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----- Otter 3.3f, August 2004 -----
The process was started by beeson on Michael-Beesons-iMac.local,
Sat Jul  5 12:26:21 2014
The command was "otter".  The process ID is 6146.

set(hyper_res).
set(para_into).
set(para_from).
set(binary_res).
   dependent: set(factor).
   dependent: set(unit_deletion).
set(ur_res).
set(order_history).
assign(report,5400).
assign(max_seconds,10000).
assign(max_mem,840000).
set(input_sos_first).
set(ancestor_subsume).
assign(max_weight,12).
assign(max_distinct_vars,5).
assign(pick_given_ratio,4).
WARNING: assign(max_proofs,1) already has that value.
assign(max_proofs,1).
assign(bsub_hint_wt,-1).
assign(fsub_hint_wt,-1).
set(keep_hint_subsumers).

weight_list(pick_and_purge).
end_of_list.

list(usable).
1 [] E(x,y,y,x).
2 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
3 [] -E(x,y,z,z)|x=y.
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).
7 [] -T(x,y,x)|x=y.
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).
10 [] -T(alpha,beta,gamma).
11 [] -T(beta,gamma,alpha).
12 [] -T(gamma,alpha,beta).
13 [] E(x,y,x,y).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
15 [] -E(xa,xb,xc,xd)|E(xb,xa,xc,xd).
16 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
17 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
18 [] E(x,x,y,y).
19 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
20 [] xq=xa| -T(xq,xa,u)| -E(xa,u,xc,xd)|ext(xq,xa,xc,xd)=u.
21 [] T(x,y,y).
22 [] -T(xa,xb,xc)|T(xc,xb,xa).
23 [] T(xa,xa,xb).
24 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
25 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
26 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xc,xd).
27 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
28 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
29 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xc,xd).
30 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
31 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xc,xd).
32 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xb,xd).
33 [] -IFS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xb,xd,xb1,xd1).
34 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xc,xa1,xc1)| -E(xb,xc,xb1,xc1)|E(xa,xb,xa1,xb1).
35 [] alpha!=beta.
36 [] beta!=gamma.
37 [] alpha!=gamma.
38 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
39 [] xb!=ext(xa,xb,alpha,gamma).
40 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|T(xa,xb,xc).
41 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|T(za,zb,zc).
42 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xa,xc,za,zc).
43 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xb,xc,zb,zc).
44 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xa,xd,za,zd).
45 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xc,xd,zc,zd).
46 [] -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).
47 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa1,xa2,xb1,xb2).
48 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa1,xa3,xb1,xb3).
49 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa2,xa3,xb2,xb3).
50 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
51 [] -T(xa,xb,xc)| -E(xa,xc,xa1,xc1)|T(xa1,insert(xa,xb,xa1,xc1),xc1).
52 [] -T(xa,xb,xc)| -E(xa,xc,xa1,xc1)|E3(xa,xb,xc,xa1,insert(xa,xb,xa1,xc1),xc1).
53 [] insert(xa,xb,xa1,xc1)=ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
