [binary,39039.1,15.1] E(cx,p1,cx,p).
39315 [hyper,20,610,1527,2441,39039] E(r,p,r1,p1).
39780 [ur,210,38142,39159,8590] -Col(a,cx,r).
39951 [hyper,149,1527,610,664,39192,3591,1395] T(m,cx,a).
40001 [hyper,76,38142,2289,39192,unit_del,39159] E(b,p1,b,p).
40185 [hyper,3,39315,2] E(r1,p1,p,r).
40304 [binary,39780.1,59.1] -T(a,cx,r).
40734 [binary,39951.1,59.2] Col(m,cx,a).
41425 [ur,149,1067,39192,14,1395,127,40304] -T(p1,cx,r).
41490 [ur,26,22,40304] -T(cx,r,cx).
41507 [binary,40734.1,65.1] Col(cx,m,a).
41508 [binary,40734.1,64.1] Col(a,cx,m).
41900 [ur,28,1067,41490] -T(p,r,cx).
42161 [hyper,210,38142,41508,unit_del,39159] Col(a,b,m).
42229 [binary,41900.1,111.2,unit_del,1048] sameside(p,r,cx).
42342 [binary,42161.1,63.1] Col(m,a,b).
42361 [hyper,173,2856,2028,42161] R(r,b,m).
42434 [binary,42229.1,105.1] cx!=r.
42749 [binary,42361.1,160.1] R(m,b,r).
43007 [ur,32,1067,42434,36448] -T(cx,r,p1).
43100 [ur,164,42749,42749,4464] -T(m,r,m).
43131 [binary,43007.1,23.2] -T(p1,r,cx).
43291 [ur,28,4242,43100] -T(r1,r,m).
43336 [ur,81,665,41425,43131] -T(p1,r,r1).
43416 [binary,43291.1,111.2,unit_del,4268] sameside(r1,r,m).
43527 [binary,43336.1,23.2] -T(r1,r,p1).
43616 [binary,43416.1,104.1] r1!=r.
43637 [hyper,104,43416,112] sameside(r1,r,r1).
43786 [ur,129,3591,43616] -M(r1,m,r1).
43935 [binary,43637.1,109.1] Col(r1,r,r1).
43950 [binary,43786.1,125.3,unit_del,14] -T(r1,m,r1).
43971 [hyper,210,4268,43935,unit_del,43616] Col(r1,m,r1).
44029 [binary,43950.1,111.2,unit_del,43971] sameside(r1,m,r1).
44178 [binary,44029.1,105.1] r1!=m.
44386 [ur,79,44178,4242,37731,43527] -T(r1,m,p1).
44505 [ur,31,1527,44386] -T(r1,m,cx).
44620 [ur,26,22,44505] -T(m,cx,m).
44724 [ur,26,39951,44620] -T(cx,m,a).
44735 [binary,44724.1,111.2,unit_del,41507] sameside(cx,m,a).
44830 [binary,44735.1,105.1] a!=m.
44831 [binary,44735.1,104.1] cx!=m.
45094 [ur,161,4553,44831,40734] R(a,m,r).
45283 [hyper,161,45094,42342,unit_del,44830] R(b,m,r).
45341 [binary,45283.1,160.1] R(r,m,b).
45396 [binary,45341.1,165.1,unit_del,42361] m=b.
45486 [para_from,45396.1.1,3593.1.2] T(r,b,r1).
45491 [para_from,45396.1.1,2446.1.2] M(r,b,r1).
46370 [binary,45491.1,124.1] E(b,r,b,r1).
46546 [hyper,3,46370,853] E(b,r1,a,p).
46625 [hyper,20,45486,2290,3895,46546] E(r,r1,p1,p).
49912 [ur,148,35935,693,1930,2077,38142,221] -E(a,r,b,p).
50046 [ur,3,40001,49912] -E(b,p1,a,r).
50066 [binary,50046.1,34.2] -IFS(x,b,y,p1,z,a,u,r).
50131 [ur,49,45486,2290,46625,46546,40185,50066] -E(r,p1,p1,r).
50132 [binary,50131.1,2.1] $F.