1 CLASH, statistics insufficient
3 4578: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
5 multiply ?5 ?6 =?= multiply ?6 ?5
6 [6, 5] by commutativity_of_multiply ?5 ?6
8 add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
9 [10, 9, 8] by distributivity1 ?8 ?9 ?10
11 add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
12 [14, 13, 12] by distributivity2 ?12 ?13 ?14
14 multiply (add ?16 ?17) ?18
16 add (multiply ?16 ?18) (multiply ?17 ?18)
17 [18, 17, 16] by distributivity3 ?16 ?17 ?18
19 multiply ?20 (add ?21 ?22)
21 add (multiply ?20 ?21) (multiply ?20 ?22)
22 [22, 21, 20] by distributivity4 ?20 ?21 ?22
24 add ?24 (inverse ?24) =>= multiplicative_identity
25 [24] by additive_inverse1 ?24
27 add (inverse ?26) ?26 =>= multiplicative_identity
28 [26] by additive_inverse2 ?26
30 multiply ?28 (inverse ?28) =>= additive_identity
31 [28] by multiplicative_inverse1 ?28
33 multiply (inverse ?30) ?30 =>= additive_identity
34 [30] by multiplicative_inverse2 ?30
36 multiply ?32 multiplicative_identity =>= ?32
37 [32] by multiplicative_id1 ?32
39 multiply multiplicative_identity ?34 =>= ?34
40 [34] by multiplicative_id2 ?34
41 4578: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
42 4578: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
45 multiply a (multiply b c) =<= multiply (multiply a b) c
46 [] by prove_associativity
50 4578: additive_identity 4 0 0
51 4578: multiplicative_identity 4 0 0
53 4578: add 16 2 0 multiply
54 4578: multiply 20 2 4 0,2add
58 CLASH, statistics insufficient
60 4579: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
62 multiply ?5 ?6 =?= multiply ?6 ?5
63 [6, 5] by commutativity_of_multiply ?5 ?6
65 add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
66 [10, 9, 8] by distributivity1 ?8 ?9 ?10
68 add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
69 [14, 13, 12] by distributivity2 ?12 ?13 ?14
71 multiply (add ?16 ?17) ?18
73 add (multiply ?16 ?18) (multiply ?17 ?18)
74 [18, 17, 16] by distributivity3 ?16 ?17 ?18
76 multiply ?20 (add ?21 ?22)
78 add (multiply ?20 ?21) (multiply ?20 ?22)
79 [22, 21, 20] by distributivity4 ?20 ?21 ?22
81 add ?24 (inverse ?24) =>= multiplicative_identity
82 [24] by additive_inverse1 ?24
84 add (inverse ?26) ?26 =>= multiplicative_identity
85 [26] by additive_inverse2 ?26
87 multiply ?28 (inverse ?28) =>= additive_identity
88 [28] by multiplicative_inverse1 ?28
90 multiply (inverse ?30) ?30 =>= additive_identity
91 [30] by multiplicative_inverse2 ?30
93 multiply ?32 multiplicative_identity =>= ?32
94 [32] by multiplicative_id1 ?32
96 multiply multiplicative_identity ?34 =>= ?34
97 [34] by multiplicative_id2 ?34
98 4579: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
99 4579: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
102 multiply a (multiply b c) =<= multiply (multiply a b) c
103 [] by prove_associativity
107 4579: additive_identity 4 0 0
108 4579: multiplicative_identity 4 0 0
110 4579: add 16 2 0 multiply
111 4579: multiply 20 2 4 0,2add
115 CLASH, statistics insufficient
117 4580: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
119 multiply ?5 ?6 =?= multiply ?6 ?5
120 [6, 5] by commutativity_of_multiply ?5 ?6
122 add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
123 [10, 9, 8] by distributivity1 ?8 ?9 ?10
125 add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
126 [14, 13, 12] by distributivity2 ?12 ?13 ?14
128 multiply (add ?16 ?17) ?18
130 add (multiply ?16 ?18) (multiply ?17 ?18)
131 [18, 17, 16] by distributivity3 ?16 ?17 ?18
133 multiply ?20 (add ?21 ?22)
135 add (multiply ?20 ?21) (multiply ?20 ?22)
136 [22, 21, 20] by distributivity4 ?20 ?21 ?22
138 add ?24 (inverse ?24) =>= multiplicative_identity
139 [24] by additive_inverse1 ?24
141 add (inverse ?26) ?26 =>= multiplicative_identity
142 [26] by additive_inverse2 ?26
144 multiply ?28 (inverse ?28) =>= additive_identity
145 [28] by multiplicative_inverse1 ?28
147 multiply (inverse ?30) ?30 =>= additive_identity
148 [30] by multiplicative_inverse2 ?30
150 multiply ?32 multiplicative_identity =>= ?32
151 [32] by multiplicative_id1 ?32
153 multiply multiplicative_identity ?34 =>= ?34
154 [34] by multiplicative_id2 ?34
155 4580: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
156 4580: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
159 multiply a (multiply b c) =<= multiply (multiply a b) c
160 [] by prove_associativity
164 4580: additive_identity 4 0 0
165 4580: multiplicative_identity 4 0 0
167 4580: add 16 2 0 multiply
168 4580: multiply 20 2 4 0,2add
174 Found proof, 16.914436s
175 % SZS status Unsatisfiable for BOO007-2.p
176 % SZS output start CNFRefutation for BOO007-2.p
177 Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
178 Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
179 Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
180 Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
181 Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
182 Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
183 Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
184 Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
185 Id : 31, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80
186 Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
187 Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
188 Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
189 Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
190 Id : 65, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3
191 Id : 46, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3
192 Id : 58, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 46 with 5 at 2
193 Id : 32, {_}: add (multiply ?82 ?83) ?84 =<= multiply (add ?82 ?84) (add ?84 ?83) [84, 83, 82] by Super 31 with 2 at 2,3
194 Id : 121, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3
195 Id : 2169, {_}: add ?2910 (multiply (inverse ?2910) ?2911) =>= add ?2910 ?2911 [2911, 2910] by Demod 121 with 13 at 3
196 Id : 2179, {_}: add ?2938 additive_identity =<= add ?2938 (inverse (inverse ?2938)) [2938] by Super 2169 with 10 at 2,2
197 Id : 2230, {_}: ?2938 =<= add ?2938 (inverse (inverse ?2938)) [2938] by Demod 2179 with 14 at 2
198 Id : 2429, {_}: add (multiply ?3159 (inverse (inverse ?3160))) ?3160 =>= multiply (add ?3159 ?3160) ?3160 [3160, 3159] by Super 32 with 2230 at 2,3
199 Id : 2455, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply (add ?3159 ?3160) ?3160 [3159, 3160] by Demod 2429 with 2 at 2
200 Id : 2456, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply ?3160 (add ?3159 ?3160) [3159, 3160] by Demod 2455 with 3 at 3
201 Id : 248, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3
202 Id : 2457, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2456 with 248 at 3
203 Id : 120, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3
204 Id : 124, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 120 with 3 at 3
205 Id : 3170, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 124 with 13 at 3
206 Id : 144, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3
207 Id : 3378, {_}: multiply ?4138 (add (inverse ?4138) ?4139) =>= multiply ?4138 ?4139 [4139, 4138] by Demod 144 with 15 at 3
208 Id : 3399, {_}: multiply ?4195 (inverse ?4195) =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Super 3378 with 2230 at 2,2
209 Id : 3488, {_}: additive_identity =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Demod 3399 with 10 at 2
210 Id : 3900, {_}: add (inverse (inverse ?4844)) additive_identity =?= add (inverse (inverse ?4844)) ?4844 [4844] by Super 3170 with 3488 at 2,2
211 Id : 3924, {_}: add additive_identity (inverse (inverse ?4844)) =<= add (inverse (inverse ?4844)) ?4844 [4844] by Demod 3900 with 2 at 2
212 Id : 3925, {_}: add additive_identity (inverse (inverse ?4844)) =?= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3924 with 2 at 3
213 Id : 3926, {_}: inverse (inverse ?4844) =<= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3925 with 15 at 2
214 Id : 3927, {_}: inverse (inverse ?4844) =>= ?4844 [4844] by Demod 3926 with 2230 at 3
215 Id : 6845, {_}: add ?3160 (multiply ?3159 ?3160) =?= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2457 with 3927 at 2,2,2
216 Id : 1130, {_}: add (multiply additive_identity ?1671) ?1672 =<= multiply ?1672 (add ?1671 ?1672) [1672, 1671] by Super 4 with 15 at 1,3
217 Id : 1134, {_}: add (multiply additive_identity ?1683) (inverse ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Super 1130 with 8 at 2,3
218 Id : 1186, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Demod 1134 with 2 at 2
219 Id : 1187, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply multiplicative_identity (inverse ?1683) [1683] by Demod 1186 with 3 at 3
220 Id : 1188, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= inverse ?1683 [1683] by Demod 1187 with 13 at 3
221 Id : 3360, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 144 with 15 at 3
222 Id : 3364, {_}: add (inverse (add (inverse additive_identity) ?4095)) (multiply additive_identity ?4095) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Super 1188 with 3360 at 2,2
223 Id : 3442, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Demod 3364 with 2 at 2
224 Id : 249, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2
225 Id : 3443, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3442 with 249 at 1,1,3
226 Id : 3444, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3443 with 249 at 1,1,2,2
227 Id : 2180, {_}: add ?2940 (inverse ?2940) =>= add ?2940 multiplicative_identity [2940] by Super 2169 with 12 at 2,2
228 Id : 2231, {_}: multiplicative_identity =<= add ?2940 multiplicative_identity [2940] by Demod 2180 with 8 at 2
229 Id : 2263, {_}: add multiplicative_identity ?3015 =>= multiplicative_identity [3015] by Super 2 with 2231 at 3
230 Id : 3445, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse multiplicative_identity [4095] by Demod 3444 with 2263 at 1,3
231 Id : 3446, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4095] by Demod 3445 with 2263 at 1,2,2
232 Id : 191, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2
233 Id : 3447, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= additive_identity [4095] by Demod 3446 with 191 at 3
234 Id : 3448, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3447 with 2 at 2
235 Id : 3449, {_}: add additive_identity (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3448 with 191 at 1,2
236 Id : 3450, {_}: multiply additive_identity ?4095 =>= additive_identity [4095] by Demod 3449 with 15 at 2
237 Id : 6846, {_}: add ?3160 (multiply ?3159 ?3160) =>= add additive_identity ?3160 [3159, 3160] by Demod 6845 with 3450 at 1,3
238 Id : 6847, {_}: add ?3160 (multiply ?3159 ?3160) =>= ?3160 [3159, 3160] by Demod 6846 with 15 at 3
239 Id : 6852, {_}: add ?8316 (multiply ?8316 ?8317) =>= ?8316 [8317, 8316] by Super 58 with 6847 at 3
240 Id : 7003, {_}: add (multiply ?8541 (multiply ?8542 ?8543)) (multiply ?8541 ?8543) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8543, 8542, 8541] by Super 65 with 6852 at 1,3
241 Id : 7114, {_}: add (multiply ?8541 ?8543) (multiply ?8541 (multiply ?8542 ?8543)) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7003 with 2 at 2
242 Id : 7115, {_}: multiply ?8541 (add ?8543 (multiply ?8542 ?8543)) =?= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7114 with 7 at 2
243 Id : 21444, {_}: multiply ?30534 ?30535 =<= multiply ?30534 (multiply (add ?30536 ?30534) ?30535) [30536, 30535, 30534] by Demod 7115 with 6847 at 2,2
244 Id : 21466, {_}: multiply (multiply ?30625 ?30626) ?30627 =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30626, 30625] by Super 21444 with 6847 at 1,2,3
245 Id : 147, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3
246 Id : 152, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 147 with 3 at 2
247 Id : 4375, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 152 with 15 at 3
248 Id : 532, {_}: add (multiply ?866 ?867) ?868 =<= multiply (add ?866 ?868) (add ?868 ?867) [868, 867, 866] by Super 31 with 2 at 2,3
249 Id : 547, {_}: add (multiply ?925 ?926) (inverse ?925) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Super 532 with 8 at 1,3
250 Id : 583, {_}: add (inverse ?925) (multiply ?925 ?926) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Demod 547 with 2 at 2
251 Id : 584, {_}: add (inverse ?925) (multiply ?925 ?926) =>= add (inverse ?925) ?926 [926, 925] by Demod 583 with 13 at 3
252 Id : 4646, {_}: multiply (inverse (inverse ?5719)) (add (inverse ?5719) ?5720) =>= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5720, 5719] by Super 4375 with 584 at 2,2
253 Id : 4685, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5719, 5720] by Demod 4646 with 4375 at 2
254 Id : 4686, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4685 with 3 at 3
255 Id : 4687, {_}: multiply ?5720 ?5719 =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4686 with 3927 at 2,2
256 Id : 4688, {_}: multiply ?5720 ?5719 =<= multiply ?5719 (multiply ?5719 ?5720) [5719, 5720] by Demod 4687 with 3927 at 1,3
257 Id : 21467, {_}: multiply (multiply ?30629 ?30630) ?30631 =<= multiply (multiply ?30629 ?30630) (multiply ?30629 ?30631) [30631, 30630, 30629] by Super 21444 with 6852 at 1,2,3
258 Id : 36399, {_}: multiply (multiply ?58815 ?58816) (multiply ?58815 ?58817) =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Super 4688 with 21467 at 2,3
259 Id : 36627, {_}: multiply (multiply ?58815 ?58816) ?58817 =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Demod 36399 with 21467 at 2
260 Id : 36628, {_}: multiply (multiply ?58815 ?58816) ?58817 =>= multiply ?58816 (multiply ?58815 ?58817) [58817, 58816, 58815] by Demod 36627 with 4688 at 3
261 Id : 36893, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 21466 with 36628 at 2
262 Id : 36894, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply ?30626 (multiply ?30625 (multiply ?30626 ?30627)) [30627, 30625, 30626] by Demod 36893 with 36628 at 3
263 Id : 3522, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 248 with 3450 at 1,2
264 Id : 3543, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3522 with 15 at 2
265 Id : 7020, {_}: add (multiply ?8599 (multiply ?8600 ?8601)) ?8600 =>= multiply (add ?8599 ?8600) ?8600 [8601, 8600, 8599] by Super 32 with 6852 at 2,3
266 Id : 7087, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply (add ?8599 ?8600) ?8600 [8601, 8599, 8600] by Demod 7020 with 2 at 2
267 Id : 7088, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply ?8600 (add ?8599 ?8600) [8601, 8599, 8600] by Demod 7087 with 3 at 3
268 Id : 7089, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= ?8600 [8601, 8599, 8600] by Demod 7088 with 3543 at 3
269 Id : 20142, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply (multiply ?27776 (multiply ?27777 ?27778)) ?27777 [27778, 27777, 27776] by Super 3543 with 7089 at 2,3
270 Id : 20329, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply ?27777 (multiply ?27776 (multiply ?27777 ?27778)) [27778, 27777, 27776] by Demod 20142 with 3 at 3
271 Id : 36895, {_}: multiply ?30626 (multiply ?30625 ?30627) =?= multiply ?30625 (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 36894 with 20329 at 3
272 Id : 34, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 31 with 2 at 1,3
273 Id : 6868, {_}: add (multiply (multiply ?8366 ?8367) ?8368) ?8367 =>= multiply ?8367 (add ?8368 ?8367) [8368, 8367, 8366] by Super 34 with 6847 at 1,3
274 Id : 6940, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= multiply ?8367 (add ?8368 ?8367) [8368, 8366, 8367] by Demod 6868 with 2 at 2
275 Id : 6941, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= ?8367 [8368, 8366, 8367] by Demod 6940 with 3543 at 3
276 Id : 19816, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply (multiply (multiply ?27180 ?27181) ?27182) ?27181 [27182, 27181, 27180] by Super 3543 with 6941 at 2,3
277 Id : 19977, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27181, 27180] by Demod 19816 with 3 at 3
278 Id : 36891, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27180, 27181] by Demod 19977 with 36628 at 2
279 Id : 36892, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply ?27181 (multiply ?27180 ?27182)) [27182, 27180, 27181] by Demod 36891 with 36628 at 2,3
280 Id : 36900, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply (multiply ?27180 ?27182) ?27181 [27182, 27180, 27181] by Demod 36892 with 4688 at 3
281 Id : 36901, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply ?27182 (multiply ?27180 ?27181) [27182, 27180, 27181] by Demod 36900 with 36628 at 3
282 Id : 37364, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 37363 with 3 at 2,2
283 Id : 37363, {_}: multiply c (multiply a b) =?= multiply c (multiply b a) [] by Demod 37362 with 3 at 2,3
284 Id : 37362, {_}: multiply c (multiply a b) =?= multiply c (multiply a b) [] by Demod 37361 with 36901 at 2
285 Id : 37361, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 37360 with 3 at 3
286 Id : 37360, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 36895 at 2
287 Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
288 % SZS output end CNFRefutation for BOO007-2.p
289 4579: solved BOO007-2.p in 8.372523 using kbo
290 4579: status Unsatisfiable for BOO007-2.p
291 CLASH, statistics insufficient
293 4588: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
295 multiply ?5 ?6 =?= multiply ?6 ?5
296 [6, 5] by commutativity_of_multiply ?5 ?6
298 add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
299 [10, 9, 8] by distributivity1 ?8 ?9 ?10
301 multiply ?12 (add ?13 ?14)
303 add (multiply ?12 ?13) (multiply ?12 ?14)
304 [14, 13, 12] by distributivity2 ?12 ?13 ?14
305 4588: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
307 multiply ?18 multiplicative_identity =>= ?18
308 [18] by multiplicative_id1 ?18
310 add ?20 (inverse ?20) =>= multiplicative_identity
311 [20] by additive_inverse1 ?20
313 multiply ?22 (inverse ?22) =>= additive_identity
314 [22] by multiplicative_inverse1 ?22
317 multiply a (multiply b c) =<= multiply (multiply a b) c
318 [] by prove_associativity
323 4588: multiplicative_identity 2 0 0
324 4588: additive_identity 2 0 0
325 4588: add 9 2 0 multiply
326 4588: multiply 13 2 4 0,2add
330 CLASH, statistics insufficient
332 4589: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
334 multiply ?5 ?6 =?= multiply ?6 ?5
335 [6, 5] by commutativity_of_multiply ?5 ?6
337 add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
338 [10, 9, 8] by distributivity1 ?8 ?9 ?10
340 multiply ?12 (add ?13 ?14)
342 add (multiply ?12 ?13) (multiply ?12 ?14)
343 [14, 13, 12] by distributivity2 ?12 ?13 ?14
344 4589: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
346 multiply ?18 multiplicative_identity =>= ?18
347 [18] by multiplicative_id1 ?18
349 add ?20 (inverse ?20) =>= multiplicative_identity
350 [20] by additive_inverse1 ?20
352 multiply ?22 (inverse ?22) =>= additive_identity
353 [22] by multiplicative_inverse1 ?22
356 multiply a (multiply b c) =<= multiply (multiply a b) c
357 [] by prove_associativity
362 4589: multiplicative_identity 2 0 0
363 4589: additive_identity 2 0 0
364 4589: add 9 2 0 multiply
365 4589: multiply 13 2 4 0,2add
369 CLASH, statistics insufficient
371 4590: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
373 multiply ?5 ?6 =?= multiply ?6 ?5
374 [6, 5] by commutativity_of_multiply ?5 ?6
376 add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
377 [10, 9, 8] by distributivity1 ?8 ?9 ?10
379 multiply ?12 (add ?13 ?14)
381 add (multiply ?12 ?13) (multiply ?12 ?14)
382 [14, 13, 12] by distributivity2 ?12 ?13 ?14
383 4590: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
385 multiply ?18 multiplicative_identity =>= ?18
386 [18] by multiplicative_id1 ?18
388 add ?20 (inverse ?20) =>= multiplicative_identity
389 [20] by additive_inverse1 ?20
391 multiply ?22 (inverse ?22) =>= additive_identity
392 [22] by multiplicative_inverse1 ?22
395 multiply a (multiply b c) =<= multiply (multiply a b) c
396 [] by prove_associativity
401 4590: multiplicative_identity 2 0 0
402 4590: additive_identity 2 0 0
403 4590: add 9 2 0 multiply
404 4590: multiply 13 2 4 0,2add
410 Found proof, 23.495904s
411 % SZS status Unsatisfiable for BOO007-4.p
412 % SZS output start CNFRefutation for BOO007-4.p
413 Id : 44, {_}: multiply ?112 (add ?113 ?114) =<= add (multiply ?112 ?113) (multiply ?112 ?114) [114, 113, 112] by distributivity2 ?112 ?113 ?114
414 Id : 4, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
415 Id : 9, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22
416 Id : 5, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
417 Id : 7, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18
418 Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
419 Id : 8, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20
420 Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
421 Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
422 Id : 25, {_}: add ?62 (multiply ?63 ?64) =<= multiply (add ?62 ?63) (add ?62 ?64) [64, 63, 62] by distributivity1 ?62 ?63 ?64
423 Id : 516, {_}: add ?742 (multiply ?743 ?744) =<= multiply (add ?742 ?743) (add ?744 ?742) [744, 743, 742] by Super 25 with 2 at 2,3
424 Id : 530, {_}: add ?796 (multiply additive_identity ?797) =<= multiply ?796 (add ?797 ?796) [797, 796] by Super 516 with 6 at 1,3
425 Id : 1019, {_}: add ?1448 (multiply additive_identity ?1449) =<= multiply ?1448 (add ?1449 ?1448) [1449, 1448] by Super 516 with 6 at 1,3
426 Id : 1024, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply (inverse ?1462) multiplicative_identity [1462] by Super 1019 with 8 at 2,3
427 Id : 1064, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply multiplicative_identity (inverse ?1462) [1462] by Demod 1024 with 3 at 3
428 Id : 75, {_}: multiply multiplicative_identity ?178 =>= ?178 [178] by Super 3 with 7 at 3
429 Id : 1065, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= inverse ?1462 [1462] by Demod 1064 with 75 at 3
430 Id : 97, {_}: multiply ?204 (add (inverse ?204) ?205) =>= add additive_identity (multiply ?204 ?205) [205, 204] by Super 5 with 9 at 1,3
431 Id : 63, {_}: add additive_identity ?160 =>= ?160 [160] by Super 2 with 6 at 3
432 Id : 2714, {_}: multiply ?204 (add (inverse ?204) ?205) =>= multiply ?204 ?205 [205, 204] by Demod 97 with 63 at 3
433 Id : 2718, {_}: add (inverse (add (inverse additive_identity) ?3390)) (multiply additive_identity ?3390) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Super 1065 with 2714 at 2,2
434 Id : 2791, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Demod 2718 with 2 at 2
435 Id : 184, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 63 at 2
436 Id : 2792, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2791 with 184 at 1,1,3
437 Id : 2793, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2792 with 184 at 1,1,2,2
438 Id : 86, {_}: add ?193 (multiply (inverse ?193) ?194) =>= multiply multiplicative_identity (add ?193 ?194) [194, 193] by Super 4 with 8 at 1,3
439 Id : 1836, {_}: add ?2310 (multiply (inverse ?2310) ?2311) =>= add ?2310 ?2311 [2311, 2310] by Demod 86 with 75 at 3
440 Id : 1846, {_}: add ?2338 (inverse ?2338) =>= add ?2338 multiplicative_identity [2338] by Super 1836 with 7 at 2,2
441 Id : 1890, {_}: multiplicative_identity =<= add ?2338 multiplicative_identity [2338] by Demod 1846 with 8 at 2
442 Id : 1917, {_}: add multiplicative_identity ?2407 =>= multiplicative_identity [2407] by Super 2 with 1890 at 3
443 Id : 2794, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse multiplicative_identity [3390] by Demod 2793 with 1917 at 1,3
444 Id : 2795, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= inverse multiplicative_identity [3390] by Demod 2794 with 1917 at 1,2,2
445 Id : 476, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 9 with 75 at 2
446 Id : 2796, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= additive_identity [3390] by Demod 2795 with 476 at 3
447 Id : 2797, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2796 with 2 at 2
448 Id : 2798, {_}: add additive_identity (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2797 with 476 at 1,2
449 Id : 2799, {_}: multiply additive_identity ?3390 =>= additive_identity [3390] by Demod 2798 with 63 at 2
450 Id : 2854, {_}: add ?796 additive_identity =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 530 with 2799 at 2,2
451 Id : 2870, {_}: ?796 =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 2854 with 6 at 2
452 Id : 2113, {_}: add (multiply ?2595 ?2596) (multiply ?2597 (multiply ?2595 ?2598)) =<= multiply (add (multiply ?2595 ?2596) ?2597) (multiply ?2595 (add ?2596 ?2598)) [2598, 2597, 2596, 2595] by Super 4 with 5 at 2,3
453 Id : 2126, {_}: add (multiply ?2655 multiplicative_identity) (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Super 2113 with 1917 at 2,2,3
454 Id : 2201, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Demod 2126 with 7 at 1,2
455 Id : 2202, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (multiply ?2655 multiplicative_identity) (add (multiply ?2655 multiplicative_identity) ?2656) [2657, 2656, 2655] by Demod 2201 with 3 at 3
456 Id : 62, {_}: add ?157 (multiply additive_identity ?158) =<= multiply ?157 (add ?157 ?158) [158, 157] by Super 4 with 6 at 1,3
457 Id : 2203, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= add (multiply ?2655 multiplicative_identity) (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2202 with 62 at 3
458 Id : 2204, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2203 with 7 at 1,3
459 Id : 12654, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 additive_identity [2657, 2656, 2655] by Demod 2204 with 2799 at 2,3
460 Id : 12655, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= ?2655 [2657, 2656, 2655] by Demod 12654 with 6 at 3
461 Id : 12666, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply (multiply ?15534 (multiply ?15535 ?15536)) ?15535 [15536, 15535, 15534] by Super 2870 with 12655 at 2,3
462 Id : 21339, {_}: multiply ?30912 (multiply ?30913 ?30914) =<= multiply ?30913 (multiply ?30912 (multiply ?30913 ?30914)) [30914, 30913, 30912] by Demod 12666 with 3 at 3
463 Id : 21342, {_}: multiply ?30924 (multiply ?30925 ?30926) =<= multiply ?30925 (multiply ?30924 (multiply ?30926 ?30925)) [30926, 30925, 30924] by Super 21339 with 3 at 2,2,3
464 Id : 28, {_}: add ?74 (multiply ?75 ?76) =<= multiply (add ?75 ?74) (add ?74 ?76) [76, 75, 74] by Super 25 with 2 at 1,3
465 Id : 4808, {_}: multiply ?5796 (add ?5797 ?5798) =<= add (multiply ?5796 ?5797) (multiply ?5798 ?5796) [5798, 5797, 5796] by Super 44 with 3 at 2,3
466 Id : 4837, {_}: multiply ?5913 (add multiplicative_identity ?5914) =?= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Super 4808 with 7 at 1,3
467 Id : 4917, {_}: multiply ?5913 multiplicative_identity =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4837 with 1917 at 2,2
468 Id : 4918, {_}: ?5913 =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4917 with 7 at 2
469 Id : 5091, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply (add ?6287 ?6286) ?6286 [6288, 6287, 6286] by Super 28 with 4918 at 2,3
470 Id : 5151, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply ?6286 (add ?6287 ?6286) [6288, 6287, 6286] by Demod 5091 with 3 at 3
471 Id : 5152, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= ?6286 [6288, 6287, 6286] by Demod 5151 with 2870 at 3
472 Id : 19536, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply (multiply ?27546 (multiply ?27547 ?27548)) ?27548 [27548, 27547, 27546] by Super 2870 with 5152 at 2,3
473 Id : 19689, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply ?27548 (multiply ?27546 (multiply ?27547 ?27548)) [27548, 27547, 27546] by Demod 19536 with 3 at 3
474 Id : 31289, {_}: multiply ?30924 (multiply ?30925 ?30926) =?= multiply ?30924 (multiply ?30926 ?30925) [30926, 30925, 30924] by Demod 21342 with 19689 at 3
475 Id : 521, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply (add (inverse ?761) ?762) multiplicative_identity [762, 761] by Super 516 with 8 at 2,3
476 Id : 550, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply multiplicative_identity (add (inverse ?761) ?762) [762, 761] by Demod 521 with 3 at 3
477 Id : 551, {_}: add (inverse ?761) (multiply ?762 ?761) =>= add (inverse ?761) ?762 [762, 761] by Demod 550 with 75 at 3
478 Id : 3740, {_}: multiply ?4638 (add (inverse ?4638) ?4639) =>= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Super 2714 with 551 at 2,2
479 Id : 3782, {_}: multiply ?4638 ?4639 =<= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Demod 3740 with 2714 at 2
480 Id : 3863, {_}: multiply ?4768 (add ?4769 (multiply ?4770 ?4768)) =>= add (multiply ?4768 ?4769) (multiply ?4768 ?4770) [4770, 4769, 4768] by Super 5 with 3782 at 2,3
481 Id : 15840, {_}: multiply ?20984 (add ?20985 (multiply ?20986 ?20984)) =>= multiply ?20984 (add ?20985 ?20986) [20986, 20985, 20984] by Demod 3863 with 5 at 3
482 Id : 15903, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add (multiply ?21235 ?21236) ?21235) [21236, 21235, 21234] by Super 15840 with 5 at 2,2
483 Id : 16059, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add ?21235 (multiply ?21235 ?21236)) [21236, 21235, 21234] by Demod 15903 with 2 at 2,3
484 Id : 4814, {_}: multiply ?5818 (add ?5819 multiplicative_identity) =?= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Super 4808 with 75 at 2,3
485 Id : 4891, {_}: multiply ?5818 multiplicative_identity =<= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Demod 4814 with 1890 at 2,2
486 Id : 4892, {_}: multiply ?5818 multiplicative_identity =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4891 with 2 at 3
487 Id : 4893, {_}: ?5818 =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4892 with 7 at 2
488 Id : 26804, {_}: multiply ?40743 (multiply ?40744 (add ?40745 ?40743)) =>= multiply ?40743 ?40744 [40745, 40744, 40743] by Demod 16059 with 4893 at 2,3
489 Id : 26854, {_}: multiply (multiply ?40962 ?40963) (multiply ?40964 ?40962) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Super 26804 with 4893 at 2,2,2
490 Id : 38294, {_}: multiply (multiply ?63621 ?63622) (multiply ?63621 ?63623) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Super 31289 with 26854 at 3
491 Id : 26855, {_}: multiply (multiply ?40966 ?40967) (multiply ?40968 ?40967) =>= multiply (multiply ?40966 ?40967) ?40968 [40968, 40967, 40966] by Super 26804 with 4918 at 2,2,2
492 Id : 38958, {_}: multiply (multiply ?65058 ?65059) (multiply ?65059 ?65060) =>= multiply (multiply ?65058 ?65059) ?65060 [65060, 65059, 65058] by Super 31289 with 26855 at 3
493 Id : 38330, {_}: multiply (multiply ?63784 ?63785) (multiply ?63785 ?63786) =>= multiply (multiply ?63785 ?63786) ?63784 [63786, 63785, 63784] by Super 3 with 26854 at 3
494 Id : 46713, {_}: multiply (multiply ?65059 ?65060) ?65058 =?= multiply (multiply ?65058 ?65059) ?65060 [65058, 65060, 65059] by Demod 38958 with 38330 at 2
495 Id : 46797, {_}: multiply ?81775 (multiply ?81776 ?81777) =<= multiply (multiply ?81775 ?81776) ?81777 [81777, 81776, 81775] by Super 3 with 46713 at 3
496 Id : 47389, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Demod 38294 with 46797 at 2
497 Id : 47390, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply ?63621 (multiply ?63622 ?63623) [63623, 63622, 63621] by Demod 47389 with 46797 at 3
498 Id : 12809, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply ?15535 (multiply ?15534 (multiply ?15535 ?15536)) [15536, 15535, 15534] by Demod 12666 with 3 at 3
499 Id : 47391, {_}: multiply ?63622 (multiply ?63621 ?63623) =?= multiply ?63621 (multiply ?63622 ?63623) [63623, 63621, 63622] by Demod 47390 with 12809 at 2
500 Id : 47371, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Demod 26854 with 46797 at 2
501 Id : 47372, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply ?40962 (multiply ?40963 ?40964) [40964, 40963, 40962] by Demod 47371 with 46797 at 3
502 Id : 47409, {_}: multiply ?40963 (multiply ?40964 ?40962) =?= multiply ?40962 (multiply ?40963 ?40964) [40962, 40964, 40963] by Demod 47372 with 19689 at 2
503 Id : 47847, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 47846 with 3 at 2,3
504 Id : 47846, {_}: multiply c (multiply b a) =?= multiply c (multiply a b) [] by Demod 47845 with 47409 at 2
505 Id : 47845, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 47844 with 3 at 3
506 Id : 47844, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 47391 at 2
507 Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
508 % SZS output end CNFRefutation for BOO007-4.p
509 4589: solved BOO007-4.p in 11.664728 using kbo
510 4589: status Unsatisfiable for BOO007-4.p
511 CLASH, statistics insufficient
514 add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
516 multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
517 [4, 3, 2] by distributivity ?2 ?3 ?4
519 add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
520 [8, 7, 6] by l1 ?6 ?7 ?8
522 add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
523 [12, 11, 10] by l3 ?10 ?11 ?12
525 multiply (add ?14 (inverse ?14)) ?15 =>= ?15
526 [15, 14] by property3 ?14 ?15
528 multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
529 [19, 18, 17] by l2 ?17 ?18 ?19
531 multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
532 [23, 22, 21] by l4 ?21 ?22 ?23
534 add (multiply ?25 (inverse ?25)) ?26 =>= ?26
535 [26, 25] by property3_dual ?25 ?26
536 4606: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
538 multiply ?30 (inverse ?30) =>= n0
539 [30] by multiplicative_inverse ?30
541 add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
542 [34, 33, 32] by associativity_of_add ?32 ?33 ?34
544 multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
545 [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
548 multiply a (add b c) =<= add (multiply b a) (multiply c a)
549 [] by prove_multiply_add_property
556 4606: multiply 22 2 3 0,2add
557 4606: add 21 2 2 0,2,2multiply
561 CLASH, statistics insufficient
564 add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
566 multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
567 [4, 3, 2] by distributivity ?2 ?3 ?4
569 add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
570 [8, 7, 6] by l1 ?6 ?7 ?8
572 add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
573 [12, 11, 10] by l3 ?10 ?11 ?12
575 multiply (add ?14 (inverse ?14)) ?15 =>= ?15
576 [15, 14] by property3 ?14 ?15
578 multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
579 [19, 18, 17] by l2 ?17 ?18 ?19
581 multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
582 [23, 22, 21] by l4 ?21 ?22 ?23
584 add (multiply ?25 (inverse ?25)) ?26 =>= ?26
585 [26, 25] by property3_dual ?25 ?26
586 4607: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
588 multiply ?30 (inverse ?30) =>= n0
589 [30] by multiplicative_inverse ?30
591 add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
592 [34, 33, 32] by associativity_of_add ?32 ?33 ?34
593 CLASH, statistics insufficient
596 add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
598 multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
599 [4, 3, 2] by distributivity ?2 ?3 ?4
601 add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
602 [8, 7, 6] by l1 ?6 ?7 ?8
604 add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
605 [12, 11, 10] by l3 ?10 ?11 ?12
607 multiply (add ?14 (inverse ?14)) ?15 =>= ?15
608 [15, 14] by property3 ?14 ?15
610 multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
611 [19, 18, 17] by l2 ?17 ?18 ?19
613 multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
614 [23, 22, 21] by l4 ?21 ?22 ?23
616 add (multiply ?25 (inverse ?25)) ?26 =>= ?26
617 [26, 25] by property3_dual ?25 ?26
618 4608: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
620 multiply ?30 (inverse ?30) =>= n0
621 [30] by multiplicative_inverse ?30
623 add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
624 [34, 33, 32] by associativity_of_add ?32 ?33 ?34
626 multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
627 [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
630 multiply a (add b c) =<= add (multiply b a) (multiply c a)
631 [] by prove_multiply_add_property
638 4607: multiply 22 2 3 0,2add
639 4607: add 21 2 2 0,2,2multiply
644 multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
645 [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
648 multiply a (add b c) =<= add (multiply b a) (multiply c a)
649 [] by prove_multiply_add_property
656 4608: multiply 22 2 3 0,2add
657 4608: add 21 2 2 0,2,2multiply
663 Found proof, 44.648027s
664 % SZS status Unsatisfiable for BOO031-1.p
665 % SZS output start CNFRefutation for BOO031-1.p
666 Id : 7, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23
667 Id : 10, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30
668 Id : 8, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26
669 Id : 12, {_}: multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
670 Id : 52, {_}: multiply (multiply (add ?189 ?190) (add ?190 ?191)) ?190 =>= ?190 [191, 190, 189] by l4 ?189 ?190 ?191
671 Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
672 Id : 5, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15
673 Id : 2, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4
674 Id : 18, {_}: add (add (multiply ?58 ?59) (multiply ?59 ?60)) ?59 =>= ?59 [60, 59, 58] by l3 ?58 ?59 ?60
675 Id : 11, {_}: add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34
676 Id : 4, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12
677 Id : 37, {_}: multiply ?128 (add ?129 (add ?128 ?130)) =>= ?128 [130, 129, 128] by l2 ?128 ?129 ?130
678 Id : 6, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19
679 Id : 3, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8
680 Id : 35, {_}: add ?121 (multiply ?122 ?121) =>= ?121 [122, 121] by Super 3 with 6 at 2,2,2
681 Id : 42, {_}: multiply ?149 (add ?149 ?150) =>= ?149 [150, 149] by Super 37 with 4 at 2,2
682 Id : 1579, {_}: add (add ?2436 ?2437) ?2436 =>= add ?2436 ?2437 [2437, 2436] by Super 35 with 42 at 2,2
683 Id : 1609, {_}: add ?2436 (add ?2437 ?2436) =>= add ?2436 ?2437 [2437, 2436] by Demod 1579 with 11 at 2
684 Id : 19, {_}: add (multiply ?62 ?63) ?63 =>= ?63 [63, 62] by Super 18 with 3 at 1,2
685 Id : 39, {_}: multiply ?137 (add ?138 ?137) =>= ?137 [138, 137] by Super 37 with 3 at 2,2,2
686 Id : 1363, {_}: add ?2089 (add ?2090 ?2089) =>= add ?2090 ?2089 [2090, 2089] by Super 19 with 39 at 1,2
687 Id : 2844, {_}: add ?2437 ?2436 =?= add ?2436 ?2437 [2436, 2437] by Demod 1609 with 1363 at 2
688 Id : 32, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add (multiply ?109 ?107) ?107) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Super 2 with 6 at 2,2,2
689 Id : 5786, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 32 with 2844 at 2,2
690 Id : 5787, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 5786 with 11 at 1,3
691 Id : 1088, {_}: add (multiply ?1721 ?1722) ?1722 =>= ?1722 [1722, 1721] by Super 18 with 3 at 1,2
692 Id : 1091, {_}: add ?1730 (add ?1731 (add ?1730 ?1732)) =>= add ?1731 (add ?1730 ?1732) [1732, 1731, 1730] by Super 1088 with 6 at 1,2
693 Id : 5788, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5787 with 1091 at 2,2,3
694 Id : 5789, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5788 with 35 at 2,2
695 Id : 5790, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add ?107 (add ?108 ?109))) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5789 with 11 at 2,1,3
696 Id : 5814, {_}: add ?7785 (multiply (add ?7786 (add ?7785 ?7787)) ?7788) =<= multiply (add ?7786 (add ?7785 (add ?7787 ?7788))) (multiply (add ?7788 ?7785) (add ?7786 (add ?7785 ?7787))) [7788, 7787, 7786, 7785] by Demod 5790 with 2844 at 2
697 Id : 79, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 5 with 9 at 1,2
698 Id : 1095, {_}: add ?1743 ?1743 =>= ?1743 [1743] by Super 1088 with 79 at 1,2
699 Id : 5853, {_}: add ?7982 (multiply (add (add ?7982 ?7983) (add ?7982 ?7983)) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Super 5814 with 1095 at 2,2,3
700 Id : 6183, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Demod 5853 with 11 at 1,2,2
701 Id : 1663, {_}: multiply (add ?2570 ?2571) ?2571 =>= ?2571 [2571, 2570] by Super 52 with 6 at 1,2
702 Id : 1673, {_}: multiply ?2601 (multiply ?2602 ?2601) =>= multiply ?2602 ?2601 [2602, 2601] by Super 1663 with 35 at 1,2
703 Id : 1365, {_}: multiply ?2095 (add ?2096 ?2095) =>= ?2095 [2096, 2095] by Super 37 with 3 at 2,2,2
704 Id : 22, {_}: add ?71 (multiply ?71 ?72) =>= ?71 [72, 71] by Super 3 with 5 at 2,2
705 Id : 1374, {_}: multiply (multiply ?2123 ?2124) ?2123 =>= multiply ?2123 ?2124 [2124, 2123] by Super 1365 with 22 at 2,2
706 Id : 1408, {_}: multiply ?2123 (multiply ?2124 ?2123) =>= multiply ?2123 ?2124 [2124, 2123] by Demod 1374 with 12 at 2
707 Id : 2987, {_}: multiply ?2601 ?2602 =?= multiply ?2602 ?2601 [2602, 2601] by Demod 1673 with 1408 at 2
708 Id : 6184, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6183 with 2987 at 3
709 Id : 6185, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6184 with 1091 at 1,2,2
710 Id : 6186, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6185 with 12 at 3
711 Id : 6187, {_}: add ?7982 (multiply (add ?7982 ?7983) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6186 with 1363 at 1,2,2
712 Id : 13074, {_}: add ?18195 (multiply (add ?18195 ?18196) ?18197) =>= multiply (add ?18197 ?18195) (add ?18195 ?18196) [18197, 18196, 18195] by Demod 6187 with 42 at 2,3
713 Id : 16401, {_}: add ?22734 (multiply (add ?22735 ?22734) ?22736) =>= multiply (add ?22736 ?22734) (add ?22734 ?22735) [22736, 22735, 22734] by Super 13074 with 2844 at 1,2,2
714 Id : 18162, {_}: add ?24925 (multiply ?24926 (add ?24927 ?24925)) =>= multiply (add ?24926 ?24925) (add ?24925 ?24927) [24927, 24926, 24925] by Super 16401 with 2987 at 2,2
715 Id : 18171, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add (multiply ?24963 ?24964) ?24964) [24965, 24964, 24963] by Super 18162 with 35 at 2,2,2
716 Id : 18379, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add ?24964 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18171 with 2844 at 2,3
717 Id : 18380, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply (add ?24965 (multiply ?24963 ?24964)) ?24964 [24965, 24964, 24963] by Demod 18379 with 35 at 2,3
718 Id : 18381, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18380 with 2987 at 3
719 Id : 1575, {_}: multiply ?2421 ?2422 =<= multiply ?2421 (multiply (add ?2421 ?2423) ?2422) [2423, 2422, 2421] by Super 12 with 42 at 1,2
720 Id : 16456, {_}: add ?22968 (multiply ?22969 (add ?22970 ?22968)) =>= multiply (add ?22969 ?22968) (add ?22968 ?22970) [22970, 22969, 22968] by Super 16401 with 2987 at 2,2
721 Id : 1247, {_}: add ?1879 ?1880 =<= add ?1879 (add (multiply ?1879 ?1881) ?1880) [1881, 1880, 1879] by Super 11 with 22 at 1,2
722 Id : 6619, {_}: multiply (multiply ?8607 ?8608) (add ?8607 ?8609) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Super 6 with 1247 at 2,2
723 Id : 6763, {_}: multiply ?8607 (multiply ?8608 (add ?8607 ?8609)) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Demod 6619 with 12 at 2
724 Id : 65, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =<= multiply (add ?237 ?238) (multiply (add ?238 (inverse ?238)) (add (inverse ?238) ?237)) [238, 237] by Super 2 with 8 at 2,2
725 Id : 76, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =>= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 65 with 5 at 2,3
726 Id : 18170, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add (multiply ?24959 ?24960) ?24959) [24961, 24960, 24959] by Super 18162 with 22 at 2,2,2
727 Id : 18376, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add ?24959 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18170 with 2844 at 2,3
728 Id : 18377, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply (add ?24961 (multiply ?24959 ?24960)) ?24959 [24961, 24960, 24959] by Demod 18376 with 22 at 2,3
729 Id : 18378, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply ?24959 (add ?24961 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18377 with 2987 at 3
730 Id : 22657, {_}: multiply ?237 (add (inverse ?238) (multiply ?237 ?238)) =<= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 76 with 18378 at 2
731 Id : 22699, {_}: multiply (inverse ?30910) (multiply ?30911 (add (inverse ?30910) (multiply ?30911 ?30910))) =>= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Super 6763 with 22657 at 2,2
732 Id : 22814, {_}: multiply (inverse ?30910) ?30911 =<= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Demod 22699 with 6763 at 2
733 Id : 23609, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add (inverse ?31619) ?31619) (add ?31619 ?31620) [31620, 31619] by Super 16456 with 22814 at 2,2
734 Id : 23775, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add ?31619 (inverse ?31619)) (add ?31619 ?31620) [31620, 31619] by Demod 23609 with 2844 at 1,3
735 Id : 23776, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =>= multiply n1 (add ?31619 ?31620) [31620, 31619] by Demod 23775 with 9 at 1,3
736 Id : 24286, {_}: add ?32553 (multiply (inverse ?32553) ?32554) =>= add ?32553 ?32554 [32554, 32553] by Demod 23776 with 79 at 3
737 Id : 13130, {_}: add ?18432 (multiply ?18433 (add ?18432 ?18434)) =>= multiply (add ?18433 ?18432) (add ?18432 ?18434) [18434, 18433, 18432] by Super 13074 with 2987 at 2,2
738 Id : 22705, {_}: multiply ?30931 (add (inverse ?30932) (multiply ?30931 ?30932)) =<= multiply (add ?30931 ?30932) (add (inverse ?30932) ?30931) [30932, 30931] by Demod 76 with 18378 at 2
739 Id : 22751, {_}: multiply ?31084 (add (inverse (inverse ?31084)) (multiply ?31084 (inverse ?31084))) =>= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Super 22705 with 9 at 1,3
740 Id : 23065, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =?= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Demod 22751 with 10 at 2,2,2
741 Id : 23066, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =>= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23065 with 79 at 3
742 Id : 130, {_}: multiply (add ?21 ?22) (multiply (add ?22 ?23) ?22) =>= ?22 [23, 22, 21] by Demod 7 with 12 at 2
743 Id : 89, {_}: n0 =<= inverse n1 [] by Super 79 with 10 at 2
744 Id : 360, {_}: add n1 n0 =>= n1 [] by Super 9 with 89 at 2,2
745 Id : 382, {_}: multiply n1 (multiply (add n0 ?765) n0) =>= n0 [765] by Super 130 with 360 at 1,2
746 Id : 422, {_}: multiply (add n0 ?765) n0 =>= n0 [765] by Demod 382 with 79 at 2
747 Id : 88, {_}: add n0 ?26 =>= ?26 [26] by Demod 8 with 10 at 1,2
748 Id : 423, {_}: multiply ?765 n0 =>= n0 [765] by Demod 422 with 88 at 1,2
749 Id : 831, {_}: add ?1448 (multiply ?1449 n0) =>= ?1448 [1449, 1448] by Super 3 with 423 at 2,2,2
750 Id : 867, {_}: add ?1448 n0 =>= ?1448 [1448] by Demod 831 with 423 at 2,2
751 Id : 23067, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23066 with 867 at 2,2
752 Id : 23068, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23067 with 2844 at 3
753 Id : 23215, {_}: add ?31334 (multiply ?31335 (multiply ?31334 (inverse (inverse ?31334)))) =>= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Super 13130 with 23068 at 2,2,2
754 Id : 23280, {_}: ?31334 =<= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23215 with 3 at 2
755 Id : 23281, {_}: ?31334 =<= multiply (add ?31335 ?31334) (multiply ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23280 with 23068 at 2,3
756 Id : 2547, {_}: multiply (multiply ?3698 ?3699) ?3700 =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Super 12 with 1408 at 1,2
757 Id : 2578, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Demod 2547 with 12 at 2
758 Id : 2579, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply ?3699 (multiply ?3698 ?3700)) [3700, 3699, 3698] by Demod 2578 with 12 at 2,3
759 Id : 1667, {_}: multiply ?2583 (multiply ?2584 (multiply ?2583 ?2585)) =>= multiply ?2584 (multiply ?2583 ?2585) [2585, 2584, 2583] by Super 1663 with 3 at 1,2
760 Id : 12236, {_}: multiply ?3698 (multiply ?3699 ?3700) =?= multiply ?3699 (multiply ?3698 ?3700) [3700, 3699, 3698] by Demod 2579 with 1667 at 3
761 Id : 23282, {_}: ?31334 =<= multiply ?31334 (multiply (add ?31335 ?31334) (inverse (inverse ?31334))) [31335, 31334] by Demod 23281 with 12236 at 3
762 Id : 1360, {_}: multiply ?2077 ?2078 =<= multiply ?2077 (multiply (add ?2079 ?2077) ?2078) [2079, 2078, 2077] by Super 12 with 39 at 1,2
763 Id : 23283, {_}: ?31334 =<= multiply ?31334 (inverse (inverse ?31334)) [31334] by Demod 23282 with 1360 at 3
764 Id : 23386, {_}: add (inverse (inverse ?31435)) ?31435 =>= inverse (inverse ?31435) [31435] by Super 35 with 23283 at 2,2
765 Id : 23494, {_}: add ?31435 (inverse (inverse ?31435)) =>= inverse (inverse ?31435) [31435] by Demod 23386 with 2844 at 2
766 Id : 23374, {_}: ?31084 =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23068 with 23283 at 2
767 Id : 23495, {_}: ?31435 =<= inverse (inverse ?31435) [31435] by Demod 23494 with 23374 at 2
768 Id : 24293, {_}: add (inverse ?32572) (multiply ?32572 ?32573) =>= add (inverse ?32572) ?32573 [32573, 32572] by Super 24286 with 23495 at 1,2,2
769 Id : 23619, {_}: multiply (multiply (inverse ?31653) ?31654) ?31655 =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Super 12 with 22814 at 1,2
770 Id : 23754, {_}: multiply (inverse ?31653) (multiply ?31654 ?31655) =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Demod 23619 with 12 at 2
771 Id : 77768, {_}: add (inverse (inverse ?103133)) (multiply (inverse ?103133) (multiply ?103134 ?103135)) =>= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Super 24293 with 23754 at 2,2
772 Id : 78028, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =<= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 77768 with 24293 at 2
773 Id : 78029, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =?= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78028 with 23495 at 1,3
774 Id : 78030, {_}: add ?103133 (multiply ?103134 ?103135) =<= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78029 with 23495 at 1,2
775 Id : 13094, {_}: add ?18275 (multiply (add ?18276 ?18275) ?18277) =>= multiply (add ?18277 ?18275) (add ?18275 ?18276) [18277, 18276, 18275] by Super 13074 with 2844 at 1,2,2
776 Id : 78031, {_}: add ?103133 (multiply ?103134 ?103135) =<= multiply (add ?103135 ?103133) (add ?103133 ?103134) [103135, 103134, 103133] by Demod 78030 with 13094 at 3
777 Id : 78812, {_}: multiply ?104288 (add ?104289 ?104290) =<= multiply ?104288 (add ?104289 (multiply ?104290 ?104288)) [104290, 104289, 104288] by Super 1575 with 78031 at 2,3
778 Id : 80954, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 ?24963) [24965, 24964, 24963] by Demod 18381 with 78812 at 3
779 Id : 81595, {_}: multiply a (add c b) =?= multiply a (add c b) [] by Demod 81594 with 2844 at 2,3
780 Id : 81594, {_}: multiply a (add c b) =?= multiply a (add b c) [] by Demod 81593 with 80954 at 3
781 Id : 81593, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 81592 with 2844 at 3
782 Id : 81592, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 1 with 2844 at 2,2
783 Id : 1, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property
784 % SZS output end CNFRefutation for BOO031-1.p
785 4607: solved BOO031-1.p in 22.309393 using kbo
786 4607: status Unsatisfiable for BOO031-1.p
787 NO CLASH, using fixed ground order
791 (add (inverse (add (inverse (add ?2 ?3)) ?4))
793 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
796 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
798 4619: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
806 NO CLASH, using fixed ground order
810 (add (inverse (add (inverse (add ?2 ?3)) ?4))
812 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
815 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
817 4620: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
825 NO CLASH, using fixed ground order
829 (add (inverse (add (inverse (add ?2 ?3)) ?4))
831 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
834 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
836 4621: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
846 Found proof, 56.468020s
847 % SZS status Unsatisfiable for BOO072-1.p
848 % SZS output start CNFRefutation for BOO072-1.p
849 Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
850 Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
851 Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
852 Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
853 Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
854 Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
855 Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
856 Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
857 Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
858 Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
859 Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
860 Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
861 Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
862 Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
863 Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
864 Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
865 Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
866 Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
867 Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
868 Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
869 Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
870 Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
871 Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
872 Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
873 Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
874 Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
875 Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
876 Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
877 Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
878 Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
879 Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
880 Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
881 Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
882 Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
883 Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
884 Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
885 Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
886 Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
887 Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
888 Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
889 Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
890 Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
891 Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
892 Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
893 Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
894 Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
895 Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
896 Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
897 Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
898 Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
899 Id : 12127, {_}: inverse (inverse (add ?22871 (inverse (inverse ?22872)))) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Super 1761 with 11260 at 1,2,3
900 Id : 12312, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12127 with 1733 at 2
901 Id : 12313, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12312 with 1733 at 2,1,2,1,1,3
902 Id : 12314, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12313 with 1733 at 2,3
903 Id : 12315, {_}: add ?22871 ?22872 =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12314 with 1733 at 2,2
904 Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
905 Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
906 Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
907 Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
908 Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
909 Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
910 Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
911 Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
912 Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
913 Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
914 Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
915 Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
916 Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
917 Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
918 Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
919 Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
920 Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
921 Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
922 Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
923 Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
924 Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
925 Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
926 Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
927 Id : 18514, {_}: add (add ?31834 ?31835) ?31834 =<= add (inverse (add ?31834 (inverse (add ?31834 ?31835)))) ?31834 [31835, 31834] by Super 12315 with 18257 at 1,2,1,1,3
928 Id : 19938, {_}: add ?34185 ?34186 =<= add (inverse (add ?34185 (inverse (add ?34185 ?34186)))) ?34185 [34186, 34185] by Demod 18514 with 18257 at 2
929 Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