54 [] -T(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|T(xa1,xb1,xc1).
55 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
56 [] Col(xa,xb,xc)| -T(xa,xb,xc).
57 [] Col(xa,xb,xc)| -T(xb,xc,xa).
58 [] Col(xa,xb,xc)| -T(xc,xa,xb).
59 [] -Col(x,y,z)|Col(y,z,x).
60 [] -Col(x,y,z)|Col(z,x,y).
61 [] -Col(x,y,z)|Col(z,y,x).
62 [] -Col(x,y,z)|Col(y,x,z).
63 [] -Col(x,y,z)|Col(x,z,y).
64 [] Col(x,x,y).
65 [] -Col(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|Col(xa1,xb1,xc1).
66 [] -Col(xa,xb,xc)| -E(xa,xb,xa1,xb1)|E3(xa,xb,xc,xa1,xb1,insert5(xa,xb,xc,xa1,xb1)).
67 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|Col(xa,xb,xc).
68 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E3(xa,xb,xc,xa1,xb1,xc1).
69 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xa,xd,xa1,xd1).
70 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xb,xd,xb1,xd1).
71 [] -Col(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)| -E(xa,xd,xa1,xd1)| -E(xb,xd,xb1,xd1)|FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1).
72 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|xa=xb|E(xc,xd,xc1,xd1).
73 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xp,xa,xq)| -E(xb,xp,xb,xq)|E(xc,xp,xc,xq).
74 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
75 [] -T(xa,xc,xb)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
76 [] xa=xb| -T(xa,xb,xc)| -T(xa,xb,xd)|T(xa,xc,xd)|T(xa,xd,xc).
77 [] xa=xb| -T(xa,xb,xc)| -T(xa,xb,xd)|T(xb,xc,xd)|T(xb,xd,xc).
78 [] -T(xa,xb,xd)| -T(xa,xc,xd)|T(xa,xb,xc)|T(xa,xc,xb).
79 [] -T(xc,y,xd)| -E(xa,xb,xc,y)|le(xa,xb,xc,xd).
80 [] -le(xa,xb,xc,xd)|T(xc,insert(xa,xb,xc,xd),xd).
81 [] -le(xa,xb,xc,xd)|E(xa,xb,xc,insert(xa,xb,xc,xd)).
82 [] -le(xa,xb,xc,xd)|T(xa,xb,insert(xc,xd,xa,xb)).
83 [] -le(xa,xb,xc,xd)|E(xa,insert(xc,xd,xa,xb),xc,xd).
84 [] -T(xa,xb,x)| -E(xa,x,xc,xd)|le(xa,xb,xc,xd).
85 [] -le(xa,xb,xc,xd)| -E(xa,xb,xa1,xb1)| -E(xc,xd,xc1,xd1)|le(xa1,xb1,xc1,xd1).
86 [] le(xa,xb,xa,xb).
87 [] -le(xa,xb,xc,xd)| -le(xc,xd,xe,xf)|le(xa,xb,xe,xf).
88 [] -le(xa,xb,xc,xd)| -le(xc,xd,xa,xb)|E(xa,xb,xc,xd).
89 [] le(xa,xb,xc,xd)|le(xc,xd,xa,xb).
90 [] le(xa,xa,xc,xd).
91 [] sameside(xa,xp,xb)|xa=xp|xb=xp| -T(xp,xa,xb).
92 [] sameside(xa,xp,xb)|xa=xp|xb=xp| -T(xp,xb,xa).
93 [] -sameside(xa,xp,xb)|xa!=xp.
94 [] -sameside(xa,xp,xb)|xb!=xp.
95 [] -sameside(xa,xp,xb)|T(xp,xa,xb)|T(xp,xb,xa).
96 [] xa=xp|xb=xp|xc=xp| -T(xa,xp,xc)| -T(xb,xp,xc)|sameside(xa,xp,xb).
97 [] xa=xp|xb=xp|xc=xp| -T(xa,xp,xc)|T(xb,xp,xc)| -sameside(xa,xp,xb).
98 [] -sameside(xa,xp,xb)|xa!=xp.
99 [] -sameside(xa,xp,xb)|xb!=xp.
100 [] -sameside(xa,xp,xb)|f63(xa,xp,xb)!=xp.
101 [] -sameside(xa,xp,xb)|T(xa,xp,f63(xa,xp,xc)).
102 [] -sameside(xa,xp,xb)|T(xb,xp,f63(xa,xp,xc)).
103 [] xa=xp|xb=xp|xc=xp| -T(xa,xp,xc)| -T(xb,xp,xc)|sameside(xa,xp,xb).
104 [] -sameside(xa,xp,xb)|Col(xa,xp,xb).
105 [] -sameside(xa,xp,xb)| -T(xa,xp,xb).
106 [] -Col(xa,xp,xb)|T(xa,xp,xb)|sameside(xa,xp,xb).
107 [] xa=xp|sameside(xa,xp,xa).
108 [] -sameside(xa,xp,xb)|sameside(xb,xp,xa).
109 [] -sameside(xa,xp,xb)| -sameside(xb,xp,xc)|sameside(xa,xp,xc).
110 [] xr=xa|xb=xc|sameside(insert(xb,xc,xa,xr),xa,xr).
111 [] xr=xa|xb=xc|E(xa,insert(xb,xc,xa,xr),xb,xc).
112 [] xr=xa|xb=xc| -sameside(x,xa,xr)| -sameside(y,xa,xr)| -E(xa,x,xb,xc)| -E(xa,y,xb,xc)|x=y.
113 [] -sameside(xa,xp,xb)| -le(xp,xa,xp,xb)|T(xp,xa,xb).
