Sindbad~EG File Manager

Length of proof is 99.  Level of proof is 14.

---------------- 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).
15 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
16 [] -E(xa,xb,xc,xd)|E(xb,xa,xc,xd).
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).
21 [] -E(xb,xc,xa,xa)|xb=xc.
22 [] -E(xa,xb,xc,xd)|E(xb,xa,xd,xc).
23 [] -T(xa,xb,xc)| -T(xA,xB,xC)| -E(xa,xb,xB,xC)| -E(xb,xc,xA,xB)|E(xa,xc,xA,xC).
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).
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).
42 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xc,xa1,xc1)| -E(xb,xc,xb1,xc1)|E(xa,xb,xa1,xb1).
57 [] -T(xa,xc,xb)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
85 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
105 [] -M(xa,xm,xb)|M(xb,xm,xa).
107 [] M(xa,xm,xa)|xm!=xa.
108 [] M(xp,xa,s(xa,xp)).
109 [] -M(xp,xa,xr)| -M(xp,xa,xq)|xr=xq.
112 [] s(xa,xp)!=xr|s(xa,xq)!=xr|xp=xq.
114 [] s(xa,xp)!=xp|xp=xa.
115 [] s(xa,xp)=xp|xp!=xa.
138 [] Col(xa,xb,xc)| -T(xc,xa,xb).
148 [] -sameside(xa,xp,xb)|xb!=xp.
152 [] -M(xa,xm,xb)|T(xa,xm,xb).
153 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
163 [] -E(p,q,s(a,p),s(a,q)).
164 [] p1=s(a,p).
165 [] q1=s(a,q).
166 [] cx=ext(p1,p,q,a).
167 [] cy=ext(q1,q,p,a).
168 [] cx1=ext(cx,p1,q,a).
169 [] cy1=ext(cy,q1,p,a).
170 [] p=a|p!=a.
171 [] s(a,p)=p1.
172 [] s(a,q)=q1.
199 [binary,163.1,14.2,demod,171,172] -E(p1,q1,p,q).
224 [para_from,164.1.2,114.1.1] p1!=p|p=a.
226 [para_from,164.1.2,112.1.1] p1!=x|s(a,y)!=x|p=y.
229 [para_from,164.1.2,108.1.3] M(p,a,p1).
244 [para_from,165.1.2,108.1.3] M(q,a,q1).
252 [para_from,166.1.2,5.1.2] E(p,cx,q,a).
253 [para_from,166.1.2,4.1.3] T(p1,p,cx).
261 [para_from,167.1.2,5.1.2] E(q,cy,p,a).
262 [para_from,167.1.2,4.1.3] T(q1,q,cy).
270 [para_from,168.1.2,5.1.2] E(p1,cx1,q,a).
271 [para_from,168.1.2,4.1.3] T(cx,p1,cx1).
279 [para_from,169.1.2,5.1.2] E(q1,cy1,p,a).
280 [para_from,169.1.2,4.1.3] T(cy,q1,cy1).
287 [para_from,170.1.1,163.1.3.2,demod,172] -E(p,q,s(a,a),q1)|p!=a.
304 [binary,229.1,153.1] E(a,p,a,p1).
305 [binary,229.1,152.1] T(p,a,p1).
306 [binary,229.1,105.1] M(p1,a,p).
321 [binary,244.1,153.1] E(a,q,a,q1).
322 [binary,244.1,152.1] T(q,a,q1).
323 [binary,244.1,105.1] M(q1,a,q).
378 [binary,253.1,25.1] T(cx,p,p1).
539 [binary,262.1,25.1] T(cy,q,q1).
701 [binary,271.1,25.1] T(cx1,p1,cx).
864 [binary,280.1,25.1] T(cy1,q1,cy).
1000 [binary,305.1,25.1] T(p1,a,p).
1024 [hyper,57,305,13,13] a=a.
1104 [binary,1024.1,115.2] s(a,a)=a.
1107 [binary,306.1,153.1] E(a,p1,a,p).
1150 [binary,322.1,25.1] T(q1,a,q).
1250 [binary,323.1,153.1] E(a,q1,a,q).
1417 [hyper,31,378,305] T(cx,a,p1).
1423 [hyper,28,378,305] T(cx,p,a).
1647 [hyper,31,539,322] T(cy,a,q1).
1653 [hyper,28,539,322] T(cy,q,a).
1889 [hyper,28,701,253] T(cx1,p1,p).
2087 [hyper,28,864,262] T(cy1,q1,q).
2310 [hyper,29,1000,253] T(a,p,cx).
2595 [hyper,29,1150,262] T(a,q,cy).
2987 [hyper,32,1417,271] T(cx,a,cx1).