930 Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
931 Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
932 Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
933 Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
934 Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
935 Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
936 Id : 20385, {_}: add ?34911 ?34912 =<= add (inverse (add (inverse (add ?34911 ?34912)) ?34911)) ?34911 [34912, 34911] by Super 19938 with 18480 at 1,1,3
937 Id : 20390, {_}: add ?34925 (add ?34926 ?34925) =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34926, 34925] by Super 20385 with 8543 at 1,1,1,1,3
938 Id : 20500, {_}: add ?34926 ?34925 =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34925, 34926] by Demod 20390 with 8543 at 2
939 Id : 5906, {_}: inverse (add (inverse (inverse ?12265)) (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Super 136 with 5602 at 1,1,1,2
940 Id : 6067, {_}: inverse (add ?12265 (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 5906 with 1733 at 1,1,2
941 Id : 15857, {_}: add (inverse ?28730) (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Super 1785 with 15735 at 1,2,1,2,3
942 Id : 16100, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 15857 with 15735 at 2
943 Id : 16101, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 16100 with 1733 at 1,1,2,1,3
944 Id : 16102, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 ?28730)) [28731, 28730] by Demod 16101 with 1733 at 2,1,2,3
945 Id : 16103, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse ?28730) [28731, 28730] by Demod 16102 with 1724 at 1,2,3
946 Id : 18477, {_}: inverse ?28730 =<= add (inverse ?28730) (inverse (add ?28730 ?28731)) [28731, 28730] by Demod 16103 with 18257 at 3
947 Id : 21222, {_}: inverse (add ?12265 (inverse (inverse ?12266))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 6067 with 18477 at 1,2,1,2
948 Id : 21223, {_}: inverse (add ?12265 ?12266) =?= inverse (add ?12266 ?12265) [12266, 12265] by Demod 21222 with 1733 at 2,1,2
949 Id : 21386, {_}: add ?36951 ?36952 =<= add (inverse (add (inverse (add ?36952 ?36951)) ?36952)) ?36952 [36952, 36951] by Super 20500 with 21223 at 1,1,1,3
950 Id : 19969, {_}: add ?34289 ?34290 =<= add (inverse (add (inverse (add ?34289 ?34290)) ?34289)) ?34289 [34290, 34289] by Super 19938 with 18480 at 1,1,3
951 Id : 21454, {_}: add ?36951 ?36952 =?= add ?36952 ?36951 [36952, 36951] by Demod 21386 with 19969 at 3
952 Id : 21981, {_}: add a b === add a b [] by Demod 1 with 21454 at 2
953 Id : 1, {_}: add b a =>= add a b [] by huntinton_1
954 % SZS output end CNFRefutation for BOO072-1.p
955 4619: solved BOO072-1.p in 9.46059 using nrkbo
956 4619: status Unsatisfiable for BOO072-1.p
957 NO CLASH, using fixed ground order
961 (add (inverse (add (inverse (add ?2 ?3)) ?4))
963 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
966 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
968 4637: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
977 NO CLASH, using fixed ground order
981 (add (inverse (add (inverse (add ?2 ?3)) ?4))
983 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
986 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
988 4638: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
997 NO CLASH, using fixed ground order
1001 (add (inverse (add (inverse (add ?2 ?3)) ?4))
1003 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
1006 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
1008 4639: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
1014 4639: add 10 2 4 0,2
1017 % SZS status Timeout for BOO073-1.p
1018 NO CLASH, using fixed ground order
1022 (add (inverse (add (inverse (add ?2 ?3)) ?4))
1024 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
1027 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
1030 add (inverse (add (inverse a) b))
1031 (inverse (add (inverse a) (inverse b)))
1039 4666: b 2 0 2 2,1,1,2
1040 4666: inverse 12 1 5 0,1,2
1041 4666: a 3 0 3 1,1,1,1,2
1042 NO CLASH, using fixed ground order
1046 (add (inverse (add (inverse (add ?2 ?3)) ?4))
1048 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
1051 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
1054 add (inverse (add (inverse a) b))
1055 (inverse (add (inverse a) (inverse b)))
1063 4667: b 2 0 2 2,1,1,2
1064 4667: inverse 12 1 5 0,1,2
1065 4667: a 3 0 3 1,1,1,1,2
1066 NO CLASH, using fixed ground order
1070 (add (inverse (add (inverse (add ?2 ?3)) ?4))
1072 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
1075 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
1078 add (inverse (add (inverse a) b))
1079 (inverse (add (inverse a) (inverse b)))
1087 4668: b 2 0 2 2,1,1,2
1088 4668: inverse 12 1 5 0,1,2
1089 4668: a 3 0 3 1,1,1,1,2
1092 Found proof, 17.395929s
1093 % SZS status Unsatisfiable for BOO074-1.p
1094 % SZS output start CNFRefutation for BOO074-1.p
1095 Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
1096 Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
1097 Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
1098 Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
1099 Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
1100 Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
1101 Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
1102 Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
1103 Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
1104 Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
1105 Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
1106 Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
1107 Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
1108 Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
1109 Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
1110 Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
1111 Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
1112 Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
1113 Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
1114 Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
1115 Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
1116 Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
1117 Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
1118 Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
1119 Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
1120 Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
1121 Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
1122 Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
1123 Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
1124 Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
1125 Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
1126 Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
1127 Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
1128 Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
1129 Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
1130 Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
1131 Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
1132 Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
1133 Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
1134 Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
1135 Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
1136 Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =?= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
1137 Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
1138 Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
1139 Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
1140 Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
1141 Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
1142 Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
1143 Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
1144 Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
1145 Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
1146 Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
1147 Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
1148 Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
1149 Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
1150 Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
1151 Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
1152 Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
1153 Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
1154 Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
1155 Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
1156 Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
1157 Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
1158 Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
1159 Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
1160 Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
1161 Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
1162 Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
1163 Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
1164 Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
1165 Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
1166 Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
1167 Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
1168 Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
1169 Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
1170 Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
1171 Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
1172 Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
1173 Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
1174 Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
1175 Id : 18644, {_}: a === a [] by Demod 18643 with 1733 at 2
1176 Id : 18643, {_}: inverse (inverse a) =>= a [] by Demod 18642 with 1761 at 2
1177 Id : 18642, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse b) (inverse a))) =>= a [] by Demod 18641 with 18480 at 1,2,2
1178 Id : 18641, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse a) (inverse b))) =>= a [] by Demod 1 with 18480 at 1,1,2
1179 Id : 1, {_}: add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b))) =>= a [] by huntinton_3
1180 % SZS output end CNFRefutation for BOO074-1.p
1181 4666: solved BOO074-1.p in 8.672542 using nrkbo
1182 4666: status Unsatisfiable for BOO074-1.p
1183 NO CLASH, using fixed ground order
1186 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1187 [4, 3, 2] by b_definition ?2 ?3 ?4
1189 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1190 [7, 6] by w_definition ?6 ?7
1194 apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
1195 [] by strong_fixed_point
1198 apply strong_fixed_point fixed_pt
1200 apply fixed_pt (apply strong_fixed_point fixed_pt)
1201 [] by prove_strong_fixed_point
1207 4673: apply 19 2 3 0,2
1208 4673: fixed_pt 3 0 3 2,2
1209 4673: strong_fixed_point 3 0 2 1,2
1210 NO CLASH, using fixed ground order
1213 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1214 [4, 3, 2] by b_definition ?2 ?3 ?4
1216 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1217 [7, 6] by w_definition ?6 ?7
1221 apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
1222 [] by strong_fixed_point
1225 apply strong_fixed_point fixed_pt
1227 apply fixed_pt (apply strong_fixed_point fixed_pt)
1228 [] by prove_strong_fixed_point
1234 4674: apply 19 2 3 0,2
1235 4674: fixed_pt 3 0 3 2,2
1236 4674: strong_fixed_point 3 0 2 1,2
1237 NO CLASH, using fixed ground order
1240 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1241 [4, 3, 2] by b_definition ?2 ?3 ?4
1243 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1244 [7, 6] by w_definition ?6 ?7
1248 apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
1249 [] by strong_fixed_point
1252 apply strong_fixed_point fixed_pt
1254 apply fixed_pt (apply strong_fixed_point fixed_pt)
1255 [] by prove_strong_fixed_point
1261 4675: apply 19 2 3 0,2
1262 4675: fixed_pt 3 0 3 2,2
1263 4675: strong_fixed_point 3 0 2 1,2
1264 % SZS status Timeout for COL003-12.p
1265 NO CLASH, using fixed ground order
1268 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1269 [4, 3, 2] by b_definition ?2 ?3 ?4
1271 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1272 [7, 6] by w_definition ?6 ?7
1278 (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
1279 [] by strong_fixed_point
1282 apply strong_fixed_point fixed_pt
1284 apply fixed_pt (apply strong_fixed_point fixed_pt)
1285 [] by prove_strong_fixed_point
1291 4697: apply 20 2 3 0,2
1292 4697: fixed_pt 3 0 3 2,2
1293 4697: strong_fixed_point 3 0 2 1,2
1294 NO CLASH, using fixed ground order
1297 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1298 [4, 3, 2] by b_definition ?2 ?3 ?4
1300 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1301 [7, 6] by w_definition ?6 ?7
1307 (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
1308 [] by strong_fixed_point
1311 apply strong_fixed_point fixed_pt
1313 apply fixed_pt (apply strong_fixed_point fixed_pt)
1314 [] by prove_strong_fixed_point
1320 4698: apply 20 2 3 0,2
1321 4698: fixed_pt 3 0 3 2,2
1322 4698: strong_fixed_point 3 0 2 1,2
1323 NO CLASH, using fixed ground order
1326 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1327 [4, 3, 2] by b_definition ?2 ?3 ?4
1329 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1330 [7, 6] by w_definition ?6 ?7
1336 (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
1337 [] by strong_fixed_point
1340 apply strong_fixed_point fixed_pt
1342 apply fixed_pt (apply strong_fixed_point fixed_pt)
1343 [] by prove_strong_fixed_point
1349 4699: apply 20 2 3 0,2
1350 4699: fixed_pt 3 0 3 2,2
1351 4699: strong_fixed_point 3 0 2 1,2
1352 % SZS status Timeout for COL003-17.p
1353 NO CLASH, using fixed ground order
1356 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1357 [4, 3, 2] by b_definition ?2 ?3 ?4
1359 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1360 [7, 6] by w_definition ?6 ?7
1364 apply (apply b (apply (apply b (apply w w)) (apply b w)))
1365 (apply (apply b b) b)
1366 [] by strong_fixed_point
1369 apply strong_fixed_point fixed_pt
1371 apply fixed_pt (apply strong_fixed_point fixed_pt)
1372 [] by prove_strong_fixed_point
1378 4971: apply 20 2 3 0,2
1379 4971: fixed_pt 3 0 3 2,2
1380 4971: strong_fixed_point 3 0 2 1,2
1381 NO CLASH, using fixed ground order
1384 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1385 [4, 3, 2] by b_definition ?2 ?3 ?4
1387 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1388 [7, 6] by w_definition ?6 ?7
1392 apply (apply b (apply (apply b (apply w w)) (apply b w)))
1393 (apply (apply b b) b)
1394 [] by strong_fixed_point
1397 apply strong_fixed_point fixed_pt
1399 apply fixed_pt (apply strong_fixed_point fixed_pt)
1400 [] by prove_strong_fixed_point
1406 4972: apply 20 2 3 0,2
1407 4972: fixed_pt 3 0 3 2,2
1408 4972: strong_fixed_point 3 0 2 1,2
1409 NO CLASH, using fixed ground order
1412 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1413 [4, 3, 2] by b_definition ?2 ?3 ?4
1415 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1416 [7, 6] by w_definition ?6 ?7
1420 apply (apply b (apply (apply b (apply w w)) (apply b w)))
1421 (apply (apply b b) b)
1422 [] by strong_fixed_point
1425 apply strong_fixed_point fixed_pt
1427 apply fixed_pt (apply strong_fixed_point fixed_pt)
1428 [] by prove_strong_fixed_point
1434 4973: apply 20 2 3 0,2
1435 4973: fixed_pt 3 0 3 2,2
1436 4973: strong_fixed_point 3 0 2 1,2
1437 % SZS status Timeout for COL003-18.p
1438 NO CLASH, using fixed ground order
1441 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1442 [4, 3, 2] by b_definition ?2 ?3 ?4
1444 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1445 [7, 6] by w_definition ?6 ?7
1451 (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
1452 [] by strong_fixed_point
1455 apply strong_fixed_point fixed_pt
1457 apply fixed_pt (apply strong_fixed_point fixed_pt)
1458 [] by prove_strong_fixed_point
1464 7458: apply 20 2 3 0,2
1465 7458: fixed_pt 3 0 3 2,2
1466 7458: strong_fixed_point 3 0 2 1,2
1467 NO CLASH, using fixed ground order
1470 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1471 [4, 3, 2] by b_definition ?2 ?3 ?4
1473 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1474 [7, 6] by w_definition ?6 ?7
1480 (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
1481 [] by strong_fixed_point
1484 apply strong_fixed_point fixed_pt
1486 apply fixed_pt (apply strong_fixed_point fixed_pt)
1487 [] by prove_strong_fixed_point
1493 7459: apply 20 2 3 0,2
1494 7459: fixed_pt 3 0 3 2,2
1495 7459: strong_fixed_point 3 0 2 1,2
1496 NO CLASH, using fixed ground order
1499 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
1500 [4, 3, 2] by b_definition ?2 ?3 ?4
1502 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
1503 [7, 6] by w_definition ?6 ?7
1509 (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
1510 [] by strong_fixed_point
1513 apply strong_fixed_point fixed_pt
1515 apply fixed_pt (apply strong_fixed_point fixed_pt)
1516 [] by prove_strong_fixed_point
1522 7460: apply 20 2 3 0,2
1523 7460: fixed_pt 3 0 3 2,2
1524 7460: strong_fixed_point 3 0 2 1,2
1525 % SZS status Timeout for COL003-19.p
1526 CLASH, statistics insufficient
1529 apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
1530 [4, 3] by o_definition ?3 ?4
1532 apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
1533 [8, 7, 6] by q1_definition ?6 ?7 ?8
1535 9903: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
1541 9903: apply 10 2 1 0,3
1542 9903: combinator 1 0 1 1,3
1543 CLASH, statistics insufficient
1546 apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
1547 [4, 3] by o_definition ?3 ?4
1549 apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
1550 [8, 7, 6] by q1_definition ?6 ?7 ?8
1552 9904: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
1558 9904: apply 10 2 1 0,3
1559 9904: combinator 1 0 1 1,3
1560 CLASH, statistics insufficient
1563 apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
1564 [4, 3] by o_definition ?3 ?4
1566 apply (apply (apply q1 ?6) ?7) ?8 =?= apply ?6 (apply ?8 ?7)
1567 [8, 7, 6] by q1_definition ?6 ?7 ?8
1569 9905: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
1575 9905: apply 10 2 1 0,3
1576 9905: combinator 1 0 1 1,3
1577 % SZS status Timeout for COL011-1.p
1578 CLASH, statistics insufficient
1581 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1582 [5, 4, 3] by b_definition ?3 ?4 ?5
1583 9926: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1585 apply (apply t ?9) ?10 =>= apply ?10 ?9
1586 [10, 9] by t_definition ?9 ?10
1589 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1590 [1] by prove_fixed_point ?1
1597 9926: apply 13 2 3 0,2
1599 CLASH, statistics insufficient
1602 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1603 [5, 4, 3] by b_definition ?3 ?4 ?5
1604 9927: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1606 apply (apply t ?9) ?10 =>= apply ?10 ?9
1607 [10, 9] by t_definition ?9 ?10
1610 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1611 [1] by prove_fixed_point ?1
1618 9927: apply 13 2 3 0,2
1620 CLASH, statistics insufficient
1623 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1624 [5, 4, 3] by b_definition ?3 ?4 ?5
1625 9928: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1627 apply (apply t ?9) ?10 =?= apply ?10 ?9
1628 [10, 9] by t_definition ?9 ?10
1631 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1632 [1] by prove_fixed_point ?1
1639 9928: apply 13 2 3 0,2
1644 Found proof, 1.513358s
1645 % SZS status Unsatisfiable for COL034-1.p
1646 % SZS output start CNFRefutation for COL034-1.p
1647 Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1648 Id : 4, {_}: apply (apply t ?9) ?10 =>= apply ?10 ?9 [10, 9] by t_definition ?9 ?10
1649 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
1650 Id : 11, {_}: apply m (apply (apply b ?29) ?30) =<= apply ?29 (apply ?30 (apply (apply b ?29) ?30)) [30, 29] by Super 2 with 3 at 2
1651 Id : 2545, {_}: apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) === apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) [] by Super 2544 with 11 at 2
1652 Id : 2544, {_}: apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1975, 1976, 1974] by Demod 2294 with 4 at 2,2
1653 Id : 2294, {_}: apply ?1974 (apply (apply t ?1975) (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))))) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1976, 1975, 1974] by Super 53 with 4 at 2,2,3
1654 Id : 53, {_}: apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80))))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Demod 39 with 2 at 2,2
1655 Id : 39, {_}: apply ?78 (apply (apply (apply b ?79) ?80) (f (apply (apply b ?78) (apply (apply b ?79) ?80)))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Super 8 with 2 at 2,2,3
1656 Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
1657 Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
1658 Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
1659 % SZS output end CNFRefutation for COL034-1.p
1660 9926: solved COL034-1.p in 0.528032 using nrkbo
1661 9926: status Unsatisfiable for COL034-1.p
1662 CLASH, statistics insufficient
1665 apply (apply (apply s ?3) ?4) ?5
1667 apply (apply ?3 ?5) (apply ?4 ?5)
1668 [5, 4, 3] by s_definition ?3 ?4 ?5
1670 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
1671 [9, 8, 7] by b_definition ?7 ?8 ?9
1673 apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
1674 [13, 12, 11] by c_definition ?11 ?12 ?13
1677 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1678 [1] by prove_fixed_point ?1
1685 9933: apply 19 2 3 0,2
1687 CLASH, statistics insufficient
1690 apply (apply (apply s ?3) ?4) ?5
1692 apply (apply ?3 ?5) (apply ?4 ?5)
1693 [5, 4, 3] by s_definition ?3 ?4 ?5
1695 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
1696 [9, 8, 7] by b_definition ?7 ?8 ?9
1698 apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
1699 [13, 12, 11] by c_definition ?11 ?12 ?13
1702 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1703 [1] by prove_fixed_point ?1
1710 9934: apply 19 2 3 0,2
1712 CLASH, statistics insufficient
1715 apply (apply (apply s ?3) ?4) ?5
1717 apply (apply ?3 ?5) (apply ?4 ?5)
1718 [5, 4, 3] by s_definition ?3 ?4 ?5
1720 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
1721 [9, 8, 7] by b_definition ?7 ?8 ?9
1723 apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
1724 [13, 12, 11] by c_definition ?11 ?12 ?13
1727 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1728 [1] by prove_fixed_point ?1
1735 9935: apply 19 2 3 0,2
1737 % SZS status Timeout for COL037-1.p
1738 CLASH, statistics insufficient
1741 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1742 [5, 4, 3] by b_definition ?3 ?4 ?5
1743 9973: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1745 apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
1746 [11, 10, 9] by c_definition ?9 ?10 ?11
1749 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1750 [1] by prove_fixed_point ?1
1757 9973: apply 15 2 3 0,2
1759 CLASH, statistics insufficient
1762 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1763 [5, 4, 3] by b_definition ?3 ?4 ?5
1764 9974: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1766 apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
1767 [11, 10, 9] by c_definition ?9 ?10 ?11
1770 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1771 [1] by prove_fixed_point ?1
1778 9974: apply 15 2 3 0,2
1780 CLASH, statistics insufficient
1783 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1784 [5, 4, 3] by b_definition ?3 ?4 ?5
1785 9975: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1787 apply (apply (apply c ?9) ?10) ?11 =?= apply (apply ?9 ?11) ?10
1788 [11, 10, 9] by c_definition ?9 ?10 ?11
1791 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1792 [1] by prove_fixed_point ?1
1799 9975: apply 15 2 3 0,2
1804 Found proof, 2.234152s
1805 % SZS status Unsatisfiable for COL041-1.p
1806 % SZS output start CNFRefutation for COL041-1.p
1807 Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
1808 Id : 4, {_}: apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 [11, 10, 9] by c_definition ?9 ?10 ?11
1809 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
1810 Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
1811 Id : 4380, {_}: apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) === apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) [] by Super 53 with 11 at 2
1812 Id : 53, {_}: apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Demod 39 with 4 at 2,2
1813 Id : 39, {_}: apply ?91 (apply (apply (apply c ?92) ?93) (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Super 8 with 4 at 2,2,3
1814 Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
1815 Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
1816 Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
1817 % SZS output end CNFRefutation for COL041-1.p
1818 9973: solved COL041-1.p in 1.13607 using nrkbo
1819 9973: status Unsatisfiable for COL041-1.p
1820 CLASH, statistics insufficient
1823 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1824 [5, 4, 3] by b_definition ?3 ?4 ?5
1826 apply (apply (apply n ?7) ?8) ?9
1828 apply (apply (apply ?7 ?9) ?8) ?9
1829 [9, 8, 7] by n_definition ?7 ?8 ?9
1832 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1833 [1] by prove_fixed_point ?1
1839 9980: apply 14 2 3 0,2
1841 CLASH, statistics insufficient
1844 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1845 [5, 4, 3] by b_definition ?3 ?4 ?5
1847 apply (apply (apply n ?7) ?8) ?9
1849 apply (apply (apply ?7 ?9) ?8) ?9
1850 [9, 8, 7] by n_definition ?7 ?8 ?9
1853 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1854 [1] by prove_fixed_point ?1
1860 9981: apply 14 2 3 0,2
1862 CLASH, statistics insufficient
1865 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1866 [5, 4, 3] by b_definition ?3 ?4 ?5
1868 apply (apply (apply n ?7) ?8) ?9
1870 apply (apply (apply ?7 ?9) ?8) ?9
1871 [9, 8, 7] by n_definition ?7 ?8 ?9
1874 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1875 [1] by prove_fixed_point ?1
1881 9982: apply 14 2 3 0,2
1886 Found proof, 76.191737s
1887 % SZS status Unsatisfiable for COL044-1.p
1888 % SZS output start CNFRefutation for COL044-1.p
1889 Id : 4, {_}: apply (apply (apply b ?11) ?12) ?13 =>= apply ?11 (apply ?12 ?13) [13, 12, 11] by b_definition ?11 ?12 ?13
1890 Id : 3, {_}: apply (apply (apply n ?7) ?8) ?9 =?= apply (apply (apply ?7 ?9) ?8) ?9 [9, 8, 7] by n_definition ?7 ?8 ?9
1891 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
1892 Id : 8, {_}: apply (apply (apply n b) ?22) ?23 =?= apply ?23 (apply ?22 ?23) [23, 22] by Super 2 with 3 at 2
1893 Id : 5, {_}: apply ?15 (apply ?16 ?17) =?= apply ?15 (apply ?16 ?17) [17, 16, 15] by Super 4 with 2 at 2
1894 Id : 83, {_}: apply (apply (apply (apply n b) ?260) (apply b ?261)) ?262 =?= apply ?261 (apply (apply ?260 (apply b ?261)) ?262) [262, 261, 260] by Super 2 with 8 at 1,2
1895 Id : 24939, {_}: apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) =?= apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) [] by Super 24245 with 83 at 1,2
1896 Id : 24245, {_}: apply (apply (apply (apply ?35313 ?35314) ?35315) ?35314) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) =?= apply (apply (apply n b) (apply (apply (apply n ?35313) ?35315) ?35314)) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) [35315, 35314, 35313] by Super 153 with 3 at 2,1,3
1897 Id : 153, {_}: apply (apply ?460 ?461) (f (apply ?460 ?461)) =<= apply (apply (apply n b) (apply ?460 ?461)) (f (apply ?460 ?461)) [461, 460] by Super 115 with 5 at 1,3
1898 Id : 115, {_}: apply ?375 (f ?375) =<= apply (apply (apply n b) ?375) (f ?375) [375] by Super 1 with 8 at 3
1899 Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
1900 % SZS output end CNFRefutation for COL044-1.p
1901 9981: solved COL044-1.p in 12.724795 using kbo
1902 9981: status Unsatisfiable for COL044-1.p
1903 CLASH, statistics insufficient
1906 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1907 [5, 4, 3] by b_definition ?3 ?4 ?5
1909 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
1910 [8, 7] by w_definition ?7 ?8
1911 9998: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
1914 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1915 [1] by prove_strong_fixed_point ?1
1922 9998: apply 14 2 3 0,2
1924 CLASH, statistics insufficient
1927 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1928 [5, 4, 3] by b_definition ?3 ?4 ?5
1930 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
1931 [8, 7] by w_definition ?7 ?8
1932 9999: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
1935 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1936 [1] by prove_strong_fixed_point ?1
1943 9999: apply 14 2 3 0,2
1945 CLASH, statistics insufficient
1948 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
1949 [5, 4, 3] by b_definition ?3 ?4 ?5
1951 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
1952 [8, 7] by w_definition ?7 ?8
1953 10000: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
1956 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
1957 [1] by prove_strong_fixed_point ?1
1964 10000: apply 14 2 3 0,2
1965 10000: f 3 1 3 0,2,2
1969 Found proof, 12.856628s
1970 % SZS status Unsatisfiable for COL049-1.p
1971 % SZS output start CNFRefutation for COL049-1.p
1972 Id : 3, {_}: apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 [8, 7] by w_definition ?7 ?8
1973 Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
1974 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
1975 Id : 226, {_}: apply (apply w (apply b ?378)) ?379 =?= apply ?378 (apply ?379 ?379) [379, 378] by Super 2 with 3 at 2
1976 Id : 231, {_}: apply (apply w (apply b ?393)) ?394 =>= apply ?393 (apply m ?394) [394, 393] by Super 226 with 4 at 2,3
1977 Id : 289, {_}: apply m (apply w (apply b ?503)) =<= apply ?503 (apply m (apply w (apply b ?503))) [503] by Super 4 with 231 at 3
1978 Id : 15983, {_}: apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) === apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) [] by Super 72 with 289 at 2
1979 Id : 72, {_}: apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125))))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Demod 59 with 2 at 2,2
1980 Id : 59, {_}: apply ?123 (apply (apply (apply b ?124) ?125) (f (apply (apply b ?123) (apply (apply b ?124) ?125)))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Super 8 with 2 at 2,2,3
1981 Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
1982 Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
1983 Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
1984 % SZS output end CNFRefutation for COL049-1.p
1985 9998: solved COL049-1.p in 6.372397 using nrkbo
1986 9998: status Unsatisfiable for COL049-1.p
1987 CLASH, statistics insufficient
1990 apply (apply (apply s ?3) ?4) ?5
1992 apply (apply ?3 ?5) (apply ?4 ?5)
1993 [5, 4, 3] by s_definition ?3 ?4 ?5
1995 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
1996 [9, 8, 7] by b_definition ?7 ?8 ?9
1998 apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
1999 [13, 12, 11] by c_definition ?11 ?12 ?13
2000 10010: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
2003 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
2004 [1] by prove_strong_fixed_point ?1
2012 10010: apply 20 2 3 0,2
2013 10010: f 3 1 3 0,2,2
2014 CLASH, statistics insufficient
2017 apply (apply (apply s ?3) ?4) ?5
2019 apply (apply ?3 ?5) (apply ?4 ?5)
2020 [5, 4, 3] by s_definition ?3 ?4 ?5
2022 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
2023 [9, 8, 7] by b_definition ?7 ?8 ?9
2025 apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
2026 [13, 12, 11] by c_definition ?11 ?12 ?13
2027 10011: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
2030 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
2031 [1] by prove_strong_fixed_point ?1
2039 10011: apply 20 2 3 0,2
2040 10011: f 3 1 3 0,2,2
2041 CLASH, statistics insufficient
2044 apply (apply (apply s ?3) ?4) ?5
2046 apply (apply ?3 ?5) (apply ?4 ?5)
2047 [5, 4, 3] by s_definition ?3 ?4 ?5
2049 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
2050 [9, 8, 7] by b_definition ?7 ?8 ?9
2052 apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
2053 [13, 12, 11] by c_definition ?11 ?12 ?13
2054 10012: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
2057 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
2058 [1] by prove_strong_fixed_point ?1
2066 10012: apply 20 2 3 0,2
2067 10012: f 3 1 3 0,2,2
2071 Found proof, 12.629405s
2072 % SZS status Unsatisfiable for COL057-1.p
2073 % SZS output start CNFRefutation for COL057-1.p
2074 Id : 3, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9
2075 Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
2076 Id : 2, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5
2077 Id : 37, {_}: apply (apply (apply s i) ?141) ?142 =?= apply ?142 (apply ?141 ?142) [142, 141] by Super 2 with 5 at 1,3
2078 Id : 16, {_}: apply (apply (apply s (apply b ?64)) ?65) ?66 =?= apply ?64 (apply ?66 (apply ?65 ?66)) [66, 65, 64] by Super 2 with 3 at 3
2079 Id : 9068, {_}: apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) === apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) [] by Super 9059 with 5 at 2,1,2
2080 Id : 9059, {_}: apply (apply ?16932 (apply ?16933 ?16932)) (f (apply ?16932 (apply ?16933 ?16932))) =?= apply (apply (apply (apply s (apply b (apply s i))) ?16933) ?16932) (f (apply ?16932 (apply ?16933 ?16932))) [16933, 16932] by Super 9058 with 16 at 1,3
2081 Id : 9058, {_}: apply ?16930 (f ?16930) =<= apply (apply (apply s i) ?16930) (f ?16930) [16930] by Super 1 with 37 at 3
2082 Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
2083 % SZS output end CNFRefutation for COL057-1.p
2084 10010: solved COL057-1.p in 2.124132 using nrkbo
2085 10010: status Unsatisfiable for COL057-1.p
2086 NO CLASH, using fixed ground order
2093 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
2094 ?5) (inverse (multiply ?3 ?5))))
2097 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
2100 multiply a (multiply b c) =<= multiply (multiply a b) c
2101 [] by prove_associativity
2105 10025: inverse 5 1 0
2106 10025: multiply 10 2 4 0,2
2107 10025: c 2 0 2 2,2,2
2108 10025: b 2 0 2 1,2,2
2110 NO CLASH, using fixed ground order
2117 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
2118 ?5) (inverse (multiply ?3 ?5))))
2121 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
2124 multiply a (multiply b c) =<= multiply (multiply a b) c
2125 [] by prove_associativity
2129 10026: inverse 5 1 0
2130 10026: multiply 10 2 4 0,2
2131 10026: c 2 0 2 2,2,2
2132 10026: b 2 0 2 1,2,2
2134 NO CLASH, using fixed ground order
2141 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
2142 ?5) (inverse (multiply ?3 ?5))))
2145 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
2148 multiply a (multiply b c) =<= multiply (multiply a b) c
2149 [] by prove_associativity
2153 10027: inverse 5 1 0
2154 10027: multiply 10 2 4 0,2
2155 10027: c 2 0 2 2,2,2
2156 10027: b 2 0 2 1,2,2
2160 Found proof, 20.319552s
2161 % SZS status Unsatisfiable for GRP014-1.p
2162 % SZS output start CNFRefutation for GRP014-1.p
2163 Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
2164 Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
2165 Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
2166 Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
2167 Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2
2168 Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2
2169 Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2
2170 Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2
2171 Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3
2172 Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2
2173 Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2
2174 Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2
2175 Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2
2176 Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2
2177 Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2
2178 Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2
2179 Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2
2180 Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2
2181 Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2
2182 Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2
2183 Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3
2184 Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2
2185 Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2
2186 Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3
2187 Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2
2188 Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2
2189 Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2
2190 Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
2191 Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2
2192 Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3
2193 Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2
2194 Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3
2195 Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2
2196 Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2
2197 Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2
2198 Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2
2199 Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2
2200 Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2
2201 Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2
2202 Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2
2203 Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3
2204 Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2
2205 Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2
2206 Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2
2207 Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2
2208 Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2
2209 Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2
2210 Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2
2211 Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2
2212 Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2
2213 Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2
2214 Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2
2215 Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2
2216 Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2
2217 Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2
2218 Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2
2219 Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2
2220 Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2
2221 Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2
2222 Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2
2223 Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2
2224 Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2
2225 Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2
2226 Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2
2227 Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2
2228 Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2
2229 Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2
2230 Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2
2231 Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2
2232 Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2
2233 Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2
2234 Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2
2235 Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2
2236 Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2
2237 Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2
2238 Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2
2239 Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2
2240 Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2
2241 Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2
2242 Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2
2243 Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2
2244 Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2
2245 Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2
2246 Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2
2247 Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3
2248 Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2
2249 Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2
2250 Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2
2251 Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2
2252 Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2
2253 Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2
2254 Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2
2255 Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2
2256 Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2
2257 Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2
2258 Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2
2259 Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2
2260 Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2
2261 Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3
2262 Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2
2263 Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2
2264 Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2
2265 Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2
2266 Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2
2267 Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2
2268 Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2
2269 Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2
2270 Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2
2271 Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3
2272 Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3
2273 Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2
2274 Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2
2275 Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3
2276 Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2
2277 Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2
2278 Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2
2279 Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2
2280 Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2
2281 Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2
2282 Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2
2283 Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2
2284 Id : 33337, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 32860 at 3
2285 Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
2286 % SZS output end CNFRefutation for GRP014-1.p
2287 10025: solved GRP014-1.p in 10.216638 using nrkbo
2288 10025: status Unsatisfiable for GRP014-1.p
2289 CLASH, statistics insufficient
2291 10036: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2292 10036: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2294 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2295 [8, 7, 6] by associativity ?6 ?7 ?8
2297 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2298 [11, 10] by symmetry_of_glb ?10 ?11
2300 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2301 [14, 13] by symmetry_of_lub ?13 ?14
2303 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2305 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2306 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2308 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2310 least_upper_bound (least_upper_bound ?20 ?21) ?22
2311 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2312 10036: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2313 10036: Id : 10, {_}:
2314 greatest_lower_bound ?26 ?26 =>= ?26
2315 [26] by idempotence_of_gld ?26
2316 10036: Id : 11, {_}:
2317 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2318 [29, 28] by lub_absorbtion ?28 ?29
2319 10036: Id : 12, {_}:
2320 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2321 [32, 31] by glb_absorbtion ?31 ?32
2322 10036: Id : 13, {_}:
2323 multiply ?34 (least_upper_bound ?35 ?36)
2325 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2326 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2327 10036: Id : 14, {_}:
2328 multiply ?38 (greatest_lower_bound ?39 ?40)
2330 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2331 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2332 10036: Id : 15, {_}:
2333 multiply (least_upper_bound ?42 ?43) ?44
2335 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2336 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2337 10036: Id : 16, {_}:
2338 multiply (greatest_lower_bound ?46 ?47) ?48
2340 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2341 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2342 10036: Id : 17, {_}:
2343 positive_part ?50 =<= least_upper_bound ?50 identity
2345 10036: Id : 18, {_}:
2346 negative_part ?52 =<= greatest_lower_bound ?52 identity
2348 10036: Id : 19, {_}:
2349 least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
2351 greatest_lower_bound (least_upper_bound ?54 ?55)
2352 (least_upper_bound ?54 ?56)
2353 [56, 55, 54] by lat4_3 ?54 ?55 ?56
2354 10036: Id : 20, {_}:
2355 greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
2357 least_upper_bound (greatest_lower_bound ?58 ?59)
2358 (greatest_lower_bound ?58 ?60)
2359 [60, 59, 58] by lat4_4 ?58 ?59 ?60
2362 a =<= multiply (positive_part a) (negative_part a)
2367 10036: least_upper_bound 19 2 0
2368 10036: greatest_lower_bound 19 2 0
2369 10036: inverse 1 1 0
2370 10036: identity 4 0 0
2371 10036: multiply 19 2 1 0,3
2372 10036: negative_part 2 1 1 0,2,3
2373 10036: positive_part 2 1 1 0,1,3
2375 CLASH, statistics insufficient
2377 10037: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2378 10037: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2380 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
2381 [8, 7, 6] by associativity ?6 ?7 ?8
2383 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2384 [11, 10] by symmetry_of_glb ?10 ?11
2386 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2387 [14, 13] by symmetry_of_lub ?13 ?14
2389 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2391 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2392 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2394 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2396 least_upper_bound (least_upper_bound ?20 ?21) ?22
2397 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2398 10037: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2399 10037: Id : 10, {_}:
2400 greatest_lower_bound ?26 ?26 =>= ?26
2401 [26] by idempotence_of_gld ?26
2402 10037: Id : 11, {_}:
2403 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2404 [29, 28] by lub_absorbtion ?28 ?29
2405 10037: Id : 12, {_}:
2406 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2407 [32, 31] by glb_absorbtion ?31 ?32
2408 10037: Id : 13, {_}:
2409 multiply ?34 (least_upper_bound ?35 ?36)
2411 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2412 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2413 10037: Id : 14, {_}:
2414 multiply ?38 (greatest_lower_bound ?39 ?40)
2416 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2417 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2418 10037: Id : 15, {_}:
2419 multiply (least_upper_bound ?42 ?43) ?44
2421 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2422 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2423 10037: Id : 16, {_}:
2424 multiply (greatest_lower_bound ?46 ?47) ?48
2426 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2427 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2428 10037: Id : 17, {_}:
2429 positive_part ?50 =<= least_upper_bound ?50 identity
2431 10037: Id : 18, {_}:
2432 negative_part ?52 =<= greatest_lower_bound ?52 identity
2434 10037: Id : 19, {_}:
2435 least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
2437 greatest_lower_bound (least_upper_bound ?54 ?55)
2438 (least_upper_bound ?54 ?56)
2439 [56, 55, 54] by lat4_3 ?54 ?55 ?56
2440 10037: Id : 20, {_}:
2441 greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
2443 least_upper_bound (greatest_lower_bound ?58 ?59)
2444 (greatest_lower_bound ?58 ?60)
2445 [60, 59, 58] by lat4_4 ?58 ?59 ?60
2448 a =<= multiply (positive_part a) (negative_part a)
2453 10037: least_upper_bound 19 2 0
2454 10037: greatest_lower_bound 19 2 0
2455 10037: inverse 1 1 0
2456 10037: identity 4 0 0
2457 10037: multiply 19 2 1 0,3
2458 10037: negative_part 2 1 1 0,2,3
2459 10037: positive_part 2 1 1 0,1,3
2461 CLASH, statistics insufficient
2463 10038: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2464 10038: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2466 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
2467 [8, 7, 6] by associativity ?6 ?7 ?8
2469 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2470 [11, 10] by symmetry_of_glb ?10 ?11
2472 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2473 [14, 13] by symmetry_of_lub ?13 ?14
2475 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2477 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2478 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2480 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2482 least_upper_bound (least_upper_bound ?20 ?21) ?22
2483 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2484 10038: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2485 10038: Id : 10, {_}:
2486 greatest_lower_bound ?26 ?26 =>= ?26
2487 [26] by idempotence_of_gld ?26
2488 10038: Id : 11, {_}:
2489 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2490 [29, 28] by lub_absorbtion ?28 ?29
2491 10038: Id : 12, {_}:
2492 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2493 [32, 31] by glb_absorbtion ?31 ?32
2494 10038: Id : 13, {_}:
2495 multiply ?34 (least_upper_bound ?35 ?36)
2497 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2498 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2499 10038: Id : 14, {_}:
2500 multiply ?38 (greatest_lower_bound ?39 ?40)
2502 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2503 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2504 10038: Id : 15, {_}:
2505 multiply (least_upper_bound ?42 ?43) ?44
2507 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2508 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2509 10038: Id : 16, {_}:
2510 multiply (greatest_lower_bound ?46 ?47) ?48
2512 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2513 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2514 10038: Id : 17, {_}:
2515 positive_part ?50 =>= least_upper_bound ?50 identity
2517 10038: Id : 18, {_}:
2518 negative_part ?52 =>= greatest_lower_bound ?52 identity
2520 10038: Id : 19, {_}:
2521 least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
2523 greatest_lower_bound (least_upper_bound ?54 ?55)
2524 (least_upper_bound ?54 ?56)
2525 [56, 55, 54] by lat4_3 ?54 ?55 ?56
2526 10038: Id : 20, {_}:
2527 greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
2529 least_upper_bound (greatest_lower_bound ?58 ?59)
2530 (greatest_lower_bound ?58 ?60)
2531 [60, 59, 58] by lat4_4 ?58 ?59 ?60
2534 a =<= multiply (positive_part a) (negative_part a)
2539 10038: least_upper_bound 19 2 0
2540 10038: greatest_lower_bound 19 2 0
2541 10038: inverse 1 1 0
2542 10038: identity 4 0 0
2543 10038: multiply 19 2 1 0,3
2544 10038: negative_part 2 1 1 0,2,3
2545 10038: positive_part 2 1 1 0,1,3
2549 Found proof, 19.804581s
2550 % SZS status Unsatisfiable for GRP167-1.p
2551 % SZS output start CNFRefutation for GRP167-1.p
2552 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
2553 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2554 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2555 Id : 134, {_}: multiply ?322 (least_upper_bound ?323 ?324) =<= least_upper_bound (multiply ?322 ?323) (multiply ?322 ?324) [324, 323, 322] by monotony_lub1 ?322 ?323 ?324
2556 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
2557 Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2558 Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2559 Id : 20, {_}: greatest_lower_bound ?58 (least_upper_bound ?59 ?60) =<= least_upper_bound (greatest_lower_bound ?58 ?59) (greatest_lower_bound ?58 ?60) [60, 59, 58] by lat4_4 ?58 ?59 ?60
2560 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
2561 Id : 17, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
2562 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2563 Id : 18, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
2564 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
2565 Id : 237, {_}: multiply (greatest_lower_bound ?514 ?515) ?516 =<= greatest_lower_bound (multiply ?514 ?516) (multiply ?515 ?516) [516, 515, 514] by monotony_glb2 ?514 ?515 ?516
2566 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2567 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2568 Id : 25, {_}: multiply (multiply ?69 ?70) ?71 =>= multiply ?69 (multiply ?70 ?71) [71, 70, 69] by associativity ?69 ?70 ?71
2569 Id : 27, {_}: multiply identity ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Super 25 with 3 at 1,2
2570 Id : 31, {_}: ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Demod 27 with 2 at 2
2571 Id : 242, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= greatest_lower_bound identity (multiply ?533 ?532) [533, 532] by Super 237 with 3 at 1,3
2572 Id : 278, {_}: greatest_lower_bound identity ?584 =>= negative_part ?584 [584] by Super 5 with 18 at 3
2573 Id : 15662, {_}: multiply (greatest_lower_bound (inverse ?19569) ?19570) ?19569 =>= negative_part (multiply ?19570 ?19569) [19570, 19569] by Demod 242 with 278 at 3
2574 Id : 15688, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part (multiply identity ?19646) [19646] by Super 15662 with 18 at 1,2
2575 Id : 15740, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part ?19646 [19646] by Demod 15688 with 2 at 1,3
2576 Id : 15765, {_}: ?19710 =<= multiply (inverse (negative_part (inverse ?19710))) (negative_part ?19710) [19710] by Super 31 with 15740 at 2,3
2577 Id : 778, {_}: ?1461 =<= multiply (inverse ?1462) (multiply ?1462 ?1461) [1462, 1461] by Demod 27 with 2 at 2
2578 Id : 782, {_}: ?1472 =<= multiply (inverse (inverse ?1472)) identity [1472] by Super 778 with 3 at 2,3
2579 Id : 1371, {_}: multiply (inverse (inverse ?2316)) (least_upper_bound ?2317 identity) =?= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Super 13 with 782 at 2,3
2580 Id : 1392, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Demod 1371 with 17 at 2,2
2581 Id : 1393, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1392 with 6 at 3
2582 Id : 786, {_}: multiply ?1484 ?1485 =<= multiply (inverse (inverse ?1484)) ?1485 [1485, 1484] by Super 778 with 31 at 2,3
2583 Id : 2137, {_}: ?1472 =<= multiply ?1472 identity [1472] by Demod 782 with 786 at 3
2584 Id : 2138, {_}: inverse (inverse ?3405) =<= multiply ?3405 identity [3405] by Super 2137 with 786 at 3
2585 Id : 2189, {_}: inverse (inverse ?3405) =>= ?3405 [3405] by Demod 2138 with 2137 at 3
2586 Id : 49575, {_}: multiply ?2316 (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1393 with 2189 at 1,2
2587 Id : 49621, {_}: multiply ?54979 (positive_part ?54980) =<= least_upper_bound ?54979 (multiply ?54979 ?54980) [54980, 54979] by Demod 49575 with 2189 at 1,2,3
2588 Id : 15768, {_}: multiply (negative_part (inverse ?19715)) ?19715 =>= negative_part ?19715 [19715] by Demod 15688 with 2 at 1,3
2589 Id : 15773, {_}: multiply (negative_part ?19724) (inverse ?19724) =>= negative_part (inverse ?19724) [19724] by Super 15768 with 2189 at 1,1,2
2590 Id : 49652, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= least_upper_bound (negative_part ?55064) (negative_part (inverse ?55064)) [55064] by Super 49621 with 15773 at 2,3
2591 Id : 865, {_}: greatest_lower_bound identity (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Super 20 with 278 at 2,3
2592 Id : 880, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Demod 865 with 278 at 2
2593 Id : 881, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (negative_part ?1569) (negative_part ?1570) [1570, 1569] by Demod 880 with 278 at 1,3
2594 Id : 49776, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= negative_part (least_upper_bound ?55064 (inverse ?55064)) [55064] by Demod 49652 with 881 at 3
2595 Id : 15757, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19686)) ?19687) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Super 16 with 15740 at 1,3
2596 Id : 859, {_}: greatest_lower_bound identity (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Super 7 with 278 at 1,3
2597 Id : 890, {_}: negative_part (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 859 with 278 at 2
2598 Id : 281, {_}: greatest_lower_bound ?591 (greatest_lower_bound ?592 identity) =>= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Super 7 with 18 at 3
2599 Id : 289, {_}: greatest_lower_bound ?591 (negative_part ?592) =<= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Demod 281 with 18 at 2,2
2600 Id : 1628, {_}: greatest_lower_bound ?1558 (negative_part ?1559) =<= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 890 with 289 at 2
2601 Id : 15802, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Demod 15757 with 1628 at 1,2
2602 Id : 15803, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19687, 19686] by Demod 15802 with 1628 at 3