114 [] -sameside(xa,xp,xb)| -T(xp,xa,xb)|le(xp,xa,xp,xb).
115 [] xp=xq|xp=xr| -T(xq,xp,xr)| -Col(xa,xp,xq)|xa=xp|sameside(xa,xp,xq)|sameside(xa,xp,xr).
116 [] xp=xq|xp=xr| -T(xq,xp,xr)| -sameside(xa,xp,xq)|Col(xa,xp,xq).
117 [] xp=xq|xp=xr| -T(xq,xp,xr)| -sameside(xa,xp,xr)|Col(xa,xp,xq).
118 [] xp=xq|xp=xr| -T(xq,xp,xr)|xa!=xp|Col(xa,xp,xq).
119 [] -M(xa,xm,xb)|T(xa,xm,xb).
120 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
121 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
122 [] -M(xa,xm,xb)|M(xb,xm,xa).
123 [] M(xa,xa,xa).
124 [] -M(xa,xm,xa)|xm=xa.
125 [] -M(x,xa,z)| -M(x,xa,y)|z=y.
126 [] M(x,xa,s(xa,x)).
127 [] -M(x,y,z)|z=s(y,x).
128 [] s(x,s(x,y))=y.
129 [] s(xa,xp)!=xr|s(xa,xq)!=xr|xp=xq.
130 [] s(xa,xp)!=s(xa,xq)|xp=xq.
131 [] s(xa,xp)!=xp|xp=xa.
132 [] xp!=xa|s(xa,xp)=xp.
133 [] E(xp,xq,s(xa,xp),s(xa,xq)).
134 [] -T(xp,xq,xr)|T(s(xa,xp),s(xa,xq),s(xa,xr)).
135 [] T(xp,xq,xr)| -T(s(xa,xp),s(xa,xq),s(xa,xr)).
136 [] -E(xp,xq,xr,xs)|E(s(xa,xp),s(xa,xq),s(xa,xr),s(xa,xs)).
137 [] E(xp,xq,xr,xs)| -E(s(xa,xp),s(xa,xq),s(xa,xr),s(xa,xs)).
138 [] -M(xp,xa,xq)| -M(xp,xb,xq)|xa=xb.
139 [] s(xa,xp)!=s(xb,xp)|xa=xb.
140 [] s(xa,s(xb,xp))!=s(xb,s(xa,xp))|xa=xb.
141 [] s(xa,s(xb,xp))=s(xb,s(xa,xp))|xa!=xb.
142 [] -Col(xa,xm,xb)| -E(xm,xa,xm,xb)|xa=xb|M(xa,xm,xb).
143 [] 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).
144 [] 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).
145 [] -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).
146 [] -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)|KF(xa1,xm1,xb1,xc,xb2,xm2,xa2).
147 [] -KF(xa1,xm1,xb1,xc,xb2,xm2,xa2)|T(xa1,xc,xa2).
148 [] -KF(xa1,xm1,xb1,xc,xb2,xm2,xa2)|T(xb1,xc,xb2).
149 [] -KF(xa1,xm1,xb1,xc,xb2,xm2,xa2)|E(xc,xa1,xc,xb1).
150 [] -KF(xa1,xm1,xb1,xc,xb2,xm2,xa2)|E(xc,xa2,xc,xb2).
151 [] -KF(xa1,xm1,xb1,xc,xb2,xm2,xa2)|M(xa1,xm1,xb1).
152 [] -KF(xa1,xm1,xb1,xc,xb2,xm2,xa2)|M(xa2,xm2,xb2).
153 [] -E(xc,xa,xc,xb)|M(xa,midpoint(xa,xb),xb).
154 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
155 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
156 [] -R(xa,xb,xc)|R(xc,xb,xa).
157 [] -R(xa,xb,xc)|xa=xb| -Col(xb,xa,xa1)|R(xa1,xb,xc).
158 [] -R(xa,xb,xc)|R(xa,xb,s(xb,xc)).
159 [] R(x,y,y).
160 [] -R(xa,xb,xc)| -R(xa1,xb,xc)| -T(xa,xc,xa1)|xb=xc.
161 [] -R(xa,xb,xc)| -R(xa,xc,xb)|xb=xc.
162 [] -R(xa,xb,xa)|xa=xb.
163 [] -R(xa,xb,xc)| -Col(xa,xb,xc)|xa=xb|xc=xb.
164 [] -R(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|R(xa1,xb1,xc1).
165 [] -perpAt(y,z,x,y1,z1)|Col(y,z,x).
166 [] -perpAt(y,z,x,y1,z1)|Col(y1,z1,x).
167 [] -perpAt(y,z,x,y1,z1)|y!=z.
168 [] -perpAt(y,z,x,y1,z1)|y1!=z1.
169 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
170 [] perpAt(y,z,x,y1,z1)|y=z|y1=z1| -Col(y,z,x)| -Col(y1,z1,x)|Col(y,z,f811(y,z,y1,z1,x)).
171 [] perpAt(y,z,x,y1,z1)|y=z|y1=z1| -Col(y,z,x)| -Col(y1,z1,x)|Col(y1,z1,g811(y,z,y1,z1,x)).
172 [] perpAt(y,z,x,y1,z1)|y=z|y1=z1| -Col(y,z,x)| -Col(y1,z1,x)|R(f811(y,z,y1,z1,x),x,g811(y,z,y1,z1,x)).
173 [] -perp(xp,xq,xp1,xq1)|xp=xq|xp1=xq1|perpAt(xp,xq,il(xp,xq,xp1,xq1),xp1,xq1).
174 [] perp(xp,xq,xp1,xq1)| -perpAt(xp,xq,x,xp1,xq1).
175 [] expressions.
176 [] -perpAt(x,y,z,u,v)|perpAt(u,v,z,x,y).
177 [] -perp(x,y,u,v)|perp(u,v,x,y).
178 [] -perpAt(xa,xb,x,xp,xq)|xa!=xb.
179 [] -perpAt(xa,xb,x,xp,xq)|xp!=xq.
180 [] -perpAt(xa,xb,x,xp,xq)|Col(xa,xb,x).