2992 [hyper,29,1417,271] T(a,p1,cx1).
3232 [binary,1423.1,138.2] Col(p,a,cx).
3752 [hyper,32,1647,280] T(cy,a,cy1).
3757 [hyper,29,1647,280] T(a,q1,cy1).
4512 [hyper,31,1889,1000] T(cx1,a,p).
4517 [hyper,28,1889,1000] T(cx1,p1,a).
4905 [hyper,31,2087,1150] T(cy1,a,q).
4910 [hyper,28,2087,1150] T(cy1,q1,a).
8695 [binary,4517.1,138.2] Col(p1,a,cx1).
13127 [binary,252.1,22.1] E(cx,p,a,q).
13130 [binary,252.1,16.1] E(cx,p,q,a).
13133 [binary,252.1,14.1] E(q,a,p,cx).
13317 [binary,261.1,22.1] E(cy,q,a,p).
13319 [binary,261.1,17.1] E(q,cy,a,p).
13320 [binary,261.1,16.1] E(cy,q,p,a).
13376 [hyper,2,261,1] E(p,a,cy,q).
13601 [binary,270.1,17.1] E(p1,cx1,a,q).
13771 [binary,279.1,14.1] E(p,a,q1,cy1).
13826 [hyper,2,279,1] E(p,a,cy1,q1).
13923 [binary,304.1,22.1] E(p,a,p1,a).
13926 [binary,304.1,16.1] E(p,a,a,p1).
13978 [hyper,42,1000,305,1,304] E(p1,a,p,a).
14031 [binary,321.1,22.1] E(q,a,q1,a).
15802 [para_from,1104.1.2,321.1.3] E(a,q,s(a,a),q1).
16207 [para_into,287.1.1,170.1.1,unit_del,15802,factor_simp] p!=a.
16216 [binary,16207.1,224.2] p1!=p.
16253 [ur,226,1104,16207] p1!=a.
16294 [ur,27,2310,16207] -T(p,a,cx).
16371 [binary,16216.1,21.2] -E(p1,p,x,x).
16382 [ur,109,306,16216] -M(p1,a,p1).
16545 [ur,27,2992,16253] -T(p1,a,cx1).
16930 [binary,16294.1,85.3,unit_del,3232] sameside(p,a,cx).
17582 [binary,16382.1,107.1] a!=p1.
18364 [binary,16545.1,85.3,unit_del,8695] sameside(p1,a,cx1).
19123 [binary,16930.1,148.1] cx!=a.
21201 [binary,18364.1,148.1] cx1!=a.
35345 [hyper,2,13127,1] E(a,q,p,cx).
35608 [hyper,15,270,13133] E(p1,cx1,p,cx).
36644 [hyper,2,13317,1] E(a,p,q,cy).
38243 [hyper,23,1423,1653,13130,13376] E(cx,a,cy,a).
38458 [hyper,15,13601,321] E(p1,cx1,a,q1).
40804 [hyper,15,13320,13826] E(cy,q,cy1,q1).
40999 [hyper,2,13923,13376] E(p1,a,cy,q).
41003 [ur,6,13923,1107,1250,305,1000,16207,199] -E(p,q1,p1,q).
41246 [hyper,2,13926,13771] E(a,p1,q1,cy1).
78767 [hyper,23,2595,2310,35345,13319] E(a,cy,a,cx).
79461 [hyper,19,2992,2310,1107,35608] E(a,cx1,a,cx).
79467 [hyper,6,1107,35608,18,13978,2992,2310,unit_del,17582] E(cx1,a,cx,a).
91263 [hyper,19,1653,4910,40804,14031] E(cy,a,cy1,a).
109925 [ur,23,1000,40999,36644,16371] -T(q,cy,q).
110264 [ur,29,2595,109925] -T(a,cy,q).
111918 [ur,32,26,110264] -T(a,cy,a).
117143 [binary,111918.1,152.2] -M(a,cy,a).
119322 [binary,117143.1,107.1] cy!=a.
121212 [hyper,23,2992,3757,41246,38458] E(a,cx1,a,cy1).
208840 [ur,6,79467,304,1250,4512,1417,21201,41003] -E(cx1,q1,cx,q).
326851 [hyper,6,38243,121212,1,78767,2987,3752,unit_del,19123] E(cx1,cy,cy1,cx).
470641 [binary,208840.1,22.2] -E(q1,cx1,q,cx).
591853 [binary,326851.1,16.1] E(cy,cx1,cy1,cx).
653846 [ur,6,91263,1250,79461,1647,4905,119322,470641] -E(cy,cx1,cy1,cx).
653847 [binary,653846.1,591853.1] $F.