2603 Id : 15650, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= negative_part (multiply ?533 ?532) [533, 532] by Demod 242 with 278 at 3
2604 Id : 15804, {_}: negative_part (multiply (negative_part ?19687) ?19686) =<= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19686, 19687] by Demod 15803 with 15650 at 2
2605 Id : 49651, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part (inverse ?55062)) (negative_part ?55062) [55062] by Super 49621 with 15740 at 2,3
2606 Id : 49774, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part ?55062) (negative_part (inverse ?55062)) [55062] by Demod 49651 with 6 at 3
2607 Id : 49775, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= negative_part (least_upper_bound ?55062 (inverse ?55062)) [55062] by Demod 49774 with 881 at 3
2608 Id : 49840, {_}: negative_part (multiply (negative_part (negative_part (inverse ?55170))) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Super 15804 with 49775 at 1,2,3
2609 Id : 268, {_}: greatest_lower_bound ?569 (positive_part ?569) =>= ?569 [569] by Super 12 with 17 at 2,2
2610 Id : 139, {_}: multiply (inverse ?340) (least_upper_bound ?340 ?341) =>= least_upper_bound identity (multiply (inverse ?340) ?341) [341, 340] by Super 134 with 3 at 1,3
2611 Id : 264, {_}: least_upper_bound identity ?559 =>= positive_part ?559 [559] by Super 6 with 17 at 3
2612 Id : 4901, {_}: multiply (inverse ?7380) (least_upper_bound ?7380 ?7381) =>= positive_part (multiply (inverse ?7380) ?7381) [7381, 7380] by Demod 139 with 264 at 3
2613 Id : 4921, {_}: multiply (inverse ?7441) (positive_part ?7441) =?= positive_part (multiply (inverse ?7441) identity) [7441] by Super 4901 with 17 at 2,2
2614 Id : 4985, {_}: multiply (inverse ?7525) (positive_part ?7525) =>= positive_part (inverse ?7525) [7525] by Demod 4921 with 2137 at 1,3
2615 Id : 267, {_}: least_upper_bound ?566 (least_upper_bound ?567 identity) =>= positive_part (least_upper_bound ?566 ?567) [567, 566] by Super 8 with 17 at 3
2616 Id : 1187, {_}: least_upper_bound ?2080 (positive_part ?2081) =<= positive_part (least_upper_bound ?2080 ?2081) [2081, 2080] by Demod 267 with 17 at 2,2
2617 Id : 1199, {_}: least_upper_bound ?2117 (positive_part identity) =>= positive_part (positive_part ?2117) [2117] by Super 1187 with 17 at 1,3
2618 Id : 263, {_}: positive_part identity =>= identity [] by Super 9 with 17 at 2
2619 Id : 1218, {_}: least_upper_bound ?2117 identity =<= positive_part (positive_part ?2117) [2117] by Demod 1199 with 263 at 2,2
2620 Id : 1219, {_}: positive_part ?2117 =<= positive_part (positive_part ?2117) [2117] by Demod 1218 with 17 at 2
2621 Id : 4997, {_}: multiply (inverse (positive_part ?7553)) (positive_part ?7553) =>= positive_part (inverse (positive_part ?7553)) [7553] by Super 4985 with 1219 at 2,2
2622 Id : 5031, {_}: identity =<= positive_part (inverse (positive_part ?7553)) [7553] by Demod 4997 with 3 at 2
2623 Id : 5129, {_}: greatest_lower_bound (inverse (positive_part ?7677)) identity =>= inverse (positive_part ?7677) [7677] by Super 268 with 5031 at 2,2
2624 Id : 5176, {_}: greatest_lower_bound identity (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5129 with 5 at 2
2625 Id : 5177, {_}: negative_part (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5176 with 278 at 2
2626 Id : 5325, {_}: greatest_lower_bound (inverse (positive_part ?7851)) (negative_part ?7852) =>= greatest_lower_bound (inverse (positive_part ?7851)) ?7852 [7852, 7851] by Super 1628 with 5177 at 1,3
2627 Id : 15685, {_}: multiply (greatest_lower_bound (inverse (positive_part ?19637)) ?19638) (positive_part ?19637) =>= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19638, 19637] by Super 15662 with 5325 at 1,2
2628 Id : 15737, {_}: negative_part (multiply ?19638 (positive_part ?19637)) =<= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19637, 19638] by Demod 15685 with 15650 at 2
2629 Id : 49928, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Demod 49840 with 15737 at 2
2630 Id : 1648, {_}: greatest_lower_bound ?2900 (negative_part ?2901) =<= greatest_lower_bound (negative_part ?2900) ?2901 [2901, 2900] by Demod 890 with 289 at 2
2631 Id : 863, {_}: negative_part (least_upper_bound identity ?1566) =>= identity [1566] by Super 12 with 278 at 2
2632 Id : 886, {_}: negative_part (positive_part ?1566) =>= identity [1566] by Demod 863 with 264 at 1,2
2633 Id : 1653, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= greatest_lower_bound identity ?2915 [2915, 2914] by Super 1648 with 886 at 1,3
2634 Id : 1710, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= negative_part ?2915 [2915, 2914] by Demod 1653 with 278 at 3
2635 Id : 49929, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =>= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49928 with 1710 at 3
2636 Id : 49930, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =<= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49929 with 15737 at 2
2637 Id : 1014, {_}: greatest_lower_bound ?1717 (positive_part ?1717) =>= ?1717 [1717] by Super 12 with 17 at 2,2
2638 Id : 858, {_}: least_upper_bound identity (negative_part ?1556) =>= identity [1556] by Super 11 with 278 at 2,2
2639 Id : 891, {_}: positive_part (negative_part ?1556) =>= identity [1556] by Demod 858 with 264 at 2
2640 Id : 1019, {_}: greatest_lower_bound (negative_part ?1726) identity =>= negative_part ?1726 [1726] by Super 1014 with 891 at 2,2
2641 Id : 1039, {_}: greatest_lower_bound identity (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1019 with 5 at 2
2642 Id : 1040, {_}: negative_part (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1039 with 278 at 2
2643 Id : 49931, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =>= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49930 with 1040 at 3
2644 Id : 4960, {_}: multiply (inverse ?7441) (positive_part ?7441) =>= positive_part (inverse ?7441) [7441] by Demod 4921 with 2137 at 1,3
2645 Id : 49932, {_}: negative_part (positive_part (inverse ?55170)) =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49931 with 4960 at 1,2
2646 Id : 49933, {_}: identity =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49932 with 886 at 2
2647 Id : 53516, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= identity [55064] by Demod 49776 with 49933 at 3
2648 Id : 53529, {_}: positive_part (inverse ?58317) =<= multiply (inverse (negative_part ?58317)) identity [58317] by Super 31 with 53516 at 2,3
2649 Id : 53947, {_}: positive_part (inverse ?58761) =>= inverse (negative_part ?58761) [58761] by Demod 53529 with 2137 at 3
2650 Id : 53952, {_}: positive_part ?58770 =<= inverse (negative_part (inverse ?58770)) [58770] by Super 53947 with 2189 at 1,2
2651 Id : 54151, {_}: ?19710 =<= multiply (positive_part ?19710) (negative_part ?19710) [19710] by Demod 15765 with 53952 at 1,3
2652 Id : 54473, {_}: a =?= a [] by Demod 1 with 54151 at 3
2653 Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
2654 % SZS output end CNFRefutation for GRP167-1.p
2655 10037: solved GRP167-1.p in 9.872616 using kbo
2656 10037: status Unsatisfiable for GRP167-1.p
2657 CLASH, statistics insufficient
2659 10051: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2660 10051: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2662 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2663 [8, 7, 6] by associativity ?6 ?7 ?8
2665 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2666 [11, 10] by symmetry_of_glb ?10 ?11
2668 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2669 [14, 13] by symmetry_of_lub ?13 ?14
2671 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2673 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2674 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2676 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2678 least_upper_bound (least_upper_bound ?20 ?21) ?22
2679 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2680 10051: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2681 10051: Id : 10, {_}:
2682 greatest_lower_bound ?26 ?26 =>= ?26
2683 [26] by idempotence_of_gld ?26
2684 10051: Id : 11, {_}:
2685 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2686 [29, 28] by lub_absorbtion ?28 ?29
2687 10051: Id : 12, {_}:
2688 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2689 [32, 31] by glb_absorbtion ?31 ?32
2690 10051: Id : 13, {_}:
2691 multiply ?34 (least_upper_bound ?35 ?36)
2693 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2694 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2695 10051: Id : 14, {_}:
2696 multiply ?38 (greatest_lower_bound ?39 ?40)
2698 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2699 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2700 10051: Id : 15, {_}:
2701 multiply (least_upper_bound ?42 ?43) ?44
2703 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2704 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2705 10051: Id : 16, {_}:
2706 multiply (greatest_lower_bound ?46 ?47) ?48
2708 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2709 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2710 10051: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
2711 10051: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
2712 10051: Id : 19, {_}:
2713 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
2714 [54, 53] by lat4_3 ?53 ?54
2715 10051: Id : 20, {_}:
2716 positive_part ?56 =<= least_upper_bound ?56 identity
2718 10051: Id : 21, {_}:
2719 negative_part ?58 =<= greatest_lower_bound ?58 identity
2721 10051: Id : 22, {_}:
2722 least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
2724 greatest_lower_bound (least_upper_bound ?60 ?61)
2725 (least_upper_bound ?60 ?62)
2726 [62, 61, 60] by lat4_6 ?60 ?61 ?62
2727 10051: Id : 23, {_}:
2728 greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
2730 least_upper_bound (greatest_lower_bound ?64 ?65)
2731 (greatest_lower_bound ?64 ?66)
2732 [66, 65, 64] by lat4_7 ?64 ?65 ?66
2735 a =<= multiply (positive_part a) (negative_part a)
2740 10051: least_upper_bound 19 2 0
2741 10051: greatest_lower_bound 19 2 0
2742 10051: inverse 7 1 0
2743 10051: identity 6 0 0
2744 10051: multiply 21 2 1 0,3
2745 10051: negative_part 2 1 1 0,2,3
2746 10051: positive_part 2 1 1 0,1,3
2748 CLASH, statistics insufficient
2750 10052: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2751 10052: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2753 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
2754 [8, 7, 6] by associativity ?6 ?7 ?8
2756 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2757 [11, 10] by symmetry_of_glb ?10 ?11
2759 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2760 [14, 13] by symmetry_of_lub ?13 ?14
2762 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2764 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2765 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2767 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2769 least_upper_bound (least_upper_bound ?20 ?21) ?22
2770 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2771 10052: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2772 10052: Id : 10, {_}:
2773 greatest_lower_bound ?26 ?26 =>= ?26
2774 [26] by idempotence_of_gld ?26
2775 10052: Id : 11, {_}:
2776 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2777 [29, 28] by lub_absorbtion ?28 ?29
2778 10052: Id : 12, {_}:
2779 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2780 [32, 31] by glb_absorbtion ?31 ?32
2781 10052: Id : 13, {_}:
2782 multiply ?34 (least_upper_bound ?35 ?36)
2784 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2785 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2786 10052: Id : 14, {_}:
2787 multiply ?38 (greatest_lower_bound ?39 ?40)
2789 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2790 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2791 10052: Id : 15, {_}:
2792 multiply (least_upper_bound ?42 ?43) ?44
2794 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2795 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2796 10052: Id : 16, {_}:
2797 multiply (greatest_lower_bound ?46 ?47) ?48
2799 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2800 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2801 10052: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
2802 10052: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
2803 10052: Id : 19, {_}:
2804 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
2805 [54, 53] by lat4_3 ?53 ?54
2806 10052: Id : 20, {_}:
2807 positive_part ?56 =<= least_upper_bound ?56 identity
2809 10052: Id : 21, {_}:
2810 negative_part ?58 =<= greatest_lower_bound ?58 identity
2812 10052: Id : 22, {_}:
2813 least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
2815 greatest_lower_bound (least_upper_bound ?60 ?61)
2816 (least_upper_bound ?60 ?62)
2817 [62, 61, 60] by lat4_6 ?60 ?61 ?62
2818 10052: Id : 23, {_}:
2819 greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
2821 least_upper_bound (greatest_lower_bound ?64 ?65)
2822 (greatest_lower_bound ?64 ?66)
2823 [66, 65, 64] by lat4_7 ?64 ?65 ?66
2826 a =<= multiply (positive_part a) (negative_part a)
2831 10052: least_upper_bound 19 2 0
2832 10052: greatest_lower_bound 19 2 0
2833 10052: inverse 7 1 0
2834 10052: identity 6 0 0
2835 10052: multiply 21 2 1 0,3
2836 10052: negative_part 2 1 1 0,2,3
2837 10052: positive_part 2 1 1 0,1,3
2839 CLASH, statistics insufficient
2841 10053: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2842 10053: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2844 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
2845 [8, 7, 6] by associativity ?6 ?7 ?8
2847 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2848 [11, 10] by symmetry_of_glb ?10 ?11
2850 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2851 [14, 13] by symmetry_of_lub ?13 ?14
2853 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2855 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2856 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2858 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2860 least_upper_bound (least_upper_bound ?20 ?21) ?22
2861 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2862 10053: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2863 10053: Id : 10, {_}:
2864 greatest_lower_bound ?26 ?26 =>= ?26
2865 [26] by idempotence_of_gld ?26
2866 10053: Id : 11, {_}:
2867 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2868 [29, 28] by lub_absorbtion ?28 ?29
2869 10053: Id : 12, {_}:
2870 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2871 [32, 31] by glb_absorbtion ?31 ?32
2872 10053: Id : 13, {_}:
2873 multiply ?34 (least_upper_bound ?35 ?36)
2875 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2876 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2877 10053: Id : 14, {_}:
2878 multiply ?38 (greatest_lower_bound ?39 ?40)
2880 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2881 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2882 10053: Id : 15, {_}:
2883 multiply (least_upper_bound ?42 ?43) ?44
2885 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2886 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2887 10053: Id : 16, {_}:
2888 multiply (greatest_lower_bound ?46 ?47) ?48
2890 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2891 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2892 10053: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
2893 10053: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
2894 10053: Id : 19, {_}:
2895 inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
2896 [54, 53] by lat4_3 ?53 ?54
2897 10053: Id : 20, {_}:
2898 positive_part ?56 =>= least_upper_bound ?56 identity
2900 10053: Id : 21, {_}:
2901 negative_part ?58 =>= greatest_lower_bound ?58 identity
2903 10053: Id : 22, {_}:
2904 least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
2906 greatest_lower_bound (least_upper_bound ?60 ?61)
2907 (least_upper_bound ?60 ?62)
2908 [62, 61, 60] by lat4_6 ?60 ?61 ?62
2909 10053: Id : 23, {_}:
2910 greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
2912 least_upper_bound (greatest_lower_bound ?64 ?65)
2913 (greatest_lower_bound ?64 ?66)
2914 [66, 65, 64] by lat4_7 ?64 ?65 ?66
2917 a =<= multiply (positive_part a) (negative_part a)
2922 10053: least_upper_bound 19 2 0
2923 10053: greatest_lower_bound 19 2 0
2924 10053: inverse 7 1 0
2925 10053: identity 6 0 0
2926 10053: multiply 21 2 1 0,3
2927 10053: negative_part 2 1 1 0,2,3
2928 10053: positive_part 2 1 1 0,1,3
2932 Found proof, 6.844655s
2933 % SZS status Unsatisfiable for GRP167-2.p
2934 % SZS output start CNFRefutation for GRP167-2.p
2935 Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by lat4_3 ?53 ?54
2936 Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2937 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2938 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
2939 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
2940 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2941 Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62
2942 Id : 210, {_}: multiply (least_upper_bound ?453 ?454) ?455 =<= least_upper_bound (multiply ?453 ?455) (multiply ?454 ?455) [455, 454, 453] by monotony_lub2 ?453 ?454 ?455
2943 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
2944 Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58
2945 Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2946 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
2947 Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56
2948 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2949 Id : 286, {_}: inverse (multiply ?614 ?615) =<= multiply (inverse ?615) (inverse ?614) [615, 614] by lat4_3 ?614 ?615
2950 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2951 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2952 Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =>= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77
2953 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
2954 Id : 30, {_}: multiply identity ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Super 28 with 3 at 1,2
2955 Id : 34, {_}: ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Demod 30 with 2 at 2
2956 Id : 288, {_}: inverse (multiply (inverse ?619) ?620) =>= multiply (inverse ?620) ?619 [620, 619] by Super 286 with 18 at 2,3
2957 Id : 997, {_}: ?1719 =<= multiply (inverse ?1720) (multiply ?1720 ?1719) [1720, 1719] by Demod 30 with 2 at 2
2958 Id : 1001, {_}: ?1730 =<= multiply (inverse (inverse ?1730)) identity [1730] by Super 997 with 3 at 2,3
2959 Id : 1026, {_}: ?1730 =<= multiply ?1730 identity [1730] by Demod 1001 with 18 at 1,3
2960 Id : 1045, {_}: multiply ?1785 (least_upper_bound ?1786 identity) =?= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Super 13 with 1026 at 2,3
2961 Id : 1078, {_}: multiply ?1785 (positive_part ?1786) =<= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Demod 1045 with 20 at 2,2
2962 Id : 5086, {_}: multiply ?7297 (positive_part ?7298) =<= least_upper_bound ?7297 (multiply ?7297 ?7298) [7298, 7297] by Demod 1078 with 6 at 3
2963 Id : 5090, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound (inverse ?7308) identity [7308] by Super 5086 with 3 at 2,3
2964 Id : 5133, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound identity (inverse ?7308) [7308] by Demod 5090 with 6 at 3
2965 Id : 298, {_}: least_upper_bound identity ?640 =>= positive_part ?640 [640] by Super 6 with 20 at 3
2966 Id : 5134, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= positive_part (inverse ?7308) [7308] by Demod 5133 with 298 at 3
2967 Id : 5356, {_}: inverse (positive_part (inverse ?7872)) =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Super 288 with 5134 at 1,2
2968 Id : 1051, {_}: multiply ?1799 (greatest_lower_bound ?1800 identity) =?= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Super 14 with 1026 at 2,3
2969 Id : 1072, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Demod 1051 with 21 at 2,2
2970 Id : 4381, {_}: multiply ?6565 (negative_part ?6566) =<= greatest_lower_bound ?6565 (multiply ?6565 ?6566) [6566, 6565] by Demod 1072 with 5 at 3
2971 Id : 270, {_}: multiply ?567 (inverse ?567) =>= identity [567] by Super 3 with 18 at 1,2
2972 Id : 4388, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= greatest_lower_bound ?6585 identity [6585] by Super 4381 with 270 at 2,3
2973 Id : 4428, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 4388 with 21 at 3
2974 Id : 1073, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound ?1799 (multiply ?1799 ?1800) [1800, 1799] by Demod 1072 with 5 at 3
2975 Id : 215, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= least_upper_bound identity (multiply ?472 ?471) [472, 471] by Super 210 with 3 at 1,3
2976 Id : 11818, {_}: multiply (least_upper_bound (inverse ?15728) ?15729) ?15728 =>= positive_part (multiply ?15729 ?15728) [15729, 15728] by Demod 215 with 298 at 3
2977 Id : 11845, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part (multiply identity ?15810) [15810] by Super 11818 with 20 at 1,2
2978 Id : 12179, {_}: multiply (positive_part (inverse ?16312)) ?16312 =>= positive_part ?16312 [16312] by Demod 11845 with 2 at 1,3
2979 Id : 12183, {_}: multiply (positive_part ?16319) (inverse ?16319) =>= positive_part (inverse ?16319) [16319] by Super 12179 with 18 at 1,1,2
2980 Id : 12264, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= greatest_lower_bound (positive_part ?16391) (positive_part (inverse ?16391)) [16391] by Super 1073 with 12183 at 2,3
2981 Id : 849, {_}: least_upper_bound identity (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Super 22 with 298 at 2,3
2982 Id : 877, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Demod 849 with 298 at 2
2983 Id : 878, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (positive_part ?1555) (positive_part ?1556) [1556, 1555] by Demod 877 with 298 at 1,3
2984 Id : 12306, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= positive_part (greatest_lower_bound ?16391 (inverse ?16391)) [16391] by Demod 12264 with 878 at 3
2985 Id : 853, {_}: least_upper_bound identity (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Super 8 with 298 at 1,3
2986 Id : 874, {_}: positive_part (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 853 with 298 at 2
2987 Id : 297, {_}: least_upper_bound ?637 (least_upper_bound ?638 identity) =>= positive_part (least_upper_bound ?637 ?638) [638, 637] by Super 8 with 20 at 3
2988 Id : 307, {_}: least_upper_bound ?637 (positive_part ?638) =<= positive_part (least_upper_bound ?637 ?638) [638, 637] by Demod 297 with 20 at 2,2
2989 Id : 1518, {_}: least_upper_bound ?1564 (positive_part ?1565) =<= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 874 with 307 at 2
2990 Id : 309, {_}: least_upper_bound ?657 (negative_part ?657) =>= ?657 [657] by Super 11 with 21 at 2,2
2991 Id : 4385, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound (inverse ?6576) identity [6576] by Super 4381 with 3 at 2,3
2992 Id : 4422, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound identity (inverse ?6576) [6576] by Demod 4385 with 5 at 3
2993 Id : 312, {_}: greatest_lower_bound identity ?665 =>= negative_part ?665 [665] by Super 5 with 21 at 3
2994 Id : 4454, {_}: multiply (inverse ?6658) (negative_part ?6658) =>= negative_part (inverse ?6658) [6658] by Demod 4422 with 312 at 3
2995 Id : 1166, {_}: greatest_lower_bound ?1914 (positive_part ?1914) =>= ?1914 [1914] by Super 12 with 20 at 2,2
2996 Id : 898, {_}: least_upper_bound identity (negative_part ?1605) =>= identity [1605] by Super 11 with 312 at 2,2
2997 Id : 922, {_}: positive_part (negative_part ?1605) =>= identity [1605] by Demod 898 with 298 at 2
2998 Id : 1171, {_}: greatest_lower_bound (negative_part ?1923) identity =>= negative_part ?1923 [1923] by Super 1166 with 922 at 2,2
2999 Id : 1191, {_}: greatest_lower_bound identity (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1171 with 5 at 2
3000 Id : 1192, {_}: negative_part (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1191 with 312 at 2
3001 Id : 4460, {_}: multiply (inverse (negative_part ?6669)) (negative_part ?6669) =>= negative_part (inverse (negative_part ?6669)) [6669] by Super 4454 with 1192 at 2,2
3002 Id : 4502, {_}: identity =<= negative_part (inverse (negative_part ?6669)) [6669] by Demod 4460 with 3 at 2
3003 Id : 4607, {_}: least_upper_bound (inverse (negative_part ?6821)) identity =>= inverse (negative_part ?6821) [6821] by Super 309 with 4502 at 2,2
3004 Id : 4660, {_}: least_upper_bound identity (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4607 with 6 at 2
3005 Id : 4661, {_}: positive_part (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4660 with 298 at 2
3006 Id : 4799, {_}: least_upper_bound (inverse (negative_part ?6984)) (positive_part ?6985) =>= least_upper_bound (inverse (negative_part ?6984)) ?6985 [6985, 6984] by Super 1518 with 4661 at 1,3
3007 Id : 11842, {_}: multiply (least_upper_bound (inverse (negative_part ?15801)) ?15802) (negative_part ?15801) =>= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15802, 15801] by Super 11818 with 4799 at 1,2
3008 Id : 11803, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= positive_part (multiply ?472 ?471) [472, 471] by Demod 215 with 298 at 3
3009 Id : 11889, {_}: positive_part (multiply ?15802 (negative_part ?15801)) =<= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15801, 15802] by Demod 11842 with 11803 at 2
3010 Id : 11892, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part ?15810 [15810] by Demod 11845 with 2 at 1,3
3011 Id : 12165, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part (inverse ?16276)) (positive_part ?16276) [16276] by Super 1073 with 11892 at 2,3
3012 Id : 12217, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part ?16276) (positive_part (inverse ?16276)) [16276] by Demod 12165 with 5 at 3
3013 Id : 12218, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= positive_part (greatest_lower_bound ?16276 (inverse ?16276)) [16276] by Demod 12217 with 878 at 3
3014 Id : 12981, {_}: positive_part (multiply (inverse ?17147) (negative_part ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Super 11889 with 12218 at 1,3
3015 Id : 4423, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= negative_part (inverse ?6576) [6576] by Demod 4422 with 312 at 3
3016 Id : 13027, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Demod 12981 with 4423 at 1,2
3017 Id : 1230, {_}: least_upper_bound ?1974 (positive_part ?1975) =<= positive_part (least_upper_bound ?1974 ?1975) [1975, 1974] by Demod 297 with 20 at 2,2
3018 Id : 1242, {_}: least_upper_bound ?2011 (positive_part identity) =>= positive_part (positive_part ?2011) [2011] by Super 1230 with 20 at 1,3
3019 Id : 300, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2
3020 Id : 1261, {_}: least_upper_bound ?2011 identity =<= positive_part (positive_part ?2011) [2011] by Demod 1242 with 300 at 2,2
3021 Id : 1262, {_}: positive_part ?2011 =<= positive_part (positive_part ?2011) [2011] by Demod 1261 with 20 at 2
3022 Id : 13028, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13027 with 1262 at 3
3023 Id : 13029, {_}: identity =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13028 with 922 at 2
3024 Id : 14199, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= identity [16391] by Demod 12306 with 13029 at 3
3025 Id : 14209, {_}: negative_part (inverse ?18032) =<= multiply (inverse (positive_part ?18032)) identity [18032] by Super 34 with 14199 at 2,3
3026 Id : 14275, {_}: negative_part (inverse ?18032) =>= inverse (positive_part ?18032) [18032] by Demod 14209 with 1026 at 3
3027 Id : 14351, {_}: multiply ?6585 (inverse (positive_part ?6585)) =>= negative_part ?6585 [6585] by Demod 4428 with 14275 at 2,2
3028 Id : 290, {_}: inverse (multiply ?624 (inverse ?625)) =>= multiply ?625 (inverse ?624) [625, 624] by Super 286 with 18 at 1,3
3029 Id : 12177, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part (inverse (inverse ?16308)))) [16308] by Super 290 with 11892 at 1,2
3030 Id : 12203, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part ?16308)) [16308] by Demod 12177 with 18 at 1,1,2,3
3031 Id : 14356, {_}: inverse (positive_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 14351 with 12203 at 2
3032 Id : 14357, {_}: negative_part ?7872 =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Demod 5356 with 14356 at 2
3033 Id : 13168, {_}: multiply (inverse (greatest_lower_bound ?17321 (inverse ?17321))) identity =>= positive_part (inverse (greatest_lower_bound ?17321 (inverse ?17321))) [17321] by Super 5134 with 13029 at 2,2
3034 Id : 15132, {_}: inverse (greatest_lower_bound ?18904 (inverse ?18904)) =<= positive_part (inverse (greatest_lower_bound ?18904 (inverse ?18904))) [18904] by Demod 13168 with 1026 at 2
3035 Id : 15140, {_}: inverse (greatest_lower_bound (positive_part (inverse ?18921)) (inverse (positive_part (inverse ?18921)))) =>= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Super 15132 with 14356 at 2,1,1,3
3036 Id : 899, {_}: greatest_lower_bound identity (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Super 7 with 312 at 1,3
3037 Id : 921, {_}: negative_part (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 899 with 312 at 2
3038 Id : 311, {_}: greatest_lower_bound ?662 (greatest_lower_bound ?663 identity) =>= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Super 7 with 21 at 3
3039 Id : 321, {_}: greatest_lower_bound ?662 (negative_part ?663) =<= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Demod 311 with 21 at 2,2
3040 Id : 1610, {_}: greatest_lower_bound ?2637 (negative_part ?2638) =<= greatest_lower_bound (negative_part ?2637) ?2638 [2638, 2637] by Demod 921 with 321 at 2
3041 Id : 903, {_}: negative_part (least_upper_bound identity ?1615) =>= identity [1615] by Super 12 with 312 at 2
3042 Id : 917, {_}: negative_part (positive_part ?1615) =>= identity [1615] by Demod 903 with 298 at 1,2
3043 Id : 1615, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= greatest_lower_bound identity ?2652 [2652, 2651] by Super 1610 with 917 at 1,3
3044 Id : 1662, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= negative_part ?2652 [2652, 2651] by Demod 1615 with 312 at 3
3045 Id : 4459, {_}: multiply (inverse (positive_part ?6667)) identity =>= negative_part (inverse (positive_part ?6667)) [6667] by Super 4454 with 917 at 2,2
3046 Id : 4501, {_}: inverse (positive_part ?6667) =<= negative_part (inverse (positive_part ?6667)) [6667] by Demod 4459 with 1026 at 2
3047 Id : 4523, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= negative_part (inverse (positive_part ?6722)) [6722, 6721] by Super 1662 with 4501 at 2,2
3048 Id : 4568, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= inverse (positive_part ?6722) [6722, 6721] by Demod 4523 with 4501 at 3
3049 Id : 15267, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Demod 15140 with 4568 at 1,2
3050 Id : 4810, {_}: positive_part (inverse (negative_part ?7011)) =>= inverse (negative_part ?7011) [7011] by Demod 4660 with 298 at 2
3051 Id : 4822, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (negative_part (greatest_lower_bound ?7038 ?7039)) [7039, 7038] by Super 4810 with 321 at 1,1,2
3052 Id : 4871, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (greatest_lower_bound ?7038 (negative_part ?7039)) [7039, 7038] by Demod 4822 with 321 at 1,3
3053 Id : 15268, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15267 with 4871 at 3
3054 Id : 15269, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15268 with 18 at 2
3055 Id : 15270, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (negative_part ?18921) (positive_part (inverse ?18921))) [18921] by Demod 15269 with 5 at 1,3
3056 Id : 1594, {_}: greatest_lower_bound ?1607 (negative_part ?1608) =<= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 921 with 321 at 2
3057 Id : 15271, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 (negative_part (positive_part (inverse ?18921)))) [18921] by Demod 15270 with 1594 at 1,3
3058 Id : 15272, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 identity) [18921] by Demod 15271 with 917 at 2,1,3
3059 Id : 15273, {_}: positive_part (inverse ?18921) =>= inverse (negative_part ?18921) [18921] by Demod 15272 with 21 at 1,3
3060 Id : 15393, {_}: negative_part (inverse ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Super 14357 with 15273 at 1,1,3
3061 Id : 15435, {_}: inverse (positive_part ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Demod 15393 with 14275 at 2
3062 Id : 15436, {_}: inverse (positive_part ?19045) =<= inverse (multiply ?19045 (inverse (negative_part ?19045))) [19045] by Demod 15435 with 19 at 3
3063 Id : 15437, {_}: inverse (positive_part ?19045) =<= multiply (negative_part ?19045) (inverse ?19045) [19045] by Demod 15436 with 290 at 3
3064 Id : 15800, {_}: inverse ?19405 =<= multiply (inverse (negative_part ?19405)) (inverse (positive_part ?19405)) [19405] by Super 34 with 15437 at 2,3
3065 Id : 15843, {_}: inverse ?19405 =<= inverse (multiply (positive_part ?19405) (negative_part ?19405)) [19405] by Demod 15800 with 19 at 3
3066 Id : 20580, {_}: inverse (inverse ?23723) =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Super 18 with 15843 at 1,2
3067 Id : 20668, {_}: ?23723 =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Demod 20580 with 18 at 2
3068 Id : 20964, {_}: a =?= a [] by Demod 1 with 20668 at 3
3069 Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
3070 % SZS output end CNFRefutation for GRP167-2.p
3071 10052: solved GRP167-2.p in 3.352209 using kbo
3072 10052: status Unsatisfiable for GRP167-2.p
3073 NO CLASH, using fixed ground order
3075 10058: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3076 10058: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3078 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
3079 [8, 7, 6] by associativity ?6 ?7 ?8
3081 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3082 [11, 10] by symmetry_of_glb ?10 ?11
3084 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3085 [14, 13] by symmetry_of_lub ?13 ?14
3087 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3089 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3090 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3092 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3094 least_upper_bound (least_upper_bound ?20 ?21) ?22
3095 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3096 10058: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3097 10058: Id : 10, {_}:
3098 greatest_lower_bound ?26 ?26 =>= ?26
3099 [26] by idempotence_of_gld ?26
3100 10058: Id : 11, {_}:
3101 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3102 [29, 28] by lub_absorbtion ?28 ?29
3103 10058: Id : 12, {_}:
3104 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3105 [32, 31] by glb_absorbtion ?31 ?32
3106 10058: Id : 13, {_}:
3107 multiply ?34 (least_upper_bound ?35 ?36)
3109 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3110 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3111 10058: Id : 14, {_}:
3112 multiply ?38 (greatest_lower_bound ?39 ?40)
3114 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3115 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3116 10058: Id : 15, {_}:
3117 multiply (least_upper_bound ?42 ?43) ?44
3119 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3120 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3121 10058: Id : 16, {_}:
3122 multiply (greatest_lower_bound ?46 ?47) ?48
3124 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3125 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3126 10058: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
3127 10058: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
3128 10058: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
3129 10058: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
3132 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
3137 10058: least_upper_bound 16 2 0
3138 10058: inverse 1 1 0
3139 10058: identity 6 0 0
3140 10058: greatest_lower_bound 16 2 2 0,2
3141 10058: multiply 19 2 1 0,2,2
3142 10058: c 4 0 2 2,2,2
3143 10058: b 4 0 1 1,2,2
3145 NO CLASH, using fixed ground order
3147 10059: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3148 10059: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3150 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3151 [8, 7, 6] by associativity ?6 ?7 ?8
3153 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3154 [11, 10] by symmetry_of_glb ?10 ?11
3156 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3157 [14, 13] by symmetry_of_lub ?13 ?14
3159 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3161 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3162 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3164 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3166 least_upper_bound (least_upper_bound ?20 ?21) ?22
3167 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3168 NO CLASH, using fixed ground order
3170 10060: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3171 10060: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3173 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3174 [8, 7, 6] by associativity ?6 ?7 ?8
3176 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3177 [11, 10] by symmetry_of_glb ?10 ?11
3179 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3180 [14, 13] by symmetry_of_lub ?13 ?14
3182 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3184 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3185 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3186 10059: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3187 10059: Id : 10, {_}:
3188 greatest_lower_bound ?26 ?26 =>= ?26
3189 [26] by idempotence_of_gld ?26
3190 10059: Id : 11, {_}:
3191 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3192 [29, 28] by lub_absorbtion ?28 ?29
3193 10059: Id : 12, {_}:
3194 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3195 [32, 31] by glb_absorbtion ?31 ?32
3196 10059: Id : 13, {_}:
3197 multiply ?34 (least_upper_bound ?35 ?36)
3199 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3200 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3201 10059: Id : 14, {_}:
3202 multiply ?38 (greatest_lower_bound ?39 ?40)
3204 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3205 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3206 10059: Id : 15, {_}:
3207 multiply (least_upper_bound ?42 ?43) ?44
3209 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3210 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3211 10059: Id : 16, {_}:
3212 multiply (greatest_lower_bound ?46 ?47) ?48
3214 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3215 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3216 10059: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
3217 10059: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
3218 10059: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
3219 10059: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
3222 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
3227 10059: least_upper_bound 16 2 0
3228 10059: inverse 1 1 0
3229 10059: identity 6 0 0
3230 10059: greatest_lower_bound 16 2 2 0,2
3231 10059: multiply 19 2 1 0,2,2
3232 10059: c 4 0 2 2,2,2
3233 10059: b 4 0 1 1,2,2
3236 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3238 least_upper_bound (least_upper_bound ?20 ?21) ?22
3239 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3240 10060: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3241 10060: Id : 10, {_}:
3242 greatest_lower_bound ?26 ?26 =>= ?26
3243 [26] by idempotence_of_gld ?26
3244 10060: Id : 11, {_}:
3245 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3246 [29, 28] by lub_absorbtion ?28 ?29
3247 10060: Id : 12, {_}:
3248 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3249 [32, 31] by glb_absorbtion ?31 ?32
3250 10060: Id : 13, {_}:
3251 multiply ?34 (least_upper_bound ?35 ?36)
3253 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3254 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3255 10060: Id : 14, {_}:
3256 multiply ?38 (greatest_lower_bound ?39 ?40)
3258 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3259 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3260 10060: Id : 15, {_}:
3261 multiply (least_upper_bound ?42 ?43) ?44
3263 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3264 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3265 10060: Id : 16, {_}:
3266 multiply (greatest_lower_bound ?46 ?47) ?48
3268 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3269 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3270 10060: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
3271 10060: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
3272 10060: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
3273 10060: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
3276 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
3281 10060: least_upper_bound 16 2 0
3282 10060: inverse 1 1 0
3283 10060: identity 6 0 0
3284 10060: greatest_lower_bound 16 2 2 0,2
3285 10060: multiply 19 2 1 0,2,2
3286 10060: c 4 0 2 2,2,2
3287 10060: b 4 0 1 1,2,2
3289 % SZS status Timeout for GRP178-1.p
3290 NO CLASH, using fixed ground order
3292 10102: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3293 10102: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3295 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
3296 [8, 7, 6] by associativity ?6 ?7 ?8
3298 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3299 [11, 10] by symmetry_of_glb ?10 ?11
3301 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3302 [14, 13] by symmetry_of_lub ?13 ?14
3304 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3306 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3307 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3309 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3311 least_upper_bound (least_upper_bound ?20 ?21) ?22
3312 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3313 10102: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3314 10102: Id : 10, {_}:
3315 greatest_lower_bound ?26 ?26 =>= ?26
3316 [26] by idempotence_of_gld ?26
3317 10102: Id : 11, {_}:
3318 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3319 [29, 28] by lub_absorbtion ?28 ?29
3320 10102: Id : 12, {_}:
3321 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3322 [32, 31] by glb_absorbtion ?31 ?32
3323 10102: Id : 13, {_}:
3324 multiply ?34 (least_upper_bound ?35 ?36)
3326 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3327 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3328 10102: Id : 14, {_}:
3329 multiply ?38 (greatest_lower_bound ?39 ?40)
3331 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3332 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3333 10102: Id : 15, {_}:
3334 multiply (least_upper_bound ?42 ?43) ?44
3336 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3337 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3338 10102: Id : 16, {_}:
3339 multiply (greatest_lower_bound ?46 ?47) ?48
3341 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3342 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3343 10102: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
3344 10102: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
3345 10102: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
3346 10102: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
3349 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
3354 10102: least_upper_bound 13 2 0
3355 10102: inverse 1 1 0
3356 10102: identity 9 0 0
3357 10102: greatest_lower_bound 19 2 2 0,2
3358 10102: multiply 19 2 1 0,2,2
3359 10102: c 3 0 2 2,2,2
3360 10102: b 3 0 1 1,2,2
3362 NO CLASH, using fixed ground order
3364 10103: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3365 10103: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3367 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3368 [8, 7, 6] by associativity ?6 ?7 ?8
3370 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3371 [11, 10] by symmetry_of_glb ?10 ?11
3373 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3374 [14, 13] by symmetry_of_lub ?13 ?14
3376 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3378 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3379 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3381 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3383 least_upper_bound (least_upper_bound ?20 ?21) ?22
3384 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3385 10103: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3386 10103: Id : 10, {_}:
3387 greatest_lower_bound ?26 ?26 =>= ?26
3388 [26] by idempotence_of_gld ?26
3389 10103: Id : 11, {_}:
3390 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3391 [29, 28] by lub_absorbtion ?28 ?29
3392 10103: Id : 12, {_}:
3393 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3394 [32, 31] by glb_absorbtion ?31 ?32
3395 10103: Id : 13, {_}:
3396 multiply ?34 (least_upper_bound ?35 ?36)
3398 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3399 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3400 10103: Id : 14, {_}:
3401 multiply ?38 (greatest_lower_bound ?39 ?40)
3403 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3404 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3405 10103: Id : 15, {_}:
3406 multiply (least_upper_bound ?42 ?43) ?44
3408 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3409 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3410 10103: Id : 16, {_}:
3411 multiply (greatest_lower_bound ?46 ?47) ?48
3413 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3414 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3415 10103: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
3416 10103: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
3417 10103: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
3418 10103: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
3421 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
3426 10103: least_upper_bound 13 2 0
3427 10103: inverse 1 1 0
3428 10103: identity 9 0 0
3429 10103: greatest_lower_bound 19 2 2 0,2
3430 10103: multiply 19 2 1 0,2,2
3431 10103: c 3 0 2 2,2,2
3432 10103: b 3 0 1 1,2,2
3434 NO CLASH, using fixed ground order
3436 10104: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3437 10104: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3439 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3440 [8, 7, 6] by associativity ?6 ?7 ?8
3442 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3443 [11, 10] by symmetry_of_glb ?10 ?11
3445 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3446 [14, 13] by symmetry_of_lub ?13 ?14
3448 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3450 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3451 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3453 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3455 least_upper_bound (least_upper_bound ?20 ?21) ?22
3456 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3457 10104: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3458 10104: Id : 10, {_}:
3459 greatest_lower_bound ?26 ?26 =>= ?26
3460 [26] by idempotence_of_gld ?26
3461 10104: Id : 11, {_}:
3462 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3463 [29, 28] by lub_absorbtion ?28 ?29
3464 10104: Id : 12, {_}:
3465 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3466 [32, 31] by glb_absorbtion ?31 ?32
3467 10104: Id : 13, {_}:
3468 multiply ?34 (least_upper_bound ?35 ?36)
3470 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3471 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3472 10104: Id : 14, {_}:
3473 multiply ?38 (greatest_lower_bound ?39 ?40)
3475 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3476 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3477 10104: Id : 15, {_}:
3478 multiply (least_upper_bound ?42 ?43) ?44
3480 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3481 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3482 10104: Id : 16, {_}:
3483 multiply (greatest_lower_bound ?46 ?47) ?48
3485 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3486 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3487 10104: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
3488 10104: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
3489 10104: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
3490 10104: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
3493 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
3498 10104: least_upper_bound 13 2 0
3499 10104: inverse 1 1 0
3500 10104: identity 9 0 0
3501 10104: greatest_lower_bound 19 2 2 0,2
3502 10104: multiply 19 2 1 0,2,2
3503 10104: c 3 0 2 2,2,2
3504 10104: b 3 0 1 1,2,2
3506 % SZS status Timeout for GRP178-2.p
3507 CLASH, statistics insufficient
3509 10125: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3510 10125: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3512 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
3513 [8, 7, 6] by associativity ?6 ?7 ?8
3515 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3516 [11, 10] by symmetry_of_glb ?10 ?11
3518 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3519 [14, 13] by symmetry_of_lub ?13 ?14
3521 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3523 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3524 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3526 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3528 least_upper_bound (least_upper_bound ?20 ?21) ?22
3529 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3530 10125: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3531 10125: Id : 10, {_}:
3532 greatest_lower_bound ?26 ?26 =>= ?26
3533 [26] by idempotence_of_gld ?26
3534 10125: Id : 11, {_}:
3535 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3536 [29, 28] by lub_absorbtion ?28 ?29
3537 10125: Id : 12, {_}:
3538 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3539 [32, 31] by glb_absorbtion ?31 ?32
3540 10125: Id : 13, {_}:
3541 multiply ?34 (least_upper_bound ?35 ?36)
3543 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3544 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3545 10125: Id : 14, {_}:
3546 multiply ?38 (greatest_lower_bound ?39 ?40)
3548 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3549 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3550 10125: Id : 15, {_}:
3551 multiply (least_upper_bound ?42 ?43) ?44
3553 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3554 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3555 10125: Id : 16, {_}:
3556 multiply (greatest_lower_bound ?46 ?47) ?48
3558 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3559 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3560 10125: Id : 17, {_}:
3561 greatest_lower_bound a c =>= greatest_lower_bound b c
3563 10125: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
3564 10125: Id : 19, {_}:
3565 inverse (greatest_lower_bound ?52 ?53)
3567 least_upper_bound (inverse ?52) (inverse ?53)
3568 [53, 52] by p12x_3 ?52 ?53
3569 10125: Id : 20, {_}:
3570 inverse (least_upper_bound ?55 ?56)
3572 greatest_lower_bound (inverse ?55) (inverse ?56)
3573 [56, 55] by p12x_4 ?55 ?56
3575 10125: Id : 1, {_}: a =>= b [] by prove_p12x
3580 10125: least_upper_bound 17 2 0
3581 10125: greatest_lower_bound 17 2 0
3582 10125: inverse 7 1 0
3583 10125: multiply 18 2 0
3584 10125: identity 2 0 0
3587 CLASH, statistics insufficient
3589 10126: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3590 10126: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3592 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3593 [8, 7, 6] by associativity ?6 ?7 ?8
3595 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3596 [11, 10] by symmetry_of_glb ?10 ?11
3598 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3599 [14, 13] by symmetry_of_lub ?13 ?14
3601 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3603 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3604 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3606 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3608 least_upper_bound (least_upper_bound ?20 ?21) ?22
3609 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3610 10126: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3611 10126: Id : 10, {_}:
3612 greatest_lower_bound ?26 ?26 =>= ?26
3613 [26] by idempotence_of_gld ?26
3614 10126: Id : 11, {_}:
3615 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3616 [29, 28] by lub_absorbtion ?28 ?29
3617 10126: Id : 12, {_}:
3618 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3619 [32, 31] by glb_absorbtion ?31 ?32
3620 10126: Id : 13, {_}:
3621 multiply ?34 (least_upper_bound ?35 ?36)
3623 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3624 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3625 10126: Id : 14, {_}:
3626 multiply ?38 (greatest_lower_bound ?39 ?40)
3628 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3629 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3630 10126: Id : 15, {_}:
3631 multiply (least_upper_bound ?42 ?43) ?44
3633 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3634 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3635 10126: Id : 16, {_}:
3636 multiply (greatest_lower_bound ?46 ?47) ?48
3638 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3639 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3640 10126: Id : 17, {_}:
3641 greatest_lower_bound a c =>= greatest_lower_bound b c
3643 10126: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
3644 10126: Id : 19, {_}:
3645 inverse (greatest_lower_bound ?52 ?53)
3647 least_upper_bound (inverse ?52) (inverse ?53)
3648 [53, 52] by p12x_3 ?52 ?53
3649 10126: Id : 20, {_}:
3650 inverse (least_upper_bound ?55 ?56)
3652 greatest_lower_bound (inverse ?55) (inverse ?56)
3653 [56, 55] by p12x_4 ?55 ?56
3655 10126: Id : 1, {_}: a =>= b [] by prove_p12x
3660 10126: least_upper_bound 17 2 0
3661 10126: greatest_lower_bound 17 2 0
3662 10126: inverse 7 1 0
3663 10126: multiply 18 2 0
3664 10126: identity 2 0 0
3667 CLASH, statistics insufficient
3669 10127: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3670 10127: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3672 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3673 [8, 7, 6] by associativity ?6 ?7 ?8
3675 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3676 [11, 10] by symmetry_of_glb ?10 ?11
3678 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3679 [14, 13] by symmetry_of_lub ?13 ?14
3681 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3683 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3684 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3686 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3688 least_upper_bound (least_upper_bound ?20 ?21) ?22
3689 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3690 10127: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3691 10127: Id : 10, {_}:
3692 greatest_lower_bound ?26 ?26 =>= ?26
3693 [26] by idempotence_of_gld ?26
3694 10127: Id : 11, {_}:
3695 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3696 [29, 28] by lub_absorbtion ?28 ?29
3697 10127: Id : 12, {_}:
3698 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3699 [32, 31] by glb_absorbtion ?31 ?32
3700 10127: Id : 13, {_}:
3701 multiply ?34 (least_upper_bound ?35 ?36)
3703 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3704 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3705 10127: Id : 14, {_}:
3706 multiply ?38 (greatest_lower_bound ?39 ?40)
3708 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3709 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3710 10127: Id : 15, {_}:
3711 multiply (least_upper_bound ?42 ?43) ?44
3713 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3714 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3715 10127: Id : 16, {_}:
3716 multiply (greatest_lower_bound ?46 ?47) ?48
3718 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3719 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3720 10127: Id : 17, {_}:
3721 greatest_lower_bound a c =>= greatest_lower_bound b c
3723 10127: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
3724 10127: Id : 19, {_}:
3725 inverse (greatest_lower_bound ?52 ?53)
3727 least_upper_bound (inverse ?52) (inverse ?53)
3728 [53, 52] by p12x_3 ?52 ?53
3729 10127: Id : 20, {_}:
3730 inverse (least_upper_bound ?55 ?56)
3732 greatest_lower_bound (inverse ?55) (inverse ?56)
3733 [56, 55] by p12x_4 ?55 ?56
3735 10127: Id : 1, {_}: a =>= b [] by prove_p12x
3740 10127: least_upper_bound 17 2 0
3741 10127: greatest_lower_bound 17 2 0
3742 10127: inverse 7 1 0
3743 10127: multiply 18 2 0
3744 10127: identity 2 0 0
3747 % SZS status Timeout for GRP181-3.p
3748 NO CLASH, using fixed ground order
3750 10150: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3751 10150: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3753 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
3754 [8, 7, 6] by associativity ?6 ?7 ?8
3756 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3757 [11, 10] by symmetry_of_glb ?10 ?11
3759 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3760 [14, 13] by symmetry_of_lub ?13 ?14
3762 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3764 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3765 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3767 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3769 least_upper_bound (least_upper_bound ?20 ?21) ?22