181 [] -perpAt(xa,xb,x,xp,xq)|Col(xp,xq,x).
182 [] -perpAt(xa,xb,x,xp,xq)|R(xa,x,xp).
183 [] -perpAt(xa,xb,x,xp,xq)|R(xb,x,xp).
184 [] -perpAt(xa,xb,x,xp,xq)|R(xa,x,xq).
185 [] -perpAt(xa,xb,x,xp,xq)|R(xb,x,xq).
186 [] -Col(xa,xb,x)| -Col(xp,xq,x)|xa=xb|xp=xq| -Col(xa,xb,u)| -Col(xp,xq,v)|u=x|v=x| -R(u,x,v)|perpAt(xa,xb,x,xp,xq).
187 [] -perp(xa,xb,xp,xq)| -Col(xa,xb,xp)| -Col(xa,xb,xq).
188 [] -perpAt(xa,xb,xc,xp,xq)|Col(xa,xb,xc).
189 [] -perpAt(xa,xb,xc,xp,xq)|Col(xp,xq,xc).
190 [] -perpAt(xa,xb,xc,xp,xq)|xc=il(xa,xb,xp,xq).
191 [] xa=xb| -Col(xa,xb,x)| -perp(xa,xb,xc,x)|perpAt(xa,xb,x,xc,x).
192 [] xa=xb| -Col(xa,xb,x)|perp(xa,xb,xc,x)| -perpAt(xa,xb,x,xc,x).
193 [] Col(xa,xb,xc)| -Col(xa,xb,xp)| -Col(xa,xb,xq)| -perp(xa,xb,xc,xp)| -perp(xa,xb,xc,xq)|xp=xq.
194 [] Col(xa,xb,xc)|Col(xa,xb,foot(xa,xb,xc)).
195 [] Col(xa,xb,xc)|perp(xa,xb,xc,foot(xa,xb,xc)).
196 [] Col(xa,xb,xc)| -Col(xa,xb,z)| -Col(xa,xb,y)| -perp(xa,xb,xc,z)| -perp(xa,xb,xc,y)|y=z.
197 [] -R(xa,xb,xc)| -M(s(xa,xc),xp,s(xb,xc))|R(xb,xa,xp).
198 [] -R(xa,xb,xc)| -M(s(xa,xc),xp,s(xb,xc))| -R(xb,xa,xp)|xb=xc|xa!=xp.
199 [] -perp(x,y,u,v)|perp(y,x,u,v).
200 [] xa=xb|perp(xa,xb,erect(xa,xb,xc),xa).
201 [] xa=xb|Col(xa,xb,erectAux(xa,xb,xc)).
202 [] xa=xb|T(xc,erectAux(xa,xb,xc),erect(xa,xb,xc)).
203 [] M(xa,midpoint(xa,xb),xb).
204 [] xp=xq|Col(xp,xq,xa)|Col(xp,xq,xb)| -T(xa,xt,xb)| -Col(xp,xq,xt)|opposite(xa,xp,xq,xb).
205 [] -opposite(xa,xp,xq,xb)| -Col(xp,xq,xa).
206 [] -opposite(xa,xp,xq,xb)| -Col(xp,xq,xb).
207 [] -opposite(xa,xp,xq,xb)|T(xa,il(xa,xb,xp,xq),xb).
208 [] -opposite(xa,xp,xq,xb)|Col(xp,xq,il(xa,xb,xp,xq)).
209 [] -opposite(xa,xp,xq,xb)|opposite(xb,xp,xq,xa).
210 [] -opposite(xa,xp,xq,xc)| -Col(xp,xq,xr)| -sameside(xa,xr,xb)|opposite(xb,xp,xq,xc).
211 [] -T(xa,xc,xp)| -T(xb,xq,xc)|T(xa,op(xq,xb,xp,xc,xa),xb).
212 [] -T(xa,xc,xp)| -T(xb,xq,xc)|T(xp,xq,op(xq,xb,xp,xc,xa)).
213 [] -T(xa,xu,xc)| -T(xb,xv,xc)| -Col(xp,xq,xu)| -Col(xp,xq,xv)|xp=xq|xc=xu|xc=xv|xa=xu|xb=xv|Col(xp,xq,xa)|Col(xp,xq,xb)|samesideline(xa,xb,xp,xq).
214 [] -samesideline(xa,xb,xp,xq)|Col(xp,xq,ss1(xa,xb,xp,xq)).
215 [] -samesideline(xa,xb,xp,xq)|Col(xp,xq,ss2(xa,xb,xp,xq)).
216 [] -samesideline(xa,xb,xp,xq)|T(xa,ss1(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
217 [] -samesideline(xa,xb,xp,xq)|T(xb,ss2(xa,xb,xp,xq),ss3(xa,xb,xp,xq)).
218 [] -samesideline(xa,xb,xp,xq)|xa!=ss1(xa,xb,xp,xq).
219 [] -samesideline(xa,xb,xp,xq)|xb!=ss2(xa,xb,xp,xq).
220 [] -samesideline(xa,xb,xp,xq)|ss3(xa,xb,xp,xq)!=ss1(xa,xb,xp,xq).
221 [] -samesideline(xa,xb,xp,xq)|ss3(xa,xb,xp,xq)!=ss2(xa,xb,xp,xq).
222 [] -samesideline(xa,xb,xp,xq)|xp!=xq.
223 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xa).
224 [] -samesideline(xa,xb,xp,xq)| -Col(xp,xq,xb).
225 [] -opposite(xa,xp,xq,xc)| -opposite(xb,xp,xq,xc)|samesideline(xa,xb,xp,xq).
226 [] -opposite(xa,xp,xq,xc)|opposite(xb,xp,xq,xc)| -samesideline(xa,xb,xp,xq).
227 [] xa=xb|Col(xa,xb,midpoint(u,reflect(xa,xb,u))).
228 [] xa=xb|u=reflect(xa,xb,u)|perp(xa,xb,u,reflect(xa,xb,u)).
229 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))| -perp(xa,xb,xp,xp1)|xp1=reflect(xa,xb,xp).
230 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))|xp!=xp1|xp1=reflect(xa,xb,xp).
231 [] xa=xb| -Col(xa,xb,xp)|xp=reflect(xa,xb,xp).
232 [] xa!=xb|reflect(xa,xb,z)=s(xa,z).
233 [] xa=xb|reflect(xa,xb,xp)!=xp1|reflect(xa,xb,xp1)=xp.
end_of_list.

list(hints).
234 [] reflect(a,b,x)!=p.
235 [] reflect(a,b,p)!=x.
236 [] -R(reflect(a,b,p),x,reflect(a,b,p)).
end_of_list.

list(passive).
end_of_list.

list(sos).
237 [] a!=b.
238 [] reflect(a,b,reflect(a,b,p))!=p.
end_of_list.

======= end of input processing =======

=========== start of search ===========

given clause #1: (wt=-2147483647) 237 [] a!=b.
** KEPT (pick-wt=12): 239 [binary,237.1,233.1] reflect(a,b,x)!=y|reflect(a,b,y)=x.
** KEPT (pick-wt=10): 240 [binary,237.1,231.1] -Col(a,b,x)|x=reflect(a,b,x).
** KEPT (pick-wt=9): 241 [binary,237.1,227.1] Col(a,b,midpoint(x,reflect(a,b,x))).
** KEPT (pick-wt=10): 242 [binary,237.1,202.1] T(x,erectAux(a,b,x),erect(a,b,x)).
** KEPT (pick-wt=7): 243 [binary,237.1,201.1] Col(a,b,erectAux(a,b,x)).
** KEPT (pick-wt=8): 244 [binary,237.1,200.1] perp(a,b,erect(a,b,x),a).
** KEPT (pick-wt=11): 245 [binary,237.1,163.4] -R(x,b,a)| -Col(x,b,a)|x=b.
** KEPT (pick-wt=11): 246 [binary,237.1,163.3] -R(a,b,x)| -Col(a,b,x)|x=b.
** KEPT (pick-wt=4): 247 [binary,237.1,162.2] -R(a,b,a).
** KEPT (pick-wt=8): 248 [binary,237.1,161.3] -R(x,a,b)| -R(x,b,a).
** KEPT (pick-wt=12): 249 [binary,237.1,160.4] -R(x,a,b)| -R(y,a,b)| -T(x,b,y).
** KEPT (pick-wt=12): 250 [binary,237.1,157.2] -R(a,b,x)| -Col(b,a,y)|R(y,b,x).
** KEPT (pick-wt=11): 251 [binary,237.1,140.2] s(a,s(b,x))!=s(b,s(a,x)).
** KEPT (pick-wt=7): 252 [binary,237.1,139.2] s(a,x)!=s(b,x).
** KEPT (pick-wt=8): 253 [binary,237.1,138.3] -M(x,a,y)| -M(x,b,y).
** KEPT (pick-wt=5): 254 [binary,237.1,131.2] s(b,a)!=a.
** KEPT (pick-wt=7): 255 [binary,237.1,130.2] s(x,a)!=s(x,b).
** KEPT (pick-wt=10): 256 [binary,237.1,129.3] s(x,a)!=y|s(x,b)!=y.
** KEPT (pick-wt=8): 257 [binary,237.1,125.3] -M(x,y,a)| -M(x,y,b).
** KEPT (pick-wt=4): 258 [binary,237.1,124.2] -M(b,a,b).
** KEPT (pick-wt=12): 259 [binary,237.1,111.2] x=y|E(y,insert(a,b,y,x),a,b).
** KEPT (pick-wt=12): 260 [binary,237.1,111.1] x=y|E(b,insert(x,y,b,a),x,y).
** KEPT (pick-wt=11): 261 [binary,237.1,110.2] x=y|sameside(insert(a,b,y,x),y,x).
** KEPT (pick-wt=11): 262 [binary,237.1,110.1] x=y|sameside(insert(x,y,b,a),b,a).
** KEPT (pick-wt=4): 263 [binary,237.1,107.1] sameside(a,b,a).
** KEPT (pick-wt=11): 264 [binary,237.1,92.3] sameside(x,b,a)|x=b| -T(b,a,x).
** KEPT (pick-wt=11): 265 [binary,237.1,92.2] sameside(a,b,x)|x=b| -T(b,x,a).
** KEPT (pick-wt=11): 266 [binary,237.1,91.3] sameside(x,b,a)|x=b| -T(b,x,a).
** KEPT (pick-wt=11): 267 [binary,237.1,91.2] sameside(a,b,x)|x=b| -T(b,a,x).
** KEPT (pick-wt=12): 268 [binary,237.1,32.3] -T(x,a,b)| -T(a,b,y)|T(x,a,y).
** KEPT (pick-wt=12): 269 [binary,237.1,31.3] -T(x,a,b)| -T(a,b,y)|T(x,b,y).
** KEPT (pick-wt=8): 270 [binary,237.1,24.3] -T(a,b,x)| -T(b,a,x).
** KEPT (pick-wt=4): 271 [binary,237.1,7.2] -T(a,b,a).
** KEPT (pick-wt=5): 272 [binary,237.1,3.2] -E(a,b,x,x).