3770 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3771 10150: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3772 10150: Id : 10, {_}:
3773 greatest_lower_bound ?26 ?26 =>= ?26
3774 [26] by idempotence_of_gld ?26
3775 10150: Id : 11, {_}:
3776 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3777 [29, 28] by lub_absorbtion ?28 ?29
3778 10150: Id : 12, {_}:
3779 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3780 [32, 31] by glb_absorbtion ?31 ?32
3781 10150: Id : 13, {_}:
3782 multiply ?34 (least_upper_bound ?35 ?36)
3784 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3785 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3786 10150: Id : 14, {_}:
3787 multiply ?38 (greatest_lower_bound ?39 ?40)
3789 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3790 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3791 10150: Id : 15, {_}:
3792 multiply (least_upper_bound ?42 ?43) ?44
3794 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3795 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3796 10150: Id : 16, {_}:
3797 multiply (greatest_lower_bound ?46 ?47) ?48
3799 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3800 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3801 10150: Id : 17, {_}: inverse identity =>= identity [] by p21_1
3802 10150: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
3803 10150: Id : 19, {_}:
3804 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
3805 [54, 53] by p21_3 ?53 ?54
3808 multiply (least_upper_bound a identity)
3809 (inverse (greatest_lower_bound a identity))
3811 multiply (inverse (greatest_lower_bound a identity))
3812 (least_upper_bound a identity)
3817 10150: multiply 22 2 2 0,2
3818 10150: inverse 9 1 2 0,2,2
3819 10150: greatest_lower_bound 15 2 2 0,1,2,2
3820 10150: least_upper_bound 15 2 2 0,1,2
3821 10150: identity 8 0 4 2,1,2
3822 10150: a 4 0 4 1,1,2
3823 NO CLASH, using fixed ground order
3825 10151: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3826 10151: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3828 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3829 [8, 7, 6] by associativity ?6 ?7 ?8
3831 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3832 [11, 10] by symmetry_of_glb ?10 ?11
3834 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3835 [14, 13] by symmetry_of_lub ?13 ?14
3837 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3839 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3840 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3842 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3844 least_upper_bound (least_upper_bound ?20 ?21) ?22
3845 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3846 10151: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3847 10151: Id : 10, {_}:
3848 greatest_lower_bound ?26 ?26 =>= ?26
3849 [26] by idempotence_of_gld ?26
3850 10151: Id : 11, {_}:
3851 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3852 [29, 28] by lub_absorbtion ?28 ?29
3853 10151: Id : 12, {_}:
3854 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3855 [32, 31] by glb_absorbtion ?31 ?32
3856 10151: Id : 13, {_}:
3857 multiply ?34 (least_upper_bound ?35 ?36)
3859 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3860 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3861 10151: Id : 14, {_}:
3862 multiply ?38 (greatest_lower_bound ?39 ?40)
3864 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3865 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3866 10151: Id : 15, {_}:
3867 multiply (least_upper_bound ?42 ?43) ?44
3869 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3870 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3871 10151: Id : 16, {_}:
3872 multiply (greatest_lower_bound ?46 ?47) ?48
3874 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3875 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3876 10151: Id : 17, {_}: inverse identity =>= identity [] by p21_1
3877 10151: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
3878 10151: Id : 19, {_}:
3879 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
3880 [54, 53] by p21_3 ?53 ?54
3883 multiply (least_upper_bound a identity)
3884 (inverse (greatest_lower_bound a identity))
3886 multiply (inverse (greatest_lower_bound a identity))
3887 (least_upper_bound a identity)
3892 10151: multiply 22 2 2 0,2
3893 10151: inverse 9 1 2 0,2,2
3894 10151: greatest_lower_bound 15 2 2 0,1,2,2
3895 10151: least_upper_bound 15 2 2 0,1,2
3896 10151: identity 8 0 4 2,1,2
3897 10151: a 4 0 4 1,1,2
3898 NO CLASH, using fixed ground order
3900 10152: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3901 10152: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3903 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
3904 [8, 7, 6] by associativity ?6 ?7 ?8
3906 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3907 [11, 10] by symmetry_of_glb ?10 ?11
3909 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3910 [14, 13] by symmetry_of_lub ?13 ?14
3912 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3914 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3915 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3917 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3919 least_upper_bound (least_upper_bound ?20 ?21) ?22
3920 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3921 10152: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3922 10152: Id : 10, {_}:
3923 greatest_lower_bound ?26 ?26 =>= ?26
3924 [26] by idempotence_of_gld ?26
3925 10152: Id : 11, {_}:
3926 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
3927 [29, 28] by lub_absorbtion ?28 ?29
3928 10152: Id : 12, {_}:
3929 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
3930 [32, 31] by glb_absorbtion ?31 ?32
3931 10152: Id : 13, {_}:
3932 multiply ?34 (least_upper_bound ?35 ?36)
3934 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
3935 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
3936 10152: Id : 14, {_}:
3937 multiply ?38 (greatest_lower_bound ?39 ?40)
3939 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
3940 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
3941 10152: Id : 15, {_}:
3942 multiply (least_upper_bound ?42 ?43) ?44
3944 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
3945 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
3946 10152: Id : 16, {_}:
3947 multiply (greatest_lower_bound ?46 ?47) ?48
3949 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
3950 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
3951 10152: Id : 17, {_}: inverse identity =>= identity [] by p21_1
3952 10152: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
3953 10152: Id : 19, {_}:
3954 inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
3955 [54, 53] by p21_3 ?53 ?54
3958 multiply (least_upper_bound a identity)
3959 (inverse (greatest_lower_bound a identity))
3961 multiply (inverse (greatest_lower_bound a identity))
3962 (least_upper_bound a identity)
3967 10152: multiply 22 2 2 0,2
3968 10152: inverse 9 1 2 0,2,2
3969 10152: greatest_lower_bound 15 2 2 0,1,2,2
3970 10152: least_upper_bound 15 2 2 0,1,2
3971 10152: identity 8 0 4 2,1,2
3972 10152: a 4 0 4 1,1,2
3973 % SZS status Timeout for GRP184-2.p
3974 NO CLASH, using fixed ground order
3976 10174: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
3977 10174: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
3979 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
3980 [8, 7, 6] by associativity ?6 ?7 ?8
3982 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
3983 [11, 10] by symmetry_of_glb ?10 ?11
3985 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
3986 [14, 13] by symmetry_of_lub ?13 ?14
3988 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
3990 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
3991 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
3993 least_upper_bound ?20 (least_upper_bound ?21 ?22)
3995 least_upper_bound (least_upper_bound ?20 ?21) ?22
3996 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
3997 10174: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
3998 10174: Id : 10, {_}:
3999 greatest_lower_bound ?26 ?26 =>= ?26
4000 [26] by idempotence_of_gld ?26
4001 10174: Id : 11, {_}:
4002 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
4003 [29, 28] by lub_absorbtion ?28 ?29
4004 10174: Id : 12, {_}:
4005 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
4006 [32, 31] by glb_absorbtion ?31 ?32
4007 10174: Id : 13, {_}:
4008 multiply ?34 (least_upper_bound ?35 ?36)
4010 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
4011 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4012 10174: Id : 14, {_}:
4013 multiply ?38 (greatest_lower_bound ?39 ?40)
4015 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
4016 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
4017 10174: Id : 15, {_}:
4018 multiply (least_upper_bound ?42 ?43) ?44
4020 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
4021 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4022 10174: Id : 16, {_}:
4023 multiply (greatest_lower_bound ?46 ?47) ?48
4025 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
4026 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
4029 least_upper_bound (least_upper_bound (multiply a b) identity)
4030 (multiply (least_upper_bound a identity)
4031 (least_upper_bound b identity))
4033 multiply (least_upper_bound a identity)
4034 (least_upper_bound b identity)
4039 10174: greatest_lower_bound 13 2 0
4040 10174: inverse 1 1 0
4041 10174: least_upper_bound 19 2 6 0,2
4042 10174: identity 7 0 5 2,1,2
4043 10174: multiply 21 2 3 0,1,1,2
4044 10174: b 3 0 3 2,1,1,2
4045 10174: a 3 0 3 1,1,1,2
4046 NO CLASH, using fixed ground order
4048 10175: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4049 10175: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
4051 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
4052 [8, 7, 6] by associativity ?6 ?7 ?8
4054 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
4055 [11, 10] by symmetry_of_glb ?10 ?11
4057 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
4058 [14, 13] by symmetry_of_lub ?13 ?14
4060 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
4062 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
4063 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
4065 least_upper_bound ?20 (least_upper_bound ?21 ?22)
4067 least_upper_bound (least_upper_bound ?20 ?21) ?22
4068 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
4069 10175: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
4070 10175: Id : 10, {_}:
4071 greatest_lower_bound ?26 ?26 =>= ?26
4072 [26] by idempotence_of_gld ?26
4073 10175: Id : 11, {_}:
4074 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
4075 [29, 28] by lub_absorbtion ?28 ?29
4076 10175: Id : 12, {_}:
4077 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
4078 [32, 31] by glb_absorbtion ?31 ?32
4079 10175: Id : 13, {_}:
4080 multiply ?34 (least_upper_bound ?35 ?36)
4082 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
4083 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4084 10175: Id : 14, {_}:
4085 multiply ?38 (greatest_lower_bound ?39 ?40)
4087 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
4088 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
4089 10175: Id : 15, {_}:
4090 multiply (least_upper_bound ?42 ?43) ?44
4092 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
4093 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4094 10175: Id : 16, {_}:
4095 multiply (greatest_lower_bound ?46 ?47) ?48
4097 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
4098 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
4101 least_upper_bound (least_upper_bound (multiply a b) identity)
4102 (multiply (least_upper_bound a identity)
4103 (least_upper_bound b identity))
4105 multiply (least_upper_bound a identity)
4106 (least_upper_bound b identity)
4111 10175: greatest_lower_bound 13 2 0
4112 10175: inverse 1 1 0
4113 10175: least_upper_bound 19 2 6 0,2
4114 10175: identity 7 0 5 2,1,2
4115 10175: multiply 21 2 3 0,1,1,2
4116 10175: b 3 0 3 2,1,1,2
4117 10175: a 3 0 3 1,1,1,2
4118 NO CLASH, using fixed ground order
4120 10176: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4121 10176: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
4123 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
4124 [8, 7, 6] by associativity ?6 ?7 ?8
4126 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
4127 [11, 10] by symmetry_of_glb ?10 ?11
4129 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
4130 [14, 13] by symmetry_of_lub ?13 ?14
4132 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
4134 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
4135 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
4137 least_upper_bound ?20 (least_upper_bound ?21 ?22)
4139 least_upper_bound (least_upper_bound ?20 ?21) ?22
4140 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
4141 10176: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
4142 10176: Id : 10, {_}:
4143 greatest_lower_bound ?26 ?26 =>= ?26
4144 [26] by idempotence_of_gld ?26
4145 10176: Id : 11, {_}:
4146 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
4147 [29, 28] by lub_absorbtion ?28 ?29
4148 10176: Id : 12, {_}:
4149 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
4150 [32, 31] by glb_absorbtion ?31 ?32
4151 10176: Id : 13, {_}:
4152 multiply ?34 (least_upper_bound ?35 ?36)
4154 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
4155 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4156 10176: Id : 14, {_}:
4157 multiply ?38 (greatest_lower_bound ?39 ?40)
4159 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
4160 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
4161 10176: Id : 15, {_}:
4162 multiply (least_upper_bound ?42 ?43) ?44
4164 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
4165 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4166 10176: Id : 16, {_}:
4167 multiply (greatest_lower_bound ?46 ?47) ?48
4169 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
4170 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
4173 least_upper_bound (least_upper_bound (multiply a b) identity)
4174 (multiply (least_upper_bound a identity)
4175 (least_upper_bound b identity))
4177 multiply (least_upper_bound a identity)
4178 (least_upper_bound b identity)
4183 10176: greatest_lower_bound 13 2 0
4184 10176: inverse 1 1 0
4185 10176: least_upper_bound 19 2 6 0,2
4186 10176: identity 7 0 5 2,1,2
4187 10176: multiply 21 2 3 0,1,1,2
4188 10176: b 3 0 3 2,1,1,2
4189 10176: a 3 0 3 1,1,1,2
4192 Found proof, 4.014671s
4193 % SZS status Unsatisfiable for GRP185-1.p
4194 % SZS output start CNFRefutation for GRP185-1.p
4195 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
4196 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
4197 Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
4198 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4199 Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4200 Id : 67, {_}: least_upper_bound ?151 (least_upper_bound ?152 ?153) =<= least_upper_bound (least_upper_bound ?151 ?152) ?153 [153, 152, 151] by associativity_of_lub ?151 ?152 ?153
4201 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
4202 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4203 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
4204 Id : 68, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =<= least_upper_bound (least_upper_bound ?156 ?155) ?157 [157, 156, 155] by Super 67 with 6 at 1,3
4205 Id : 74, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =?= least_upper_bound ?156 (least_upper_bound ?155 ?157) [157, 156, 155] by Demod 68 with 8 at 3
4206 Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
4207 Id : 562, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
4208 Id : 564, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 562 with 3 at 2,3
4209 Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
4210 Id : 570, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 562 with 27 at 2,3
4211 Id : 855, {_}: ?599 =<= multiply ?599 identity [599] by Demod 564 with 570 at 3
4212 Id : 65, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
4213 Id : 85, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3
4214 Id : 5149, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) === least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5148 with 74 at 2,2
4215 Id : 5148, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5147 with 9 at 2,2,2,2
4216 Id : 5147, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5146 with 2 at 1,2,2,2
4217 Id : 5146, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5145 with 85 at 2
4218 Id : 5145, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5144 with 74 at 3
4219 Id : 5144, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5143 with 65 at 2,2,2,2
4220 Id : 5143, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5142 with 855 at 1,2,2,2
4221 Id : 5142, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5141 with 2 at 1,2,2
4222 Id : 5141, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5140 with 855 at 1,2,2,3
4223 Id : 5140, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5139 with 2 at 1,2,3
4224 Id : 5139, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5138 with 8 at 2,2
4225 Id : 5138, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5137 with 8 at 2,3
4226 Id : 5137, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5136 with 2 at 1,3
4227 Id : 5136, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5135 with 74 at 2,2
4228 Id : 5135, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5134 with 74 at 3
4229 Id : 5134, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5133 with 15 at 2,2,2,2
4230 Id : 5133, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5132 with 15 at 1,2,2,2
4231 Id : 5132, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5131 with 15 at 2,3
4232 Id : 5131, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 5130 with 15 at 1,3
4233 Id : 5130, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 237 with 74 at 2
4234 Id : 237, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 236 with 6 at 1,2,2,2,2
4235 Id : 236, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 235 with 6 at 1,1,2,2,2
4236 Id : 235, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 234 with 6 at 1,2,3
4237 Id : 234, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b) [] by Demod 233 with 6 at 1,1,3
4238 Id : 233, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 232 with 6 at 2,2,2
4239 Id : 232, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 231 with 6 at 3
4240 Id : 231, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 230 with 13 at 2,2,2
4241 Id : 230, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 229 with 13 at 3
4242 Id : 229, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 8 at 2
4243 Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
4244 % SZS output end CNFRefutation for GRP185-1.p
4245 10176: solved GRP185-1.p in 1.916119 using lpo
4246 10176: status Unsatisfiable for GRP185-1.p
4247 NO CLASH, using fixed ground order
4249 10187: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4250 10187: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
4252 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
4253 [8, 7, 6] by associativity ?6 ?7 ?8
4255 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
4256 [11, 10] by symmetry_of_glb ?10 ?11
4258 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
4259 [14, 13] by symmetry_of_lub ?13 ?14
4261 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
4263 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
4264 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
4266 least_upper_bound ?20 (least_upper_bound ?21 ?22)
4268 least_upper_bound (least_upper_bound ?20 ?21) ?22
4269 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
4270 10187: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
4271 10187: Id : 10, {_}:
4272 greatest_lower_bound ?26 ?26 =>= ?26
4273 [26] by idempotence_of_gld ?26
4274 10187: Id : 11, {_}:
4275 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
4276 [29, 28] by lub_absorbtion ?28 ?29
4277 10187: Id : 12, {_}:
4278 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
4279 [32, 31] by glb_absorbtion ?31 ?32
4280 10187: Id : 13, {_}:
4281 multiply ?34 (least_upper_bound ?35 ?36)
4283 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
4284 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4285 10187: Id : 14, {_}:
4286 multiply ?38 (greatest_lower_bound ?39 ?40)
4288 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
4289 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
4290 10187: Id : 15, {_}:
4291 multiply (least_upper_bound ?42 ?43) ?44
4293 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
4294 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4295 10187: Id : 16, {_}:
4296 multiply (greatest_lower_bound ?46 ?47) ?48
4298 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
4299 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
4300 10187: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
4301 10187: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
4302 10187: Id : 19, {_}:
4303 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
4304 [54, 53] by p22a_3 ?53 ?54
4307 least_upper_bound (least_upper_bound (multiply a b) identity)
4308 (multiply (least_upper_bound a identity)
4309 (least_upper_bound b identity))
4311 multiply (least_upper_bound a identity)
4312 (least_upper_bound b identity)
4317 10187: greatest_lower_bound 13 2 0
4318 10187: inverse 7 1 0
4319 10187: least_upper_bound 19 2 6 0,2
4320 10187: identity 9 0 5 2,1,2
4321 10187: multiply 23 2 3 0,1,1,2
4322 10187: b 3 0 3 2,1,1,2
4323 10187: a 3 0 3 1,1,1,2
4324 NO CLASH, using fixed ground order
4326 10188: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4327 10188: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
4329 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
4330 [8, 7, 6] by associativity ?6 ?7 ?8
4332 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
4333 [11, 10] by symmetry_of_glb ?10 ?11
4335 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
4336 [14, 13] by symmetry_of_lub ?13 ?14
4338 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
4340 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
4341 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
4343 least_upper_bound ?20 (least_upper_bound ?21 ?22)
4345 least_upper_bound (least_upper_bound ?20 ?21) ?22
4346 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
4347 10188: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
4348 10188: Id : 10, {_}:
4349 greatest_lower_bound ?26 ?26 =>= ?26
4350 [26] by idempotence_of_gld ?26
4351 10188: Id : 11, {_}:
4352 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
4353 [29, 28] by lub_absorbtion ?28 ?29
4354 10188: Id : 12, {_}:
4355 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
4356 [32, 31] by glb_absorbtion ?31 ?32
4357 10188: Id : 13, {_}:
4358 multiply ?34 (least_upper_bound ?35 ?36)
4360 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
4361 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4362 10188: Id : 14, {_}:
4363 multiply ?38 (greatest_lower_bound ?39 ?40)
4365 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
4366 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
4367 10188: Id : 15, {_}:
4368 multiply (least_upper_bound ?42 ?43) ?44
4370 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
4371 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4372 10188: Id : 16, {_}:
4373 multiply (greatest_lower_bound ?46 ?47) ?48
4375 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
4376 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
4377 10188: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
4378 10188: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
4379 10188: Id : 19, {_}:
4380 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
4381 [54, 53] by p22a_3 ?53 ?54
4384 least_upper_bound (least_upper_bound (multiply a b) identity)
4385 (multiply (least_upper_bound a identity)
4386 (least_upper_bound b identity))
4388 multiply (least_upper_bound a identity)
4389 (least_upper_bound b identity)
4394 10188: greatest_lower_bound 13 2 0
4395 10188: inverse 7 1 0
4396 10188: least_upper_bound 19 2 6 0,2
4397 10188: identity 9 0 5 2,1,2
4398 10188: multiply 23 2 3 0,1,1,2
4399 10188: b 3 0 3 2,1,1,2
4400 10188: a 3 0 3 1,1,1,2
4401 NO CLASH, using fixed ground order
4403 10189: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4404 10189: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
4406 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
4407 [8, 7, 6] by associativity ?6 ?7 ?8
4409 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
4410 [11, 10] by symmetry_of_glb ?10 ?11
4412 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
4413 [14, 13] by symmetry_of_lub ?13 ?14
4415 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
4417 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
4418 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
4420 least_upper_bound ?20 (least_upper_bound ?21 ?22)
4422 least_upper_bound (least_upper_bound ?20 ?21) ?22
4423 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
4424 10189: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
4425 10189: Id : 10, {_}:
4426 greatest_lower_bound ?26 ?26 =>= ?26
4427 [26] by idempotence_of_gld ?26
4428 10189: Id : 11, {_}:
4429 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
4430 [29, 28] by lub_absorbtion ?28 ?29
4431 10189: Id : 12, {_}:
4432 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
4433 [32, 31] by glb_absorbtion ?31 ?32
4434 10189: Id : 13, {_}:
4435 multiply ?34 (least_upper_bound ?35 ?36)
4437 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
4438 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4439 10189: Id : 14, {_}:
4440 multiply ?38 (greatest_lower_bound ?39 ?40)
4442 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
4443 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
4444 10189: Id : 15, {_}:
4445 multiply (least_upper_bound ?42 ?43) ?44
4447 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
4448 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4449 10189: Id : 16, {_}:
4450 multiply (greatest_lower_bound ?46 ?47) ?48
4452 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
4453 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
4454 10189: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
4455 10189: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
4456 10189: Id : 19, {_}:
4457 inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
4458 [54, 53] by p22a_3 ?53 ?54
4461 least_upper_bound (least_upper_bound (multiply a b) identity)
4462 (multiply (least_upper_bound a identity)
4463 (least_upper_bound b identity))
4465 multiply (least_upper_bound a identity)
4466 (least_upper_bound b identity)
4471 10189: greatest_lower_bound 13 2 0
4472 10189: inverse 7 1 0
4473 10189: least_upper_bound 19 2 6 0,2
4474 10189: identity 9 0 5 2,1,2
4475 10189: multiply 23 2 3 0,1,1,2
4476 10189: b 3 0 3 2,1,1,2
4477 10189: a 3 0 3 1,1,1,2
4480 Found proof, 5.587205s
4481 % SZS status Unsatisfiable for GRP185-2.p
4482 % SZS output start CNFRefutation for GRP185-2.p
4483 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
4484 Id : 17, {_}: inverse identity =>= identity [] by p22a_1
4485 Id : 506, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521
4486 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4487 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
4488 Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
4489 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
4490 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
4491 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
4492 Id : 782, {_}: least_upper_bound ?667 (least_upper_bound ?667 ?668) =>= least_upper_bound ?667 ?668 [668, 667] by Super 8 with 9 at 1,3
4493 Id : 1203, {_}: least_upper_bound ?943 (least_upper_bound ?944 ?943) =>= least_upper_bound ?943 ?944 [944, 943] by Super 782 with 6 at 2,2
4494 Id : 1211, {_}: least_upper_bound ?966 (least_upper_bound ?967 (least_upper_bound ?968 ?966)) =>= least_upper_bound ?966 (least_upper_bound ?967 ?968) [968, 967, 966] by Super 1203 with 8 at 2,2
4495 Id : 507, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 506 with 17 at 2,3
4496 Id : 571, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 507 with 2 at 1,2
4497 Id : 573, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 571 with 18 at 1,3
4498 Id : 581, {_}: ?572 =<= multiply ?572 identity [572] by Demod 573 with 18 at 2
4499 Id : 88, {_}: least_upper_bound ?186 (least_upper_bound ?186 ?187) =>= least_upper_bound ?186 ?187 [187, 186] by Super 8 with 9 at 1,3
4500 Id : 3310, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) === least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3309 with 88 at 2
4501 Id : 3309, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3308 with 2 at 1,2,2,2,2
4502 Id : 3308, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3307 with 581 at 1,2,2,2
4503 Id : 3307, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3306 with 2 at 1,2,2
4504 Id : 3306, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3305 with 8 at 2,2
4505 Id : 3305, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3304 with 8 at 2,2
4506 Id : 3304, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b)) (multiply a b)) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3303 with 6 at 2,2
4507 Id : 3303, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3302 with 2 at 1,2,2,3
4508 Id : 3302, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3301 with 581 at 1,2,3
4509 Id : 3301, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3300 with 2 at 1,3
4510 Id : 3300, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3299 with 1211 at 2,2
4511 Id : 3299, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3298 with 8 at 3
4512 Id : 3298, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3297 with 15 at 2,2,2,2
4513 Id : 3297, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3296 with 15 at 1,2,2,2
4514 Id : 3296, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3295 with 15 at 2,3
4515 Id : 3295, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 3294 with 15 at 1,3
4516 Id : 3294, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3293 with 13 at 2,2,2
4517 Id : 3293, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3292 with 13 at 3
4518 Id : 3292, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 67 with 8 at 2
4519 Id : 67, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 66 with 6 at 2,3
4520 Id : 66, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound identity a) (least_upper_bound b identity) [] by Demod 65 with 6 at 1,3
4521 Id : 65, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 64 with 6 at 2,2,2
4522 Id : 64, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound b identity)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 63 with 6 at 1,2,2
4523 Id : 63, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 6 at 1,2
4524 Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
4525 % SZS output end CNFRefutation for GRP185-2.p
4526 10189: solved GRP185-2.p in 0.988061 using lpo
4527 10189: status Unsatisfiable for GRP185-2.p
4528 CLASH, statistics insufficient
4530 10194: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4531 10194: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4533 multiply ?6 (left_division ?6 ?7) =>= ?7
4534 [7, 6] by multiply_left_division ?6 ?7
4536 left_division ?9 (multiply ?9 ?10) =>= ?10
4537 [10, 9] by left_division_multiply ?9 ?10
4539 multiply (right_division ?12 ?13) ?13 =>= ?12
4540 [13, 12] by multiply_right_division ?12 ?13
4542 right_division (multiply ?15 ?16) ?16 =>= ?15
4543 [16, 15] by right_division_multiply ?15 ?16
4545 multiply ?18 (right_inverse ?18) =>= identity
4546 [18] by right_inverse ?18
4548 multiply (left_inverse ?20) ?20 =>= identity
4549 [20] by left_inverse ?20
4550 10194: Id : 10, {_}:
4551 multiply (multiply ?22 (multiply ?23 ?24)) ?22
4553 multiply (multiply ?22 ?23) (multiply ?24 ?22)
4554 [24, 23, 22] by moufang1 ?22 ?23 ?24
4557 multiply (multiply (multiply a b) c) b
4559 multiply a (multiply b (multiply c b))
4560 [] by prove_moufang2
4564 10194: left_inverse 1 1 0
4565 10194: right_inverse 1 1 0
4566 10194: right_division 2 2 0
4567 10194: left_division 2 2 0
4568 10194: identity 4 0 0
4569 10194: c 2 0 2 2,1,2
4570 10194: multiply 20 2 6 0,2
4571 10194: b 4 0 4 2,1,1,2
4572 10194: a 2 0 2 1,1,1,2
4573 CLASH, statistics insufficient
4575 10195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4576 10195: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4578 multiply ?6 (left_division ?6 ?7) =>= ?7
4579 [7, 6] by multiply_left_division ?6 ?7
4581 left_division ?9 (multiply ?9 ?10) =>= ?10
4582 [10, 9] by left_division_multiply ?9 ?10
4584 multiply (right_division ?12 ?13) ?13 =>= ?12
4585 [13, 12] by multiply_right_division ?12 ?13
4587 right_division (multiply ?15 ?16) ?16 =>= ?15
4588 [16, 15] by right_division_multiply ?15 ?16
4590 multiply ?18 (right_inverse ?18) =>= identity
4591 [18] by right_inverse ?18
4593 multiply (left_inverse ?20) ?20 =>= identity
4594 [20] by left_inverse ?20
4595 10195: Id : 10, {_}:
4596 multiply (multiply ?22 (multiply ?23 ?24)) ?22
4598 multiply (multiply ?22 ?23) (multiply ?24 ?22)
4599 [24, 23, 22] by moufang1 ?22 ?23 ?24
4602 multiply (multiply (multiply a b) c) b
4604 multiply a (multiply b (multiply c b))
4605 [] by prove_moufang2
4609 10195: left_inverse 1 1 0
4610 10195: right_inverse 1 1 0
4611 10195: right_division 2 2 0
4612 10195: left_division 2 2 0
4613 10195: identity 4 0 0
4614 10195: c 2 0 2 2,1,2
4615 10195: multiply 20 2 6 0,2
4616 10195: b 4 0 4 2,1,1,2
4617 10195: a 2 0 2 1,1,1,2
4618 CLASH, statistics insufficient
4620 10196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4621 10196: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4623 multiply ?6 (left_division ?6 ?7) =>= ?7
4624 [7, 6] by multiply_left_division ?6 ?7
4626 left_division ?9 (multiply ?9 ?10) =>= ?10
4627 [10, 9] by left_division_multiply ?9 ?10
4629 multiply (right_division ?12 ?13) ?13 =>= ?12
4630 [13, 12] by multiply_right_division ?12 ?13
4632 right_division (multiply ?15 ?16) ?16 =>= ?15
4633 [16, 15] by right_division_multiply ?15 ?16
4635 multiply ?18 (right_inverse ?18) =>= identity
4636 [18] by right_inverse ?18
4638 multiply (left_inverse ?20) ?20 =>= identity
4639 [20] by left_inverse ?20
4640 10196: Id : 10, {_}:
4641 multiply (multiply ?22 (multiply ?23 ?24)) ?22
4643 multiply (multiply ?22 ?23) (multiply ?24 ?22)
4644 [24, 23, 22] by moufang1 ?22 ?23 ?24
4647 multiply (multiply (multiply a b) c) b
4649 multiply a (multiply b (multiply c b))
4650 [] by prove_moufang2
4654 10196: left_inverse 1 1 0
4655 10196: right_inverse 1 1 0
4656 10196: right_division 2 2 0
4657 10196: left_division 2 2 0
4658 10196: identity 4 0 0
4659 10196: c 2 0 2 2,1,2
4660 10196: multiply 20 2 6 0,2
4661 10196: b 4 0 4 2,1,1,2
4662 10196: a 2 0 2 1,1,1,2
4663 % SZS status Timeout for GRP200-1.p
4664 CLASH, statistics insufficient
4666 10959: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4667 10959: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4669 multiply ?6 (left_division ?6 ?7) =>= ?7
4670 [7, 6] by multiply_left_division ?6 ?7
4672 left_division ?9 (multiply ?9 ?10) =>= ?10
4673 [10, 9] by left_division_multiply ?9 ?10
4675 multiply (right_division ?12 ?13) ?13 =>= ?12
4676 [13, 12] by multiply_right_division ?12 ?13
4678 right_division (multiply ?15 ?16) ?16 =>= ?15
4679 [16, 15] by right_division_multiply ?15 ?16
4681 multiply ?18 (right_inverse ?18) =>= identity
4682 [18] by right_inverse ?18
4684 multiply (left_inverse ?20) ?20 =>= identity
4685 [20] by left_inverse ?20
4686 10959: Id : 10, {_}:
4687 multiply (multiply (multiply ?22 ?23) ?24) ?23
4689 multiply ?22 (multiply ?23 (multiply ?24 ?23))
4690 [24, 23, 22] by moufang2 ?22 ?23 ?24
4693 multiply (multiply (multiply a b) a) c
4695 multiply a (multiply b (multiply a c))
4696 [] by prove_moufang3
4700 10959: left_inverse 1 1 0
4701 10959: right_inverse 1 1 0
4702 10959: right_division 2 2 0
4703 10959: left_division 2 2 0
4704 10959: identity 4 0 0
4706 10959: multiply 20 2 6 0,2
4707 10959: b 2 0 2 2,1,1,2
4708 10959: a 4 0 4 1,1,1,2
4709 CLASH, statistics insufficient
4711 10960: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4712 10960: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4714 multiply ?6 (left_division ?6 ?7) =>= ?7
4715 [7, 6] by multiply_left_division ?6 ?7
4717 left_division ?9 (multiply ?9 ?10) =>= ?10
4718 [10, 9] by left_division_multiply ?9 ?10
4720 multiply (right_division ?12 ?13) ?13 =>= ?12
4721 [13, 12] by multiply_right_division ?12 ?13
4723 right_division (multiply ?15 ?16) ?16 =>= ?15
4724 [16, 15] by right_division_multiply ?15 ?16
4726 multiply ?18 (right_inverse ?18) =>= identity
4727 [18] by right_inverse ?18
4729 multiply (left_inverse ?20) ?20 =>= identity
4730 [20] by left_inverse ?20
4731 10960: Id : 10, {_}:
4732 multiply (multiply (multiply ?22 ?23) ?24) ?23
4734 multiply ?22 (multiply ?23 (multiply ?24 ?23))
4735 [24, 23, 22] by moufang2 ?22 ?23 ?24
4738 multiply (multiply (multiply a b) a) c
4740 multiply a (multiply b (multiply a c))
4741 [] by prove_moufang3
4745 10960: left_inverse 1 1 0
4746 10960: right_inverse 1 1 0
4747 10960: right_division 2 2 0
4748 10960: left_division 2 2 0
4749 10960: identity 4 0 0
4751 10960: multiply 20 2 6 0,2
4752 10960: b 2 0 2 2,1,1,2
4753 10960: a 4 0 4 1,1,1,2
4754 CLASH, statistics insufficient
4756 10961: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4757 10961: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4759 multiply ?6 (left_division ?6 ?7) =>= ?7
4760 [7, 6] by multiply_left_division ?6 ?7
4762 left_division ?9 (multiply ?9 ?10) =>= ?10
4763 [10, 9] by left_division_multiply ?9 ?10
4765 multiply (right_division ?12 ?13) ?13 =>= ?12
4766 [13, 12] by multiply_right_division ?12 ?13
4768 right_division (multiply ?15 ?16) ?16 =>= ?15
4769 [16, 15] by right_division_multiply ?15 ?16
4771 multiply ?18 (right_inverse ?18) =>= identity
4772 [18] by right_inverse ?18
4774 multiply (left_inverse ?20) ?20 =>= identity
4775 [20] by left_inverse ?20
4776 10961: Id : 10, {_}:
4777 multiply (multiply (multiply ?22 ?23) ?24) ?23
4779 multiply ?22 (multiply ?23 (multiply ?24 ?23))
4780 [24, 23, 22] by moufang2 ?22 ?23 ?24
4783 multiply (multiply (multiply a b) a) c
4785 multiply a (multiply b (multiply a c))
4786 [] by prove_moufang3
4790 10961: left_inverse 1 1 0
4791 10961: right_inverse 1 1 0
4792 10961: right_division 2 2 0
4793 10961: left_division 2 2 0
4794 10961: identity 4 0 0
4796 10961: multiply 20 2 6 0,2
4797 10961: b 2 0 2 2,1,1,2
4798 10961: a 4 0 4 1,1,1,2
4801 Found proof, 24.390962s
4802 % SZS status Unsatisfiable for GRP201-1.p
4803 % SZS output start CNFRefutation for GRP201-1.p
4804 Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
4805 Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
4806 Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
4807 Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
4808 Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4809 Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
4810 Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?24) ?23 =>= multiply ?22 (multiply ?23 (multiply ?24 ?23)) [24, 23, 22] by moufang2 ?22 ?23 ?24
4811 Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
4812 Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
4813 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4814 Id : 54, {_}: multiply (multiply (multiply ?119 ?120) ?121) ?120 =>= multiply ?119 (multiply ?120 (multiply ?121 ?120)) [121, 120, 119] by moufang2 ?119 ?120 ?121
4815 Id : 55, {_}: multiply (multiply ?123 ?124) ?123 =<= multiply identity (multiply ?123 (multiply ?124 ?123)) [124, 123] by Super 54 with 2 at 1,1,2
4816 Id : 71, {_}: multiply (multiply ?123 ?124) ?123 =>= multiply ?123 (multiply ?124 ?123) [124, 123] by Demod 55 with 2 at 3
4817 Id : 897, {_}: right_division (multiply ?1221 (multiply ?1222 (multiply ?1223 ?1222))) ?1222 =>= multiply (multiply ?1221 ?1222) ?1223 [1223, 1222, 1221] by Super 7 with 10 at 1,2
4818 Id : 904, {_}: right_division (multiply ?1247 (multiply ?1248 identity)) ?1248 =>= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Super 897 with 9 at 2,2,1,2
4819 Id : 944, {_}: right_division (multiply ?1247 ?1248) ?1248 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 904 with 3 at 2,1,2
4820 Id : 945, {_}: ?1247 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 944 with 7 at 2
4821 Id : 1320, {_}: left_division (multiply ?1774 ?1775) ?1774 =>= left_inverse ?1775 [1775, 1774] by Super 5 with 945 at 2,2
4822 Id : 1325, {_}: left_division ?1787 ?1788 =<= left_inverse (left_division ?1788 ?1787) [1788, 1787] by Super 1320 with 4 at 1,2
4823 Id : 1124, {_}: ?1512 =<= multiply (multiply ?1512 ?1513) (left_inverse ?1513) [1513, 1512] by Demod 944 with 7 at 2
4824 Id : 1136, {_}: right_division ?1545 ?1546 =<= multiply ?1545 (left_inverse ?1546) [1546, 1545] by Super 1124 with 6 at 1,3
4825 Id : 1239, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (multiply ?1665 (left_inverse ?1664)) [1665, 1664] by Super 71 with 1136 at 2
4826 Id : 1291, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1239 with 1136 at 2,3
4827 Id : 621, {_}: right_division (multiply ?874 (multiply ?875 ?874)) ?874 =>= multiply ?874 ?875 [875, 874] by Super 7 with 71 at 1,2
4828 Id : 2721, {_}: right_division (multiply (left_inverse ?3427) (multiply ?3427 (multiply ?3428 ?3427))) ?3427 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Super 1291 with 621 at 2,3
4829 Id : 53, {_}: right_division (multiply ?115 (multiply ?116 (multiply ?117 ?116))) ?116 =>= multiply (multiply ?115 ?116) ?117 [117, 116, 115] by Super 7 with 10 at 1,2
4830 Id : 2757, {_}: multiply (multiply (left_inverse ?3427) ?3427) ?3428 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Demod 2721 with 53 at 2
4831 Id : 2758, {_}: multiply identity ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2757 with 9 at 1,2
4832 Id : 2759, {_}: ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2758 with 2 at 2
4833 Id : 3344, {_}: left_division (left_inverse ?4254) ?4255 =>= multiply ?4254 ?4255 [4255, 4254] by Super 5 with 2759 at 2,2
4834 Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
4835 Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
4836 Id : 425, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
4837 Id : 626, {_}: multiply (multiply ?892 ?893) ?892 =>= multiply ?892 (multiply ?893 ?892) [893, 892] by Demod 55 with 2 at 3
4838 Id : 633, {_}: multiply identity ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Super 626 with 8 at 1,2
4839 Id : 654, {_}: ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Demod 633 with 2 at 2
4840 Id : 727, {_}: left_division ?1053 ?1053 =<= multiply (right_inverse ?1053) ?1053 [1053] by Super 5 with 654 at 2,2
4841 Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
4842 Id : 754, {_}: identity =<= multiply (right_inverse ?1053) ?1053 [1053] by Demod 727 with 24 at 2
4843 Id : 784, {_}: right_division identity ?1115 =>= right_inverse ?1115 [1115] by Super 7 with 754 at 1,2
4844 Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
4845 Id : 808, {_}: left_inverse ?1115 =<= right_inverse ?1115 [1115] by Demod 784 with 45 at 2
4846 Id : 829, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 425 with 808 at 2
4847 Id : 3348, {_}: left_division ?4266 ?4267 =<= multiply (left_inverse ?4266) ?4267 [4267, 4266] by Super 3344 with 829 at 1,2
4848 Id : 3417, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =<= multiply (left_inverse ?4342) (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Super 10 with 3348 at 1,1,2
4849 Id : 3495, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Demod 3417 with 3348 at 3
4850 Id : 3351, {_}: left_division (left_division ?4274 ?4275) ?4276 =<= multiply (left_division ?4275 ?4274) ?4276 [4276, 4275, 4274] by Super 3344 with 1325 at 1,2
4851 Id : 9541, {_}: multiply (left_division (left_division ?4343 ?4342) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4342, 4343] by Demod 3495 with 3351 at 1,2
4852 Id : 9542, {_}: left_division (left_division ?4344 (left_division ?4343 ?4342)) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4342, 4343, 4344] by Demod 9541 with 3351 at 2
4853 Id : 9554, {_}: left_division ?10951 (left_division ?10952 (left_division ?10951 ?10953)) =<= left_inverse (left_division ?10953 (multiply ?10951 (multiply ?10952 ?10951))) [10953, 10952, 10951] by Super 1325 with 9542 at 1,3
4854 Id : 27037, {_}: left_division ?28025 (left_division ?28026 (left_division ?28025 ?28027)) =<= left_division (multiply ?28025 (multiply ?28026 ?28025)) ?28027 [28027, 28026, 28025] by Demod 9554 with 1325 at 3
4855 Id : 27055, {_}: left_division (left_inverse ?28099) (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Super 27037 with 1136 at 2,1,3
4856 Id : 3143, {_}: left_division (left_inverse ?4011) ?4012 =>= multiply ?4011 ?4012 [4012, 4011] by Super 5 with 2759 at 2,2
4857 Id : 27191, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27055 with 3143 at 2
4858 Id : 27192, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27191 with 3348 at 1,3
4859 Id : 1117, {_}: right_division ?1491 (left_inverse ?1492) =>= multiply ?1491 ?1492 [1492, 1491] by Super 7 with 945 at 1,2
4860 Id : 1524, {_}: right_division ?2086 (left_division ?2087 ?2088) =<= multiply ?2086 (left_division ?2088 ?2087) [2088, 2087, 2086] by Super 1117 with 1325 at 2,2
4861 Id : 27193, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28100, 28101, 28099] by Demod 27192 with 1524 at 2
4862 Id : 3400, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1291 with 3348 at 1,2
4863 Id : 3401, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= left_division ?1664 (right_division ?1665 ?1664) [1665, 1664] by Demod 3400 with 3348 at 3
4864 Id : 27194, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (right_division (left_division ?28099 ?28100) ?28099) ?28101 [28100, 28101, 28099] by Demod 27193 with 3401 at 1,3
4865 Id : 40132, {_}: right_division ?42719 (left_division (multiply ?42719 ?42720) ?42721) =<= left_division (right_division (left_division ?42719 ?42721) ?42719) ?42720 [42721, 42720, 42719] by Demod 27194 with 3143 at 1,2,2
4866 Id : 1118, {_}: left_division (multiply ?1494 ?1495) ?1494 =>= left_inverse ?1495 [1495, 1494] by Super 5 with 945 at 2,2
4867 Id : 3133, {_}: left_division ?3978 (left_inverse ?3979) =>= left_inverse (multiply ?3979 ?3978) [3979, 3978] by Super 1118 with 2759 at 1,2
4868 Id : 40144, {_}: right_division ?42768 (left_division (multiply ?42768 ?42769) (left_inverse ?42770)) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42770, 42769, 42768] by Super 40132 with 3133 at 1,1,3
4869 Id : 40468, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42769, 42770, 42768] by Demod 40144 with 3133 at 2,2
4870 Id : 3414, {_}: right_division (left_inverse ?4334) ?4335 =<= left_division ?4334 (left_inverse ?4335) [4335, 4334] by Super 1136 with 3348 at 3
4871 Id : 3502, {_}: right_division (left_inverse ?4334) ?4335 =>= left_inverse (multiply ?4335 ?4334) [4335, 4334] by Demod 3414 with 3133 at 3
4872 Id : 40469, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40468 with 3502 at 1,3
4873 Id : 40470, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40469 with 1117 at 2
4874 Id : 40471, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= multiply (multiply ?42768 (multiply ?42770 ?42768)) ?42769 [42769, 42770, 42768] by Demod 40470 with 3143 at 3
4875 Id : 50862, {_}: multiply a (multiply b (multiply a c)) =?= multiply a (multiply b (multiply a c)) [] by Demod 50861 with 40471 at 2
4876 Id : 50861, {_}: multiply (multiply a (multiply b a)) c =>= multiply a (multiply b (multiply a c)) [] by Demod 1 with 71 at 1,2
4877 Id : 1, {_}: multiply (multiply (multiply a b) a) c =>= multiply a (multiply b (multiply a c)) [] by prove_moufang3
4878 % SZS output end CNFRefutation for GRP201-1.p
4879 10960: solved GRP201-1.p in 12.208762 using kbo
4880 10960: status Unsatisfiable for GRP201-1.p
4881 CLASH, statistics insufficient
4883 10977: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4884 10977: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4886 multiply ?6 (left_division ?6 ?7) =>= ?7
4887 [7, 6] by multiply_left_division ?6 ?7
4889 left_division ?9 (multiply ?9 ?10) =>= ?10
4890 [10, 9] by left_division_multiply ?9 ?10
4892 multiply (right_division ?12 ?13) ?13 =>= ?12
4893 [13, 12] by multiply_right_division ?12 ?13
4895 right_division (multiply ?15 ?16) ?16 =>= ?15
4896 [16, 15] by right_division_multiply ?15 ?16
4898 multiply ?18 (right_inverse ?18) =>= identity
4899 [18] by right_inverse ?18
4901 multiply (left_inverse ?20) ?20 =>= identity
4902 [20] by left_inverse ?20
4903 10977: Id : 10, {_}:
4904 multiply (multiply (multiply ?22 ?23) ?22) ?24
4906 multiply ?22 (multiply ?23 (multiply ?22 ?24))
4907 [24, 23, 22] by moufang3 ?22 ?23 ?24
4910 multiply (multiply a (multiply b c)) a
4912 multiply (multiply a b) (multiply c a)
4913 [] by prove_moufang1
4917 10977: left_inverse 1 1 0
4918 10977: right_inverse 1 1 0
4919 10977: right_division 2 2 0
4920 10977: left_division 2 2 0
4921 10977: identity 4 0 0
4922 10977: multiply 20 2 6 0,2
4923 10977: c 2 0 2 2,2,1,2
4924 10977: b 2 0 2 1,2,1,2
4925 10977: a 4 0 4 1,1,2
4926 CLASH, statistics insufficient
4928 10978: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4929 10978: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4931 multiply ?6 (left_division ?6 ?7) =>= ?7
4932 [7, 6] by multiply_left_division ?6 ?7
4934 left_division ?9 (multiply ?9 ?10) =>= ?10
4935 [10, 9] by left_division_multiply ?9 ?10
4937 multiply (right_division ?12 ?13) ?13 =>= ?12
4938 [13, 12] by multiply_right_division ?12 ?13
4940 right_division (multiply ?15 ?16) ?16 =>= ?15
4941 [16, 15] by right_division_multiply ?15 ?16
4943 multiply ?18 (right_inverse ?18) =>= identity
4944 [18] by right_inverse ?18
4946 multiply (left_inverse ?20) ?20 =>= identity
4947 [20] by left_inverse ?20
4948 10978: Id : 10, {_}:
4949 multiply (multiply (multiply ?22 ?23) ?22) ?24
4951 multiply ?22 (multiply ?23 (multiply ?22 ?24))
4952 [24, 23, 22] by moufang3 ?22 ?23 ?24
4955 multiply (multiply a (multiply b c)) a
4957 multiply (multiply a b) (multiply c a)
4958 [] by prove_moufang1
4962 10978: left_inverse 1 1 0
4963 10978: right_inverse 1 1 0
4964 10978: right_division 2 2 0
4965 10978: left_division 2 2 0
4966 10978: identity 4 0 0
4967 10978: multiply 20 2 6 0,2
4968 10978: c 2 0 2 2,2,1,2
4969 10978: b 2 0 2 1,2,1,2
4970 10978: a 4 0 4 1,1,2
4971 CLASH, statistics insufficient
4973 10979: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
4974 10979: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
4976 multiply ?6 (left_division ?6 ?7) =>= ?7
4977 [7, 6] by multiply_left_division ?6 ?7
4979 left_division ?9 (multiply ?9 ?10) =>= ?10
4980 [10, 9] by left_division_multiply ?9 ?10
4982 multiply (right_division ?12 ?13) ?13 =>= ?12
4983 [13, 12] by multiply_right_division ?12 ?13
4985 right_division (multiply ?15 ?16) ?16 =>= ?15
4986 [16, 15] by right_division_multiply ?15 ?16
4988 multiply ?18 (right_inverse ?18) =>= identity
4989 [18] by right_inverse ?18
4991 multiply (left_inverse ?20) ?20 =>= identity
4992 [20] by left_inverse ?20
4993 10979: Id : 10, {_}:
4994 multiply (multiply (multiply ?22 ?23) ?22) ?24
4996 multiply ?22 (multiply ?23 (multiply ?22 ?24))
4997 [24, 23, 22] by moufang3 ?22 ?23 ?24
5000 multiply (multiply a (multiply b c)) a
5002 multiply (multiply a b) (multiply c a)
5003 [] by prove_moufang1
5007 10979: left_inverse 1 1 0
5008 10979: right_inverse 1 1 0
5009 10979: right_division 2 2 0
5010 10979: left_division 2 2 0
5011 10979: identity 4 0 0
5012 10979: multiply 20 2 6 0,2
5013 10979: c 2 0 2 2,2,1,2
5014 10979: b 2 0 2 1,2,1,2
5015 10979: a 4 0 4 1,1,2
5018 Found proof, 29.848585s
5019 % SZS status Unsatisfiable for GRP202-1.p
5020 % SZS output start CNFRefutation for GRP202-1.p
5021 Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
5022 Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
5023 Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
5024 Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
5025 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
5026 Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
5027 Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
5028 Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
5029 Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
5030 Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
5031 Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
5032 Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
5033 Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
5034 Id : 894, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
5035 Id : 900, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 894 with 6 at 2,1,2
5036 Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
5037 Id : 2577, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
5038 Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
5039 Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
5040 Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
5041 Id : 765, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
5042 Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
5043 Id : 791, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 765 with 24 at 2
5044 Id : 819, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 791 at 1,2
5045 Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
5046 Id : 846, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 819 with 45 at 2
5047 Id : 861, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 846 at 2,2
5048 Id : 2586, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2577 with 861 at 2,2,1,2
5049 Id : 2645, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2586 with 3 at 2,1,2
5050 Id : 2833, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 900 with 2645 at 2,3
5051 Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
5052 Id : 969, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
5053 Id : 976, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 969 with 9 at 2,1,2,2,2,2
5054 Id : 1036, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 976 with 3 at 1,2,2,2,2
5055 Id : 1037, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1036 with 4 at 2,2,2
5056 Id : 1172, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1037 at 2,2
5057 Id : 2879, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2833 with 1172 at 1,2
5058 Id : 2880, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2879 with 1172 at 3
5059 Id : 2881, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2880 with 5 at 1,2
5060 Id : 2882, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2881 with 5 at 3
5061 Id : 1389, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1172 at 1,2
5062 Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
5063 Id : 1395, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1389 with 28 at 1,2
5064 Id : 3679, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
5065 Id : 3684, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3679 with 4 at 2,2,3
5066 Id : 2950, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1395 with 2882 at 1,3
5067 Id : 3037, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2882 with 2950 at 2
5068 Id : 3056, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3037 with 1172 at 1,2
5069 Id : 3057, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3056 with 1172 at 3
5070 Id : 3222, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2882 with 3057 at 2,2
5071 Id : 8079, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3684 with 3222 at 2
5072 Id : 3218, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1172 with 3057 at 1,3
5073 Id : 8080, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8079 with 3218 at 2,3
5074 Id : 8081, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8080 with 3222 at 3
5075 Id : 8094, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1395 with 8081 at 1,3
5076 Id : 8159, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8094 with 1395 at 3
5077 Id : 23778, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2882 with 8159 at 2
5078 Id : 2960, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2881 with 5 at 3
5079 Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
5080 Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
5081 Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
5082 Id : 864, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 846 at 2
5083 Id : 2964, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2960 with 864 at 2,2
5084 Id : 3107, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1172 with 2964 at 3
5085 Id : 3145, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3107 with 2950 at 3
5086 Id : 23925, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23778 with 3145 at 1,2
5087 Id : 23926, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23925 with 2964 at 2,2
5088 Id : 23927, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23926 with 3218 at 3
5089 Id : 23928, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23927 with 2950 at 2
5090 Id : 23929, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23928 with 3145 at 1,1,3
5091 Id : 1175, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1036 with 4 at 2,2,2
5092 Id : 1185, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1175 with 4 at 2,2
5093 Id : 1426, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1185 with 1395 at 1,3
5094 Id : 23930, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23929 with 1426 at 1,2
5095 Id : 23931, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23930 with 1185 at 1,3
5096 Id : 37380, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23931 with 3057 at 2
5097 Id : 37397, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37380 with 2964 at 1,1,3
5098 Id : 37604, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37397 with 2882 at 2,2
5099 Id : 37605, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37604 with 1426 at 1,3
5100 Id : 8101, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8080 with 3222 at 3
5101 Id : 8114, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8101 with 3145 at 2,2
5102 Id : 8186, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8114 with 2882 at 2
5103 Id : 8187, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8186 with 2950 at 3
5104 Id : 8188, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8187 with 2964 at 1,2
5105 Id : 8189, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8188 with 3218 at 1,3
5106 Id : 8190, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8189 with 1426 at 2
5107 Id : 8191, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8190 with 3057 at 3
5108 Id : 8192, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8191 with 3145 at 1,2,3
5109 Id : 24138, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8192 with 1185 at 2,3
5110 Id : 24175, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24138 with 2882 at 1,2
5111 Id : 24394, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24175 with 2964 at 1,2,3
5112 Id : 24395, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24394 with 1426 at 2,3
5113 Id : 47972, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37605 with 24395 at 2
5114 Id : 1255, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1172 at 1,3
5115 Id : 1319, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1255 with 1172 at 2
5116 Id : 3086, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1319 with 2964 at 2,2
5117 Id : 3087, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3086 with 2964 at 3
5118 Id : 48040, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47972 with 3087 at 1,3
5119 Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
5120 Id : 3668, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
5121 Id : 7892, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3668 with 3218 at 3
5122 Id : 7900, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3057 with 7892 at 1,2
5123 Id : 7969, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7900 with 3057 at 2
5124 Id : 22647, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3145 with 7969 at 2
5125 Id : 22730, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22647 with 1172 at 1,2
5126 Id : 22731, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22730 with 3145 at 2,2
5127 Id : 22732, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22731 with 2964 at 1,2,1,3
5128 Id : 22733, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22732 with 3145 at 2
5129 Id : 22734, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22733 with 1426 at 2,1,3
5130 Id : 22735, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22734 with 3222 at 1,2
5131 Id : 22736, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22735 with 3222 at 1,3
5132 Id : 22737, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22736 with 1395 at 2
5133 Id : 33406, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22737 with 1395 at 3
5134 Id : 33487, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33406 with 1185 at 1,3
5135 Id : 33773, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33487 with 1185 at 1,2
5136 Id : 2967, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2960 with 1395 at 2,2
5137 Id : 33774, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33773 with 2967 at 1,3
5138 Id : 48410, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 48040 with 33774 at 1,2,2
5139 Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
5140 Id : 1260, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1172 at 2,1,2
5141 Id : 1315, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1260 with 1172 at 2,3
5142 Id : 5054, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1315 with 3222 at 1,2
5143 Id : 5055, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5054 with 3222 at 3
5144 Id : 5056, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5055 with 1426 at 2
5145 Id : 48411, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48410 with 5056 at 3
5146 Id : 3100, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2964 at 2,1,2
5147 Id : 3156, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3100 with 1172 at 1,2
5148 Id : 3157, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3156 with 1172 at 3
5149 Id : 3158, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3157 with 3087 at 1,2
5150 Id : 3159, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3158 with 1172 at 2,2,3
5151 Id : 3160, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3159 with 1426 at 2
5152 Id : 7103, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3160 with 3222 at 2,3
5153 Id : 7119, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3145 with 7103 at 2
5154 Id : 7221, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7119 with 1185 at 2,2,2
5155 Id : 7222, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7221 with 2967 at 1,3
5156 Id : 7223, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7222 with 1395 at 3
5157 Id : 21525, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3057 with 7223 at 1,2
5158 Id : 21646, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21525 with 1395 at 2
5159 Id : 48412, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48411 with 21646 at 2,2
5160 Id : 48413, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48412 with 1426 at 1,2,3
5161 Id : 3103, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2964 at 2,2
5162 Id : 48414, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48413 with 3103 at 2
5163 Id : 48415, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48414 with 28 at 1,2,3
5164 Id : 48416, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48415 with 1395 at 2
5165 Id : 52586, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1395 with 48416 at 1,3
5166 Id : 52816, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52586 with 1395 at 3
5167 Id : 55129, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2882 with 52816 at 2
5168 Id : 55322, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55129 with 1185 at 1,2
5169 Id : 55323, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55322 with 2950 at 2,2
5170 Id : 55324, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55323 with 3218 at 3
5171 Id : 55325, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55324 with 2882 at 2
5172 Id : 55326, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55325 with 3145 at 1,3
5173 Id : 55327, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55326 with 1185 at 3
5174 Id : 55328, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55327 with 70 at 3
5175 Id : 57081, {_}: multiply a (multiply (multiply b c) a) =?= multiply a (multiply (multiply b c) a) [] by Demod 57080 with 55328 at 3
5176 Id : 57080, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 1 with 70 at 2
5177 Id : 1, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1
5178 % SZS output end CNFRefutation for GRP202-1.p
5179 10978: solved GRP202-1.p in 14.864928 using kbo
5180 10978: status Unsatisfiable for GRP202-1.p
5181 NO CLASH, using fixed ground order
5186 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
5187 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
5190 [4, 3, 2] by single_axiom ?2 ?3 ?4
5193 multiply (multiply (inverse b2) b2) a2 =>= a2
5194 [] by prove_these_axioms_2
5199 10984: multiply 8 2 2 0,2
5200 10984: inverse 6 1 1 0,1,1,2
5201 10984: b2 2 0 2 1,1,1,2
5202 NO CLASH, using fixed ground order
5207 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
5208 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
5211 [4, 3, 2] by single_axiom ?2 ?3 ?4
5214 multiply (multiply (inverse b2) b2) a2 =>= a2
5215 [] by prove_these_axioms_2
5220 10985: multiply 8 2 2 0,2
5221 10985: inverse 6 1 1 0,1,1,2
5222 10985: b2 2 0 2 1,1,1,2
5223 NO CLASH, using fixed ground order
5228 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
5229 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
5232 [4, 3, 2] by single_axiom ?2 ?3 ?4
5235 multiply (multiply (inverse b2) b2) a2 =>= a2
5236 [] by prove_these_axioms_2
5241 10986: multiply 8 2 2 0,2
5242 10986: inverse 6 1 1 0,1,1,2
5243 10986: b2 2 0 2 1,1,1,2
5244 % SZS status Timeout for GRP404-1.p
5245 NO CLASH, using fixed ground order
5250 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
5251 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
5254 [4, 3, 2] by single_axiom ?2 ?3 ?4
5257 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5258 [] by prove_these_axioms_3
5262 11033: inverse 5 1 0
5264 11033: multiply 10 2 4 0,2
5265 11033: b3 2 0 2 2,1,2
5266 11033: a3 2 0 2 1,1,2
5267 NO CLASH, using fixed ground order
5272 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
5273 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
5276 [4, 3, 2] by single_axiom ?2 ?3 ?4
5279 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5280 [] by prove_these_axioms_3
5284 11034: inverse 5 1 0
5286 11034: multiply 10 2 4 0,2
5287 11034: b3 2 0 2 2,1,2
5288 11034: a3 2 0 2 1,1,2
5289 NO CLASH, using fixed ground order
5294 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
5295 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
5298 [4, 3, 2] by single_axiom ?2 ?3 ?4
5301 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5302 [] by prove_these_axioms_3
5306 11035: inverse 5 1 0
5308 11035: multiply 10 2 4 0,2
5309 11035: b3 2 0 2 2,1,2
5310 11035: a3 2 0 2 1,1,2
5311 % SZS status Timeout for GRP405-1.p
5312 NO CLASH, using fixed ground order
5316 (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
5317 (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
5320 [4, 3, 2] by single_axiom ?2 ?3 ?4
5323 multiply (multiply (inverse b2) b2) a2 =>= a2
5324 [] by prove_these_axioms_2
5329 11052: multiply 8 2 2 0,2
5330 11052: inverse 6 1 1 0,1,1,2
5331 11052: b2 2 0 2 1,1,1,2
5332 NO CLASH, using fixed ground order
5336 (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
5337 (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
5340 [4, 3, 2] by single_axiom ?2 ?3 ?4
5343 multiply (multiply (inverse b2) b2) a2 =>= a2
5344 [] by prove_these_axioms_2
5349 11053: multiply 8 2 2 0,2
5350 11053: inverse 6 1 1 0,1,1,2
5351 11053: b2 2 0 2 1,1,1,2
5352 NO CLASH, using fixed ground order
5356 (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
5357 (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
5360 [4, 3, 2] by single_axiom ?2 ?3 ?4
5363 multiply (multiply (inverse b2) b2) a2 =>= a2
5364 [] by prove_these_axioms_2
5369 11054: multiply 8 2 2 0,2
5370 11054: inverse 6 1 1 0,1,1,2
5371 11054: b2 2 0 2 1,1,1,2
5372 % SZS status Timeout for GRP410-1.p
5373 NO CLASH, using fixed ground order
5377 (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
5378 (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
5381 [4, 3, 2] by single_axiom ?2 ?3 ?4
5384 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5385 [] by prove_these_axioms_3
5389 11087: inverse 5 1 0
5391 11087: multiply 10 2 4 0,2
5392 11087: b3 2 0 2 2,1,2
5393 11087: a3 2 0 2 1,1,2
5394 NO CLASH, using fixed ground order
5398 (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
5399 (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
5402 [4, 3, 2] by single_axiom ?2 ?3 ?4
5405 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5406 [] by prove_these_axioms_3
5410 11088: inverse 5 1 0
5412 11088: multiply 10 2 4 0,2
5413 11088: b3 2 0 2 2,1,2
5414 11088: a3 2 0 2 1,1,2
5415 NO CLASH, using fixed ground order
5419 (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
5420 (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
5423 [4, 3, 2] by single_axiom ?2 ?3 ?4
5426 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5427 [] by prove_these_axioms_3
5431 11089: inverse 5 1 0
5433 11089: multiply 10 2 4 0,2
5434 11089: b3 2 0 2 2,1,2
5435 11089: a3 2 0 2 1,1,2
5436 % SZS status Timeout for GRP411-1.p
5437 NO CLASH, using fixed ground order
5445 (multiply (inverse ?3)
5447 (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
5451 [4, 3, 2] by single_axiom ?2 ?3 ?4
5454 multiply (multiply (inverse b2) b2) a2 =>= a2
5455 [] by prove_these_axioms_2
5460 11106: multiply 8 2 2 0,2
5461 11106: inverse 8 1 1 0,1,1,2
5462 11106: b2 2 0 2 1,1,1,2
5463 NO CLASH, using fixed ground order
5471 (multiply (inverse ?3)
5473 (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
5477 [4, 3, 2] by single_axiom ?2 ?3 ?4
5480 multiply (multiply (inverse b2) b2) a2 =>= a2
5481 [] by prove_these_axioms_2
5486 11107: multiply 8 2 2 0,2
5487 11107: inverse 8 1 1 0,1,1,2
5488 11107: b2 2 0 2 1,1,1,2
5489 NO CLASH, using fixed ground order
5497 (multiply (inverse ?3)
5499 (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
5503 [4, 3, 2] by single_axiom ?2 ?3 ?4
5506 multiply (multiply (inverse b2) b2) a2 =>= a2
5507 [] by prove_these_axioms_2
5512 11108: multiply 8 2 2 0,2
5513 11108: inverse 8 1 1 0,1,1,2
5514 11108: b2 2 0 2 1,1,1,2
5515 % SZS status Timeout for GRP419-1.p
5516 NO CLASH, using fixed ground order
5524 (multiply (inverse ?3)
5525 (multiply (inverse ?4)
5526 (inverse (multiply (inverse ?4) ?4)))))))
5530 [4, 3, 2] by single_axiom ?2 ?3 ?4
5533 multiply (multiply (inverse b2) b2) a2 =>= a2
5534 [] by prove_these_axioms_2
5539 11140: multiply 8 2 2 0,2
5540 11140: inverse 8 1 1 0,1,1,2
5541 11140: b2 2 0 2 1,1,1,2
5542 NO CLASH, using fixed ground order
5550 (multiply (inverse ?3)
5551 (multiply (inverse ?4)
5552 (inverse (multiply (inverse ?4) ?4)))))))
5556 [4, 3, 2] by single_axiom ?2 ?3 ?4
5559 multiply (multiply (inverse b2) b2) a2 =>= a2
5560 [] by prove_these_axioms_2
5565 11141: multiply 8 2 2 0,2
5566 11141: inverse 8 1 1 0,1,1,2
5567 11141: b2 2 0 2 1,1,1,2
5568 NO CLASH, using fixed ground order
5576 (multiply (inverse ?3)
5577 (multiply (inverse ?4)
5578 (inverse (multiply (inverse ?4) ?4)))))))
5582 [4, 3, 2] by single_axiom ?2 ?3 ?4
5585 multiply (multiply (inverse b2) b2) a2 =>= a2
5586 [] by prove_these_axioms_2
5591 11142: multiply 8 2 2 0,2
5592 11142: inverse 8 1 1 0,1,1,2
5593 11142: b2 2 0 2 1,1,1,2
5594 % SZS status Timeout for GRP422-1.p
5595 NO CLASH, using fixed ground order
5597 NO CLASH, using fixed ground order
5605 (multiply (inverse ?3)
5606 (multiply (inverse ?4)
5607 (inverse (multiply (inverse ?4) ?4)))))))
5611 [4, 3, 2] by single_axiom ?2 ?3 ?4
5614 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5615 [] by prove_these_axioms_3
5619 11164: inverse 7 1 0
5621 11164: multiply 10 2 4 0,2
5622 11164: b3 2 0 2 2,1,2
5623 11164: a3 2 0 2 1,1,2
5624 NO CLASH, using fixed ground order
5632 (multiply (inverse ?3)
5633 (multiply (inverse ?4)
5634 (inverse (multiply (inverse ?4) ?4)))))))
5638 [4, 3, 2] by single_axiom ?2 ?3 ?4
5641 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5642 [] by prove_these_axioms_3
5646 11163: inverse 7 1 0
5648 11163: multiply 10 2 4 0,2
5649 11163: b3 2 0 2 2,1,2
5650 11163: a3 2 0 2 1,1,2
5657 (multiply (inverse ?3)
5658 (multiply (inverse ?4)
5659 (inverse (multiply (inverse ?4) ?4)))))))
5663 [4, 3, 2] by single_axiom ?2 ?3 ?4
5666 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5667 [] by prove_these_axioms_3
5671 11162: inverse 7 1 0
5673 11162: multiply 10 2 4 0,2
5674 11162: b3 2 0 2 2,1,2
5675 11162: a3 2 0 2 1,1,2
5676 % SZS status Timeout for GRP423-1.p
5677 NO CLASH, using fixed ground order
5684 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
5685 ?5) (inverse (multiply ?3 ?5))))
5688 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
5691 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5692 [] by prove_these_axioms_3
5696 11197: inverse 5 1 0
5698 11197: multiply 10 2 4 0,2
5699 11197: b3 2 0 2 2,1,2
5700 11197: a3 2 0 2 1,1,2
5701 NO CLASH, using fixed ground order
5708 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
5709 ?5) (inverse (multiply ?3 ?5))))
5712 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
5715 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5716 [] by prove_these_axioms_3
5720 11198: inverse 5 1 0
5722 11198: multiply 10 2 4 0,2
5723 11198: b3 2 0 2 2,1,2
5724 11198: a3 2 0 2 1,1,2
5725 NO CLASH, using fixed ground order
5732 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
5733 ?5) (inverse (multiply ?3 ?5))))
5736 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
5739 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5740 [] by prove_these_axioms_3
5744 11196: inverse 5 1 0
5746 11196: multiply 10 2 4 0,2
5747 11196: b3 2 0 2 2,1,2
5748 11196: a3 2 0 2 1,1,2
5751 Found proof, 60.632898s
5752 % SZS status Unsatisfiable for GRP429-1.p
5753 % SZS output start CNFRefutation for GRP429-1.p
5754 Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
5755 Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
5756 Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
5757 Id : 1086, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5854) (multiply (inverse (inverse ?5855)) (multiply (inverse ?5855) ?5856)))) ?5857) (inverse (multiply ?5854 ?5857))) =>= ?5856 [5857, 5856, 5855, 5854] by Super 2 with 5 at 2
5758 Id : 473, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1916) (multiply (inverse (inverse ?1917)) (multiply (inverse ?1917) ?1918)))) ?1919) (inverse (multiply ?1916 ?1919))) =>= ?1918 [1919, 1918, 1917, 1916] by Super 2 with 5 at 2
5759 Id : 1106, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?5983) (multiply (inverse (inverse ?5984)) (multiply (inverse ?5984) ?5985)))) ?5986) (inverse (multiply ?5983 ?5986))))) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5986, 5985, 5984, 5983, 5982] by Super 1086 with 473 at 1,2,2,1,1,1,1,2
5760 Id : 2050, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?13160) (multiply (inverse ?13161) (multiply ?13161 ?13162)))) ?13163) (inverse (multiply ?13160 ?13163))) =>= ?13162 [13163, 13162, 13161, 13160] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2
5761 Id : 472, {_}: multiply (inverse ?1911) (multiply ?1911 (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912, 1911] by Super 2 with 5 at 2,2
5762 Id : 1697, {_}: multiply (inverse ?11063) (multiply ?11063 ?11064) =?= multiply (inverse (inverse ?11065)) (multiply (inverse ?11065) ?11064) [11065, 11064, 11063] by Super 472 with 473 at 2,2,2
5763 Id : 1084, {_}: multiply (inverse ?5842) (multiply ?5842 ?5843) =?= multiply (inverse (inverse ?5844)) (multiply (inverse ?5844) ?5843) [5844, 5843, 5842] by Super 472 with 473 at 2,2,2
5764 Id : 1735, {_}: multiply (inverse ?11276) (multiply ?11276 ?11277) =?= multiply (inverse ?11278) (multiply ?11278 ?11277) [11278, 11277, 11276] by Super 1697 with 1084 at 3
5765 Id : 2837, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18056) (multiply ?18056 (multiply ?18057 ?18058)))) ?18059) (inverse (multiply (inverse ?18057) ?18059))) =>= ?18058 [18059, 18058, 18057, 18056] by Super 2050 with 1735 at 1,1,1,1,2
5766 Id : 2876, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18341) (multiply ?18341 (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342, 18341] by Super 2837 with 1735 at 2,2,1,1,1,1,2
5767 Id : 930, {_}: multiply (inverse ?5077) (multiply ?5077 (inverse (multiply (multiply (inverse (multiply (inverse ?5078) ?5079)) ?5080) (inverse (multiply ?5078 ?5080))))) =>= ?5079 [5080, 5079, 5078, 5077] by Super 2 with 5 at 2,2
5768 Id : 983, {_}: multiply (inverse ?5420) (multiply ?5420 (multiply ?5421 (inverse (multiply (multiply (inverse (multiply (inverse ?5422) ?5423)) ?5424) (inverse (multiply ?5422 ?5424)))))) =>= multiply (inverse (inverse ?5421)) ?5423 [5424, 5423, 5422, 5421, 5420] by Super 930 with 5 at 2,2,2
5769 Id : 1838, {_}: multiply (inverse ?11737) (multiply ?11737 (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738, 11737] by Super 472 with 1735 at 1,1,1,1,2,2,2
5770 Id : 2618, {_}: multiply ?16805 (inverse (multiply (multiply (inverse (multiply (inverse ?16806) (multiply ?16806 ?16807))) ?16808) (inverse (multiply (inverse ?16805) ?16808)))) =>= ?16807 [16808, 16807, 16806, 16805] by Super 2 with 1735 at 1,1,1,1,2,2
5771 Id : 7049, {_}: multiply ?47447 (inverse (multiply (multiply (inverse (multiply (inverse ?47448) (multiply ?47448 ?47449))) (multiply ?47447 ?47450)) (inverse (multiply (inverse ?47451) (multiply ?47451 ?47450))))) =>= ?47449 [47451, 47450, 47449, 47448, 47447] by Super 2618 with 1735 at 1,2,1,2,2
5772 Id : 7182, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse (multiply (inverse ?48548) (multiply ?48548 (inverse (multiply (multiply (inverse (multiply (inverse ?48549) ?48547)) ?48550) (inverse (multiply ?48549 ?48550))))))))) =>= ?48546 [48550, 48549, 48548, 48547, 48546, 48545] by Super 7049 with 472 at 1,1,2,2
5773 Id : 7272, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse ?48547))) =>= ?48546 [48547, 48546, 48545] by Demod 7182 with 472 at 1,2,1,2,2
5774 Id : 7322, {_}: multiply (inverse (multiply (inverse ?48938) (multiply ?48938 ?48939))) ?48939 =?= multiply (inverse (multiply (inverse ?48940) (multiply ?48940 ?48941))) ?48941 [48941, 48940, 48939, 48938] by Super 1838 with 7272 at 2,2
5775 Id : 9244, {_}: multiply (inverse (inverse (multiply (inverse ?63609) (multiply ?63609 (inverse (multiply (multiply (inverse (multiply (inverse ?63610) ?63611)) ?63612) (inverse (multiply ?63610 ?63612)))))))) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63612, 63611, 63610, 63609] by Super 472 with 7322 at 2,2
5776 Id : 9553, {_}: multiply (inverse (inverse ?63611)) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63611] by Demod 9244 with 472 at 1,1,1,2
5777 Id : 9607, {_}: multiply (inverse ?66347) (multiply ?66347 (multiply ?66348 (inverse (multiply (multiply (inverse ?66349) ?66350) (inverse (multiply (inverse ?66349) ?66350)))))) =?= multiply (inverse (inverse ?66348)) (multiply (inverse (multiply (inverse ?66351) (multiply ?66351 ?66352))) ?66352) [66352, 66351, 66350, 66349, 66348, 66347] by Super 983 with 9553 at 1,1,1,1,2,2,2,2
5778 Id : 13028, {_}: multiply (inverse ?88877) (multiply ?88877 (multiply ?88878 (inverse (multiply (multiply (inverse ?88879) ?88880) (inverse (multiply (inverse ?88879) ?88880)))))) =>= ?88878 [88880, 88879, 88878, 88877] by Demod 9607 with 9553 at 3
5779 Id : 2125, {_}: inverse (multiply (multiply (inverse ?13666) (multiply ?13666 ?13667)) (inverse (multiply ?13668 (multiply (multiply (inverse ?13668) (multiply (inverse ?13669) (multiply ?13669 ?13670))) ?13667)))) =>= ?13670 [13670, 13669, 13668, 13667, 13666] by Super 2050 with 1735 at 1,1,2
5780 Id : 7292, {_}: inverse (multiply (multiply (inverse ?48720) (multiply ?48720 (inverse (multiply ?48721 (inverse ?48721))))) (inverse (multiply (inverse ?48722) (multiply ?48722 ?48723)))) =>= ?48723 [48723, 48722, 48721, 48720] by Super 2125 with 7272 at 2,1,2,1,2
5781 Id : 13145, {_}: multiply (inverse ?89741) (multiply ?89741 (multiply ?89742 (inverse (multiply ?89743 (inverse ?89743))))) =>= ?89742 [89743, 89742, 89741] by Super 13028 with 7292 at 2,2,2,2
5782 Id : 1878, {_}: multiply ?12021 (inverse (multiply (multiply (inverse ?12022) (multiply ?12022 ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12022, 12021] by Super 2 with 1735 at 1,1,2,2
5783 Id : 13510, {_}: multiply (inverse (inverse ?91449)) (multiply (inverse ?91450) (multiply ?91450 (inverse (multiply ?91451 (inverse ?91451))))) =>= ?91449 [91451, 91450, 91449] by Super 9553 with 13145 at 1,1,2,2
5784 Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
5785 Id : 98, {_}: multiply ?266 (inverse (multiply (multiply (inverse (multiply (inverse ?267) ?268)) ?269) (inverse (multiply ?267 ?269)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?270) (multiply (inverse (inverse ?266)) ?268))) (inverse (multiply (multiply (inverse (multiply (inverse ?271) (multiply (inverse ?270) ?272))) ?273) (inverse (multiply ?271 ?273))))) (inverse ?272)) [273, 272, 271, 270, 269, 268, 267, 266] by Super 2 with 4 at 2,1,1,1,1,2,2
5786 Id : 13781, {_}: multiply ?92573 (inverse (multiply (multiply (inverse (multiply (inverse ?92574) (multiply (inverse ?92573) (inverse (multiply ?92575 (inverse ?92575)))))) ?92576) (inverse (multiply ?92574 ?92576)))) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92576, 92575, 92574, 92573] by Super 98 with 13510 at 1,1,1,1,3
5787 Id : 13970, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92575] by Demod 13781 with 2 at 2
5788 Id : 13971, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply ?92579 (inverse ?92579)) [92579, 92575] by Demod 13970 with 2 at 1,1,3
5789 Id : 14410, {_}: multiply (inverse (inverse (multiply ?96419 (inverse ?96419)))) (multiply (inverse ?96420) (multiply ?96420 (inverse (multiply ?96421 (inverse ?96421))))) =?= multiply ?96422 (inverse ?96422) [96422, 96421, 96420, 96419] by Super 13510 with 13971 at 1,1,2
5790 Id : 14473, {_}: multiply ?96419 (inverse ?96419) =?= multiply ?96422 (inverse ?96422) [96422, 96419] by Demod 14410 with 13510 at 2
5791 Id : 14531, {_}: multiply (multiply (inverse ?96810) (multiply ?96811 (inverse ?96811))) (inverse (multiply ?96812 (inverse ?96812))) =>= inverse ?96810 [96812, 96811, 96810] by Super 7272 with 14473 at 2,1,2
5792 Id : 15237, {_}: multiply ?101459 (inverse (multiply (multiply (inverse ?101460) (multiply ?101460 (inverse (multiply ?101461 (inverse ?101461))))) (inverse (multiply ?101462 (inverse ?101462))))) =>= inverse (inverse ?101459) [101462, 101461, 101460, 101459] by Super 1878 with 14531 at 2,1,2,1,2,2
5793 Id : 15353, {_}: multiply ?101459 (inverse (inverse (multiply ?101461 (inverse ?101461)))) =>= inverse (inverse ?101459) [101461, 101459] by Demod 15237 with 7272 at 1,2,2
5794 Id : 16356, {_}: multiply (inverse (inverse ?111717)) (multiply (inverse (multiply (inverse ?111718) (inverse (inverse ?111718)))) (inverse (inverse (multiply ?111719 (inverse ?111719))))) =>= ?111717 [111719, 111718, 111717] by Super 9553 with 15353 at 2,1,1,2,2
5795 Id : 18221, {_}: multiply (inverse (inverse ?121427)) (inverse (inverse (inverse (multiply (inverse ?121428) (inverse (inverse ?121428)))))) =>= ?121427 [121428, 121427] by Demod 16356 with 15353 at 2,2
5796 Id : 16345, {_}: multiply ?111675 (inverse ?111675) =?= inverse (inverse (inverse (multiply ?111676 (inverse ?111676)))) [111676, 111675] by Super 14473 with 15353 at 3
5797 Id : 18293, {_}: multiply (inverse (inverse ?121732)) (multiply ?121733 (inverse ?121733)) =>= ?121732 [121733, 121732] by Super 18221 with 16345 at 2,2
5798 Id : 18567, {_}: multiply ?122956 (inverse (multiply ?122957 (inverse ?122957))) =>= inverse (inverse ?122956) [122957, 122956] by Super 7272 with 18293 at 1,2
5799 Id : 18716, {_}: multiply (inverse ?89741) (multiply ?89741 (inverse (inverse ?89742))) =>= ?89742 [89742, 89741] by Demod 13145 with 18567 at 2,2,2
5800 Id : 18916, {_}: multiply (inverse (inverse ?124642)) (inverse (inverse (multiply ?124643 (inverse ?124643)))) =>= ?124642 [124643, 124642] by Super 18293 with 18567 at 2,2
5801 Id : 18985, {_}: inverse (inverse (inverse (inverse ?124642))) =>= ?124642 [124642] by Demod 18916 with 15353 at 2
5802 Id : 19175, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= inverse (inverse ?124948) [124948, 124947] by Super 18716 with 18985 at 2,2,2
5803 Id : 19474, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342] by Demod 2876 with 19175 at 1,1,1,1,2
5804 Id : 19475, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19474 with 19175 at 1,1,1,1,1,1,2
5805 Id : 19512, {_}: inverse (multiply (multiply (inverse ?18343) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19475 with 18985 at 1,1,1,2
5806 Id : 19345, {_}: multiply ?126114 (multiply ?126115 (inverse ?126115)) =>= inverse (inverse ?126114) [126115, 126114] by Super 18293 with 18985 at 1,2
5807 Id : 19935, {_}: inverse (multiply (multiply (inverse ?128594) (multiply ?128595 (inverse ?128595))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128595, 128594] by Super 19512 with 19345 at 1,2,1,2
5808 Id : 19990, {_}: inverse (multiply (inverse (inverse (inverse ?128594))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128594] by Demod 19935 with 19345 at 1,1,2
5809 Id : 20507, {_}: inverse (multiply (inverse (inverse (inverse ?130153))) (inverse ?130154)) =>= multiply ?130154 ?130153 [130154, 130153] by Demod 19990 with 18985 at 2,1,2
5810 Id : 20571, {_}: inverse (multiply ?130433 (inverse ?130434)) =>= multiply ?130434 (inverse ?130433) [130434, 130433] by Super 20507 with 18985 at 1,1,2
5811 Id : 21794, {_}: multiply (multiply (inverse (inverse ?18345)) ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 19512 with 20571 at 2
5812 Id : 21760, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 21, 22, 20, 19] by Demod 5 with 20571 at 2,2
5813 Id : 21761, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 22, 20, 19] by Demod 21760 with 20571 at 3
5814 Id : 19480, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912] by Demod 472 with 19175 at 2
5815 Id : 21790, {_}: inverse (inverse (multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)))) =>= ?1913 [1913, 1914, 1912] by Demod 19480 with 20571 at 1,1,2
5816 Id : 21791, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))) =>= ?1913 [1914, 1913, 1912] by Demod 21790 with 20571 at 1,2
5817 Id : 21792, {_}: multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)) =>= ?1913 [1913, 1914, 1912] by Demod 21791 with 20571 at 2
5818 Id : 21810, {_}: multiply ?19 ?21 =<= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 19] by Demod 21761 with 21792 at 2,2
5819 Id : 21811, {_}: multiply ?19 ?21 =<= multiply (inverse (inverse ?19)) ?21 [21, 19] by Demod 21810 with 21792 at 3
5820 Id : 21822, {_}: multiply (multiply ?18345 ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 21794 with 21811 at 1,2
5821 Id : 21949, {_}: multiply (multiply ?139581 (inverse ?139582)) (multiply ?139582 (inverse (inverse ?139583))) =>= multiply ?139581 ?139583 [139583, 139582, 139581] by Super 21822 with 20571 at 2,2
5822 Id : 19491, {_}: multiply ?12021 (inverse (multiply (inverse (inverse ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12021] by Demod 1878 with 19175 at 1,1,2,2
5823 Id : 21735, {_}: multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse (inverse (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 19491 with 20571 at 2,2
5824 Id : 3075, {_}: multiply (inverse ?19377) (multiply ?19377 (multiply ?19378 (inverse (multiply (multiply (inverse (multiply (inverse ?19379) ?19380)) ?19381) (inverse (multiply ?19379 ?19381)))))) =>= multiply (inverse (inverse ?19378)) ?19380 [19381, 19380, 19379, 19378, 19377] by Super 930 with 5 at 2,2,2
5825 Id : 1191, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse ?5985) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5985, 5982] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2
5826 Id : 3153, {_}: multiply (inverse ?20008) (multiply ?20008 (multiply ?20009 ?20010)) =?= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009, 20008] by Super 3075 with 1191 at 2,2,2,2
5827 Id : 19484, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009] by Demod 3153 with 19175 at 2
5828 Id : 19485, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (inverse (inverse ?20010)) [20010, 20009] by Demod 19484 with 19175 at 2,3
5829 Id : 21818, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply ?20009 (inverse (inverse ?20010)) [20010, 20009] by Demod 19485 with 21811 at 3
5830 Id : 21880, {_}: multiply ?12021 (inverse (inverse (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21735 with 21818 at 2,2
5831 Id : 21881, {_}: inverse (inverse (multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21880 with 21818 at 2
5832 Id : 1840, {_}: multiply (inverse ?11749) (multiply ?11749 (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750, 11749] by Super 472 with 1735 at 1,1,2,2,2
5833 Id : 19489, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750] by Demod 1840 with 19175 at 2
5834 Id : 19490, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751] by Demod 19489 with 19175 at 1,1,1,1,2
5835 Id : 21784, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))))) =>= ?11753 [11751, 11753, 11752] by Demod 19490 with 20571 at 1,1,2
5836 Id : 21785, {_}: inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21784 with 20571 at 1,2
5837 Id : 21786, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21785 with 20571 at 2
5838 Id : 21834, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21786 with 21818 at 2
5839 Id : 21842, {_}: inverse (multiply ?11751 (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21834 with 20571 at 1,2
5840 Id : 21843, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751) =>= ?11753 [11751, 11753, 11752] by Demod 21842 with 20571 at 2
5841 Id : 21882, {_}: inverse (inverse (multiply ?12021 (multiply (inverse ?12021) ?12025))) =>= ?12025 [12025, 12021] by Demod 21881 with 21843 at 2,1,1,2
5842 Id : 1876, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (multiply (inverse ?12012) (multiply ?12012 ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12012, 12011] by Super 2 with 1735 at 1,1,1,1,2,2
5843 Id : 19478, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (inverse (inverse ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12011] by Demod 1876 with 19175 at 1,1,1,1,2,2
5844 Id : 21793, {_}: multiply ?12011 (multiply (multiply (inverse ?12011) ?12014) (inverse (multiply (inverse (inverse (inverse ?12013))) ?12014))) =>= ?12013 [12013, 12014, 12011] by Demod 19478 with 20571 at 2,2
5845 Id : 19486, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738] by Demod 1838 with 19175 at 2
5846 Id : 19487, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 19486 with 19175 at 1,1,1,1,1,1,2
5847 Id : 21787, {_}: inverse (inverse (multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)))) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 19487 with 20571 at 1,1,2
5848 Id : 21788, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 21787 with 20571 at 1,2
5849 Id : 21789, {_}: multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 21788 with 20571 at 2
5850 Id : 21802, {_}: multiply ?12011 (multiply (inverse ?12011) ?12013) =>= ?12013 [12013, 12011] by Demod 21793 with 21789 at 2,2
5851 Id : 21883, {_}: inverse (inverse ?12025) =>= ?12025 [12025] by Demod 21882 with 21802 at 1,1,2
5852 Id : 22088, {_}: multiply (multiply ?140028 (inverse ?140029)) (multiply ?140029 ?140030) =>= multiply ?140028 ?140030 [140030, 140029, 140028] by Demod 21949 with 21883 at 2,2,2
5853 Id : 21892, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= ?124948 [124948, 124947] by Demod 19175 with 21883 at 3
5854 Id : 22102, {_}: multiply (multiply ?140094 (inverse (inverse ?140095))) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Super 22088 with 21892 at 2,2
5855 Id : 22180, {_}: multiply (multiply ?140094 ?140095) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Demod 22102 with 21883 at 2,1,2
5856 Id : 22441, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 22180 at 2
5857 Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
5858 % SZS output end CNFRefutation for GRP429-1.p
5859 11197: solved GRP429-1.p in 30.365897 using kbo
5860 11197: status Unsatisfiable for GRP429-1.p
5861 NO CLASH, using fixed ground order
5867 (multiply (multiply ?4 (inverse ?4))
5868 (inverse (multiply ?5 (multiply ?2 ?3))))))
5871 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
5874 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5875 [] by prove_these_axioms_3
5879 11215: inverse 3 1 0
5881 11215: multiply 10 2 4 0,2
5882 11215: b3 2 0 2 2,1,2
5883 11215: a3 2 0 2 1,1,2
5884 NO CLASH, using fixed ground order
5890 (multiply (multiply ?4 (inverse ?4))
5891 (inverse (multiply ?5 (multiply ?2 ?3))))))
5894 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
5897 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5898 [] by prove_these_axioms_3
5902 11216: inverse 3 1 0
5904 11216: multiply 10 2 4 0,2
5905 11216: b3 2 0 2 2,1,2
5906 11216: a3 2 0 2 1,1,2
5907 NO CLASH, using fixed ground order
5913 (multiply (multiply ?4 (inverse ?4))
5914 (inverse (multiply ?5 (multiply ?2 ?3))))))
5917 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
5920 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
5921 [] by prove_these_axioms_3
5925 11217: inverse 3 1 0
5927 11217: multiply 10 2 4 0,2
5928 11217: b3 2 0 2 2,1,2
5929 11217: a3 2 0 2 1,1,2
5930 % SZS status Timeout for GRP444-1.p
5931 NO CLASH, using fixed ground order
5933 NO CLASH, using fixed ground order
5937 (divide (divide ?2 ?2)
5938 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
5942 [4, 3, 2] by single_axiom ?2 ?3 ?4
5944 multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
5945 [8, 7, 6] by multiply ?6 ?7 ?8
5947 inverse ?10 =<= divide (divide ?11 ?11) ?10
5948 [11, 10] by inverse ?10 ?11
5951 multiply (multiply (inverse b2) b2) a2 =>= a2
5952 [] by prove_these_axioms_2
5956 11236: divide 13 2 0
5958 11236: multiply 3 2 2 0,2
5959 11236: inverse 2 1 1 0,1,1,2
5960 11236: b2 2 0 2 1,1,1,2
5961 NO CLASH, using fixed ground order
5965 (divide (divide ?2 ?2)
5966 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
5970 [4, 3, 2] by single_axiom ?2 ?3 ?4
5972 multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7)
5973 [8, 7, 6] by multiply ?6 ?7 ?8
5975 inverse ?10 =?= divide (divide ?11 ?11) ?10
5976 [11, 10] by inverse ?10 ?11
5979 multiply (multiply (inverse b2) b2) a2 =>= a2
5980 [] by prove_these_axioms_2
5984 11237: divide 13 2 0
5986 11237: multiply 3 2 2 0,2
5987 11237: inverse 2 1 1 0,1,1,2
5988 11237: b2 2 0 2 1,1,1,2
5991 (divide (divide ?2 ?2)
5992 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
5996 [4, 3, 2] by single_axiom ?2 ?3 ?4
5998 multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
5999 [8, 7, 6] by multiply ?6 ?7 ?8
6001 inverse ?10 =<= divide (divide ?11 ?11) ?10
6002 [11, 10] by inverse ?10 ?11
6005 multiply (multiply (inverse b2) b2) a2 =>= a2
6006 [] by prove_these_axioms_2
6010 11235: divide 13 2 0
6012 11235: multiply 3 2 2 0,2
6013 11235: inverse 2 1 1 0,1,1,2
6014 11235: b2 2 0 2 1,1,1,2
6017 Found proof, 1.775197s
6018 % SZS status Unsatisfiable for GRP452-1.p
6019 % SZS output start CNFRefutation for GRP452-1.p
6020 Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
6021 Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
6022 Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
6023 Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
6024 Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
6025 Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
6026 Id : 122, {_}: multiply (divide ?250 ?250) ?251 =>= inverse (inverse ?251) [251, 250] by Super 29 with 4 at 3
6027 Id : 128, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= inverse (inverse ?269) [269, 268] by Super 122 with 29 at 1,2
6028 Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
6029 Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
6030 Id : 481, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
6031 Id : 482, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 481 with 4 at 1,2,1,1,1,2
6032 Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
6033 Id : 483, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 482 with 36 at 2,1,1,1,2
6034 Id : 484, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 483 with 29 at 1,1,1,2
6035 Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
6036 Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
6037 Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
6038 Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
6039 Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
6040 Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
6041 Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
6042 Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
6043 Id : 896, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
6044 Id : 911, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 896 with 36 at 2,1,1,3
6045 Id : 944, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 911 with 4 at 1,1,2
6046 Id : 978, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 911 with 4 at 1,1,2
6047 Id : 989, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =?= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 978 with 32 at 1,1,3
6048 Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
6049 Id : 1018, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 989 with 223 at 2
6050 Id : 1036, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1018 at 2,3
6051 Id : 1074, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1036 with 29 at 3
6052 Id : 1107, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 944 with 1074 at 1,1,3
6053 Id : 1180, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1107 with 29 at 2
6054 Id : 1223, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 944 with 1180 at 1,1,3
6055 Id : 1540, {_}: multiply (inverse (inverse (inverse (inverse ?3274)))) ?3275 =<= inverse (inverse (inverse (inverse (multiply ?3274 ?3275)))) [3275, 3274] by Demod 1223 with 29 at 2
6056 Id : 10, {_}: divide (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) (divide (divide ?37 ?37) ?36) =>= ?35 [37, 36, 35, 34] by Super 2 with 3 at 2,2,2,1,2
6057 Id : 24, {_}: multiply (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 10 with 3 at 2
6058 Id : 793, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 24 with 4 at 1,2
6059 Id : 794, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (inverse ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 793 with 4 at 1,2,2,1,1,2
6060 Id : 1550, {_}: multiply (inverse (inverse (inverse (inverse (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))))))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Super 1540 with 794 at 1,1,1,1,3
6061 Id : 1600, {_}: multiply (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Demod 1550 with 1018 at 1,2
6062 Id : 1601, {_}: ?3308 =<= inverse (inverse (inverse (inverse ?3308))) [3308] by Demod 1600 with 794 at 2
6063 Id : 1634, {_}: multiply ?3404 (inverse (inverse (inverse ?3405))) =>= divide ?3404 ?3405 [3405, 3404] by Super 29 with 1601 at 2,3
6064 Id : 1707, {_}: divide (inverse (inverse ?3544)) (inverse (inverse ?3545)) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Super 944 with 1634 at 1,1,3
6065 Id : 1741, {_}: multiply (inverse (inverse ?3544)) (inverse ?3545) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Demod 1707 with 29 at 2
6066 Id : 1807, {_}: divide (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) (inverse ?3667) =>= inverse (inverse ?3666) [3667, 3666] by Super 484 with 1741 at 1,1,1,2
6067 Id : 1849, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1807 with 29 at 2
6068 Id : 1850, {_}: multiply (divide ?3666 ?3667) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1849 with 1601 at 1,2
6069 Id : 1880, {_}: inverse (inverse ?3792) =<= divide (divide ?3792 (inverse (inverse (inverse ?3793)))) ?3793 [3793, 3792] by Super 1634 with 1850 at 2
6070 Id : 2688, {_}: inverse (inverse ?5905) =<= divide (multiply ?5905 (inverse (inverse ?5906))) ?5906 [5906, 5905] by Demod 1880 with 29 at 1,3
6071 Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
6072 Id : 2714, {_}: inverse (inverse (inverse (inverse (divide ?5996 ?5996)))) =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Super 2688 with 224 at 1,3
6073 Id : 2767, {_}: divide ?5996 ?5996 =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Demod 2714 with 1601 at 2
6074 Id : 2768, {_}: divide ?5996 ?5996 =?= divide ?5997 ?5997 [5997, 5996] by Demod 2767 with 1601 at 1,3
6075 Id : 2830, {_}: divide (inverse (divide ?6176 (divide (inverse ?6177) (divide (inverse ?6176) ?6178)))) ?6178 =?= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6178, 6177, 6176] by Super 145 with 2768 at 2,1,3
6076 Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
6077 Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
6078 Id : 2905, {_}: inverse ?6177 =<= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6177] by Demod 2830 with 31 at 2
6079 Id : 2962, {_}: divide ?6532 (divide ?6533 ?6533) =?= inverse (inverse (inverse (inverse ?6532))) [6533, 6532] by Super 1601 with 2905 at 1,1,1,3
6080 Id : 3014, {_}: divide ?6532 (divide ?6533 ?6533) =>= ?6532 [6533, 6532] by Demod 2962 with 1601 at 3
6081 Id : 3088, {_}: divide (inverse (divide ?6789 ?6790)) (divide ?6791 ?6791) =>= inverse (inverse (multiply ?6790 (inverse ?6789))) [6791, 6790, 6789] by Super 250 with 3014 at 2,1,1,3
6082 Id : 3148, {_}: inverse (divide ?6789 ?6790) =<= inverse (inverse (multiply ?6790 (inverse ?6789))) [6790, 6789] by Demod 3088 with 3014 at 2
6083 Id : 3149, {_}: inverse (divide ?6789 ?6790) =<= divide (inverse (inverse ?6790)) ?6789 [6790, 6789] by Demod 3148 with 944 at 3
6084 Id : 3377, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 484 with 3149 at 2
6085 Id : 3423, {_}: inverse (divide ?7500 ?7501) =<= divide (inverse (inverse ?7501)) ?7500 [7501, 7500] by Demod 3148 with 944 at 3
6086 Id : 3441, {_}: inverse (divide ?7566 (inverse (inverse ?7567))) =>= divide ?7567 ?7566 [7567, 7566] by Super 3423 with 1601 at 1,3
6087 Id : 3536, {_}: inverse (multiply ?7566 (inverse ?7567)) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3441 with 29 at 1,2
6088 Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
6089 Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
6090 Id : 3378, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3149 at 3
6091 Id : 3383, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3378 with 29 at 1,3
6092 Id : 3089, {_}: multiply ?6793 (divide ?6794 ?6794) =>= inverse (inverse ?6793) [6794, 6793] by Super 1850 with 3014 at 1,2
6093 Id : 3760, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3383 with 3089 at 1,3
6094 Id : 3763, {_}: multiply ?3404 (inverse ?3405) =>= divide ?3404 ?3405 [3405, 3404] by Demod 1634 with 3760 at 2,2
6095 Id : 3764, {_}: inverse (divide ?7566 ?7567) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3536 with 3763 at 1,2
6096 Id : 3776, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3377 with 3764 at 2
6097 Id : 1886, {_}: multiply (divide ?3813 ?3814) ?3814 =>= inverse (inverse ?3813) [3814, 3813] by Demod 1849 with 1601 at 1,2
6098 Id : 1895, {_}: multiply (multiply ?3842 ?3843) (inverse ?3843) =>= inverse (inverse ?3842) [3843, 3842] by Super 1886 with 29 at 1,2
6099 Id : 3766, {_}: divide (multiply ?3842 ?3843) ?3843 =>= inverse (inverse ?3842) [3843, 3842] by Demod 1895 with 3763 at 2
6100 Id : 3800, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3776 with 3766 at 2
6101 Id : 3806, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= ?269 [269, 268] by Demod 128 with 3800 at 3
6102 Id : 3889, {_}: a2 =?= a2 [] by Demod 1 with 3806 at 2
6103 Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
6104 % SZS output end CNFRefutation for GRP452-1.p
6105 11236: solved GRP452-1.p in 0.984061 using kbo
6106 11236: status Unsatisfiable for GRP452-1.p
6107 NO CLASH, using fixed ground order
6110 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6111 (divide (divide ?5 ?4) ?2)
6114 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6116 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6117 [8, 7] by multiply ?7 ?8
6120 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
6121 [] by prove_these_axioms_1
6126 11242: b1 2 0 2 1,1,3
6127 11242: multiply 3 2 2 0,2
6128 11242: inverse 4 1 2 0,1,2
6129 11242: a1 2 0 2 1,1,2
6130 NO CLASH, using fixed ground order
6133 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6134 (divide (divide ?5 ?4) ?2)
6137 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6139 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6140 [8, 7] by multiply ?7 ?8
6143 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
6144 [] by prove_these_axioms_1
6149 11243: b1 2 0 2 1,1,3
6150 11243: multiply 3 2 2 0,2
6151 11243: inverse 4 1 2 0,1,2
6152 11243: a1 2 0 2 1,1,2
6153 NO CLASH, using fixed ground order
6156 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6157 (divide (divide ?5 ?4) ?2)
6160 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6162 multiply ?7 ?8 =?= divide ?7 (inverse ?8)
6163 [8, 7] by multiply ?7 ?8
6166 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
6167 [] by prove_these_axioms_1
6172 11244: b1 2 0 2 1,1,3
6173 11244: multiply 3 2 2 0,2
6174 11244: inverse 4 1 2 0,1,2
6175 11244: a1 2 0 2 1,1,2
6176 % SZS status Timeout for GRP469-1.p
6177 NO CLASH, using fixed ground order
6180 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6181 (divide (divide ?5 ?4) ?2)
6184 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6186 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6187 [8, 7] by multiply ?7 ?8
6190 multiply (multiply (inverse b2) b2) a2 =>= a2
6191 [] by prove_these_axioms_2
6197 11271: multiply 3 2 2 0,2
6198 11271: inverse 3 1 1 0,1,1,2
6199 11271: b2 2 0 2 1,1,1,2
6200 NO CLASH, using fixed ground order
6203 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6204 (divide (divide ?5 ?4) ?2)
6207 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6209 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6210 [8, 7] by multiply ?7 ?8
6213 multiply (multiply (inverse b2) b2) a2 =>= a2
6214 [] by prove_these_axioms_2
6220 11272: multiply 3 2 2 0,2
6221 11272: inverse 3 1 1 0,1,1,2
6222 11272: b2 2 0 2 1,1,1,2
6223 NO CLASH, using fixed ground order
6226 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6227 (divide (divide ?5 ?4) ?2)
6230 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6232 multiply ?7 ?8 =?= divide ?7 (inverse ?8)
6233 [8, 7] by multiply ?7 ?8
6236 multiply (multiply (inverse b2) b2) a2 =>= a2
6237 [] by prove_these_axioms_2
6243 11273: multiply 3 2 2 0,2
6244 11273: inverse 3 1 1 0,1,1,2
6245 11273: b2 2 0 2 1,1,1,2
6248 Found proof, 64.719986s
6249 % SZS status Unsatisfiable for GRP470-1.p
6250 % SZS output start CNFRefutation for GRP470-1.p
6251 Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
6252 Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6253 Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
6254 Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2
6255 Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2
6256 Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2
6257 Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2
6258 Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2
6259 Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3
6260 Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3
6261 Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2
6262 Id : 7613, {_}: ?38021 =<= multiply (multiply (divide (inverse ?38022) ?38023) (divide (multiply ?38023 ?38022) (divide ?38024 ?38021))) ?38024 [38024, 38023, 38022, 38021] by Super 7101 with 3 at 1,2,1,3
6263 Id : 7678, {_}: ?38552 =<= multiply (multiply (multiply (inverse ?38553) ?38554) (divide (multiply (inverse ?38554) ?38553) (divide ?38555 ?38552))) ?38555 [38555, 38554, 38553, 38552] by Super 7613 with 3 at 1,1,3
6264 Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2
6265 Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2
6266 Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2
6267 Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2
6268 Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2
6269 Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3
6270 Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2
6271 Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3
6272 Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3
6273 Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2
6274 Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2
6275 Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3
6276 Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3
6277 Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2
6278 Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3
6279 Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3
6280 Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3
6281 Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2
6282 Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3
6283 Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3
6284 Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3
6285 Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3
6286 Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3
6287 Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2
6288 Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3
6289 Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3
6290 Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3
6291 Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3
6292 Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3
6293 Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3
6294 Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3
6295 Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3
6296 Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3
6297 Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3
6298 Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2
6299 Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2
6300 Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2
6301 Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3
6302 Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3
6303 Id : 12991, {_}: inverse (inverse (divide (divide ?67798 ?67799) (multiply ?67800 (multiply (inverse ?67801) ?67802)))) =>= multiply ?67798 (multiply (inverse ?67799) (inverse (multiply (divide ?67800 ?67801) ?67802))) [67802, 67801, 67800, 67799, 67798] by Super 12770 with 12807 at 1,1,2
6304 Id : 15565, {_}: inverse (inverse (divide (divide ?82879 ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883)))) =>= multiply ?82879 (divide (inverse ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883))) [82883, 82882, 82881, 82880, 82879] by Demod 12991 with 12807 at 2,3
6305 Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2
6306 Id : 15584, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =<= multiply ?83055 (divide (inverse ?83056) (multiply (multiply (divide ?83058 ?83059) (divide (divide ?83059 ?83058) (divide (multiply (inverse ?83060) ?83061) ?83057))) (multiply (inverse ?83060) ?83061))) [83061, 83060, 83059, 83058, 83057, 83056, 83055] by Super 15565 with 6973 at 2,1,1,2
6307 Id : 15659, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =>= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15584 with 6973 at 2,2,3
6308 Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3
6309 Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =>= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2
6310 Id : 13083, {_}: inverse (inverse (divide (multiply ?68472 ?68473) (multiply ?68474 (multiply (inverse ?68475) ?68476)))) =>= multiply ?68472 (multiply (inverse (inverse ?68473)) (inverse (multiply (divide ?68474 ?68475) ?68476))) [68476, 68475, 68474, 68473, 68472] by Super 12858 with 12807 at 1,1,2
6311 Id : 14137, {_}: inverse (inverse (divide (multiply ?73757 ?73758) (multiply ?73759 (multiply (inverse ?73760) ?73761)))) =>= multiply ?73757 (divide (inverse (inverse ?73758)) (multiply ?73759 (multiply (inverse ?73760) ?73761))) [73761, 73760, 73759, 73758, 73757] by Demod 13083 with 12807 at 2,3
6312 Id : 14155, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =<= multiply ?73925 (divide (inverse (inverse ?73926)) (multiply (multiply (divide ?73928 ?73929) (divide (divide ?73929 ?73928) (divide (multiply (inverse ?73930) ?73931) ?73927))) (multiply (inverse ?73930) ?73931))) [73931, 73930, 73929, 73928, 73927, 73926, 73925] by Super 14137 with 6973 at 2,1,1,2
6313 Id : 14212, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =>= multiply ?73925 (divide (inverse (inverse ?73926)) ?73927) [73927, 73926, 73925] by Demod 14155 with 6973 at 2,2,3
6314 Id : 15715, {_}: multiply ?83687 (inverse (divide (divide ?83688 ?83689) ?83690)) =>= divide ?83687 (multiply ?83688 (divide (inverse ?83689) ?83690)) [83690, 83689, 83688, 83687] by Super 3 with 15659 at 2,3
6315 Id : 15912, {_}: divide (divide ?84886 (divide (inverse ?84887) ?84888)) (divide ?84889 ?84890) =<= divide (multiply ?84886 ?84888) (multiply ?84889 (divide (inverse ?84890) ?84887)) [84890, 84889, 84888, 84887, 84886] by Super 9552 with 15715 at 3