** KEPT (pick-wt=8): 273 [factor,249.1.2] -R(x,a,b)| -T(x,b,x).
** KEPT (pick-wt=6): 274 [ur,138,126,237] -M(x,a,s(b,x)).
** KEPT (pick-wt=6): 275 [ur,138,126,237] -M(x,b,s(a,x)).
** KEPT (pick-wt=4): 276 [ur,138,123,237] -M(a,b,a).
** KEPT (pick-wt=6): 277 [ur,125,203,237] -M(x,midpoint(x,b),a).
** KEPT (pick-wt=4): 278 [ur,125,123,237] -M(b,b,a).
** KEPT (pick-wt=6): 279 [ur,125,203,237] -M(x,midpoint(x,a),b).
** KEPT (pick-wt=4): 280 [ur,125,123,237] -M(a,a,b).
** KEPT (pick-wt=8): 281 [ur,118,237,39,38,128] Col(s(x,s(x,a)),a,b).
** KEPT (pick-wt=9): 282 [ur,111,237,237] E(b,insert(a,b,b,a),a,b).
** KEPT (pick-wt=9): 283 [ur,111,37,237] E(gamma,insert(a,b,gamma,alpha),a,b).
** KEPT (pick-wt=9): 284 [ur,111,36,237] E(gamma,insert(a,b,gamma,beta),a,b).
** KEPT (pick-wt=9): 285 [ur,111,35,237] E(beta,insert(a,b,beta,alpha),a,b).
** KEPT (pick-wt=9): 286 [ur,111,237,37] E(b,insert(alpha,gamma,b,a),alpha,gamma).
** KEPT (pick-wt=9): 287 [ur,111,237,36] E(b,insert(beta,gamma,b,a),beta,gamma).
** KEPT (pick-wt=9): 288 [ur,111,237,35] E(b,insert(alpha,beta,b,a),alpha,beta).
** KEPT (pick-wt=8): 289 [ur,110,237,237] sameside(insert(a,b,b,a),b,a).
** KEPT (pick-wt=8): 290 [ur,110,37,237] sameside(insert(a,b,gamma,alpha),gamma,alpha).
** KEPT (pick-wt=8): 291 [ur,110,36,237] sameside(insert(a,b,gamma,beta),gamma,beta).
** KEPT (pick-wt=8): 292 [ur,110,35,237] sameside(insert(a,b,beta,alpha),beta,alpha).
** KEPT (pick-wt=12): 293 [ur,110,237,39] sameside(insert(x,ext(y,x,alpha,gamma),b,a),b,a).
** KEPT (pick-wt=8): 294 [ur,110,237,37] sameside(insert(alpha,gamma,b,a),b,a).
** KEPT (pick-wt=8): 295 [ur,110,237,36] sameside(insert(beta,gamma,b,a),b,a).
** KEPT (pick-wt=8): 296 [ur,110,237,35] sameside(insert(alpha,beta,b,a),b,a).
** KEPT (pick-wt=8): 297 [ur,24,38,237] -T(a,b,ext(b,a,alpha,gamma)).
** KEPT (pick-wt=8): 298 [ur,24,4,237] -T(a,b,ext(b,a,x,y)).
** KEPT (pick-wt=8): 299 [ur,24,38,237] -T(b,a,ext(a,b,alpha,gamma)).
** KEPT (pick-wt=4): 300 [ur,24,21,237] -T(b,a,b).
** KEPT (pick-wt=8): 301 [ur,24,4,237] -T(b,a,ext(a,b,x,y)).
** KEPT (pick-wt=11): 302 [ur,20,237,38,5] ext(a,b,alpha,gamma)=ext(a,b,alpha,gamma).
** KEPT (pick-wt=11): 303 [ur,20,237,21,133] ext(a,b,s(x,b),s(x,b))=b.
** KEPT (pick-wt=7): 304 [ur,20,237,21,18] ext(a,b,x,x)=b.
** KEPT (pick-wt=11): 305 [ur,20,237,4,5] ext(a,b,x,y)=ext(a,b,x,y).
** KEPT (pick-wt=9): 306 [ur,6,13,5,18,13,4,21,237] E(ext(a,b,b,b),a,b,a).
** KEPT (pick-wt=9): 307 [ur,6,13,5,13,18,4,21,237] E(ext(a,b,b,b),b,b,b).
** KEPT (pick-wt=9): 308 [ur,6,13,5,13,13,4,21,237] E(ext(a,b,b,b),x,b,x).
** KEPT (pick-wt=9): 309 [ur,6,1,5,18,1,4,21,237] E(ext(a,b,a,a),a,a,b).
** KEPT (pick-wt=9): 310 [ur,6,1,5,1,18,4,21,237] E(ext(a,b,a,a),b,a,a).
298 back subsumes 297.
301 back subsumes 299.
304 back subsumes 303.
305 back subsumes 302.
308 back subsumes 307.
308 back subsumes 306.