6316 Id : 16736, {_}: inverse (inverse (divide (divide ?88411 (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415))) =>= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Super 14212 with 15912 at 1,1,2
6317 Id : 16823, {_}: multiply ?88411 (divide (inverse (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415)) =<= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Demod 16736 with 15659 at 2
6318 Id : 19503, {_}: inverse (divide (inverse (inverse ?101466)) (multiply ?101467 (divide (inverse ?101468) ?101469))) =<= multiply (multiply (divide (inverse ?101470) ?101471) (divide (multiply ?101471 ?101470) (multiply ?101472 (divide (inverse (divide (inverse ?101469) ?101466)) (divide ?101467 ?101468))))) ?101472 [101472, 101471, 101470, 101469, 101468, 101467, 101466] by Super 7337 with 16823 at 2,2,1,3
6319 Id : 20509, {_}: inverse (divide (inverse (inverse ?107024)) (multiply ?107025 (divide (inverse ?107026) ?107027))) =>= inverse (divide (inverse (divide (inverse ?107027) ?107024)) (divide ?107025 ?107026)) [107027, 107026, 107025, 107024] by Demod 19503 with 7337 at 3
6320 Id : 15122, {_}: multiply ?80264 (inverse (divide (multiply ?80265 ?80266) ?80267)) =<= divide ?80264 (multiply ?80265 (divide (inverse (inverse ?80266)) ?80267)) [80267, 80266, 80265, 80264] by Super 3 with 14212 at 2,3
6321 Id : 20594, {_}: inverse (multiply (inverse (inverse ?107698)) (inverse (divide (multiply ?107699 ?107700) ?107701))) =>= inverse (divide (inverse (divide (inverse ?107701) ?107698)) (divide ?107699 (inverse ?107700))) [107701, 107700, 107699, 107698] by Super 20509 with 15122 at 1,2
6322 Id : 20893, {_}: inverse (multiply (inverse (inverse ?108369)) (inverse (divide (multiply ?108370 ?108371) ?108372))) =>= inverse (divide (inverse (divide (inverse ?108372) ?108369)) (multiply ?108370 ?108371)) [108372, 108371, 108370, 108369] by Demod 20594 with 3 at 2,1,3
6323 Id : 20903, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =<= inverse (divide (inverse (divide (inverse ?108449) ?108447)) (multiply (multiply (divide ?108450 ?108451) (divide (divide ?108451 ?108450) (divide ?108452 ?108448))) ?108452)) [108452, 108451, 108450, 108449, 108448, 108447] by Super 20893 with 6973 at 1,1,2,1,2
6324 Id : 21279, {_}: inverse (multiply (inverse (inverse ?109423)) (inverse (divide ?109424 ?109425))) =>= inverse (divide (inverse (divide (inverse ?109425) ?109423)) ?109424) [109425, 109424, 109423] by Demod 20903 with 6973 at 2,1,3
6325 Id : 21354, {_}: inverse (multiply (multiply ?109942 (divide (inverse ?109943) ?109944)) (inverse (divide ?109945 ?109946))) =>= inverse (divide (inverse (divide (inverse ?109946) (divide (divide ?109942 ?109943) ?109944))) ?109945) [109946, 109945, 109944, 109943, 109942] by Super 21279 with 15659 at 1,1,2
6326 Id : 25671, {_}: inverse (divide (divide ?128948 (divide (inverse ?128949) (divide (inverse ?128950) ?128951))) ?128952) =<= inverse (divide (inverse (divide (inverse ?128949) (divide (divide ?128948 ?128950) ?128951))) ?128952) [128952, 128951, 128950, 128949, 128948] by Demod 21354 with 9552 at 1,2
6327 Id : 25729, {_}: inverse (divide (divide ?129446 (divide (inverse (divide ?129447 (divide (divide ?129448 (divide (divide ?129449 ?129450) ?129447)) (divide ?129450 ?129449)))) (divide (inverse ?129451) ?129452))) ?129453) =>= inverse (divide (inverse (divide ?129448 (divide (divide ?129446 ?129451) ?129452))) ?129453) [129453, 129452, 129451, 129450, 129449, 129448, 129447, 129446] by Super 25671 with 53 at 1,1,1,1,3
6328 Id : 26075, {_}: inverse (divide (divide ?131096 (divide ?131097 (divide (inverse ?131098) ?131099))) ?131100) =<= inverse (divide (inverse (divide ?131097 (divide (divide ?131096 ?131098) ?131099))) ?131100) [131100, 131099, 131098, 131097, 131096] by Demod 25729 with 53 at 1,2,1,1,2
6329 Id : 26111, {_}: inverse (divide (divide ?131425 (divide ?131426 (divide (inverse (inverse ?131427)) ?131428))) ?131429) =>= inverse (divide (inverse (divide ?131426 (divide (multiply ?131425 ?131427) ?131428))) ?131429) [131429, 131428, 131427, 131426, 131425] by Super 26075 with 3 at 1,2,1,1,1,3
6330 Id : 30666, {_}: inverse (inverse (divide (inverse (divide ?153822 (divide (multiply ?153823 ?153824) ?153825))) ?153826)) =>= multiply ?153823 (divide (inverse (divide ?153822 (divide (inverse (inverse ?153824)) ?153825))) ?153826) [153826, 153825, 153824, 153823, 153822] by Super 15659 with 26111 at 1,2
6331 Id : 30731, {_}: inverse (inverse (multiply ?154370 ?154371)) =<= multiply ?154370 (divide (inverse (divide ?154372 (divide (inverse (inverse ?154371)) (divide ?154373 ?154374)))) (divide (divide ?154374 ?154373) ?154372)) [154374, 154373, 154372, 154371, 154370] by Super 30666 with 2 at 1,1,2
6332 Id : 31025, {_}: inverse (inverse (multiply ?155310 ?155311)) =>= multiply ?155310 (inverse (inverse ?155311)) [155311, 155310] by Demod 30731 with 2 at 2,3
6333 Id : 7367, {_}: inverse ?36880 =<= multiply (multiply (multiply ?36881 ?36882) (divide (divide (inverse ?36882) ?36881) (multiply ?36883 ?36880))) ?36883 [36883, 36882, 36881, 36880] by Super 7303 with 3 at 1,1,3
6334 Id : 15740, {_}: inverse (inverse (divide (divide ?83867 ?83868) ?83869)) =>= multiply ?83867 (divide (inverse ?83868) ?83869) [83869, 83868, 83867] by Demod 15584 with 6973 at 2,2,3
6335 Id : 15787, {_}: inverse (inverse (multiply (multiply ?84179 ?84180) (inverse (multiply ?84181 ?84182)))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Super 15740 with 9554 at 1,1,2
6336 Id : 15809, {_}: multiply ?84179 (multiply (inverse (inverse ?84180)) (inverse (multiply ?84181 ?84182))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Demod 15787 with 12858 at 2
6337 Id : 16238, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =<= multiply (multiply (multiply ?86043 ?86044) (divide (divide (inverse ?86044) ?86043) (multiply ?86045 (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041)))) ?86045 [86045, 86044, 86043, 86042, 86041, 86040] by Super 7367 with 15809 at 2,2,1,3
6338 Id : 16326, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =>= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86042, 86041, 86040] by Demod 16238 with 7367 at 3
6339 Id : 31064, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?155519)) ?155520)) ?155521)) =>= multiply (inverse (inverse ?155520)) (inverse (inverse (inverse (multiply ?155521 ?155519)))) [155521, 155520, 155519] by Super 31025 with 16326 at 1,2
6340 Id : 30884, {_}: inverse (inverse (multiply ?154370 ?154371)) =>= multiply ?154370 (inverse (inverse ?154371)) [154371, 154370] by Demod 30731 with 2 at 2,3
6341 Id : 32647, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?161221)) ?161222)) ?161223)) =>= multiply (inverse (inverse ?161222)) (inverse (multiply ?161223 (inverse (inverse ?161221)))) [161223, 161222, 161221] by Demod 31064 with 30884 at 1,2,3
6342 Id : 32648, {_}: inverse (inverse (divide (inverse (divide (inverse ?161225) ?161226)) ?161227)) =<= multiply (inverse (inverse ?161226)) (inverse (multiply ?161227 (inverse (inverse (divide ?161228 (divide (divide ?161225 (divide (divide ?161229 ?161230) ?161228)) (divide ?161230 ?161229))))))) [161230, 161229, 161228, 161227, 161226, 161225] by Super 32647 with 53 at 1,1,1,1,1,1,2
6343 Id : 33188, {_}: inverse (inverse (divide (inverse (divide (inverse ?162681) ?162682)) ?162683)) =>= multiply (inverse (inverse ?162682)) (inverse (multiply ?162683 (inverse ?162681))) [162683, 162682, 162681] by Demod 32648 with 53 at 1,2,1,2,3
6344 Id : 33189, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =<= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 (inverse (divide ?162688 (divide (divide ?162685 (divide (divide ?162689 ?162690) ?162688)) (divide ?162690 ?162689)))))) [162690, 162689, 162688, 162687, 162686, 162685] by Super 33188 with 53 at 1,1,1,1,1,2
6345 Id : 33732, {_}: inverse (inverse (divide (inverse (divide ?164373 ?164374)) ?164375)) =>= multiply (inverse (inverse ?164374)) (inverse (multiply ?164375 ?164373)) [164375, 164374, 164373] by Demod 33189 with 53 at 2,1,2,3
6346 Id : 33815, {_}: inverse (inverse (multiply (inverse (divide ?164946 ?164947)) ?164948)) =<= multiply (inverse (inverse ?164947)) (inverse (multiply (inverse ?164948) ?164946)) [164948, 164947, 164946] by Super 33732 with 3 at 1,1,2
6347 Id : 34748, {_}: multiply (inverse (divide ?166758 ?166759)) (inverse (inverse ?166760)) =<= multiply (inverse (inverse ?166759)) (inverse (multiply (inverse ?166760) ?166758)) [166760, 166759, 166758] by Demod 33815 with 30884 at 2
6348 Id : 34749, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse (inverse (divide ?166764 (divide (divide ?166765 (divide (divide ?166766 ?166767) ?166764)) (divide ?166767 ?166766))))) =>= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166767, 166766, 166765, 166764, 166763, 166762] by Super 34748 with 53 at 1,1,2,3
6349 Id : 35052, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse ?166765) =<= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166765, 166763, 166762] by Demod 34749 with 53 at 1,2,2
6350 Id : 35278, {_}: multiply (inverse (divide ?167869 ?167870)) (inverse (divide ?167871 ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Super 12807 with 35052 at 2
6351 Id : 33419, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 ?162685)) [162687, 162686, 162685] by Demod 33189 with 53 at 2,1,2,3
6352 Id : 35198, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (divide ?162685 ?162686)) (inverse ?162687) [162687, 162686, 162685] by Demod 33419 with 35052 at 3
6353 Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2
6354 Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2
6355 Id : 38131, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =<= multiply (inverse (divide (inverse (divide ?178376 (divide ?178374 (multiply (divide ?178377 ?178378) (divide ?178378 (divide ?178379 (multiply (divide (divide ?178380 ?178381) ?178382) (divide ?178382 (divide ?178377 (divide ?178381 ?178380)))))))))) (divide ?178379 ?178376))) (inverse ?178375) [178382, 178381, 178380, 178379, 178378, 178377, 178376, 178375, 178374] by Super 35198 with 38 at 1,1,1,1,2
6356 Id : 38834, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =>= multiply (inverse ?178374) (inverse ?178375) [178375, 178374] by Demod 38131 with 38 at 1,1,3
6357 Id : 39627, {_}: multiply ?187316 (inverse (divide (inverse ?187317) ?187318)) =>= divide ?187316 (multiply (inverse ?187317) (inverse ?187318)) [187318, 187317, 187316] by Super 3 with 38834 at 2,3
6358 Id : 39628, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =<= divide ?187320 (multiply (inverse (divide ?187323 (divide (divide ?187321 (divide (divide ?187324 ?187325) ?187323)) (divide ?187325 ?187324)))) (inverse ?187322)) [187325, 187324, 187323, 187322, 187321, 187320] by Super 39627 with 53 at 1,1,2,2
6359 Id : 39950, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =>= divide ?187320 (multiply ?187321 (inverse ?187322)) [187322, 187321, 187320] by Demod 39628 with 53 at 1,2,3
6360 Id : 45468, {_}: divide (inverse (divide ?167869 ?167870)) (multiply ?167871 (inverse ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Demod 35278 with 39950 at 2
6361 Id : 45552, {_}: divide (inverse ?204144) (multiply (divide ?204145 ?204146) (divide (divide ?204146 ?204145) (divide ?204144 (divide (inverse (divide ?204147 ?204148)) (multiply ?204149 (inverse ?204150)))))) =>= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204150, 204149, 204148, 204147, 204146, 204145, 204144] by Super 362 with 45468 at 2,2,2,2,2
6362 Id : 45856, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204148, 204147, 204150, 204149] by Demod 45552 with 362 at 2
6363 Id : 45857, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= multiply (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse ?204148) [204148, 204147, 204150, 204149] by Demod 45856 with 3 at 3
6364 Id : 46240, {_}: multiply (multiply ?206273 (inverse ?206274)) (divide ?206275 ?206276) =<= multiply (multiply ?206273 (multiply (inverse ?206274) ?206275)) (inverse ?206276) [206276, 206275, 206274, 206273] by Demod 45857 with 3 at 2
6365 Id : 30915, {_}: multiply (multiply ?67174 ?67175) (inverse (inverse ?67176)) =?= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 30884 at 2
6366 Id : 46333, {_}: multiply (multiply ?207013 (inverse (inverse ?207014))) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Super 46240 with 30915 at 1,3
6367 Id : 1890, {_}: divide (inverse (divide (divide ?8674 ?8675) ?8676)) ?8677 =<= inverse (divide (inverse (divide ?8678 ?8677)) (divide ?8676 (divide ?8678 (divide ?8675 ?8674)))) [8678, 8677, 8676, 8675, 8674] by Super 7 with 1266 at 2,2
6368 Id : 1908, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide ?8836 ?8835)) (divide ?8834 (divide ?8836 (multiply ?8833 ?8832)))) [8836, 8835, 8834, 8833, 8832] by Super 1890 with 3 at 2,2,2,1,3
6369 Id : 61, {_}: divide (inverse (divide ?349 ?350)) (divide (divide ?351 (divide ?352 ?353)) ?349) =>= inverse (divide ?351 (divide ?350 (divide ?353 ?352))) [353, 352, 351, 350, 349] by Super 4 with 2 at 2,1,1,2
6370 Id : 65, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide ?384 (divide ?383 (divide (inverse ?386) ?385))) [386, 385, 384, 383, 382] by Super 61 with 3 at 2,1,2,2
6371 Id : 16676, {_}: divide (inverse ?87869) (multiply (divide ?87870 ?87871) (divide (divide ?87871 ?87870) (divide ?87869 (divide (divide ?87872 (divide (inverse ?87873) ?87874)) (divide ?87875 ?87876))))) =>= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87876, 87875, 87874, 87873, 87872, 87871, 87870, 87869] by Super 362 with 15912 at 2,2,2,2,2
6372 Id : 16850, {_}: divide (divide ?87875 ?87876) (divide ?87872 (divide (inverse ?87873) ?87874)) =<= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87874, 87873, 87872, 87876, 87875] by Demod 16676 with 362 at 2
6373 Id : 17219, {_}: inverse (inverse (divide (divide ?91192 ?91193) (divide ?91194 (divide (inverse ?91195) ?91196)))) =>= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Super 14212 with 16850 at 1,1,2
6374 Id : 17309, {_}: multiply ?91192 (divide (inverse ?91193) (divide ?91194 (divide (inverse ?91195) ?91196))) =<= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Demod 17219 with 15659 at 2
6375 Id : 22082, {_}: inverse (divide (inverse (inverse (divide (inverse ?112093) ?112094))) (multiply ?112095 ?112096)) =<= multiply (multiply (divide (inverse ?112097) ?112098) (divide (multiply ?112098 ?112097) (multiply ?112099 (divide (inverse ?112093) (divide ?112095 (divide (inverse ?112094) ?112096)))))) ?112099 [112099, 112098, 112097, 112096, 112095, 112094, 112093] by Super 7337 with 17309 at 2,2,1,3
6376 Id : 22476, {_}: inverse (divide (inverse (inverse (divide (inverse ?113967) ?113968))) (multiply ?113969 ?113970)) =>= inverse (divide (inverse ?113967) (divide ?113969 (divide (inverse ?113968) ?113970))) [113970, 113969, 113968, 113967] by Demod 22082 with 7337 at 3
6377 Id : 22508, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =<= inverse (divide (inverse (divide ?114208 (divide (divide ?114204 (divide (divide ?114209 ?114210) ?114208)) (divide ?114210 ?114209)))) (divide ?114206 (divide (inverse ?114205) ?114207))) [114210, 114209, 114208, 114207, 114206, 114205, 114204] by Super 22476 with 53 at 1,1,1,1,1,2
6378 Id : 22780, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =>= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22508 with 53 at 1,1,3
6379 Id : 40158, {_}: inverse (inverse (divide ?188657 ?188658)) =<= multiply (multiply (multiply ?188659 ?188660) (divide (divide (inverse ?188660) ?188659) (divide ?188661 (multiply ?188657 (inverse ?188658))))) ?188661 [188661, 188660, 188659, 188658, 188657] by Super 7367 with 39950 at 2,2,1,3
6380 Id : 7191, {_}: ?36095 =<= multiply (multiply (multiply ?36096 ?36097) (divide (divide (inverse ?36097) ?36096) (divide ?36098 ?36095))) ?36098 [36098, 36097, 36096, 36095] by Super 7101 with 3 at 1,1,3
6381 Id : 40350, {_}: inverse (inverse (divide ?188657 ?188658)) =>= multiply ?188657 (inverse ?188658) [188658, 188657] by Demod 40158 with 7191 at 3
6382 Id : 40577, {_}: inverse (divide (multiply ?114204 (inverse ?114205)) (multiply ?114206 ?114207)) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22780 with 40350 at 1,1,2
6383 Id : 40645, {_}: divide (divide ?189801 (divide (multiply ?189802 (inverse ?189803)) ?189804)) ?189805 =<= multiply (multiply ?189801 ?189804) (inverse (multiply ?189805 (divide ?189802 ?189803))) [189805, 189804, 189803, 189802, 189801] by Super 9554 with 40350 at 1,2,1,2
6384 Id : 30968, {_}: multiply ?154958 (inverse (multiply ?154959 ?154960)) =<= divide ?154958 (multiply ?154959 (inverse (inverse ?154960))) [154960, 154959, 154958] by Super 3 with 30884 at 2,3
6385 Id : 40629, {_}: multiply ?189704 (inverse (multiply ?189705 (divide ?189706 ?189707))) =>= divide ?189704 (multiply ?189705 (multiply ?189706 (inverse ?189707))) [189707, 189706, 189705, 189704] by Super 30968 with 40350 at 2,2,3
6386 Id : 62131, {_}: divide (divide ?257834 (divide (multiply ?257835 (inverse ?257836)) ?257837)) ?257838 =<= divide (multiply ?257834 ?257837) (multiply ?257838 (multiply ?257835 (inverse ?257836))) [257838, 257837, 257836, 257835, 257834] by Demod 40645 with 40629 at 3
6387 Id : 62178, {_}: divide (divide ?258249 (divide (multiply (multiply (divide ?258250 ?258251) (divide (divide ?258251 ?258250) (divide (inverse ?258252) ?258253))) (inverse ?258252)) ?258254)) ?258255 =>= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258252, 258251, 258250, 258249] by Super 62131 with 6973 at 2,2,3
6388 Id : 62493, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =<= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258249] by Demod 62178 with 6973 at 1,2,1,2
6389 Id : 62632, {_}: inverse (divide (divide ?114204 (divide ?114207 (inverse ?114205))) ?114206) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 40577 with 62493 at 1,2
6390 Id : 62637, {_}: inverse (divide (divide ?114204 (multiply ?114207 ?114205)) ?114206) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 62632 with 3 at 2,1,1,2
6391 Id : 62641, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide (divide ?384 (multiply ?385 ?386)) ?383) [386, 385, 384, 383, 382] by Demod 65 with 62637 at 3
6392 Id : 19, {_}: divide (inverse ?90) (divide (divide ?91 ?92) (inverse (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93)))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Super 2 with 15 at 1,1,2
6393 Id : 40, {_}: divide (inverse ?90) (multiply (divide ?91 ?92) (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Demod 19 with 3 at 2,2
6394 Id : 89822, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =?= inverse (divide (divide (inverse ?333800) (multiply (divide ?333801 ?333802) (divide (divide ?333802 ?333801) (divide ?333800 (multiply (divide (divide ?333803 ?333804) ?333805) (divide ?333805 (divide ?333799 (divide ?333804 ?333803)))))))) ?333798) [333805, 333804, 333803, 333802, 333801, 333800, 333799, 333798, 333797] by Super 62641 with 40 at 1,2,2
6395 Id : 90396, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =>= inverse (divide ?333799 ?333798) [333799, 333798, 333797] by Demod 89822 with 40 at 1,1,3
6396 Id : 101099, {_}: inverse (divide (divide ?31 (divide ?32 ?33)) ?30) =?= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [30, 33, 32, 31] by Demod 7 with 90396 at 2
6397 Id : 101112, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (divide (inverse (divide ?8836 ?8835)) (divide (multiply ?8833 ?8832) ?8836)) ?8834) [8836, 8835, 8834, 8833, 8832] by Demod 1908 with 101099 at 3
6398 Id : 101118, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8835, 8834, 8833, 8832] by Demod 101112 with 90396 at 1,1,3
6399 Id : 101316, {_}: divide (inverse (divide (divide (inverse ?356253) ?356254) (divide ?356255 (multiply ?356254 ?356253)))) ?356256 =>= inverse (inverse (divide ?356255 ?356256)) [356256, 356255, 356254, 356253] by Super 101118 with 90396 at 1,3
6400 Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2
6401 Id : 101095, {_}: inverse (divide (divide (inverse ?56) ?55) (divide ?54 (multiply ?55 ?56))) =>= ?54 [54, 55, 56] by Demod 12 with 90396 at 2
6402 Id : 101519, {_}: divide ?356255 ?356256 =<= inverse (inverse (divide ?356255 ?356256)) [356256, 356255] by Demod 101316 with 101095 at 1,2
6403 Id : 101520, {_}: divide ?356255 ?356256 =<= multiply ?356255 (inverse ?356256) [356256, 356255] by Demod 101519 with 40350 at 3
6404 Id : 102152, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Demod 46333 with 101520 at 1,2
6405 Id : 102153, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= divide (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) ?207016 [207016, 207015, 207014, 207013] by Demod 102152 with 101520 at 3
6406 Id : 102154, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =>= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102153 with 101520 at 1,3
6407 Id : 102308, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =<= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102154 with 3 at 1,2
6408 Id : 102309, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =>= divide (multiply (multiply ?207013 ?207014) ?207015) ?207016 [207016, 207015, 207014, 207013] by Demod 102308 with 3 at 1,3
6409 Id : 102310, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38554) (multiply (inverse ?38554) ?38553)) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 7678 with 102309 at 1,3
6410 Id : 52549, {_}: multiply (multiply ?225200 (inverse (inverse ?225201))) (divide ?225202 ?225203) =<= multiply (multiply (multiply ?225200 ?225201) (inverse (inverse ?225202))) (inverse ?225203) [225203, 225202, 225201, 225200] by Super 46240 with 30915 at 1,3
6411 Id : 52684, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (divide ?226213 (inverse ?226214)) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Super 52549 with 30915 at 3
6412 Id : 53235, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 52684 with 3 at 2,2
6413 Id : 102165, {_}: multiply (divide ?226211 (inverse ?226212)) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 53235 with 101520 at 1,2
6414 Id : 102295, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 102165 with 3 at 1,2
6415 Id : 30916, {_}: multiply (divide ?66357 ?66358) (inverse (inverse ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12770 with 30884 at 2
6416 Id : 9965, {_}: divide (divide ?51846 (divide (inverse (inverse ?51847)) ?51848)) ?51849 =>= multiply (multiply ?51846 ?51848) (inverse (multiply ?51849 ?51847)) [51849, 51848, 51847, 51846] by Super 9472 with 7237 at 1,1,3
6417 Id : 9976, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (multiply ?51938 (inverse ?51940)) (inverse (multiply ?51941 ?51939)) [51941, 51940, 51939, 51938] by Super 9965 with 3 at 2,1,2
6418 Id : 40724, {_}: inverse (inverse (divide ?190294 ?190295)) =>= multiply ?190294 (inverse ?190295) [190295, 190294] by Demod 40158 with 7191 at 3
6419 Id : 40043, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= divide (multiply ?49359 ?49361) (multiply ?49362 (inverse ?49360)) [49362, 49361, 49360, 49359] by Demod 9552 with 39950 at 3
6420 Id : 40771, {_}: inverse (inverse (divide (divide ?190577 (divide (inverse ?190578) ?190579)) ?190580)) =>= multiply (multiply ?190577 ?190579) (inverse (multiply ?190580 (inverse ?190578))) [190580, 190579, 190578, 190577] by Super 40724 with 40043 at 1,1,2
6421 Id : 42949, {_}: multiply (divide ?196696 (divide (inverse ?196697) ?196698)) (inverse ?196699) =<= multiply (multiply ?196696 ?196698) (inverse (multiply ?196699 (inverse ?196697))) [196699, 196698, 196697, 196696] by Demod 40771 with 40350 at 2
6422 Id : 42950, {_}: multiply (divide ?196701 (divide (inverse (divide ?196702 (divide (divide ?196703 (divide (divide ?196704 ?196705) ?196702)) (divide ?196705 ?196704)))) ?196706)) (inverse ?196707) =>= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196705, 196704, 196703, 196702, 196701] by Super 42949 with 53 at 2,1,2,3
6423 Id : 43226, {_}: multiply (divide ?196701 (divide ?196703 ?196706)) (inverse ?196707) =<= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196703, 196701] by Demod 42950 with 53 at 1,2,1,2
6424 Id : 43404, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (divide ?51938 (divide ?51939 (inverse ?51940))) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 9976 with 43226 at 3
6425 Id : 43406, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= multiply (divide ?51938 (multiply ?51939 ?51940)) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 43404 with 3 at 2,1,3
6426 Id : 62671, {_}: divide (divide (divide ?259262 (divide ?259263 ?259264)) (inverse (inverse ?259265))) ?259266 =>= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Super 43406 with 62493 at 1,2
6427 Id : 63074, {_}: divide (multiply (divide ?259262 (divide ?259263 ?259264)) (inverse ?259265)) ?259266 =<= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Demod 62671 with 3 at 1,2
6428 Id : 84448, {_}: divide (multiply (divide ?320603 (divide ?320604 ?320605)) (inverse ?320606)) ?320607 =<= multiply (divide (divide ?320603 (divide ?320604 ?320605)) ?320606) (inverse ?320607) [320607, 320606, 320605, 320604, 320603] by Demod 63074 with 62493 at 1,3
6429 Id : 84555, {_}: divide (multiply (divide (inverse (divide ?321565 (divide ?321566 (multiply (divide (divide ?321567 ?321568) ?321569) (divide ?321569 (divide ?321570 (divide ?321568 ?321567))))))) (divide ?321570 ?321565)) (inverse ?321571)) ?321572 =>= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321570, 321569, 321568, 321567, 321566, 321565] by Super 84448 with 15 at 1,1,3
6430 Id : 85061, {_}: divide (multiply ?321566 (inverse ?321571)) ?321572 =<= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321566] by Demod 84555 with 15 at 1,1,2
6431 Id : 85186, {_}: divide (multiply ?66357 (inverse ?66358)) (inverse ?66359) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 30916 with 85061 at 2
6432 Id : 85229, {_}: multiply (multiply ?66357 (inverse ?66358)) ?66359 =?= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85186 with 3 at 2
6433 Id : 102180, {_}: multiply (divide ?66357 ?66358) ?66359 =<= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85229 with 101520 at 1,2
6434 Id : 102296, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse (inverse (inverse ?226213)))) ?226214 [226214, 226213, 226212, 226211] by Demod 102295 with 102180 at 3
6435 Id : 102297, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply (multiply ?226211 ?226212) (inverse (inverse ?226213))) ?226214 [226214, 226213, 226212, 226211] by Demod 102296 with 3 at 1,3
6436 Id : 102298, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse ?226213)) ?226214 [226214, 226213, 226212, 226211] by Demod 102297 with 101520 at 1,3
6437 Id : 102299, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =?= multiply (multiply (multiply ?226211 ?226212) ?226213) ?226214 [226214, 226213, 226212, 226211] by Demod 102298 with 3 at 1,3
6438 Id : 102317, {_}: ?38552 =<= multiply (divide (multiply (multiply (multiply (inverse ?38553) ?38554) (inverse ?38554)) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102310 with 102299 at 1,1,3
6439 Id : 102318, {_}: ?38552 =<= multiply (divide (multiply (divide (multiply (inverse ?38553) ?38554) ?38554) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102317 with 101520 at 1,1,1,3
6440 Id : 2791, {_}: divide (divide (inverse (multiply ?13892 ?13893)) (divide (divide (inverse ?13894) ?13895) ?13892)) (multiply ?13895 ?13894) =>= inverse ?13893 [13895, 13894, 13893, 13892] by Super 2771 with 3 at 2,2
6441 Id : 89847, {_}: divide (inverse ?334058) (multiply (divide ?334059 ?334060) (divide (divide ?334060 ?334059) (divide ?334058 (multiply (divide (divide ?334061 ?334062) ?334063) (divide ?334063 (divide ?334064 (divide ?334062 ?334061))))))) =>= ?334064 [334064, 334063, 334062, 334061, 334060, 334059, 334058] by Demod 19 with 3 at 2,2
6442 Id : 43403, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (divide ?49369 (divide ?49370 ?49371)) (inverse ?49372) [49372, 49371, 49370, 49369] by Demod 9554 with 43226 at 3
6443 Id : 85181, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (multiply ?49369 (inverse (divide ?49370 ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 43403 with 85061 at 3
6444 Id : 85235, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (divide ?49369 (multiply ?49370 (inverse ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 85181 with 39950 at 1,3
6445 Id : 89956, {_}: divide (inverse ?335244) (multiply (divide ?335245 ?335246) (divide (divide ?335246 ?335245) (divide ?335244 (multiply (divide (divide ?335247 ?335248) ?335249) (divide ?335249 (divide (divide ?335250 (multiply ?335251 (inverse ?335252))) (divide ?335248 ?335247))))))) =>= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250, 335249, 335248, 335247, 335246, 335245, 335244] by Super 89847 with 85235 at 2,2,2,2,2,2,2
6446 Id : 90764, {_}: divide ?335250 (multiply ?335251 (inverse ?335252)) =<= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250] by Demod 89956 with 40 at 2
6447 Id : 92959, {_}: divide (inverse (inverse ?344076)) ?344077 =<= multiply (multiply (multiply (inverse ?344078) ?344079) (divide (multiply (inverse ?344079) ?344078) (divide ?344080 (multiply ?344076 (inverse ?344077))))) ?344080 [344080, 344079, 344078, 344077, 344076] by Super 7678 with 90764 at 2,2,1,3
6448 Id : 93432, {_}: divide (inverse (inverse ?344076)) ?344077 =>= multiply ?344076 (inverse ?344077) [344077, 344076] by Demod 92959 with 7678 at 3
6449 Id : 94198, {_}: multiply (inverse (inverse ?346092)) (inverse (multiply ?346093 ?346094)) =?= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346094, 346093, 346092] by Super 30968 with 93432 at 3
6450 Id : 95063, {_}: multiply (inverse (divide ?346094 ?346092)) (inverse ?346093) =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 94198 with 35052 at 2
6451 Id : 102213, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 95063 with 101520 at 2
6452 Id : 102214, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= divide ?346092 (multiply ?346093 (inverse (inverse ?346094))) [346093, 346092, 346094] by Demod 102213 with 101520 at 3
6453 Id : 102215, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =?= divide ?346092 (divide ?346093 (inverse ?346094)) [346093, 346092, 346094] by Demod 102214 with 101520 at 2,3
6454 Id : 102222, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =>= divide ?346092 (multiply ?346093 ?346094) [346093, 346092, 346094] by Demod 102215 with 3 at 2,3
6455 Id : 102235, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8833, 8832, 8835, 8834] by Demod 101118 with 102222 at 2
6456 Id : 102236, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102235 with 102222 at 1,3
6457 Id : 35199, {_}: inverse (multiply (inverse (divide ?86042 ?86040)) (inverse ?86041)) =<= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86041, 86040, 86042] by Demod 16326 with 35052 at 1,2
6458 Id : 40695, {_}: inverse (multiply (inverse (divide (divide ?190115 ?190116) ?190117)) (inverse ?190118)) =>= inverse (divide (inverse (divide (multiply ?190115 (inverse ?190116)) ?190117)) ?190118) [190118, 190117, 190116, 190115] by Super 35199 with 40350 at 1,1,1,1,3
6459 Id : 46674, {_}: inverse (inverse (divide (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) ?207383)) =>= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Super 30884 with 40695 at 1,2
6460 Id : 47015, {_}: multiply (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) (inverse ?207383) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Demod 46674 with 40350 at 2
6461 Id : 31439, {_}: multiply ?157170 (inverse (multiply ?157171 ?157172)) =<= divide ?157170 (multiply ?157171 (inverse (inverse ?157172))) [157172, 157171, 157170] by Super 3 with 30884 at 2,3
6462 Id : 31475, {_}: multiply ?157430 (inverse (multiply ?157431 (multiply ?157432 ?157433))) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Super 31439 with 30884 at 2,2,3
6463 Id : 45490, {_}: multiply (inverse (inverse ?203652)) (inverse (multiply ?203653 (multiply (inverse ?203654) ?203655))) =>= divide (inverse (divide (inverse (inverse ?203655)) ?203652)) (multiply ?203653 (inverse ?203654)) [203655, 203654, 203653, 203652] by Super 31475 with 45468 at 3
6464 Id : 71413, {_}: multiply (inverse (divide (multiply (inverse ?287029) ?287030) ?287031)) (inverse ?287032) =<= divide (inverse (divide (inverse (inverse ?287030)) ?287031)) (multiply ?287032 (inverse ?287029)) [287032, 287031, 287030, 287029] by Demod 45490 with 35052 at 2
6465 Id : 71414, {_}: multiply (inverse (divide (multiply (inverse (divide ?287034 (divide (divide ?287035 (divide (divide ?287036 ?287037) ?287034)) (divide ?287037 ?287036)))) ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287037, 287036, 287035, 287034] by Super 71413 with 53 at 2,2,3
6466 Id : 72001, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =<= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 71414 with 53 at 1,1,1,1,2
6467 Id : 94096, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (multiply ?287038 (inverse ?287039))) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 72001 with 93432 at 1,1,3
6468 Id : 94118, {_}: divide (inverse (multiply (inverse ?207381) (inverse ?207382))) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 47015 with 94096 at 2
6469 Id : 102205, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 94118 with 101520 at 1,1,2
6470 Id : 102206, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207380, 207383, 207382, 207381] by Demod 102205 with 101520 at 3
6471 Id : 102244, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207381, 207380, 207383, 207382] by Demod 102206 with 102222 at 2
6472 Id : 102245, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102244 with 102222 at 3
6473 Id : 102246, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102245 with 101520 at 2,2
6474 Id : 85182, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= divide (multiply ?51938 (inverse (multiply ?51939 ?51940))) ?51941 [51941, 51940, 51939, 51938] by Demod 43406 with 85061 at 3
6475 Id : 89950, {_}: divide (inverse ?335180) (multiply (divide ?335181 ?335182) (divide (divide ?335182 ?335181) (divide ?335180 (multiply (divide (divide ?335183 ?335184) ?335185) (divide ?335185 (divide (multiply ?335186 (inverse (multiply ?335187 ?335188))) (divide ?335184 ?335183))))))) =>= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186, 335185, 335184, 335183, 335182, 335181, 335180] by Super 89847 with 85182 at 2,2,2,2,2,2,2
6476 Id : 90760, {_}: multiply ?335186 (inverse (multiply ?335187 ?335188)) =<= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186] by Demod 89950 with 40 at 2
6477 Id : 94126, {_}: multiply (inverse (inverse ?345644)) (inverse (multiply ?345645 ?345646)) =?= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345646, 345645, 345644] by Super 90760 with 93432 at 3
6478 Id : 95228, {_}: multiply (inverse (divide ?345646 ?345644)) (inverse ?345645) =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 94126 with 35052 at 2
6479 Id : 102219, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 95228 with 101520 at 2
6480 Id : 102220, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345645, 345644, 345646] by Demod 102219 with 101520 at 3
6481 Id : 102238, {_}: divide ?345644 (multiply ?345645 ?345646) =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345646, 345645, 345644] by Demod 102220 with 102222 at 2
6482 Id : 102247, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply ?207383 (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102246 with 102238 at 3
6483 Id : 102262, {_}: divide ?8834 (divide (multiply ?8835 (inverse ?8832)) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102236 with 102247 at 2
6484 Id : 102264, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102262 with 101520 at 1,2,2
6485 Id : 101098, {_}: inverse (divide (divide ?5 ?4) (divide ?3 (divide ?4 ?5))) =>= ?3 [3, 4, 5] by Demod 2 with 90396 at 2
6486 Id : 102493, {_}: divide (divide (inverse (divide (inverse ?357684) ?357685)) (multiply (divide ?357686 ?357687) ?357684)) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357687, 357686, 357685, 357684] by Super 2814 with 101520 at 1,1,1,2
6487 Id : 102761, {_}: divide (divide ?357685 (multiply (multiply (divide ?357686 ?357687) ?357684) (inverse ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102493 with 102222 at 1,2
6488 Id : 102131, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Demod 31475 with 101520 at 2
6489 Id : 102132, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (divide ?157432 (inverse ?157433))) [157433, 157432, 157431, 157430] by Demod 102131 with 101520 at 2,2,3
6490 Id : 102348, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (divide (multiply ?157431 ?157432) (inverse ?157433)) [157433, 157432, 157431, 157430] by Demod 102132 with 102247 at 3
6491 Id : 102349, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =?= divide ?157430 (multiply (multiply ?157431 ?157432) ?157433) [157433, 157432, 157431, 157430] by Demod 102348 with 3 at 2,3
6492 Id : 102762, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (multiply ?357684 (inverse ?357684)))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102761 with 102349 at 1,2
6493 Id : 102763, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (divide ?357684 ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102762 with 101520 at 2,2,1,2
6494 Id : 41245, {_}: multiply ?191831 (inverse (multiply ?191832 (divide ?191833 ?191834))) =>= divide ?191831 (multiply ?191832 (multiply ?191833 (inverse ?191834))) [191834, 191833, 191832, 191831] by Super 30968 with 40350 at 2,2,3
6495 Id : 40574, {_}: multiply (divide ?83055 ?83056) (inverse ?83057) =?= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15659 with 40350 at 2
6496 Id : 41328, {_}: multiply ?192465 (divide (inverse ?192466) (multiply ?192467 (divide ?192468 ?192469))) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Super 41245 with 40574 at 2
6497 Id : 85188, {_}: divide (multiply ?83055 (inverse ?83056)) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 40574 with 85061 at 2
6498 Id : 85202, {_}: divide (multiply ?192465 (inverse ?192466)) (multiply ?192467 (divide ?192468 ?192469)) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Demod 41328 with 85188 at 2
6499 Id : 85220, {_}: divide (divide ?192465 (divide (divide ?192468 ?192469) (inverse ?192466))) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85202 with 62493 at 2
6500 Id : 85221, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =<= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85220 with 3 at 2,1,2
6501 Id : 102178, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (divide ?192468 ?192469)) [192467, 192466, 192469, 192468, 192465] by Demod 85221 with 101520 at 2,2,3
6502 Id : 102288, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (divide (multiply ?192467 ?192468) ?192469) [192467, 192466, 192469, 192468, 192465] by Demod 102178 with 102247 at 3
6503 Id : 102764, {_}: divide (divide ?357685 (divide ?357684 ?357684)) (divide (multiply (divide ?357687 ?357686) ?357686) ?357687) =>= inverse (inverse ?357685) [357686, 357687, 357684, 357685] by Demod 102763 with 102288 at 2
6504 Id : 101094, {_}: divide (inverse (divide (divide ?5777 ?5778) ?5776)) (divide ?5778 ?5777) =>= ?5776 [5776, 5778, 5777] by Demod 1266 with 90396 at 1,2
6505 Id : 102237, {_}: divide ?5776 (multiply (divide ?5778 ?5777) (divide ?5777 ?5778)) =>= ?5776 [5777, 5778, 5776] by Demod 101094 with 102222 at 2
6506 Id : 102251, {_}: divide ?5776 (divide (multiply (divide ?5778 ?5777) ?5777) ?5778) =>= ?5776 [5777, 5778, 5776] by Demod 102237 with 102247 at 2
6507 Id : 102765, {_}: divide ?357685 (divide ?357684 ?357684) =>= inverse (inverse ?357685) [357684, 357685] by Demod 102764 with 102251 at 2
6508 Id : 102313, {_}: inverse ?36880 =<= multiply (divide (multiply (multiply ?36881 ?36882) (divide (inverse ?36882) ?36881)) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 7367 with 102309 at 1,3
6509 Id : 102314, {_}: inverse ?36880 =<= multiply (divide (divide (multiply (multiply ?36881 ?36882) (inverse ?36882)) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102313 with 102309 at 1,1,3
6510 Id : 102315, {_}: inverse ?36880 =<= multiply (divide (divide (divide (multiply ?36881 ?36882) ?36882) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102314 with 101520 at 1,1,1,3
6511 Id : 102533, {_}: inverse (inverse ?357905) =<= multiply (divide (divide (divide (multiply ?357906 ?357907) ?357907) ?357906) (divide ?357908 ?357905)) ?357908 [357908, 357907, 357906, 357905] by Super 102315 with 101520 at 2,1,3
6512 Id : 102311, {_}: ?36095 =<= multiply (divide (multiply (multiply ?36096 ?36097) (divide (inverse ?36097) ?36096)) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 7191 with 102309 at 1,3
6513 Id : 102312, {_}: ?36095 =<= multiply (divide (divide (multiply (multiply ?36096 ?36097) (inverse ?36097)) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102311 with 102309 at 1,1,3
6514 Id : 102316, {_}: ?36095 =<= multiply (divide (divide (divide (multiply ?36096 ?36097) ?36097) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102312 with 101520 at 1,1,1,3
6515 Id : 102664, {_}: inverse (inverse ?357905) =>= ?357905 [357905] by Demod 102533 with 102316 at 3
6516 Id : 103069, {_}: divide ?357685 (divide ?357684 ?357684) =>= ?357685 [357684, 357685] by Demod 102765 with 102664 at 3
6517 Id : 103199, {_}: inverse (divide ?359423 ?359424) =>= divide ?359424 ?359423 [359424, 359423] by Super 101098 with 103069 at 1,2
6518 Id : 103718, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =?= divide (multiply ?8834 (multiply ?8833 ?8832)) ?8835 [8833, 8832, 8835, 8834] by Demod 102264 with 103199 at 3
6519 Id : 103734, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (inverse ?13894)) (multiply ?13895 ?13894) =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 2791 with 103718 at 1,2
6520 Id : 40697, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (multiply ?190126 (inverse ?190127)) (inverse (multiply ?190128 ?190125)) [190128, 190127, 190126, 190125] by Super 35052 with 40350 at 1,3
6521 Id : 40823, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (divide ?190126 (multiply (inverse (inverse ?190125)) ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 40697 with 9976 at 3
6522 Id : 43409, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (divide ?190126 (multiply ?190125 ?190127)) (inverse ?190128) [190128, 190127, 190126, 190125] by Demod 40823 with 43406 at 3
6523 Id : 85192, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 43409 with 85061 at 3
6524 Id : 102170, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 85192 with 101520 at 2
6525 Id : 102171, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 102170 with 101520 at 1,3
6526 Id : 102293, {_}: divide (divide ?190126 ?190127) (multiply ?190128 ?190125) =?= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190125, 190128, 190127, 190126] by Demod 102171 with 102222 at 2
6527 Id : 103736, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (multiply ?13894 (inverse ?13894))) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103734 with 102293 at 2
6528 Id : 103737, {_}: divide (divide (divide (inverse (multiply ?13892 ?13893)) (divide (inverse ?13894) (multiply ?13892 ?13895))) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103736 with 62493 at 1,2
6529 Id : 40061, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (multiply ?188029 (inverse ?188030))) [188032, 188031, 188030, 188029, 188028] by Super 40043 with 39950 at 2,3
6530 Id : 102158, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =>= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188031, 188030, 188029, 188028] by Demod 40061 with 101520 at 2,2,3
6531 Id : 102302, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188029, 188031, 188030, 188028] by Demod 102158 with 102222 at 2,1,2
6532 Id : 103711, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =<= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30] by Demod 101099 with 103199 at 2
6533 Id : 103712, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =?= divide (divide ?30 (divide ?33 ?32)) ?31 [33, 32, 31, 30] by Demod 103711 with 103199 at 3
6534 Id : 103741, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =?= divide (divide (multiply ?188028 ?188031) (divide ?188030 ?188029)) ?188032 [188032, 188029, 188031, 188030, 188028] by Demod 102302 with 103712 at 3
6535 Id : 103744, {_}: divide (divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide (inverse ?13894) ?13895)) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103737 with 103741 at 1,2
6536 Id : 103708, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114205, 114207, 114204, 114206] by Demod 62637 with 103199 at 2
6537 Id : 103709, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= divide (divide ?114206 (divide (inverse ?114205) ?114207)) ?114204 [114205, 114207, 114204, 114206] by Demod 103708 with 103199 at 3
6538 Id : 103749, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide ?13894 (multiply ?13895 ?13894))) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103744 with 103709 at 1,2
6539 Id : 103750, {_}: divide (divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) (divide ?13894 ?13894)) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103749 with 103741 at 2
6540 Id : 103751, {_}: divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) ?13895 =>= inverse ?13893 [13895, 13893, 13892] by Demod 103750 with 103069 at 1,2
6541 Id : 2811, {_}: divide (divide (inverse (multiply ?14050 ?14051)) (divide (multiply ?14052 ?14053) ?14050)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Super 2771 with 3 at 1,2,1,2
6542 Id : 103699, {_}: divide (divide ?346092 ?346094) ?346093 =?= divide ?346092 (multiply ?346093 ?346094) [346093, 346094, 346092] by Demod 102222 with 103199 at 1,2
6543 Id : 103754, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =?= divide (divide (multiply ?258249 ?258254) ?258253) ?258255 [258255, 258254, 258253, 258249] by Demod 62493 with 103699 at 3
6544 Id : 103756, {_}: divide (divide (multiply (inverse (multiply ?14050 ?14051)) ?14050) (multiply ?14052 ?14053)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Demod 2811 with 103754 at 2
6545 Id : 103714, {_}: divide (divide ?54 (multiply ?55 ?56)) (divide (inverse ?56) ?55) =>= ?54 [56, 55, 54] by Demod 101095 with 103199 at 2
6546 Id : 103765, {_}: multiply (inverse (multiply ?14050 ?14051)) ?14050 =>= inverse ?14051 [14051, 14050] by Demod 103756 with 103714 at 2
6547 Id : 103766, {_}: divide (multiply (inverse ?13893) ?13895) ?13895 =>= inverse ?13893 [13895, 13893] by Demod 103751 with 103765 at 1,1,2
6548 Id : 103767, {_}: ?38552 =<= multiply (divide (multiply (inverse ?38553) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38553, 38552] by Demod 102318 with 103766 at 1,1,1,3
6549 Id : 103801, {_}: multiply ?360754 (divide ?360755 ?360756) =>= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Super 3 with 103199 at 2,3
6550 Id : 102172, {_}: divide (divide ?83055 ?83056) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 85188 with 101520 at 1,2
6551 Id : 102958, {_}: divide (divide ?358448 (inverse ?358449)) ?358450 =>= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Super 102172 with 102664 at 1,2,3
6552 Id : 103012, {_}: divide (multiply ?358448 ?358449) ?358450 =<= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Demod 102958 with 3 at 1,2
6553 Id : 104738, {_}: divide (multiply ?360754 ?360755) ?360756 =?= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Demod 103801 with 103012 at 2
6554 Id : 104742, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38553) ?38552) ?38555) ?38555 [38555, 38553, 38552] by Demod 103767 with 104738 at 1,3
6555 Id : 102256, {_}: divide (inverse ?35) (divide (multiply (divide ?36 ?37) (divide ?37 ?36)) (divide ?35 (divide ?38 ?39))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 362 with 102247 at 2
6556 Id : 102304, {_}: divide (inverse ?35) (divide (divide (divide ?36 ?37) (divide ?39 (multiply (divide ?37 ?36) ?38))) ?35) =>= divide ?39 ?38 [38, 39, 37, 36, 35] by Demod 102256 with 102302 at 2,2
6557 Id : 103730, {_}: divide (multiply (inverse ?35) (multiply ?35 (divide ?39 (multiply (divide ?37 ?36) ?38)))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 102304 with 103718 at 2
6558 Id : 104003, {_}: divide (multiply (inverse ?35) (divide (multiply ?35 ?39) (multiply (divide ?37 ?36) ?38))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 103730 with 103012 at 2,1,2
6559 Id : 104004, {_}: divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) (multiply (divide ?37 ?36) ?38)) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 104003 with 103012 at 1,2
6560 Id : 104036, {_}: divide (divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38) (divide ?37 ?36)) (divide ?36 ?37) =>= divide ?39 ?38 [36, 37, 38, 39, 35] by Demod 104004 with 103699 at 1,2
6561 Id : 103700, {_}: divide (divide ?3 (divide ?4 ?5)) (divide ?5 ?4) =>= ?3 [5, 4, 3] by Demod 101098 with 103199 at 2
6562 Id : 104037, {_}: divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104036 with 103700 at 2
6563 Id : 21134, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 20903 with 6973 at 2,1,3
6564 Id : 40046, {_}: inverse (divide (inverse (inverse ?108447)) (multiply ?108448 (inverse ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 21134 with 39950 at 1,2
6565 Id : 40707, {_}: inverse (divide (multiply ?190184 (inverse ?190185)) (multiply ?190186 (inverse ?190187))) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190187, 190186, 190185, 190184] by Super 40046 with 40350 at 1,1,2
6566 Id : 40813, {_}: inverse (divide (divide ?190184 (divide (inverse ?190187) (inverse ?190185))) ?190186) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190186, 190185, 190187, 190184] by Demod 40707 with 40043 at 1,2
6567 Id : 47405, {_}: inverse (divide (divide ?210380 (multiply (inverse ?210381) ?210382)) ?210383) =<= inverse (divide (inverse (divide (inverse ?210381) (divide ?210380 ?210382))) ?210383) [210383, 210382, 210381, 210380] by Demod 40813 with 3 at 2,1,1,2
6568 Id : 47459, {_}: inverse (divide (divide ?210809 (multiply (inverse (divide ?210810 (divide (divide ?210811 (divide (divide ?210812 ?210813) ?210810)) (divide ?210813 ?210812)))) ?210814)) ?210815) =>= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210813, 210812, 210811, 210810, 210809] by Super 47405 with 53 at 1,1,1,1,3
6569 Id : 48148, {_}: inverse (divide (divide ?212886 (multiply ?212887 ?212888)) ?212889) =<= inverse (divide (inverse (divide ?212887 (divide ?212886 ?212888))) ?212889) [212889, 212888, 212887, 212886] by Demod 47459 with 53 at 1,2,1,1,2
6570 Id : 48271, {_}: inverse (divide (divide ?213823 (multiply ?213824 ?213825)) (inverse ?213826)) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Super 48148 with 3 at 1,3
6571 Id : 48613, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Demod 48271 with 3 at 1,2
6572 Id : 103705, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =?= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213826, 213825, 213824, 213823] by Demod 48613 with 103199 at 1,1,3
6573 Id : 106200, {_}: divide (multiply ?367270 ?367271) ?367271 =>= ?367270 [367271, 367270] by Super 103069 with 104738 at 2
6574 Id : 106204, {_}: divide (inverse ?367290) ?367291 =<= inverse (multiply ?367291 ?367290) [367291, 367290] by Super 106200 with 103765 at 1,2
6575 Id : 106549, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =<= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213825, 213824, 213823, 213826] by Demod 103705 with 106204 at 2
6576 Id : 106550, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =?= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213824, 213823, 213826] by Demod 106549 with 106204 at 3
6577 Id : 47859, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =<= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210811, 210809] by Demod 47459 with 53 at 1,2,1,1,2
6578 Id : 102230, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =?= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210815, 210814, 210811, 210809] by Demod 47859 with 102222 at 1,3
6579 Id : 103696, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =<= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210814, 210811, 210809, 210815] by Demod 102230 with 103199 at 2
6580 Id : 103697, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =?= divide (multiply ?210815 ?210811) (divide ?210809 ?210814) [210814, 210811, 210809, 210815] by Demod 103696 with 103199 at 3
6581 Id : 106566, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =<= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213823, 213824, 213826] by Demod 106550 with 103697 at 2
6582 Id : 106567, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =?= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213825, 213823, 213824, 213826] by Demod 106566 with 103718 at 3
6583 Id : 106568, {_}: divide (multiply (multiply (inverse ?213826) ?213824) ?213825) ?213823 =<= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213823, 213825, 213824, 213826] by Demod 106567 with 104738 at 2
6584 Id : 106569, {_}: divide (multiply (multiply (inverse ?35) ?35) ?39) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104037 with 106568 at 2
6585 Id : 106570, {_}: ?38552 =<= multiply (divide ?38552 ?38555) ?38555 [38555, 38552] by Demod 104742 with 106569 at 1,3
6586 Id : 104876, {_}: divide (multiply ?363468 ?363469) ?363469 =>= ?363468 [363469, 363468] by Super 103069 with 104738 at 2
6587 Id : 106173, {_}: inverse ?367130 =<= divide ?367131 (multiply ?367130 ?367131) [367131, 367130] by Super 103199 with 104876 at 1,2
6588 Id : 106805, {_}: ?367778 =<= multiply (inverse ?367779) (multiply ?367779 ?367778) [367779, 367778] by Super 106570 with 106173 at 1,3
6589 Id : 106633, {_}: multiply ?367594 (multiply ?367595 ?367596) =<= divide ?367594 (divide (inverse ?367596) ?367595) [367596, 367595, 367594] by Super 3 with 106204 at 2,3
6590 Id : 104940, {_}: multiply (multiply ?363900 ?363901) ?363902 =<= divide ?363900 (divide (inverse ?363902) ?363901) [363902, 363901, 363900] by Super 3 with 104738 at 3
6591 Id : 108764, {_}: multiply ?367594 (multiply ?367595 ?367596) =?= multiply (multiply ?367594 ?367595) ?367596 [367596, 367595, 367594] by Demod 106633 with 104940 at 3
6592 Id : 109130, {_}: ?367778 =<= multiply (multiply (inverse ?367779) ?367779) ?367778 [367779, 367778] by Demod 106805 with 108764 at 3
6593 Id : 109444, {_}: a2 === a2 [] by Demod 1 with 109130 at 2
6594 Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
6595 % SZS output end CNFRefutation for GRP470-1.p
6596 11271: solved GRP470-1.p in 32.33802 using nrkbo
6597 11271: status Unsatisfiable for GRP470-1.p
6598 NO CLASH, using fixed ground order
6601 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6602 (divide (divide ?5 ?4) ?2)
6605 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6607 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6608 [8, 7] by multiply ?7 ?8
6611 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
6612 [] by prove_these_axioms_3
6616 11326: inverse 2 1 0
6619 11326: multiply 5 2 4 0,2
6620 11326: b3 2 0 2 2,1,2
6621 11326: a3 2 0 2 1,1,2
6622 NO CLASH, using fixed ground order
6625 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6626 (divide (divide ?5 ?4) ?2)
6629 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6631 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6632 [8, 7] by multiply ?7 ?8
6635 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
6636 [] by prove_these_axioms_3
6640 11327: inverse 2 1 0
6643 11327: multiply 5 2 4 0,2
6644 11327: b3 2 0 2 2,1,2
6645 11327: a3 2 0 2 1,1,2
6646 NO CLASH, using fixed ground order
6649 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
6650 (divide (divide ?5 ?4) ?2)
6653 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6655 multiply ?7 ?8 =>= divide ?7 (inverse ?8)
6656 [8, 7] by multiply ?7 ?8
6659 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
6660 [] by prove_these_axioms_3
6664 11328: inverse 2 1 0
6667 11328: multiply 5 2 4 0,2
6668 11328: b3 2 0 2 2,1,2
6669 11328: a3 2 0 2 1,1,2
6672 Found proof, 38.615883s
6673 % SZS status Unsatisfiable for GRP471-1.p
6674 % SZS output start CNFRefutation for GRP471-1.p
6675 Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
6676 Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6677 Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
6678 Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2
6679 Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2
6680 Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2
6681 Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2
6682 Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2
6683 Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3
6684 Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2
6685 Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2
6686 Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2
6687 Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2