given clause #2: (wt=-2147483647) 238 [] reflect(a,b,reflect(a,b,p))!=p.
** KEPT (pick-wt=-1): 311 [binary,238.1,233.3,unit_del,237] reflect(a,b,p)!=reflect(a,b,p).
** KEPT (pick-wt=10): 312 [binary,238.1,124.2] -M(p,reflect(a,b,reflect(a,b,p)),p).
** KEPT (pick-wt=11): 313 [binary,238.1,3.2] -E(reflect(a,b,reflect(a,b,p)),p,x,x).
** KEPT (pick-wt=12): 314 [ur,138,126,238] -M(x,reflect(a,b,reflect(a,b,p)),s(p,x)).
** KEPT (pick-wt=12): 315 [ur,138,126,238] -M(x,p,s(reflect(a,b,reflect(a,b,p)),x)).
** KEPT (pick-wt=12): 316 [ur,125,203,238] -M(x,midpoint(x,p),reflect(a,b,reflect(a,b,p))).
** KEPT (pick-wt=10): 317 [ur,125,123,238] -M(p,p,reflect(a,b,reflect(a,b,p))).
** KEPT (pick-wt=12): 318 [ur,125,203,238] -M(x,midpoint(x,reflect(a,b,reflect(a,b,p))),p).
** KEPT (pick-wt=10): 319 [ur,24,21,238] -T(p,reflect(a,b,reflect(a,b,p)),p).
** KEPT (pick-wt=-1): 320 [para_into,238.1.1.3,233.3.1,unit_del,237,factor_simp] reflect(a,b,x)!=p.
** KEPT (pick-wt=12): 321 [para_into,238.1.1,233.3.1,unit_del,237] x!=p|reflect(a,b,x)!=reflect(a,b,p).
320 back subsumes 238.