6688 Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2
6689 Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3
6690 Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2
6691 Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3
6692 Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3
6693 Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3
6694 Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2
6695 Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2
6696 Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2
6697 Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3
6698 Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3
6699 Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2
6700 Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3
6701 Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3
6702 Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3
6703 Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2
6704 Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3
6705 Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3
6706 Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3
6707 Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3
6708 Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3
6709 Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2
6710 Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3
6711 Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3
6712 Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3
6713 Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3
6714 Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3
6715 Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3
6716 Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3
6717 Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3
6718 Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3
6719 Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3
6720 Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2
6721 Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2
6722 Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2
6723 Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3
6724 Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2
6725 Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2
6726 Id : 17, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (divide (divide ?76 ?77) (inverse (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78)))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Super 2 with 15 at 2,2,1,1,2
6727 Id : 66361, {_}: divide (inverse (divide ?259836 (divide ?259837 ?259838))) (divide (multiply (divide ?259839 ?259840) (divide ?259840 (divide ?259838 (multiply (divide (divide ?259841 ?259842) ?259843) (divide ?259843 (divide ?259839 (divide ?259842 ?259841))))))) ?259836) =>= ?259837 [259843, 259842, 259841, 259840, 259839, 259838, 259837, 259836] by Demod 17 with 3 at 1,2,2
6728 Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3
6729 Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3
6730 Id : 13153, {_}: inverse (inverse (multiply (multiply ?68629 ?68630) (inverse (multiply (divide ?68631 ?68632) ?68633)))) =<= multiply ?68629 (divide (inverse (inverse ?68630)) (multiply ?68631 (multiply (inverse ?68632) ?68633))) [68633, 68632, 68631, 68630, 68629] by Super 12858 with 12807 at 2,3
6731 Id : 15503, {_}: inverse (inverse (divide (multiply ?81665 ?81666) (multiply ?81667 (multiply (inverse ?81668) ?81669)))) =<= multiply ?81665 (divide (inverse (inverse ?81666)) (multiply ?81667 (multiply (inverse ?81668) ?81669))) [81669, 81668, 81667, 81666, 81665] by Demod 13153 with 12807 at 1,1,2
6732 Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2
6733 Id : 15524, {_}: inverse (inverse (divide (multiply ?81857 ?81858) (multiply (multiply (divide ?81859 ?81860) (divide (divide ?81860 ?81859) (divide (multiply (inverse ?81861) ?81862) ?81863))) (multiply (inverse ?81861) ?81862)))) =>= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81862, 81861, 81860, 81859, 81858, 81857] by Super 15503 with 6973 at 2,2,3
6734 Id : 15656, {_}: inverse (inverse (divide (multiply ?81857 ?81858) ?81863)) =<= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81858, 81857] by Demod 15524 with 6973 at 2,1,1,2
6735 Id : 23797, {_}: divide (divide ?119374 (divide (inverse ?119375) (divide (inverse (inverse ?119376)) ?119377))) ?119378 =<= multiply (inverse (inverse (divide (multiply ?119374 ?119376) ?119377))) (inverse (divide ?119378 ?119375)) [119378, 119377, 119376, 119375, 119374] by Super 9552 with 15656 at 1,3
6736 Id : 23859, {_}: divide (divide (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) (divide (inverse ?119934) (divide (inverse (inverse ?119932)) ?119935))) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Super 23797 with 7157 at 1,1,1,1,3
6737 Id : 13062, {_}: inverse (inverse (divide (divide ?67961 ?67962) (multiply ?67963 (multiply (inverse ?67964) ?67965)))) =>= multiply ?67961 (multiply (inverse ?67962) (inverse (multiply (divide ?67963 ?67964) ?67965))) [67965, 67964, 67963, 67962, 67961] by Super 12770 with 12807 at 1,1,2
6738 Id : 16664, {_}: inverse (inverse (divide (divide ?87645 ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649)))) =>= multiply ?87645 (divide (inverse ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649))) [87649, 87648, 87647, 87646, 87645] by Demod 13062 with 12807 at 2,3
6739 Id : 16690, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =<= multiply ?87882 (divide (inverse ?87883) (multiply (multiply (divide ?87885 ?87886) (divide (divide ?87886 ?87885) (divide (multiply (inverse ?87887) ?87888) ?87884))) (multiply (inverse ?87887) ?87888))) [87888, 87887, 87886, 87885, 87884, 87883, 87882] by Super 16664 with 6973 at 2,1,1,2
6740 Id : 16778, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =>= multiply ?87882 (divide (inverse ?87883) ?87884) [87884, 87883, 87882] by Demod 16690 with 6973 at 2,2,3
6741 Id : 16836, {_}: multiply ?88530 (inverse (divide (divide ?88531 ?88532) ?88533)) =>= divide ?88530 (multiply ?88531 (divide (inverse ?88532) ?88533)) [88533, 88532, 88531, 88530] by Super 3 with 16778 at 2,3
6742 Id : 16941, {_}: divide (divide ?89130 (divide (inverse ?89131) ?89132)) (divide ?89133 ?89134) =<= divide (multiply ?89130 ?89132) (multiply ?89133 (divide (inverse ?89134) ?89131)) [89134, 89133, 89132, 89131, 89130] by Super 9552 with 16836 at 3
6743 Id : 17721, {_}: divide (inverse ?92223) (multiply (divide ?92224 ?92225) (divide (divide ?92225 ?92224) (divide ?92223 (divide (divide ?92226 (divide (inverse ?92227) ?92228)) (divide ?92229 ?92230))))) =>= divide (multiply ?92229 (divide (inverse ?92230) ?92227)) (multiply ?92226 ?92228) [92230, 92229, 92228, 92227, 92226, 92225, 92224, 92223] by Super 362 with 16941 at 2,2,2,2,2
6744 Id : 18088, {_}: divide (divide ?94725 ?94726) (divide ?94727 (divide (inverse ?94728) ?94729)) =<= divide (multiply ?94725 (divide (inverse ?94726) ?94728)) (multiply ?94727 ?94729) [94729, 94728, 94727, 94726, 94725] by Demod 17721 with 362 at 2
6745 Id : 18882, {_}: divide (divide ?99448 ?99449) (divide ?99450 (divide (inverse (inverse ?99451)) ?99452)) =>= divide (multiply ?99448 (multiply (inverse ?99449) ?99451)) (multiply ?99450 ?99452) [99452, 99451, 99450, 99449, 99448] by Super 18088 with 3 at 2,1,3
6746 Id : 18956, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =?= divide (multiply ?100120 (multiply (inverse (inverse ?100121)) ?100123)) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Super 18882 with 3 at 1,2
6747 Id : 19253, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =>= divide (inverse (inverse (multiply (multiply ?100120 ?100121) ?100123))) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Demod 18956 with 12858 at 1,3
6748 Id : 24073, {_}: divide (divide (inverse (inverse (multiply (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) ?119932))) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Demod 23859 with 19253 at 1,2
6749 Id : 24074, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =<= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24073 with 7157 at 1,1,1,1,2
6750 Id : 18174, {_}: divide (divide ?95484 (inverse ?95485)) (divide ?95486 (divide (inverse ?95487) ?95488)) =>= divide (inverse (inverse (divide (multiply ?95484 ?95485) ?95487))) (multiply ?95486 ?95488) [95488, 95487, 95486, 95485, 95484] by Super 18088 with 15656 at 1,3
6751 Id : 20071, {_}: divide (multiply ?105383 ?105384) (divide ?105385 (divide (inverse ?105386) ?105387)) =<= divide (inverse (inverse (divide (multiply ?105383 ?105384) ?105386))) (multiply ?105385 ?105387) [105387, 105386, 105385, 105384, 105383] by Demod 18174 with 3 at 1,2
6752 Id : 20108, {_}: divide (multiply (multiply (divide ?105694 ?105695) (divide (divide ?105695 ?105694) (divide ?105696 ?105697))) ?105696) (divide ?105698 (divide (inverse ?105699) ?105700)) =>= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697, 105696, 105695, 105694] by Super 20071 with 6973 at 1,1,1,1,3
6753 Id : 20428, {_}: divide ?105697 (divide ?105698 (divide (inverse ?105699) ?105700)) =<= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697] by Demod 20108 with 6973 at 1,2
6754 Id : 20476, {_}: inverse (inverse (divide (divide ?106039 (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043)) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Super 16778 with 20428 at 1,1,1,2
6755 Id : 20938, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Demod 20476 with 16778 at 2
6756 Id : 24149, {_}: inverse (inverse (multiply (multiply ?120312 (divide ?120313 ?120314)) (inverse (divide ?120315 ?120316)))) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120316, 120315, 120314, 120313, 120312] by Super 12858 with 24074 at 2,3
6757 Id : 24438, {_}: inverse (inverse (divide (divide ?120312 (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315)) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24149 with 9552 at 1,1,2
6758 Id : 24439, {_}: multiply ?120312 (divide (inverse (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24438 with 16778 at 2
6759 Id : 33216, {_}: inverse (divide (divide (inverse (inverse ?156723)) (multiply (inverse ?156724) ?156725)) ?156726) =<= multiply (multiply (divide (inverse ?156727) ?156728) (divide (multiply ?156728 ?156727) (multiply ?156729 (divide (inverse (divide (inverse ?156724) (divide ?156723 ?156725))) ?156726)))) ?156729 [156729, 156728, 156727, 156726, 156725, 156724, 156723] by Super 7337 with 24439 at 2,2,1,3
6760 Id : 33721, {_}: inverse (divide (divide (inverse (inverse ?158945)) (multiply (inverse ?158946) ?158947)) ?158948) =>= inverse (divide (inverse (divide (inverse ?158946) (divide ?158945 ?158947))) ?158948) [158948, 158947, 158946, 158945] by Demod 33216 with 7337 at 3
6761 Id : 33722, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =<= inverse (divide (inverse (divide (inverse (divide ?158954 (divide (divide ?158951 (divide (divide ?158955 ?158956) ?158954)) (divide ?158956 ?158955)))) (divide ?158950 ?158952))) ?158953) [158956, 158955, 158954, 158953, 158952, 158951, 158950] by Super 33721 with 53 at 1,2,1,1,2
6762 Id : 34010, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =>= inverse (divide (inverse (divide ?158951 (divide ?158950 ?158952))) ?158953) [158953, 158952, 158951, 158950] by Demod 33722 with 53 at 1,1,1,1,3
6763 Id : 34077, {_}: inverse (inverse (divide (inverse (divide ?159790 (divide ?159791 ?159792))) ?159793)) =<= multiply (inverse (inverse ?159791)) (divide (inverse (multiply ?159790 ?159792)) ?159793) [159793, 159792, 159791, 159790] by Super 16778 with 34010 at 1,2
6764 Id : 34441, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= inverse (inverse (divide (inverse (divide ?106040 (divide (divide ?106039 ?106041) ?106042))) ?106043)) [106043, 106042, 106041, 106040, 106039] by Demod 20938 with 34077 at 3
6765 Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2
6766 Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2
6767 Id : 43649, {_}: multiply ?191130 (divide (inverse (divide ?191131 (divide (inverse ?191132) (multiply (divide ?191133 ?191134) (divide ?191134 (divide ?191135 (multiply (divide (divide ?191136 ?191137) ?191138) (divide ?191138 (divide ?191133 (divide ?191137 ?191136)))))))))) (divide ?191135 ?191131)) =>= inverse (inverse (divide ?191130 ?191132)) [191138, 191137, 191136, 191135, 191134, 191133, 191132, 191131, 191130] by Super 34441 with 38 at 1,1,3
6768 Id : 44429, {_}: multiply ?191130 (inverse ?191132) =<= inverse (inverse (divide ?191130 ?191132)) [191132, 191130] by Demod 43649 with 38 at 2,2
6769 Id : 44886, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (multiply ?119933 (inverse ?119935)) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24074 with 44429 at 1,3
6770 Id : 44891, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (divide (inverse ?119934) (inverse ?119935))) ?119936 [119936, 119935, 119934, 119933] by Demod 44886 with 9552 at 3
6771 Id : 44892, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (multiply (inverse ?119934) ?119935)) ?119936 [119936, 119935, 119934, 119933] by Demod 44891 with 3 at 2,1,3
6772 Id : 66804, {_}: divide (inverse (divide ?265003 (divide (divide ?265004 (multiply (inverse ?265005) ?265006)) ?265007))) (divide (multiply (divide ?265008 ?265009) (divide ?265009 (divide ?265007 (multiply (divide (divide ?265010 ?265011) ?265012) (divide ?265012 (divide ?265008 (divide ?265011 ?265010))))))) ?265003) =>= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265012, 265011, 265010, 265009, 265008, 265007, 265006, 265005, 265004, 265003] by Super 66361 with 44892 at 2,1,1,2
6773 Id : 39, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (multiply (divide ?76 ?77) (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Demod 17 with 3 at 1,2,2
6774 Id : 67572, {_}: divide ?265004 (multiply (inverse ?265005) ?265006) =<= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265006, 265005, 265004] by Demod 66804 with 39 at 2
6775 Id : 67796, {_}: divide (inverse (divide ?266802 (divide ?266803 (multiply (inverse ?266804) ?266805)))) (divide (divide (inverse ?266805) (inverse ?266804)) ?266802) =>= inverse (inverse ?266803) [266805, 266804, 266803, 266802] by Super 12 with 67572 at 2,1,1,2
6776 Id : 68093, {_}: ?266803 =<= inverse (inverse ?266803) [266803] by Demod 67796 with 12 at 2
6777 Id : 68404, {_}: multiply (multiply ?67174 ?67175) ?67176 =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 68093 at 2
6778 Id : 68405, {_}: multiply (multiply ?67174 ?67175) ?67176 =?= multiply ?67174 (multiply ?67175 ?67176) [67176, 67175, 67174] by Demod 68404 with 68093 at 1,2,3
6779 Id : 68861, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 68405 at 2
6780 Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
6781 % SZS output end CNFRefutation for GRP471-1.p
6782 11326: solved GRP471-1.p in 19.353208 using nrkbo
6783 11326: status Unsatisfiable for GRP471-1.p
6784 NO CLASH, using fixed ground order
6787 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
6791 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6793 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6794 [8, 7] by multiply ?7 ?8
6797 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
6798 [] by prove_these_axioms_1
6803 11333: b1 2 0 2 1,1,3
6804 11333: multiply 3 2 2 0,2
6805 11333: inverse 4 1 2 0,1,2
6806 11333: a1 2 0 2 1,1,2
6807 NO CLASH, using fixed ground order
6810 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
6814 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6816 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6817 [8, 7] by multiply ?7 ?8
6820 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
6821 [] by prove_these_axioms_1
6826 11334: b1 2 0 2 1,1,3
6827 11334: multiply 3 2 2 0,2
6828 11334: inverse 4 1 2 0,1,2
6829 11334: a1 2 0 2 1,1,2
6830 NO CLASH, using fixed ground order
6833 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
6837 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6839 multiply ?7 ?8 =?= divide ?7 (inverse ?8)
6840 [8, 7] by multiply ?7 ?8
6843 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
6844 [] by prove_these_axioms_1
6849 11335: b1 2 0 2 1,1,3
6850 11335: multiply 3 2 2 0,2
6851 11335: inverse 4 1 2 0,1,2
6852 11335: a1 2 0 2 1,1,2
6853 % SZS status Timeout for GRP475-1.p
6854 NO CLASH, using fixed ground order
6857 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
6861 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6863 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6864 [8, 7] by multiply ?7 ?8
6867 multiply (multiply (inverse b2) b2) a2 =>= a2
6868 [] by prove_these_axioms_2
6874 11373: multiply 3 2 2 0,2
6875 11373: inverse 3 1 1 0,1,1,2
6876 11373: b2 2 0 2 1,1,1,2
6877 NO CLASH, using fixed ground order
6880 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
6884 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6886 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
6887 [8, 7] by multiply ?7 ?8
6890 multiply (multiply (inverse b2) b2) a2 =>= a2
6891 [] by prove_these_axioms_2
6897 11374: multiply 3 2 2 0,2
6898 11374: inverse 3 1 1 0,1,1,2
6899 11374: b2 2 0 2 1,1,1,2
6900 NO CLASH, using fixed ground order
6903 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
6907 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6909 multiply ?7 ?8 =?= divide ?7 (inverse ?8)
6910 [8, 7] by multiply ?7 ?8
6913 multiply (multiply (inverse b2) b2) a2 =>= a2
6914 [] by prove_these_axioms_2
6920 11375: multiply 3 2 2 0,2
6921 11375: inverse 3 1 1 0,1,1,2
6922 11375: b2 2 0 2 1,1,1,2
6925 Found proof, 60.308770s
6926 % SZS status Unsatisfiable for GRP476-1.p
6927 % SZS output start CNFRefutation for GRP476-1.p
6928 Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
6929 Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
6930 Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
6931 Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
6932 Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
6933 Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
6934 Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2
6935 Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2
6936 Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2
6937 Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2
6938 Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2
6939 Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2
6940 Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
6941 Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2
6942 Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
6943 Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2
6944 Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2
6945 Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2
6946 Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2
6947 Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3
6948 Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2
6949 Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2
6950 Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2
6951 Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2
6952 Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3
6953 Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3
6954 Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2
6955 Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2
6956 Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2
6957 Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2
6958 Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2
6959 Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2
6960 Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3
6961 Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2
6962 Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2
6963 Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
6964 Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2
6965 Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2
6966 Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2
6967 Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3
6968 Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2
6969 Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2
6970 Id : 36954, {_}: inverse (divide (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 36094 with 36681 at 1,1,2
6971 Id : 37568, {_}: divide ?167565 (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) =>= ?167565 [167567, 167566, 167565] by Demod 36954 with 37291 at 2
6972 Id : 33466, {_}: ?158075 =<= multiply (multiply ?158075 (divide ?158076 ?158077)) (divide ?158077 ?158076) [158077, 158076, 158075] by Demod 33087 with 2 at 2
6973 Id : 33531, {_}: ?158517 =<= multiply (multiply ?158517 (multiply ?158518 ?158519)) (divide (inverse ?158519) ?158518) [158519, 158518, 158517] by Super 33466 with 3 at 2,1,3
6974 Id : 36952, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (divide ?158518 (inverse ?158519)) [158519, 158518, 158517] by Demod 33531 with 36681 at 3
6975 Id : 36955, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (multiply ?158518 ?158519) [158519, 158518, 158517] by Demod 36952 with 3 at 2,3
6976 Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2
6977 Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2
6978 Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2
6979 Id : 38144, {_}: ?175420 =<= divide (multiply ?175420 (multiply (divide ?175421 ?175422) ?175422)) ?175421 [175422, 175421, 175420] by Super 36955 with 36819 at 2,3
6980 Id : 38311, {_}: ?175420 =<= divide (multiply ?175420 ?175421) ?175421 [175421, 175420] by Demod 38144 with 36819 at 2,1,3
6981 Id : 38590, {_}: divide ?177333 (divide (divide (multiply ?177334 ?177335) ?177335) ?177334) =>= ?177333 [177335, 177334, 177333] by Super 37568 with 38311 at 2,2,2
6982 Id : 38627, {_}: divide ?177333 (divide ?177334 ?177334) =>= ?177333 [177334, 177333] by Demod 38590 with 38311 at 1,2,2
6983 Id : 41488, {_}: divide (divide ?193733 ?193733) ?193734 =>= inverse ?193734 [193734, 193733] by Super 37291 with 38627 at 1,3
6984 Id : 42000, {_}: multiply (divide ?195057 ?195057) ?195058 =>= inverse (inverse ?195058) [195058, 195057] by Super 3 with 41488 at 3
6985 Id : 38603, {_}: divide ?177417 (multiply ?177418 ?177417) =>= inverse ?177418 [177418, 177417] by Super 37291 with 38311 at 1,3
6986 Id : 40108, {_}: divide (multiply ?188666 ?188667) ?188667 =>= inverse (inverse ?188666) [188667, 188666] by Super 37291 with 38603 at 1,3
6987 Id : 40636, {_}: ?188666 =<= inverse (inverse ?188666) [188666] by Demod 40108 with 38311 at 2
6988 Id : 43036, {_}: multiply (divide ?197334 ?197334) ?197335 =>= ?197335 [197335, 197334] by Demod 42000 with 40636 at 3
6989 Id : 43063, {_}: multiply (multiply (inverse ?197470) ?197470) ?197471 =>= ?197471 [197471, 197470] by Super 43036 with 3 at 1,2
6990 Id : 47549, {_}: a2 =?= a2 [] by Demod 1 with 43063 at 2
6991 Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
6992 % SZS output end CNFRefutation for GRP476-1.p
6993 11374: solved GRP476-1.p in 30.053878 using kbo
6994 11374: status Unsatisfiable for GRP476-1.p
6995 NO CLASH, using fixed ground order
6998 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
7002 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7004 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7005 [8, 7] by multiply ?7 ?8
7008 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
7009 [] by prove_these_axioms_3
7013 11392: inverse 2 1 0
7016 11392: multiply 5 2 4 0,2
7017 11392: b3 2 0 2 2,1,2
7018 11392: a3 2 0 2 1,1,2
7019 NO CLASH, using fixed ground order
7022 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
7026 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7028 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7029 [8, 7] by multiply ?7 ?8
7032 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
7033 [] by prove_these_axioms_3
7037 11393: inverse 2 1 0
7040 11393: multiply 5 2 4 0,2
7041 11393: b3 2 0 2 2,1,2
7042 11393: a3 2 0 2 1,1,2
7043 NO CLASH, using fixed ground order
7046 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
7050 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7052 multiply ?7 ?8 =>= divide ?7 (inverse ?8)
7053 [8, 7] by multiply ?7 ?8
7056 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
7057 [] by prove_these_axioms_3
7061 11395: inverse 2 1 0
7064 11395: multiply 5 2 4 0,2
7065 11395: b3 2 0 2 2,1,2
7066 11395: a3 2 0 2 1,1,2
7069 Found proof, 65.047626s
7070 % SZS status Unsatisfiable for GRP477-1.p
7071 % SZS output start CNFRefutation for GRP477-1.p
7072 Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7073 Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
7074 Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
7075 Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
7076 Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
7077 Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
7078 Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2
7079 Id : 2216, {_}: divide (divide (inverse (divide (divide (divide (inverse ?9957) ?9958) ?9959) ?9960)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9960, 9959, 9958, 9957] by Super 2201 with 3 at 2,1,2
7080 Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2
7081 Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2
7082 Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2
7083 Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2
7084 Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2
7085 Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
7086 Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2
7087 Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
7088 Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2
7089 Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2
7090 Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2
7091 Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2
7092 Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3
7093 Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2
7094 Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2
7095 Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2
7096 Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2
7097 Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3
7098 Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3
7099 Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2
7100 Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2
7101 Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2
7102 Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2
7103 Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2
7104 Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2
7105 Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3
7106 Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2
7107 Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2
7108 Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
7109 Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2
7110 Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2
7111 Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2
7112 Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3
7113 Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2
7114 Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2
7115 Id : 37631, {_}: divide (divide (divide ?9960 (divide (divide (inverse ?9957) ?9958) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9958, 9957, 9960] by Demod 2216 with 37291 at 1,1,2
7116 Id : 37745, {_}: divide ?174363 ?174364 =<= inverse (divide ?174364 ?174363) [174364, 174363] by Demod 37087 with 3370 at 2
7117 Id : 37810, {_}: divide (inverse ?174753) ?174754 =>= inverse (multiply ?174754 ?174753) [174754, 174753] by Super 37745 with 3 at 1,3
7118 Id : 38028, {_}: divide (divide (divide ?9960 (divide (inverse (multiply ?9958 ?9957)) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9957, 9958, 9960] by Demod 37631 with 37810 at 1,2,1,1,2
7119 Id : 38029, {_}: divide (divide (divide ?9960 (inverse (multiply ?9959 (multiply ?9958 ?9957)))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38028 with 37810 at 2,1,1,2
7120 Id : 38096, {_}: divide (divide (multiply ?9960 (multiply ?9959 (multiply ?9958 ?9957))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38029 with 3 at 1,1,2
7121 Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2
7122 Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2
7123 Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2
7124 Id : 51854, {_}: divide (divide ?212601 (multiply ?212602 ?212603)) ?212604 =>= divide ?212601 (multiply ?212604 (multiply ?212602 ?212603)) [212604, 212603, 212602, 212601] by Super 38096 with 36819 at 1,1,2
7125 Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3
7126 Id : 1822, {_}: multiply (divide (inverse (divide (divide (divide ?7521 ?7522) (inverse ?7523)) ?7524)) (divide ?7522 ?7521)) ?7523 =>= ?7524 [7524, 7523, 7522, 7521] by Super 18 with 20 at 1,2
7127 Id : 2348, {_}: multiply (divide (inverse (divide (multiply (divide ?10333 ?10334) ?10335) ?10336)) (divide ?10334 ?10333)) ?10335 =>= ?10336 [10336, 10335, 10334, 10333] by Demod 1822 with 3 at 1,1,1,1,2
7128 Id : 2690, {_}: multiply (divide (inverse (multiply (multiply (divide ?11645 ?11646) ?11647) ?11648)) (divide ?11646 ?11645)) ?11647 =>= inverse ?11648 [11648, 11647, 11646, 11645] by Super 2348 with 3 at 1,1,1,2
7129 Id : 2723, {_}: multiply (divide (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (divide (inverse ?11879) ?11878)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Super 2690 with 3 at 1,1,1,1,1,2
7130 Id : 38038, {_}: multiply (inverse (multiply (divide (inverse ?11879) ?11878) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11878, 11879] by Demod 2723 with 37810 at 1,2
7131 Id : 38039, {_}: multiply (inverse (multiply (inverse (multiply ?11878 ?11879)) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38038 with 37810 at 1,1,1,2
7132 Id : 38184, {_}: multiply (inverse ?175473) ?175474 =<= inverse (multiply (inverse ?175474) ?175473) [175474, 175473] by Super 3 with 37810 at 3
7133 Id : 38716, {_}: multiply (multiply (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (multiply ?11878 ?11879)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38039 with 38184 at 1,2
7134 Id : 51866, {_}: divide (divide ?212677 (inverse ?212678)) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Super 51854 with 38716 at 2,1,2
7135 Id : 52301, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Demod 51866 with 3 at 1,2
7136 Id : 52302, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (inverse ?212678)) [212679, 212678, 212677] by Demod 52301 with 38716 at 2,2,3
7137 Id : 38247, {_}: divide ?175863 (inverse ?175864) =<= inverse (inverse (multiply ?175863 ?175864)) [175864, 175863] by Super 37291 with 37810 at 1,3
7138 Id : 38843, {_}: multiply ?176435 ?176436 =<= inverse (inverse (multiply ?176435 ?176436)) [176436, 176435] by Demod 38247 with 3 at 2
7139 Id : 3670, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?16718) ?16719) ?16720) ?16721)) (multiply ?16719 ?16718)) ?16720 =>= ?16721 [16721, 16720, 16719, 16718] by Super 2348 with 3 at 2,1,2
7140 Id : 3706, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?16981) ?16982) ?16983) ?16984)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16984, 16983, 16982, 16981] by Super 3670 with 3 at 1,1,1,1,1,2
7141 Id : 37609, {_}: multiply (divide (divide ?16984 (multiply (multiply (inverse ?16981) ?16982) ?16983)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16983, 16982, 16981, 16984] by Demod 3706 with 37291 at 1,1,2
7142 Id : 38847, {_}: multiply (divide (divide ?176447 (multiply (multiply (inverse ?176448) ?176449) ?176450)) (multiply (inverse ?176449) ?176448)) ?176450 =>= inverse (inverse ?176447) [176450, 176449, 176448, 176447] by Super 38843 with 37609 at 1,1,3
7143 Id : 38880, {_}: ?176447 =<= inverse (inverse ?176447) [176447] by Demod 38847 with 37609 at 2
7144 Id : 40331, {_}: multiply ?187278 (inverse ?187279) =>= divide ?187278 ?187279 [187279, 187278] by Super 3 with 38880 at 2,3
7145 Id : 52303, {_}: divide (multiply ?212677 ?212678) ?212679 =>= divide ?212677 (divide ?212679 ?212678) [212679, 212678, 212677] by Demod 52302 with 40331 at 2,3
7146 Id : 53261, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (divide (inverse ?214474) ?214473) [214474, 214473, 214472] by Super 3 with 52303 at 3
7147 Id : 53437, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (inverse (multiply ?214473 ?214474)) [214474, 214473, 214472] by Demod 53261 with 37810 at 2,3
7148 Id : 53438, {_}: multiply (multiply ?214472 ?214473) ?214474 =>= multiply ?214472 (multiply ?214473 ?214474) [214474, 214473, 214472] by Demod 53437 with 3 at 3
7149 Id : 53834, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 53438 at 2
7150 Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
7151 % SZS output end CNFRefutation for GRP477-1.p
7152 11393: solved GRP477-1.p in 32.410025 using kbo
7153 11393: status Unsatisfiable for GRP477-1.p
7154 NO CLASH, using fixed ground order
7159 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7163 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7165 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7166 [8, 7] by multiply ?7 ?8
7169 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
7170 [] by prove_these_axioms_1
7175 11411: b1 2 0 2 1,1,3
7176 11411: multiply 3 2 2 0,2
7177 11411: inverse 4 1 2 0,1,2
7178 11411: a1 2 0 2 1,1,2
7179 NO CLASH, using fixed ground order
7184 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7188 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7190 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7191 [8, 7] by multiply ?7 ?8
7194 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
7195 [] by prove_these_axioms_1
7200 11412: b1 2 0 2 1,1,3
7201 11412: multiply 3 2 2 0,2
7202 11412: inverse 4 1 2 0,1,2
7203 11412: a1 2 0 2 1,1,2
7204 NO CLASH, using fixed ground order
7209 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7213 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7215 multiply ?7 ?8 =?= divide ?7 (inverse ?8)
7216 [8, 7] by multiply ?7 ?8
7219 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
7220 [] by prove_these_axioms_1
7225 11413: b1 2 0 2 1,1,3
7226 11413: multiply 3 2 2 0,2
7227 11413: inverse 4 1 2 0,1,2
7228 11413: a1 2 0 2 1,1,2
7229 % SZS status Timeout for GRP478-1.p
7230 NO CLASH, using fixed ground order
7235 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7239 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7241 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7242 [8, 7] by multiply ?7 ?8
7245 multiply (multiply (inverse b2) b2) a2 =>= a2
7246 [] by prove_these_axioms_2
7252 11446: multiply 3 2 2 0,2
7253 11446: inverse 3 1 1 0,1,1,2
7254 11446: b2 2 0 2 1,1,1,2
7255 NO CLASH, using fixed ground order
7260 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7264 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7266 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7267 [8, 7] by multiply ?7 ?8
7270 multiply (multiply (inverse b2) b2) a2 =>= a2
7271 [] by prove_these_axioms_2
7277 11447: multiply 3 2 2 0,2
7278 11447: inverse 3 1 1 0,1,1,2
7279 11447: b2 2 0 2 1,1,1,2
7280 NO CLASH, using fixed ground order
7285 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7289 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7291 multiply ?7 ?8 =?= divide ?7 (inverse ?8)
7292 [8, 7] by multiply ?7 ?8
7295 multiply (multiply (inverse b2) b2) a2 =>= a2
7296 [] by prove_these_axioms_2
7302 11448: multiply 3 2 2 0,2
7303 11448: inverse 3 1 1 0,1,1,2
7304 11448: b2 2 0 2 1,1,1,2
7305 % SZS status Timeout for GRP479-1.p
7306 NO CLASH, using fixed ground order
7308 NO CLASH, using fixed ground order
7313 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7317 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7319 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7320 [8, 7] by multiply ?7 ?8
7323 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
7324 [] by prove_these_axioms_3
7328 11492: inverse 2 1 0
7331 11492: multiply 5 2 4 0,2
7332 11492: b3 2 0 2 2,1,2
7333 11492: a3 2 0 2 1,1,2
7334 NO CLASH, using fixed ground order
7339 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7343 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7345 multiply ?7 ?8 =>= divide ?7 (inverse ?8)
7346 [8, 7] by multiply ?7 ?8
7349 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
7350 [] by prove_these_axioms_3
7354 11493: inverse 2 1 0
7357 11493: multiply 5 2 4 0,2
7358 11493: b3 2 0 2 2,1,2
7359 11493: a3 2 0 2 1,1,2
7363 (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
7367 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7369 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
7370 [8, 7] by multiply ?7 ?8
7373 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
7374 [] by prove_these_axioms_3
7378 11491: inverse 2 1 0
7381 11491: multiply 5 2 4 0,2
7382 11491: b3 2 0 2 2,1,2
7383 11491: a3 2 0 2 1,1,2
7386 Found proof, 69.885629s
7387 % SZS status Unsatisfiable for GRP480-1.p
7388 % SZS output start CNFRefutation for GRP480-1.p
7389 Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
7390 Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
7391 Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
7392 Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2
7393 Id : 44, {_}: multiply (inverse (divide (divide (divide ?198 ?198) ?199) (divide ?200 (multiply ?199 ?201)))) ?201 =>= ?200 [201, 200, 199, 198] by Demod 8 with 3 at 2
7394 Id : 46, {_}: multiply (inverse (divide (divide (divide ?210 ?210) ?211) ?212)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 212, 211, 210] by Super 44 with 2 at 2,1,1,2
7395 Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2
7396 Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2
7397 Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2
7398 Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2
7399 Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2
7400 Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
7401 Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2
7402 Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2
7403 Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2
7404 Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2
7405 Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2
7406 Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2
7407 Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2
7408 Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2
7409 Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2
7410 Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2
7411 Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2
7412 Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2
7413 Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2
7414 Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2
7415 Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2
7416 Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2
7417 Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2
7418 Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3
7419 Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2
7420 Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3
7421 Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2
7422 Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3
7423 Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2
7424 Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3
7425 Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3
7426 Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2
7427 Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2
7428 Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2
7429 Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2
7430 Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2
7431 Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2
7432 Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2
7433 Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2
7434 Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2
7435 Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2
7436 Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2
7437 Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2
7438 Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2
7439 Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2
7440 Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3
7441 Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2
7442 Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3
7443 Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3
7444 Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3
7445 Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2
7446 Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3
7447 Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2
7448 Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2
7449 Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2
7450 Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2
7451 Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3
7452 Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2
7453 Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2
7454 Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2
7455 Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2
7456 Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3
7457 Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2
7458 Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3
7459 Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2
7460 Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2
7461 Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2
7462 Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2
7463 Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2
7464 Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2
7465 Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2
7466 Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2
7467 Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2
7468 Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2
7469 Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3
7470 Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2
7471 Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2
7472 Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2
7473 Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2
7474 Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2
7475 Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2
7476 Id : 102474, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2
7477 Id : 102475, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102474 with 101980 at 2,2
7478 Id : 102476, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102475 at 2,3
7479 Id : 102520, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102476 with 101980 at 2,3
7480 Id : 102785, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102520 with 102475 at 1,2
7481 Id : 102786, {_}: inverse (divide ?538987 ?538988) =>= divide ?538988 ?538987 [538988, 538987] by Demod 102785 with 102475 at 3
7482 Id : 104734, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 211, 210, 212] by Demod 46 with 102786 at 1,2
7483 Id : 104735, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 210, 212] by Demod 104734 with 102786 at 3
7484 Id : 104736, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 212] by Demod 104735 with 100849 at 2,1,2
7485 Id : 104737, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104736 with 100849 at 2,3
7486 Id : 104738, {_}: multiply (multiply ?212 ?211) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104737 with 3 at 1,2
7487 Id : 104739, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) ?215 [215, 213, 211, 212] by Demod 104738 with 3 at 3
7488 Id : 104774, {_}: multiply (multiply ?542474 ?542475) ?542476 =<= multiply (divide ?542474 (divide ?542477 (multiply ?542475 ?542476))) ?542477 [542477, 542476, 542475, 542474] by Demod 104738 with 3 at 3
7489 Id : 104783, {_}: multiply (multiply ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Super 104774 with 101386 at 2,2,1,3
7490 Id : 102917, {_}: multiply ?539648 (divide ?539649 ?539650) =>= divide ?539648 (divide ?539650 ?539649) [539650, 539649, 539648] by Super 102475 with 102786 at 2,2
7491 Id : 104878, {_}: multiply (divide ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Demod 104783 with 102917 at 1,2
7492 Id : 104879, {_}: multiply ?542524 ?542526 =<= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542524] by Demod 104878 with 93111 at 1,2
7493 Id : 107171, {_}: multiply (multiply ?212 ?211) ?213 =?= multiply ?212 (multiply ?211 ?213) [213, 211, 212] by Demod 104739 with 104879 at 3
7494 Id : 107392, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 107171 at 2
7495 Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
7496 % SZS output end CNFRefutation for GRP480-1.p
7497 11491: solved GRP480-1.p in 34.906181 using nrkbo
7498 11491: status Unsatisfiable for GRP480-1.p
7499 NO CLASH, using fixed ground order
7501 11510: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
7502 11510: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
7503 11510: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
7504 11510: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
7506 meet ?12 ?13 =?= meet ?13 ?12
7507 [13, 12] by commutativity_of_meet ?12 ?13
7509 join ?15 ?16 =?= join ?16 ?15
7510 [16, 15] by commutativity_of_join ?15 ?16
7512 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
7513 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
7515 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
7516 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
7517 11510: Id : 10, {_}:
7518 meet (join ?26 ?27) (join ?26 ?28)
7521 (meet (join ?26 ?27)
7522 (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
7523 [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
7528 meet a (join b (meet (join a b) (join c (meet a b))))
7533 11510: meet 17 2 4 0,2
7534 11510: join 19 2 4 0,2,2
7535 11510: c 2 0 2 2,2,2
7536 11510: b 4 0 4 1,2,2
7538 NO CLASH, using fixed ground order
7540 11511: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
7541 11511: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
7542 11511: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
7543 11511: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
7545 meet ?12 ?13 =?= meet ?13 ?12
7546 [13, 12] by commutativity_of_meet ?12 ?13
7548 join ?15 ?16 =?= join ?16 ?15
7549 [16, 15] by commutativity_of_join ?15 ?16
7551 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
7552 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
7554 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
7555 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
7556 11511: Id : 10, {_}:
7557 meet (join ?26 ?27) (join ?26 ?28)
7560 (meet (join ?26 ?27)
7561 (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
7562 [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
7567 meet a (join b (meet (join a b) (join c (meet a b))))
7572 11511: meet 17 2 4 0,2
7573 11511: join 19 2 4 0,2,2
7574 11511: c 2 0 2 2,2,2
7575 11511: b 4 0 4 1,2,2
7577 NO CLASH, using fixed ground order
7579 11512: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
7580 11512: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
7581 11512: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
7582 11512: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
7584 meet ?12 ?13 =?= meet ?13 ?12
7585 [13, 12] by commutativity_of_meet ?12 ?13
7587 join ?15 ?16 =?= join ?16 ?15
7588 [16, 15] by commutativity_of_join ?15 ?16
7590 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
7591 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
7593 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
7594 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
7595 11512: Id : 10, {_}:
7596 meet (join ?26 ?27) (join ?26 ?28)
7599 (meet (join ?26 ?27)
7600 (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
7601 [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
7606 meet a (join b (meet (join a b) (join c (meet a b))))
7611 11512: meet 17 2 4 0,2
7612 11512: join 19 2 4 0,2,2
7613 11512: c 2 0 2 2,2,2
7614 11512: b 4 0 4 1,2,2
7616 % SZS status Timeout for LAT168-1.p
7617 NO CLASH, using fixed ground order
7619 11539: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7621 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7624 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7626 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7627 [9, 8] by wajsberg_3 ?8 ?9
7629 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7630 [12, 11] by wajsberg_4 ?11 ?12
7633 implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
7634 [] by prove_wajsberg_mv_4
7639 11539: truth 4 0 1 3
7640 11539: implies 18 2 5 0,2
7641 11539: b 3 0 3 2,1,1,2
7642 11539: a 3 0 3 1,1,1,2
7643 NO CLASH, using fixed ground order
7645 11540: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7647 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7650 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7652 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7653 [9, 8] by wajsberg_3 ?8 ?9
7655 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7656 [12, 11] by wajsberg_4 ?11 ?12
7659 implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
7660 [] by prove_wajsberg_mv_4
7665 11540: truth 4 0 1 3
7666 11540: implies 18 2 5 0,2
7667 11540: b 3 0 3 2,1,1,2
7668 11540: a 3 0 3 1,1,1,2
7669 NO CLASH, using fixed ground order
7671 11541: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7673 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7676 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7678 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7679 [9, 8] by wajsberg_3 ?8 ?9
7681 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7682 [12, 11] by wajsberg_4 ?11 ?12
7685 implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
7686 [] by prove_wajsberg_mv_4
7691 11541: truth 4 0 1 3
7692 11541: implies 18 2 5 0,2
7693 11541: b 3 0 3 2,1,1,2
7694 11541: a 3 0 3 1,1,1,2
7695 % SZS status Timeout for LCL109-2.p
7696 NO CLASH, using fixed ground order
7698 11558: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7700 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7703 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7705 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7706 [9, 8] by wajsberg_3 ?8 ?9
7708 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7709 [12, 11] by wajsberg_4 ?11 ?12
7712 implies x (implies y z) =>= implies y (implies x z)
7713 [] by prove_wajsberg_lemma
7719 11558: implies 17 2 4 0,2
7720 11558: z 2 0 2 2,2,2
7721 11558: y 2 0 2 1,2,2
7723 NO CLASH, using fixed ground order
7725 11559: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7727 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7730 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7732 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7733 [9, 8] by wajsberg_3 ?8 ?9
7735 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7736 [12, 11] by wajsberg_4 ?11 ?12
7739 implies x (implies y z) =>= implies y (implies x z)
7740 [] by prove_wajsberg_lemma
7746 11559: implies 17 2 4 0,2
7747 11559: z 2 0 2 2,2,2
7748 11559: y 2 0 2 1,2,2
7750 NO CLASH, using fixed ground order
7752 11560: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7754 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7757 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7759 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7760 [9, 8] by wajsberg_3 ?8 ?9
7762 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7763 [12, 11] by wajsberg_4 ?11 ?12
7766 implies x (implies y z) =>= implies y (implies x z)
7767 [] by prove_wajsberg_lemma
7773 11560: implies 17 2 4 0,2
7774 11560: z 2 0 2 2,2,2
7775 11560: y 2 0 2 1,2,2
7777 % SZS status Timeout for LCL138-1.p
7778 NO CLASH, using fixed ground order
7780 11593: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7782 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7785 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7787 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7788 [9, 8] by wajsberg_3 ?8 ?9
7790 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7791 [12, 11] by wajsberg_4 ?11 ?12
7793 or ?14 ?15 =<= implies (not ?14) ?15
7794 [15, 14] by or_definition ?14 ?15
7796 or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
7797 [19, 18, 17] by or_associativity ?17 ?18 ?19
7798 11593: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
7800 and ?24 ?25 =<= not (or (not ?24) (not ?25))
7801 [25, 24] by and_definition ?24 ?25
7802 11593: Id : 10, {_}:
7803 and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
7804 [29, 28, 27] by and_associativity ?27 ?28 ?29
7805 11593: Id : 11, {_}:
7806 and ?31 ?32 =?= and ?32 ?31
7807 [32, 31] by and_commutativity ?31 ?32
7808 11593: Id : 12, {_}:
7809 xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
7810 [35, 34] by xor_definition ?34 ?35
7811 11593: Id : 13, {_}:
7812 xor ?37 ?38 =?= xor ?38 ?37
7813 [38, 37] by xor_commutativity ?37 ?38
7814 11593: Id : 14, {_}:
7815 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
7816 [41, 40] by and_star_definition ?40 ?41
7817 11593: Id : 15, {_}:
7818 and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
7819 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
7820 11593: Id : 16, {_}:
7821 and_star ?47 ?48 =?= and_star ?48 ?47
7822 [48, 47] by and_star_commutativity ?47 ?48
7823 11593: Id : 17, {_}: not truth =>= falsehood [] by false_definition
7826 xor x (xor truth y) =<= xor (xor x truth) y
7827 [] by prove_alternative_wajsberg_axiom
7831 11593: falsehood 1 0 0
7832 11593: and_star 7 2 0
7836 11593: implies 14 2 0
7837 11593: xor 7 2 4 0,2
7838 11593: y 2 0 2 2,2,2
7839 11593: truth 6 0 2 1,2,2
7841 NO CLASH, using fixed ground order
7843 11594: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7845 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7848 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7850 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7851 [9, 8] by wajsberg_3 ?8 ?9
7853 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7854 [12, 11] by wajsberg_4 ?11 ?12
7856 or ?14 ?15 =<= implies (not ?14) ?15
7857 [15, 14] by or_definition ?14 ?15
7859 or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
7860 [19, 18, 17] by or_associativity ?17 ?18 ?19
7861 11594: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
7863 and ?24 ?25 =<= not (or (not ?24) (not ?25))
7864 [25, 24] by and_definition ?24 ?25
7865 11594: Id : 10, {_}:
7866 and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
7867 [29, 28, 27] by and_associativity ?27 ?28 ?29
7868 11594: Id : 11, {_}:
7869 and ?31 ?32 =?= and ?32 ?31
7870 [32, 31] by and_commutativity ?31 ?32
7871 11594: Id : 12, {_}:
7872 xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
7873 [35, 34] by xor_definition ?34 ?35
7874 11594: Id : 13, {_}:
7875 xor ?37 ?38 =?= xor ?38 ?37
7876 [38, 37] by xor_commutativity ?37 ?38
7877 11594: Id : 14, {_}:
7878 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
7879 [41, 40] by and_star_definition ?40 ?41
7880 11594: Id : 15, {_}:
7881 and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
7882 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
7883 11594: Id : 16, {_}:
7884 and_star ?47 ?48 =?= and_star ?48 ?47
7885 [48, 47] by and_star_commutativity ?47 ?48
7886 11594: Id : 17, {_}: not truth =>= falsehood [] by false_definition
7889 xor x (xor truth y) =<= xor (xor x truth) y
7890 [] by prove_alternative_wajsberg_axiom
7894 11594: falsehood 1 0 0
7895 11594: and_star 7 2 0
7899 11594: implies 14 2 0
7900 11594: xor 7 2 4 0,2
7901 11594: y 2 0 2 2,2,2
7902 11594: truth 6 0 2 1,2,2
7904 NO CLASH, using fixed ground order
7906 11595: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7908 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
7911 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7913 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
7914 [9, 8] by wajsberg_3 ?8 ?9
7916 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
7917 [12, 11] by wajsberg_4 ?11 ?12
7919 or ?14 ?15 =<= implies (not ?14) ?15
7920 [15, 14] by or_definition ?14 ?15
7922 or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
7923 [19, 18, 17] by or_associativity ?17 ?18 ?19
7924 11595: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
7926 and ?24 ?25 =<= not (or (not ?24) (not ?25))
7927 [25, 24] by and_definition ?24 ?25
7928 11595: Id : 10, {_}:
7929 and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
7930 [29, 28, 27] by and_associativity ?27 ?28 ?29
7931 11595: Id : 11, {_}:
7932 and ?31 ?32 =?= and ?32 ?31
7933 [32, 31] by and_commutativity ?31 ?32
7934 11595: Id : 12, {_}:
7935 xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35)
7936 [35, 34] by xor_definition ?34 ?35
7937 11595: Id : 13, {_}:
7938 xor ?37 ?38 =?= xor ?38 ?37
7939 [38, 37] by xor_commutativity ?37 ?38
7940 11595: Id : 14, {_}:
7941 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
7942 [41, 40] by and_star_definition ?40 ?41
7943 11595: Id : 15, {_}:
7944 and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
7945 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