given clause #3: (wt=-1) 311 [binary,238.1,233.3,unit_del,237] reflect(a,b,p)!=reflect(a,b,p).
** KEPT (pick-wt=12): 322 [binary,311.1,231.1,unit_del,64] x=reflect(reflect(a,b,p),reflect(a,b,p),x).
** KEPT (pick-wt=6): 323 [binary,311.1,230.4,unit_del,237,241] p!=reflect(a,b,p).
** KEPT (pick-wt=8): 324 [binary,311.1,229.4,unit_del,237,241] -perp(a,b,p,reflect(a,b,p)).
** KEPT (pick-wt=-1): 325 [binary,311.1,161.3,unit_del,159,159] $F.

-----> EMPTY CLAUSE at   0.04 sec ----> 325 [binary,311.1,161.3,unit_del,159,159] $F.

Length of proof is 1.  Level of proof is 1.

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

159 [] R(x,y,y).
161 [] -R(xa,xb,xc)| -R(xa,xc,xb)|xb=xc.
233 [] xa=xb|reflect(xa,xb,xp)!=xp1|reflect(xa,xb,xp1)=xp.
237 [] a!=b.
238 [] reflect(a,b,reflect(a,b,p))!=p.
311 [binary,238.1,233.3,unit_del,237] reflect(a,b,p)!=reflect(a,b,p).
325 [binary,311.1,161.3,unit_del,159,159] $F.

------------ end of proof -------------


Search stopped by max_proofs option.

============ end of search ============

-------------- statistics -------------
clauses given                  3
clauses generated            562
  binary_res generated       228
  hyper_res generated         20
  para_from generated          0
  para_into generated         12
  factors generated            1
  ur_res generated           301
demod & eval rewrites          0
clauses wt,lit,sk delete     382
tautologies deleted            2
clauses forward subsumed      91
cl not subsumed due to ancestor_subsume       0
  (subsumed by sos)           43
unit deletions                44
factor simplifications         7
clauses kept                  86
new demodulators               0
empty clauses                  1
clauses back demodulated       0
clauses back subsumed          7
usable size                  235
sos size                      79
demodulators size              0
passive size                   0
hot size                       0
Kbytes malloced             5859

----------- times (seconds) -----------
user CPU time          0.04          (0 hr, 0 min, 0 sec)
system CPU time        0.01          (0 hr, 0 min, 0 sec)
wall-clock time        0             (0 hr, 0 min, 0 sec)

That finishes the proof of the theorem.

Process 6146 finished Sat Jul  5 12:26:21 2014

Sindbad File Manager Version 1.0, Coded By Sindbad EG ~ The Terrorists