7946 11595: Id : 16, {_}:
7947 and_star ?47 ?48 =?= and_star ?48 ?47
7948 [48, 47] by and_star_commutativity ?47 ?48
7949 11595: Id : 17, {_}: not truth =>= falsehood [] by false_definition
7952 xor x (xor truth y) =<= xor (xor x truth) y
7953 [] by prove_alternative_wajsberg_axiom
7957 11595: falsehood 1 0 0
7958 11595: and_star 7 2 0
7962 11595: implies 14 2 0
7963 11595: xor 7 2 4 0,2
7964 11595: y 2 0 2 2,2,2
7965 11595: truth 6 0 2 1,2,2
7969 Found proof, 7.279985s
7970 % SZS status Unsatisfiable for LCL159-1.p
7971 % SZS output start CNFRefutation for LCL159-1.p
7972 Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
7973 Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19
7974 Id : 39, {_}: implies (implies ?111 ?112) ?112 =?= implies (implies ?112 ?111) ?111 [112, 111] by wajsberg_3 ?111 ?112
7975 Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
7976 Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
7977 Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
7978 Id : 17, {_}: not truth =>= falsehood [] by false_definition
7979 Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
7980 Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
7981 Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32
7982 Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
7983 Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
7984 Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
7985 Id : 12, {_}: xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
7986 Id : 207, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
7987 Id : 212, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 207 at 1,3
7988 Id : 213, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 212 with 207 at 2,3
7989 Id : 219, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 207 at 2
7990 Id : 220, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 219 with 207 at 3
7991 Id : 240, {_}: or truth ?463 =<= implies falsehood ?463 [463] by Super 6 with 17 at 1,3
7992 Id : 286, {_}: implies (implies ?477 falsehood) falsehood =>= implies (or truth ?477) ?477 [477] by Super 4 with 240 at 1,3
7993 Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2
7994 Id : 784, {_}: implies (implies ?990 truth) (implies ?991 (implies ?990 ?991)) =>= truth [991, 990] by Super 20 with 2 at 1,2,2
7995 Id : 785, {_}: implies (implies truth truth) (implies ?993 ?993) =>= truth [993] by Super 784 with 2 at 2,2,2
7996 Id : 818, {_}: implies truth (implies ?993 ?993) =>= truth [993] by Demod 785 with 2 at 1,2
7997 Id : 819, {_}: implies ?993 ?993 =>= truth [993] by Demod 818 with 2 at 2
7998 Id : 870, {_}: implies (implies (implies ?1070 ?1070) ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071, 1070] by Super 22 with 819 at 2,1,2,2
7999 Id : 898, {_}: implies (implies truth ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071] by Demod 870 with 819 at 1,1,2
8000 Id : 40, {_}: implies (implies ?114 truth) truth =>= implies ?114 ?114 [114] by Super 39 with 2 at 1,3
8001 Id : 864, {_}: implies (implies ?114 truth) truth =>= truth [114] by Demod 40 with 819 at 3
8002 Id : 899, {_}: implies (implies truth ?1071) truth =>= truth [1071] by Demod 898 with 864 at 2,2
8003 Id : 900, {_}: implies ?1071 truth =>= truth [1071] by Demod 899 with 2 at 1,2
8004 Id : 980, {_}: or ?1117 truth =>= truth [1117] by Super 6 with 900 at 3
8005 Id : 1078, {_}: or truth ?1157 =>= truth [1157] by Super 8 with 980 at 3
8006 Id : 1116, {_}: implies (implies ?477 falsehood) falsehood =>= implies truth ?477 [477] by Demod 286 with 1078 at 1,3
8007 Id : 1117, {_}: implies (implies ?477 falsehood) falsehood =>= ?477 [477] by Demod 1116 with 2 at 3
8008 Id : 218, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 207 at 2
8009 Id : 239, {_}: and_star truth ?461 =<= not (or falsehood (not ?461)) [461] by Super 218 with 17 at 1,1,3
8010 Id : 517, {_}: or (or falsehood (not ?805)) ?806 =<= implies (and_star truth ?805) ?806 [806, 805] by Super 6 with 239 at 1,3
8011 Id : 1565, {_}: or falsehood (or (not ?1468) ?1469) =<= implies (and_star truth ?1468) ?1469 [1469, 1468] by Demod 517 with 7 at 2
8012 Id : 1566, {_}: or falsehood (or (not ?1471) ?1472) =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Super 1565 with 220 at 1,3
8013 Id : 525, {_}: or falsehood (or (not ?805) ?806) =<= implies (and_star truth ?805) ?806 [806, 805] by Demod 517 with 7 at 2
8014 Id : 520, {_}: and_star truth ?814 =<= not (or falsehood (not ?814)) [814] by Super 218 with 17 at 1,1,3
8015 Id : 521, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 520 with 17 at 2,1,3
8016 Id : 564, {_}: or (or falsehood falsehood) ?828 =<= implies (and_star truth truth) ?828 [828] by Super 6 with 521 at 1,3
8017 Id : 589, {_}: or falsehood (or falsehood ?828) =<= implies (and_star truth truth) ?828 [828] by Demod 564 with 7 at 2
8018 Id : 1273, {_}: implies (or falsehood (or falsehood falsehood)) falsehood =>= and_star truth truth [] by Super 1117 with 589 at 1,2
8019 Id : 69, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
8020 Id : 241, {_}: implies (or ?465 falsehood) (implies truth ?465) =>= truth [465] by Super 69 with 17 at 2,1,2
8021 Id : 260, {_}: implies (or ?465 falsehood) ?465 =>= truth [465] by Demod 241 with 2 at 2,2
8022 Id : 1322, {_}: implies truth falsehood =>= or falsehood falsehood [] by Super 1117 with 260 at 1,2
8023 Id : 1344, {_}: falsehood =<= or falsehood falsehood [] by Demod 1322 with 2 at 2
8024 Id : 1375, {_}: or falsehood ?1348 =<= or falsehood (or falsehood ?1348) [1348] by Super 7 with 1344 at 1,2
8025 Id : 2080, {_}: implies (or falsehood falsehood) falsehood =>= and_star truth truth [] by Demod 1273 with 1375 at 1,2
8026 Id : 2081, {_}: truth =<= and_star truth truth [] by Demod 2080 with 260 at 2
8027 Id : 2088, {_}: or falsehood (or (not truth) ?1976) =<= implies truth ?1976 [1976] by Super 525 with 2081 at 1,3
8028 Id : 2092, {_}: or falsehood (or falsehood ?1976) =<= implies truth ?1976 [1976] by Demod 2088 with 17 at 1,2,2
8029 Id : 2093, {_}: or falsehood (or falsehood ?1976) =>= ?1976 [1976] by Demod 2092 with 2 at 3
8030 Id : 2094, {_}: or falsehood ?1976 =>= ?1976 [1976] by Demod 2093 with 1375 at 2
8031 Id : 2619, {_}: or (not ?1471) ?1472 =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Demod 1566 with 2094 at 2
8032 Id : 2636, {_}: implies (or (not ?2581) falsehood) falsehood =>= and_star ?2581 truth [2581] by Super 1117 with 2619 at 1,2
8033 Id : 2658, {_}: implies (or falsehood (not ?2581)) falsehood =>= and_star ?2581 truth [2581] by Demod 2636 with 8 at 1,2
8034 Id : 2659, {_}: implies (not ?2581) falsehood =>= and_star ?2581 truth [2581] by Demod 2658 with 2094 at 1,2
8035 Id : 2660, {_}: or ?2581 falsehood =>= and_star ?2581 truth [2581] by Demod 2659 with 6 at 2
8036 Id : 1407, {_}: or falsehood ?1358 =<= or falsehood (or falsehood ?1358) [1358] by Super 7 with 1344 at 1,2
8037 Id : 1408, {_}: or falsehood ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Super 1407 with 8 at 2,3
8038 Id : 2132, {_}: ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Demod 1408 with 2094 at 2
8039 Id : 2133, {_}: ?1360 =<= or ?1360 falsehood [1360] by Demod 2132 with 2094 at 3
8040 Id : 2661, {_}: ?2581 =<= and_star ?2581 truth [2581] by Demod 2660 with 2133 at 2
8041 Id : 2708, {_}: or (not ?1471) ?1472 =<= implies ?1471 ?1472 [1472, 1471] by Demod 2619 with 2661 at 1,3
8042 Id : 2725, {_}: or (not (implies ?477 falsehood)) falsehood =>= ?477 [477] by Demod 1117 with 2708 at 2
8043 Id : 2726, {_}: or (not (or (not ?477) falsehood)) falsehood =>= ?477 [477] by Demod 2725 with 2708 at 1,1,2
8044 Id : 2767, {_}: or falsehood (not (or (not ?477) falsehood)) =>= ?477 [477] by Demod 2726 with 8 at 2
8045 Id : 2768, {_}: not (or (not ?477) falsehood) =>= ?477 [477] by Demod 2767 with 2094 at 2
8046 Id : 2769, {_}: not (or falsehood (not ?477)) =>= ?477 [477] by Demod 2768 with 8 at 1,2
8047 Id : 2770, {_}: not (not ?477) =>= ?477 [477] by Demod 2769 with 2094 at 1,2
8048 Id : 2131, {_}: and_star truth ?461 =<= not (not ?461) [461] by Demod 239 with 2094 at 1,3
8049 Id : 2771, {_}: and_star truth ?477 =>= ?477 [477] by Demod 2770 with 2131 at 2
8050 Id : 563, {_}: and_star (or falsehood falsehood) ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Super 218 with 521 at 1,1,3
8051 Id : 3108, {_}: and_star falsehood ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Demod 563 with 2094 at 1,2
8052 Id : 3109, {_}: and_star falsehood ?826 =<= not (or truth (not ?826)) [826] by Demod 3108 with 2771 at 1,1,3
8053 Id : 3110, {_}: and_star falsehood ?826 =?= not truth [826] by Demod 3109 with 1078 at 1,3
8054 Id : 3111, {_}: and_star falsehood ?826 =>= falsehood [826] by Demod 3110 with 17 at 3
8055 Id : 2777, {_}: ?461 =<= not (not ?461) [461] by Demod 2131 with 2771 at 2
8056 Id : 3185, {_}: or (and_star y x) (and_star (not y) (not x)) === or (and_star y x) (and_star (not y) (not x)) [] by Demod 3184 with 220 at 1,2
8057 Id : 3184, {_}: or (and_star x y) (and_star (not y) (not x)) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3183 with 8 at 2
8058 Id : 3183, {_}: or (and_star (not y) (not x)) (and_star x y) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3182 with 2777 at 2,2,2
8059 Id : 3182, {_}: or (and_star (not y) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3181 with 2094 at 1,1,2
8060 Id : 3181, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3180 with 8 at 3
8061 Id : 3180, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3179 with 2094 at 1,2,2,2
8062 Id : 3179, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3178 with 3111 at 1,1,1,2
8063 Id : 3178, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3177 with 2777 at 2,2,3
8064 Id : 3177, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3176 with 3111 at 1,1,2,2,2
8065 Id : 3176, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3175 with 220 at 1,1,1,2
8066 Id : 3175, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3174 with 2094 at 1,2,2,3
8067 Id : 3174, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (or falsehood (not x)))) [] by Demod 3173 with 2094 at 2,1,3
8068 Id : 3173, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3172 with 220 at 1,1,2,2,2
8069 Id : 3172, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3171 with 8 at 1,1,2
8070 Id : 3171, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3170 with 3111 at 1,1,2,2,3
8071 Id : 3170, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3169 with 3111 at 1,2,1,3
8072 Id : 3169, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3168 with 8 at 1,2,2,2
8073 Id : 3168, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3167 with 17 at 2,2,1,1,2
8074 Id : 3167, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3166 with 2771 at 2,1,2,2,3
8075 Id : 3166, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (and_star truth (not x))))) [] by Demod 3165 with 220 at 1,1,2,2,3
8076 Id : 3165, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3164 with 2771 at 2,2,1,3
8077 Id : 3164, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3163 with 220 at 1,2,1,3
8078 Id : 3163, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3162 with 17 at 2,2,1,2,2,2
8079 Id : 3162, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3161 with 220 at 2,1,1,2
8080 Id : 3161, {_}: or (and_star (or (not y) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3160 with 2771 at 1,1,1,2
8081 Id : 3160, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3159 with 220 at 2,1,2,2,3
8082 Id : 3159, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star (not x) truth)))) [] by Demod 3158 with 17 at 2,1,1,2,2,3
8083 Id : 3158, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3157 with 220 at 2,2,1,3
8084 Id : 3157, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3156 with 17 at 2,1,2,1,3
8085 Id : 3156, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3155 with 220 at 2,1,2,2,2
8086 Id : 3155, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3154 with 2771 at 1,1,2,2,2
8087 Id : 3154, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3153 with 220 at 1,2
8088 Id : 3153, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3152 with 213 at 1,2,2,3
8089 Id : 3152, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (xor x truth))) [] by Demod 3151 with 213 at 2,1,3
8090 Id : 3151, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3150 with 213 at 1,2,2,2
8091 Id : 3150, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3149 with 213 at 2,1,2
8092 Id : 3149, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3148 with 220 at 2,3
8093 Id : 3148, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star (not (xor x truth)) y) [] by Demod 3147 with 220 at 1,3
8094 Id : 3147, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3146 with 8 at 2
8095 Id : 3146, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3145 with 213 at 3
8096 Id : 3145, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= xor (xor x truth) y [] by Demod 1 with 213 at 2
8097 Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom
8098 % SZS output end CNFRefutation for LCL159-1.p
8099 11595: solved LCL159-1.p in 3.608225 using lpo
8100 11595: status Unsatisfiable for LCL159-1.p
8101 NO CLASH, using fixed ground order
8103 11600: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8105 add ?4 additive_identity =>= ?4
8106 [4] by right_additive_identity ?4
8108 multiply additive_identity ?6 =>= additive_identity
8109 [6] by left_multiplicative_zero ?6
8111 multiply ?8 additive_identity =>= additive_identity
8112 [8] by right_multiplicative_zero ?8
8114 add (additive_inverse ?10) ?10 =>= additive_identity
8115 [10] by left_additive_inverse ?10
8117 add ?12 (additive_inverse ?12) =>= additive_identity
8118 [12] by right_additive_inverse ?12
8120 additive_inverse (additive_inverse ?14) =>= ?14
8121 [14] by additive_inverse_additive_inverse ?14
8123 multiply ?16 (add ?17 ?18)
8125 add (multiply ?16 ?17) (multiply ?16 ?18)
8126 [18, 17, 16] by distribute1 ?16 ?17 ?18
8127 11600: Id : 10, {_}:
8128 multiply (add ?20 ?21) ?22
8130 add (multiply ?20 ?22) (multiply ?21 ?22)
8131 [22, 21, 20] by distribute2 ?20 ?21 ?22
8132 11600: Id : 11, {_}:
8133 add ?24 ?25 =?= add ?25 ?24
8134 [25, 24] by commutativity_for_addition ?24 ?25
8135 11600: Id : 12, {_}:
8136 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
8137 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8138 11600: Id : 13, {_}:
8139 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
8140 [32, 31] by right_alternative ?31 ?32
8141 11600: Id : 14, {_}:
8142 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
8143 [35, 34] by left_alternative ?34 ?35
8144 11600: Id : 15, {_}:
8145 associator ?37 ?38 ?39
8147 add (multiply (multiply ?37 ?38) ?39)
8148 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8149 [39, 38, 37] by associator ?37 ?38 ?39
8150 11600: Id : 16, {_}:
8153 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8154 [42, 41] by commutator ?41 ?42
8157 associator x y (add u v)
8159 add (associator x y u) (associator x y v)
8160 [] by prove_linearised_form1
8164 11600: commutator 1 2 0
8165 11600: additive_inverse 6 1 0
8166 11600: multiply 22 2 0
8167 11600: additive_identity 8 0 0
8168 11600: associator 4 3 3 0,2
8169 11600: add 18 2 2 0,3,2
8170 11600: v 2 0 2 2,3,2
8171 11600: u 2 0 2 1,3,2
8174 NO CLASH, using fixed ground order
8176 11601: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8178 add ?4 additive_identity =>= ?4
8179 [4] by right_additive_identity ?4
8181 multiply additive_identity ?6 =>= additive_identity
8182 [6] by left_multiplicative_zero ?6
8184 multiply ?8 additive_identity =>= additive_identity
8185 [8] by right_multiplicative_zero ?8
8187 add (additive_inverse ?10) ?10 =>= additive_identity
8188 [10] by left_additive_inverse ?10
8190 add ?12 (additive_inverse ?12) =>= additive_identity
8191 [12] by right_additive_inverse ?12
8193 additive_inverse (additive_inverse ?14) =>= ?14
8194 [14] by additive_inverse_additive_inverse ?14
8196 multiply ?16 (add ?17 ?18)
8198 add (multiply ?16 ?17) (multiply ?16 ?18)
8199 [18, 17, 16] by distribute1 ?16 ?17 ?18
8200 11601: Id : 10, {_}:
8201 multiply (add ?20 ?21) ?22
8203 add (multiply ?20 ?22) (multiply ?21 ?22)
8204 [22, 21, 20] by distribute2 ?20 ?21 ?22
8205 11601: Id : 11, {_}:
8206 add ?24 ?25 =?= add ?25 ?24
8207 [25, 24] by commutativity_for_addition ?24 ?25
8208 11601: Id : 12, {_}:
8209 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
8210 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8211 11601: Id : 13, {_}:
8212 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
8213 [32, 31] by right_alternative ?31 ?32
8214 11601: Id : 14, {_}:
8215 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
8216 [35, 34] by left_alternative ?34 ?35
8217 11601: Id : 15, {_}:
8218 associator ?37 ?38 ?39
8220 add (multiply (multiply ?37 ?38) ?39)
8221 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8222 [39, 38, 37] by associator ?37 ?38 ?39
8223 11601: Id : 16, {_}:
8226 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8227 [42, 41] by commutator ?41 ?42
8230 associator x y (add u v)
8232 add (associator x y u) (associator x y v)
8233 [] by prove_linearised_form1
8237 11601: commutator 1 2 0
8238 11601: additive_inverse 6 1 0
8239 11601: multiply 22 2 0
8240 11601: additive_identity 8 0 0
8241 11601: associator 4 3 3 0,2
8242 11601: add 18 2 2 0,3,2
8243 11601: v 2 0 2 2,3,2
8244 11601: u 2 0 2 1,3,2
8247 NO CLASH, using fixed ground order
8249 11602: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8251 add ?4 additive_identity =>= ?4
8252 [4] by right_additive_identity ?4
8254 multiply additive_identity ?6 =>= additive_identity
8255 [6] by left_multiplicative_zero ?6
8257 multiply ?8 additive_identity =>= additive_identity
8258 [8] by right_multiplicative_zero ?8
8260 add (additive_inverse ?10) ?10 =>= additive_identity
8261 [10] by left_additive_inverse ?10
8263 add ?12 (additive_inverse ?12) =>= additive_identity
8264 [12] by right_additive_inverse ?12
8266 additive_inverse (additive_inverse ?14) =>= ?14
8267 [14] by additive_inverse_additive_inverse ?14
8269 multiply ?16 (add ?17 ?18)
8271 add (multiply ?16 ?17) (multiply ?16 ?18)
8272 [18, 17, 16] by distribute1 ?16 ?17 ?18
8273 11602: Id : 10, {_}:
8274 multiply (add ?20 ?21) ?22
8276 add (multiply ?20 ?22) (multiply ?21 ?22)
8277 [22, 21, 20] by distribute2 ?20 ?21 ?22
8278 11602: Id : 11, {_}:
8279 add ?24 ?25 =?= add ?25 ?24
8280 [25, 24] by commutativity_for_addition ?24 ?25
8281 11602: Id : 12, {_}:
8282 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
8283 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8284 11602: Id : 13, {_}:
8285 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
8286 [32, 31] by right_alternative ?31 ?32
8287 11602: Id : 14, {_}:
8288 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
8289 [35, 34] by left_alternative ?34 ?35
8290 11602: Id : 15, {_}:
8291 associator ?37 ?38 ?39
8293 add (multiply (multiply ?37 ?38) ?39)
8294 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8295 [39, 38, 37] by associator ?37 ?38 ?39
8296 11602: Id : 16, {_}:
8299 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8300 [42, 41] by commutator ?41 ?42
8303 associator x y (add u v)
8305 add (associator x y u) (associator x y v)
8306 [] by prove_linearised_form1
8310 11602: commutator 1 2 0
8311 11602: additive_inverse 6 1 0
8312 11602: multiply 22 2 0
8313 11602: additive_identity 8 0 0
8314 11602: associator 4 3 3 0,2
8315 11602: add 18 2 2 0,3,2
8316 11602: v 2 0 2 2,3,2
8317 11602: u 2 0 2 1,3,2
8320 % SZS status Timeout for RNG019-6.p
8321 NO CLASH, using fixed ground order
8323 11618: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8325 add ?4 additive_identity =>= ?4
8326 [4] by right_additive_identity ?4
8328 multiply additive_identity ?6 =>= additive_identity
8329 [6] by left_multiplicative_zero ?6
8331 multiply ?8 additive_identity =>= additive_identity
8332 [8] by right_multiplicative_zero ?8
8334 add (additive_inverse ?10) ?10 =>= additive_identity
8335 [10] by left_additive_inverse ?10
8337 add ?12 (additive_inverse ?12) =>= additive_identity
8338 [12] by right_additive_inverse ?12
8340 additive_inverse (additive_inverse ?14) =>= ?14
8341 [14] by additive_inverse_additive_inverse ?14
8343 multiply ?16 (add ?17 ?18)
8345 add (multiply ?16 ?17) (multiply ?16 ?18)
8346 [18, 17, 16] by distribute1 ?16 ?17 ?18
8347 11618: Id : 10, {_}:
8348 multiply (add ?20 ?21) ?22
8350 add (multiply ?20 ?22) (multiply ?21 ?22)
8351 [22, 21, 20] by distribute2 ?20 ?21 ?22
8352 11618: Id : 11, {_}:
8353 add ?24 ?25 =?= add ?25 ?24
8354 [25, 24] by commutativity_for_addition ?24 ?25
8355 11618: Id : 12, {_}:
8356 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
8357 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8358 11618: Id : 13, {_}:
8359 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
8360 [32, 31] by right_alternative ?31 ?32
8361 11618: Id : 14, {_}:
8362 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
8363 [35, 34] by left_alternative ?34 ?35
8364 11618: Id : 15, {_}:
8365 associator ?37 ?38 ?39
8367 add (multiply (multiply ?37 ?38) ?39)
8368 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8369 [39, 38, 37] by associator ?37 ?38 ?39
8370 11618: Id : 16, {_}:
8373 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8374 [42, 41] by commutator ?41 ?42
8377 associator (add u v) x y
8379 add (associator u x y) (associator v x y)
8380 [] by prove_linearised_form3
8384 11618: commutator 1 2 0
8385 11618: additive_inverse 6 1 0
8386 11618: multiply 22 2 0
8387 11618: additive_identity 8 0 0
8388 11618: associator 4 3 3 0,2
8391 11618: add 18 2 2 0,1,2
8392 11618: v 2 0 2 2,1,2
8393 11618: u 2 0 2 1,1,2
8394 NO CLASH, using fixed ground order
8396 11619: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8398 add ?4 additive_identity =>= ?4
8399 [4] by right_additive_identity ?4
8401 multiply additive_identity ?6 =>= additive_identity
8402 [6] by left_multiplicative_zero ?6
8404 multiply ?8 additive_identity =>= additive_identity
8405 [8] by right_multiplicative_zero ?8
8407 add (additive_inverse ?10) ?10 =>= additive_identity
8408 [10] by left_additive_inverse ?10
8410 add ?12 (additive_inverse ?12) =>= additive_identity
8411 [12] by right_additive_inverse ?12
8413 additive_inverse (additive_inverse ?14) =>= ?14
8414 [14] by additive_inverse_additive_inverse ?14
8416 multiply ?16 (add ?17 ?18)
8418 add (multiply ?16 ?17) (multiply ?16 ?18)
8419 [18, 17, 16] by distribute1 ?16 ?17 ?18
8420 11619: Id : 10, {_}:
8421 multiply (add ?20 ?21) ?22
8423 add (multiply ?20 ?22) (multiply ?21 ?22)
8424 [22, 21, 20] by distribute2 ?20 ?21 ?22
8425 11619: Id : 11, {_}:
8426 add ?24 ?25 =?= add ?25 ?24
8427 [25, 24] by commutativity_for_addition ?24 ?25
8428 11619: Id : 12, {_}:
8429 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
8430 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8431 11619: Id : 13, {_}:
8432 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
8433 [32, 31] by right_alternative ?31 ?32
8434 11619: Id : 14, {_}:
8435 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
8436 [35, 34] by left_alternative ?34 ?35
8437 11619: Id : 15, {_}:
8438 associator ?37 ?38 ?39
8440 add (multiply (multiply ?37 ?38) ?39)
8441 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8442 [39, 38, 37] by associator ?37 ?38 ?39
8443 11619: Id : 16, {_}:
8446 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8447 [42, 41] by commutator ?41 ?42
8450 associator (add u v) x y
8452 add (associator u x y) (associator v x y)
8453 [] by prove_linearised_form3
8457 11619: commutator 1 2 0
8458 11619: additive_inverse 6 1 0
8459 11619: multiply 22 2 0
8460 11619: additive_identity 8 0 0
8461 11619: associator 4 3 3 0,2
8464 11619: add 18 2 2 0,1,2
8465 11619: v 2 0 2 2,1,2
8466 11619: u 2 0 2 1,1,2
8467 NO CLASH, using fixed ground order
8469 11620: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8471 add ?4 additive_identity =>= ?4
8472 [4] by right_additive_identity ?4
8474 multiply additive_identity ?6 =>= additive_identity
8475 [6] by left_multiplicative_zero ?6
8477 multiply ?8 additive_identity =>= additive_identity
8478 [8] by right_multiplicative_zero ?8
8480 add (additive_inverse ?10) ?10 =>= additive_identity
8481 [10] by left_additive_inverse ?10
8483 add ?12 (additive_inverse ?12) =>= additive_identity
8484 [12] by right_additive_inverse ?12
8486 additive_inverse (additive_inverse ?14) =>= ?14
8487 [14] by additive_inverse_additive_inverse ?14
8489 multiply ?16 (add ?17 ?18)
8491 add (multiply ?16 ?17) (multiply ?16 ?18)
8492 [18, 17, 16] by distribute1 ?16 ?17 ?18
8493 11620: Id : 10, {_}:
8494 multiply (add ?20 ?21) ?22
8496 add (multiply ?20 ?22) (multiply ?21 ?22)
8497 [22, 21, 20] by distribute2 ?20 ?21 ?22
8498 11620: Id : 11, {_}:
8499 add ?24 ?25 =?= add ?25 ?24
8500 [25, 24] by commutativity_for_addition ?24 ?25
8501 11620: Id : 12, {_}:
8502 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
8503 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8504 11620: Id : 13, {_}:
8505 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
8506 [32, 31] by right_alternative ?31 ?32
8507 11620: Id : 14, {_}:
8508 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
8509 [35, 34] by left_alternative ?34 ?35
8510 11620: Id : 15, {_}:
8511 associator ?37 ?38 ?39
8513 add (multiply (multiply ?37 ?38) ?39)
8514 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8515 [39, 38, 37] by associator ?37 ?38 ?39
8516 11620: Id : 16, {_}:
8519 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8520 [42, 41] by commutator ?41 ?42
8523 associator (add u v) x y
8525 add (associator u x y) (associator v x y)
8526 [] by prove_linearised_form3
8530 11620: commutator 1 2 0
8531 11620: additive_inverse 6 1 0
8532 11620: multiply 22 2 0
8533 11620: additive_identity 8 0 0
8534 11620: associator 4 3 3 0,2
8537 11620: add 18 2 2 0,1,2
8538 11620: v 2 0 2 2,1,2
8539 11620: u 2 0 2 1,1,2
8540 % SZS status Timeout for RNG021-6.p
8541 NO CLASH, using fixed ground order
8543 11722: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8545 add ?4 additive_identity =>= ?4
8546 [4] by right_additive_identity ?4
8548 multiply additive_identity ?6 =>= additive_identity
8549 [6] by left_multiplicative_zero ?6
8551 multiply ?8 additive_identity =>= additive_identity
8552 [8] by right_multiplicative_zero ?8
8554 add (additive_inverse ?10) ?10 =>= additive_identity
8555 [10] by left_additive_inverse ?10
8557 add ?12 (additive_inverse ?12) =>= additive_identity
8558 [12] by right_additive_inverse ?12
8560 additive_inverse (additive_inverse ?14) =>= ?14
8561 [14] by additive_inverse_additive_inverse ?14
8563 multiply ?16 (add ?17 ?18)
8565 add (multiply ?16 ?17) (multiply ?16 ?18)
8566 [18, 17, 16] by distribute1 ?16 ?17 ?18
8567 11722: Id : 10, {_}:
8568 multiply (add ?20 ?21) ?22
8570 add (multiply ?20 ?22) (multiply ?21 ?22)
8571 [22, 21, 20] by distribute2 ?20 ?21 ?22
8572 11722: Id : 11, {_}:
8573 add ?24 ?25 =?= add ?25 ?24
8574 [25, 24] by commutativity_for_addition ?24 ?25
8575 11722: Id : 12, {_}:
8576 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
8577 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8578 11722: Id : 13, {_}:
8579 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
8580 [32, 31] by right_alternative ?31 ?32
8581 11722: Id : 14, {_}:
8582 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
8583 [35, 34] by left_alternative ?34 ?35
8584 11722: Id : 15, {_}:
8585 associator ?37 ?38 ?39
8587 add (multiply (multiply ?37 ?38) ?39)
8588 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8589 [39, 38, 37] by associator ?37 ?38 ?39
8590 11722: Id : 16, {_}:
8593 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8594 [42, 41] by commutator ?41 ?42
8596 11722: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
8600 11722: commutator 1 2 0
8601 11722: additive_inverse 6 1 0
8602 11722: multiply 22 2 0
8604 11722: additive_identity 9 0 1 3
8605 11722: associator 2 3 1 0,2
8608 NO CLASH, using fixed ground order
8610 11723: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8612 add ?4 additive_identity =>= ?4
8613 [4] by right_additive_identity ?4
8615 multiply additive_identity ?6 =>= additive_identity
8616 [6] by left_multiplicative_zero ?6
8618 multiply ?8 additive_identity =>= additive_identity
8619 [8] by right_multiplicative_zero ?8
8621 add (additive_inverse ?10) ?10 =>= additive_identity
8622 [10] by left_additive_inverse ?10
8624 add ?12 (additive_inverse ?12) =>= additive_identity
8625 [12] by right_additive_inverse ?12
8627 additive_inverse (additive_inverse ?14) =>= ?14
8628 [14] by additive_inverse_additive_inverse ?14
8630 multiply ?16 (add ?17 ?18)
8632 add (multiply ?16 ?17) (multiply ?16 ?18)
8633 [18, 17, 16] by distribute1 ?16 ?17 ?18
8634 11723: Id : 10, {_}:
8635 multiply (add ?20 ?21) ?22
8637 add (multiply ?20 ?22) (multiply ?21 ?22)
8638 [22, 21, 20] by distribute2 ?20 ?21 ?22
8639 11723: Id : 11, {_}:
8640 add ?24 ?25 =?= add ?25 ?24
8641 [25, 24] by commutativity_for_addition ?24 ?25
8642 11723: Id : 12, {_}:
8643 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
8644 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8645 11723: Id : 13, {_}:
8646 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
8647 [32, 31] by right_alternative ?31 ?32
8648 11723: Id : 14, {_}:
8649 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
8650 [35, 34] by left_alternative ?34 ?35
8651 11723: Id : 15, {_}:
8652 associator ?37 ?38 ?39
8654 add (multiply (multiply ?37 ?38) ?39)
8655 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8656 [39, 38, 37] by associator ?37 ?38 ?39
8657 11723: Id : 16, {_}:
8660 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8661 [42, 41] by commutator ?41 ?42
8663 11723: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
8667 11723: commutator 1 2 0
8668 11723: additive_inverse 6 1 0
8669 11723: multiply 22 2 0
8671 11723: additive_identity 9 0 1 3
8672 11723: associator 2 3 1 0,2
8675 NO CLASH, using fixed ground order
8677 11724: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
8679 add ?4 additive_identity =>= ?4
8680 [4] by right_additive_identity ?4
8682 multiply additive_identity ?6 =>= additive_identity
8683 [6] by left_multiplicative_zero ?6
8685 multiply ?8 additive_identity =>= additive_identity
8686 [8] by right_multiplicative_zero ?8
8688 add (additive_inverse ?10) ?10 =>= additive_identity
8689 [10] by left_additive_inverse ?10
8691 add ?12 (additive_inverse ?12) =>= additive_identity
8692 [12] by right_additive_inverse ?12
8694 additive_inverse (additive_inverse ?14) =>= ?14
8695 [14] by additive_inverse_additive_inverse ?14
8697 multiply ?16 (add ?17 ?18)
8699 add (multiply ?16 ?17) (multiply ?16 ?18)
8700 [18, 17, 16] by distribute1 ?16 ?17 ?18
8701 11724: Id : 10, {_}:
8702 multiply (add ?20 ?21) ?22
8704 add (multiply ?20 ?22) (multiply ?21 ?22)
8705 [22, 21, 20] by distribute2 ?20 ?21 ?22
8706 11724: Id : 11, {_}:
8707 add ?24 ?25 =?= add ?25 ?24
8708 [25, 24] by commutativity_for_addition ?24 ?25
8709 11724: Id : 12, {_}:
8710 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
8711 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
8712 11724: Id : 13, {_}:
8713 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
8714 [32, 31] by right_alternative ?31 ?32
8715 11724: Id : 14, {_}:
8716 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
8717 [35, 34] by left_alternative ?34 ?35
8718 11724: Id : 15, {_}:
8719 associator ?37 ?38 ?39
8721 add (multiply (multiply ?37 ?38) ?39)
8722 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
8723 [39, 38, 37] by associator ?37 ?38 ?39
8724 11724: Id : 16, {_}:
8727 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
8728 [42, 41] by commutator ?41 ?42
8730 11724: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
8734 11724: commutator 1 2 0
8735 11724: additive_inverse 6 1 0
8736 11724: multiply 22 2 0
8738 11724: additive_identity 9 0 1 3
8739 11724: associator 2 3 1 0,2
8742 % SZS status Timeout for RNG025-6.p
8743 NO CLASH, using fixed ground order
8745 11740: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
8747 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
8748 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
8750 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
8753 [10, 9] by robbins_axiom ?9 ?10
8754 11740: Id : 5, {_}: add c c =>= c [] by idempotence
8757 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
8760 [] by prove_huntingtons_axiom
8765 11740: add 13 2 3 0,2
8766 11740: negate 9 1 5 0,1,2
8767 11740: b 3 0 3 1,2,1,1,2
8768 11740: a 2 0 2 1,1,1,2
8769 NO CLASH, using fixed ground order
8771 11741: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
8773 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
8774 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
8776 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
8779 [10, 9] by robbins_axiom ?9 ?10
8780 11741: Id : 5, {_}: add c c =>= c [] by idempotence
8783 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
8786 [] by prove_huntingtons_axiom
8791 11741: add 13 2 3 0,2
8792 11741: negate 9 1 5 0,1,2
8793 11741: b 3 0 3 1,2,1,1,2
8794 11741: a 2 0 2 1,1,1,2
8795 NO CLASH, using fixed ground order
8797 11742: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
8799 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
8800 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
8802 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
8805 [10, 9] by robbins_axiom ?9 ?10
8806 11742: Id : 5, {_}: add c c =>= c [] by idempotence
8809 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
8812 [] by prove_huntingtons_axiom
8817 11742: add 13 2 3 0,2
8818 11742: negate 9 1 5 0,1,2
8819 11742: b 3 0 3 1,2,1,1,2
8820 11742: a 2 0 2 1,1,1,2
8821 % SZS status Timeout for ROB005-1.p
8822 NO CLASH, using fixed ground order
8825 multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
8827 multiply ?2 ?3 (multiply ?4 ?5 ?6)
8828 [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
8829 11769: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
8831 multiply (inverse ?11) ?11 ?12 =>= ?12
8832 [12, 11] by left_inverse ?11 ?12
8834 multiply ?14 ?15 (inverse ?15) =>= ?14
8835 [15, 14] by right_inverse ?14 ?15
8837 11769: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
8841 11769: inverse 2 1 0
8842 11769: multiply 9 3 1 0,2
8845 NO CLASH, using fixed ground order
8848 multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
8850 multiply ?2 ?3 (multiply ?4 ?5 ?6)
8851 [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
8852 11770: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
8854 multiply (inverse ?11) ?11 ?12 =>= ?12
8855 [12, 11] by left_inverse ?11 ?12
8857 multiply ?14 ?15 (inverse ?15) =>= ?14
8858 [15, 14] by right_inverse ?14 ?15
8860 11770: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
8864 11770: inverse 2 1 0
8865 11770: multiply 9 3 1 0,2
8868 NO CLASH, using fixed ground order
8871 multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
8873 multiply ?2 ?3 (multiply ?4 ?5 ?6)
8874 [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
8875 11771: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
8877 multiply (inverse ?11) ?11 ?12 =>= ?12
8878 [12, 11] by left_inverse ?11 ?12
8880 multiply ?14 ?15 (inverse ?15) =>= ?14
8881 [15, 14] by right_inverse ?14 ?15
8883 11771: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
8887 11771: inverse 2 1 0
8888 11771: multiply 9 3 1 0,2
8891 % SZS status Timeout for BOO019-1.p
8892 CLASH, statistics insufficient
8895 add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
8896 [4, 3, 2] by l1 ?2 ?3 ?4
8898 add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
8899 [8, 7, 6] by l3 ?6 ?7 ?8
8901 multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
8902 [11, 10] by b1 ?10 ?11
8904 multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
8905 [14, 13] by majority1 ?13 ?14
8907 multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
8908 [17, 16] by majority2 ?16 ?17
8910 multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
8911 [20, 19] by majority3 ?19 ?20
8913 11791: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
8918 11791: multiply 11 2 0
8919 11791: inverse 3 1 2 0,2
8920 11791: a 2 0 2 1,1,2
8921 CLASH, statistics insufficient
8924 add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
8925 [4, 3, 2] by l1 ?2 ?3 ?4
8927 add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
8928 [8, 7, 6] by l3 ?6 ?7 ?8
8930 multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
8931 [11, 10] by b1 ?10 ?11
8933 multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
8934 [14, 13] by majority1 ?13 ?14
8936 multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
8937 [17, 16] by majority2 ?16 ?17
8939 multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
8940 [20, 19] by majority3 ?19 ?20
8942 11792: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
8947 11792: multiply 11 2 0
8948 11792: inverse 3 1 2 0,2
8949 11792: a 2 0 2 1,1,2
8950 CLASH, statistics insufficient
8953 add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
8954 [4, 3, 2] by l1 ?2 ?3 ?4
8956 add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
8957 [8, 7, 6] by l3 ?6 ?7 ?8
8959 multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
8960 [11, 10] by b1 ?10 ?11
8962 multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
8963 [14, 13] by majority1 ?13 ?14
8965 multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
8966 [17, 16] by majority2 ?16 ?17
8968 multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
8969 [20, 19] by majority3 ?19 ?20
8971 11793: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
8976 11793: multiply 11 2 0
8977 11793: inverse 3 1 2 0,2
8978 11793: a 2 0 2 1,1,2
8979 % SZS status Timeout for BOO030-1.p
8980 CLASH, statistics insufficient
8983 add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
8984 [4, 3, 2] by l1 ?2 ?3 ?4
8986 add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
8987 [8, 7, 6] by l3 ?6 ?7 ?8
8989 multiply (add ?10 (inverse ?10)) ?11 =>= ?11
8990 [11, 10] by property3 ?10 ?11
8992 multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
8993 [15, 14, 13] by l2 ?13 ?14 ?15
8995 multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
8996 [19, 18, 17] by l4 ?17 ?18 ?19
8998 add (multiply ?21 (inverse ?21)) ?22 =>= ?22
8999 [22, 21] by property3_dual ?21 ?22
9001 add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
9002 [25, 24] by majority1 ?24 ?25
9004 add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
9005 [28, 27] by majority2 ?27 ?28
9006 11822: Id : 10, {_}:
9007 add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
9008 [31, 30] by majority3 ?30 ?31
9009 11822: Id : 11, {_}:
9010 multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
9011 [34, 33] by majority1_dual ?33 ?34
9012 11822: Id : 12, {_}:
9013 multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
9014 [37, 36] by majority2_dual ?36 ?37
9015 11822: Id : 13, {_}:
9016 multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
9017 [40, 39] by majority3_dual ?39 ?40
9019 11822: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
9024 11822: multiply 21 2 0
9025 11822: inverse 4 1 2 0,2
9026 11822: a 2 0 2 1,1,2
9027 CLASH, statistics insufficient
9030 add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
9031 [4, 3, 2] by l1 ?2 ?3 ?4
9033 add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
9034 [8, 7, 6] by l3 ?6 ?7 ?8
9036 multiply (add ?10 (inverse ?10)) ?11 =>= ?11
9037 [11, 10] by property3 ?10 ?11
9039 multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
9040 [15, 14, 13] by l2 ?13 ?14 ?15
9042 multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
9043 [19, 18, 17] by l4 ?17 ?18 ?19
9045 add (multiply ?21 (inverse ?21)) ?22 =>= ?22
9046 [22, 21] by property3_dual ?21 ?22
9048 add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
9049 [25, 24] by majority1 ?24 ?25
9051 add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
9052 [28, 27] by majority2 ?27 ?28
9053 11821: Id : 10, {_}:
9054 add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
9055 [31, 30] by majority3 ?30 ?31
9056 11821: Id : 11, {_}:
9057 multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
9058 [34, 33] by majority1_dual ?33 ?34
9059 11821: Id : 12, {_}:
9060 multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
9061 [37, 36] by majority2_dual ?36 ?37
9062 11821: Id : 13, {_}:
9063 multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
9064 [40, 39] by majority3_dual ?39 ?40
9066 11821: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
9071 11821: multiply 21 2 0
9072 11821: inverse 4 1 2 0,2
9073 11821: a 2 0 2 1,1,2
9074 CLASH, statistics insufficient
9077 add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
9078 [4, 3, 2] by l1 ?2 ?3 ?4
9080 add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
9081 [8, 7, 6] by l3 ?6 ?7 ?8
9083 multiply (add ?10 (inverse ?10)) ?11 =>= ?11
9084 [11, 10] by property3 ?10 ?11
9086 multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
9087 [15, 14, 13] by l2 ?13 ?14 ?15
9089 multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
9090 [19, 18, 17] by l4 ?17 ?18 ?19
9092 add (multiply ?21 (inverse ?21)) ?22 =>= ?22
9093 [22, 21] by property3_dual ?21 ?22
9095 add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
9096 [25, 24] by majority1 ?24 ?25
9098 add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
9099 [28, 27] by majority2 ?27 ?28
9100 11820: Id : 10, {_}:
9101 add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
9102 [31, 30] by majority3 ?30 ?31
9103 11820: Id : 11, {_}:
9104 multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
9105 [34, 33] by majority1_dual ?33 ?34
9106 11820: Id : 12, {_}:
9107 multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
9108 [37, 36] by majority2_dual ?36 ?37
9109 11820: Id : 13, {_}:
9110 multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
9111 [40, 39] by majority3_dual ?39 ?40
9113 11820: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
9118 11820: multiply 21 2 0
9119 11820: inverse 4 1 2 0,2
9120 11820: a 2 0 2 1,1,2
9121 % SZS status Timeout for BOO032-1.p
9122 NO CLASH, using fixed ground order
9125 add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
9127 multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
9128 [4, 3, 2] by distributivity ?2 ?3 ?4
9130 add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
9131 [8, 7, 6] by l1 ?6 ?7 ?8
9133 add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
9134 [12, 11, 10] by l3 ?10 ?11 ?12
9136 multiply (add ?14 (inverse ?14)) ?15 =>= ?15
9137 [15, 14] by property3 ?14 ?15
9139 multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
9140 [18, 17] by majority1 ?17 ?18
9142 multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
9143 [21, 20] by majority2 ?20 ?21
9145 multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
9146 [24, 23] by majority3 ?23 ?24
9148 11838: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
9152 11838: add 15 2 0 multiply
9153 11838: multiply 16 2 0 add
9154 11838: inverse 3 1 2 0,2
9155 11838: a 2 0 2 1,1,2
9156 NO CLASH, using fixed ground order
9159 add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
9161 multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
9162 [4, 3, 2] by distributivity ?2 ?3 ?4
9164 add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
9165 [8, 7, 6] by l1 ?6 ?7 ?8
9167 add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
9168 [12, 11, 10] by l3 ?10 ?11 ?12
9170 multiply (add ?14 (inverse ?14)) ?15 =>= ?15
9171 [15, 14] by property3 ?14 ?15
9173 multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
9174 [18, 17] by majority1 ?17 ?18
9176 multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
9177 [21, 20] by majority2 ?20 ?21
9179 multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
9180 [24, 23] by majority3 ?23 ?24
9182 11839: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
9186 11839: add 15 2 0 multiply
9187 11839: multiply 16 2 0 add
9188 11839: inverse 3 1 2 0,2
9189 11839: a 2 0 2 1,1,2
9190 NO CLASH, using fixed ground order
9193 add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
9195 multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
9196 [4, 3, 2] by distributivity ?2 ?3 ?4
9198 add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
9199 [8, 7, 6] by l1 ?6 ?7 ?8
9201 add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
9202 [12, 11, 10] by l3 ?10 ?11 ?12
9204 multiply (add ?14 (inverse ?14)) ?15 =>= ?15
9205 [15, 14] by property3 ?14 ?15
9207 multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
9208 [18, 17] by majority1 ?17 ?18
9210 multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
9211 [21, 20] by majority2 ?20 ?21
9213 multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
9214 [24, 23] by majority3 ?23 ?24
9216 11840: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
9220 11840: add 15 2 0 multiply
9221 11840: multiply 16 2 0 add
9222 11840: inverse 3 1 2 0,2
9223 11840: a 2 0 2 1,1,2
9224 % SZS status Timeout for BOO033-1.p
9225 NO CLASH, using fixed ground order
9228 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
9229 [4, 3, 2] by b_definition ?2 ?3 ?4
9231 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
9232 [7, 6] by w_definition ?6 ?7
9236 apply (apply b (apply w w))
9237 (apply (apply b (apply b w)) (apply (apply b b) b))
9238 [] by strong_fixed_point
9241 apply strong_fixed_point fixed_pt
9243 apply fixed_pt (apply strong_fixed_point fixed_pt)
9244 [] by prove_strong_fixed_point
9250 11868: apply 20 2 3 0,2
9251 11868: fixed_pt 3 0 3 2,2
9252 11868: strong_fixed_point 3 0 2 1,2
9253 NO CLASH, using fixed ground order
9256 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
9257 [4, 3, 2] by b_definition ?2 ?3 ?4
9259 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
9260 [7, 6] by w_definition ?6 ?7
9264 apply (apply b (apply w w))
9265 (apply (apply b (apply b w)) (apply (apply b b) b))
9266 [] by strong_fixed_point
9269 apply strong_fixed_point fixed_pt
9271 apply fixed_pt (apply strong_fixed_point fixed_pt)
9272 [] by prove_strong_fixed_point
9278 11869: apply 20 2 3 0,2
9279 11869: fixed_pt 3 0 3 2,2
9280 11869: strong_fixed_point 3 0 2 1,2
9281 NO CLASH, using fixed ground order
9284 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
9285 [4, 3, 2] by b_definition ?2 ?3 ?4
9287 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
9288 [7, 6] by w_definition ?6 ?7
9292 apply (apply b (apply w w))
9293 (apply (apply b (apply b w)) (apply (apply b b) b))
9294 [] by strong_fixed_point
9297 apply strong_fixed_point fixed_pt
9299 apply fixed_pt (apply strong_fixed_point fixed_pt)
9300 [] by prove_strong_fixed_point
9306 11870: apply 20 2 3 0,2
9307 11870: fixed_pt 3 0 3 2,2
9308 11870: strong_fixed_point 3 0 2 1,2
9309 % SZS status Timeout for COL003-20.p
9310 NO CLASH, using fixed ground order
9311 NO CLASH, using fixed ground order
9314 apply (apply (apply s ?2) ?3) ?4
9316 apply (apply ?2 ?4) (apply ?3 ?4)
9317 [4, 3, 2] by s_definition ?2 ?3 ?4
9318 11889: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
9323 (apply (apply s (apply k (apply s (apply (apply s k) k))))
9324 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
9327 apply y (apply (apply x x) y)
9328 [] by prove_u_combinator
9333 11889: x 3 0 3 2,1,2
9334 11889: apply 25 2 17 0,2
9335 11889: k 8 0 7 1,2,1,1,1,2
9336 11889: s 7 0 6 1,1,1,1,2
9339 apply (apply (apply s ?2) ?3) ?4
9341 apply (apply ?2 ?4) (apply ?3 ?4)
9342 [4, 3, 2] by s_definition ?2 ?3 ?4
9343 11888: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
9348 (apply (apply s (apply k (apply s (apply (apply s k) k))))
9349 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
9352 apply y (apply (apply x x) y)
9353 [] by prove_u_combinator
9358 11888: x 3 0 3 2,1,2
9359 11888: apply 25 2 17 0,2
9360 11888: k 8 0 7 1,2,1,1,1,2
9361 11888: s 7 0 6 1,1,1,1,2
9362 NO CLASH, using fixed ground order
9365 apply (apply (apply s ?2) ?3) ?4
9367 apply (apply ?2 ?4) (apply ?3 ?4)
9368 [4, 3, 2] by s_definition ?2 ?3 ?4
9369 11890: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
9374 (apply (apply s (apply k (apply s (apply (apply s k) k))))
9375 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
9378 apply y (apply (apply x x) y)
9379 [] by prove_u_combinator
9384 11890: x 3 0 3 2,1,2
9385 11890: apply 25 2 17 0,2
9386 11890: k 8 0 7 1,2,1,1,1,2
9387 11890: s 7 0 6 1,1,1,1,2
9390 Found proof, 0.014068s
9391 % SZS status Unsatisfiable for COL004-3.p
9392 % SZS output start CNFRefutation for COL004-3.p
9393 Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
9394 Id : 2, {_}: apply (apply (apply s ?2) ?3) ?4 =?= apply (apply ?2 ?4) (apply ?3 ?4) [4, 3, 2] by s_definition ?2 ?3 ?4
9395 Id : 35, {_}: apply y (apply (apply x x) y) === apply y (apply (apply x x) y) [] by Demod 34 with 3 at 1,2
9396 Id : 34, {_}: apply (apply (apply k y) (apply k y)) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 33 with 2 at 1,2
9397 Id : 33, {_}: apply (apply (apply (apply s k) k) y) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 32 with 2 at 2
9398 Id : 32, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x x)) y =>= apply y (apply (apply x x) y) [] by Demod 31 with 3 at 2,2,1,2
9399 Id : 31, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 30 with 3 at 1,2,1,2
9400 Id : 30, {_}: apply (apply (apply s (apply (apply s k) k)) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 20 with 3 at 1,1,2
9401 Id : 20, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 19 with 2 at 2,2,1,2
9402 Id : 19, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 18 with 2 at 1,2,1,2
9403 Id : 18, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply (apply s k) k) x) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 17 with 2 at 2,1,2
9404 Id : 17, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)) x)) y =>= apply y (apply (apply x x) y) [] by Demod 1 with 2 at 1,2
9405 Id : 1, {_}: apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y =>= apply y (apply (apply x x) y) [] by prove_u_combinator
9406 % SZS output end CNFRefutation for COL004-3.p
9407 11890: solved COL004-3.p in 0.020001 using lpo
9408 11890: status Unsatisfiable for COL004-3.p
9409 CLASH, statistics insufficient
9412 apply (apply (apply s ?3) ?4) ?5
9414 apply (apply ?3 ?5) (apply ?4 ?5)
9415 [5, 4, 3] by s_definition ?3 ?4 ?5
9417 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
9418 [8, 7] by w_definition ?7 ?8
9420 11895: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
9426 11895: apply 11 2 1 0,3
9427 11895: combinator 1 0 1 1,3
9428 CLASH, statistics insufficient
9431 apply (apply (apply s ?3) ?4) ?5
9433 apply (apply ?3 ?5) (apply ?4 ?5)
9434 [5, 4, 3] by s_definition ?3 ?4 ?5
9436 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
9437 [8, 7] by w_definition ?7 ?8
9439 11896: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
9445 11896: apply 11 2 1 0,3
9446 11896: combinator 1 0 1 1,3
9447 CLASH, statistics insufficient
9450 apply (apply (apply s ?3) ?4) ?5
9452 apply (apply ?3 ?5) (apply ?4 ?5)
9453 [5, 4, 3] by s_definition ?3 ?4 ?5
9455 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
9456 [8, 7] by w_definition ?7 ?8
9458 11897: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
9464 11897: apply 11 2 1 0,3
9465 11897: combinator 1 0 1 1,3
9466 % SZS status Timeout for COL005-1.p
9467 CLASH, statistics insufficient
9470 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9471 [5, 4, 3] by b_definition ?3 ?4 ?5
9472 11929: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
9474 apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
9475 [11, 10, 9] by v_definition ?9 ?10 ?11
9478 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9479 [1] by prove_fixed_point ?1
9486 11929: apply 15 2 3 0,2
9487 11929: f 3 1 3 0,2,2
9488 CLASH, statistics insufficient
9491 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9492 [5, 4, 3] by b_definition ?3 ?4 ?5
9493 11930: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
9495 apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
9496 [11, 10, 9] by v_definition ?9 ?10 ?11
9499 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9500 [1] by prove_fixed_point ?1
9507 11930: apply 15 2 3 0,2
9508 11930: f 3 1 3 0,2,2
9509 CLASH, statistics insufficient
9512 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9513 [5, 4, 3] by b_definition ?3 ?4 ?5
9514 11931: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
9516 apply (apply (apply v ?9) ?10) ?11 =?= apply (apply ?11 ?9) ?10
9517 [11, 10, 9] by v_definition ?9 ?10 ?11
9520 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9521 [1] by prove_fixed_point ?1
9528 11931: apply 15 2 3 0,2
9529 11931: f 3 1 3 0,2,2
9533 Found proof, 6.233757s
9534 % SZS status Unsatisfiable for COL038-1.p
9535 % SZS output start CNFRefutation for COL038-1.p
9536 Id : 4, {_}: apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 [11, 10, 9] by v_definition ?9 ?10 ?11
9537 Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
9538 Id : 19, {_}: apply (apply (apply v ?47) ?48) ?49 =>= apply (apply ?49 ?47) ?48 [49, 48, 47] by v_definition ?47 ?48 ?49
9539 Id : 5, {_}: apply (apply (apply b ?13) ?14) ?15 =>= apply ?13 (apply ?14 ?15) [15, 14, 13] by b_definition ?13 ?14 ?15
9540 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
9541 Id : 6, {_}: apply ?17 (apply ?18 ?19) =?= apply ?17 (apply ?18 ?19) [19, 18, 17] by Super 5 with 2 at 2
9542 Id : 1244, {_}: apply (apply m (apply v ?1596)) ?1597 =?= apply (apply ?1597 ?1596) (apply v ?1596) [1597, 1596] by Super 19 with 3 at 1,2
9543 Id : 18, {_}: apply m (apply (apply v ?44) ?45) =<= apply (apply (apply (apply v ?44) ?45) ?44) ?45 [45, 44] by Super 3 with 4 at 3
9544 Id : 224, {_}: apply m (apply (apply v ?485) ?486) =<= apply (apply (apply ?485 ?485) ?486) ?486 [486, 485] by Demod 18 with 4 at 1,3
9545 Id : 232, {_}: apply m (apply (apply v ?509) ?510) =<= apply (apply (apply m ?509) ?510) ?510 [510, 509] by Super 224 with 3 at 1,1,3
9546 Id : 7751, {_}: apply (apply m (apply v ?7787)) (apply (apply m ?7788) ?7787) =<= apply (apply m (apply (apply v ?7788) ?7787)) (apply v ?7787) [7788, 7787] by Super 1244 with 232 at 1,3
9547 Id : 9, {_}: apply (apply (apply m b) ?24) ?25 =>= apply b (apply ?24 ?25) [25, 24] by Super 2 with 3 at 1,1,2
9548 Id : 236, {_}: apply m (apply (apply v (apply v ?521)) ?522) =<= apply (apply (apply ?522 ?521) (apply v ?521)) ?522 [522, 521] by Super 224 with 4 at 1,3
9549 Id : 2866, {_}: apply m (apply (apply v (apply v b)) m) =>= apply b (apply (apply v b) m) [] by Super 9 with 236 at 2
9550 Id : 7790, {_}: apply (apply m (apply v m)) (apply (apply m (apply v b)) m) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Super 7751 with 2866 at 1,3
9551 Id : 20, {_}: apply (apply m (apply v ?51)) ?52 =?= apply (apply ?52 ?51) (apply v ?51) [52, 51] by Super 19 with 3 at 1,2
9552 Id : 7860, {_}: apply (apply m (apply v m)) (apply (apply m b) (apply v b)) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Demod 7790 with 20 at 2,2
9553 Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
9554 Id : 9568, {_}: apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) =?= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) [] by Super 9567 with 11 at 2
9555 Id : 9567, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m)) [8771] by Demod 9566 with 2 at 2,3
9556 Id : 9566, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9565 with 2 at 2
9557 Id : 9565, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9564 with 4 at 1,2,3
9558 Id : 9564, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9563 with 4 at 1,2
9559 Id : 9563, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9562 with 4 at 2,3
9560 Id : 9562, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9561 with 4 at 2
9561 Id : 9561, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9560 with 2 at 2,3
9562 Id : 9560, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9559 with 2 at 2
9563 Id : 9559, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9558 with 7860 at 1,2,3
9564 Id : 9558, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9557 with 7860 at 2,1,1,1,3
9565 Id : 9557, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9556 with 7860 at 2,1,1,2,2,2
9566 Id : 9556, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9078 with 7860 at 1,2
9567 Id : 9078, {_}: apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Super 174 with 7860 at 2,1,1,2,2,2,3
9568 Id : 174, {_}: apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381))) =<= apply (f (apply (apply b (apply ?379 ?380)) ?381)) (apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381)))) [381, 380, 379] by Super 8 with 6 at 1,1,2,2,2,3
9569 Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
9570 Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
9571 Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
9572 % SZS output end CNFRefutation for COL038-1.p
9573 11930: solved COL038-1.p in 3.116194 using kbo
9574 11930: status Unsatisfiable for COL038-1.p
9575 CLASH, statistics insufficient
9578 apply (apply (apply s ?3) ?4) ?5
9580 apply (apply ?3 ?5) (apply ?4 ?5)
9581 [5, 4, 3] by s_definition ?3 ?4 ?5
9583 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
9584 [9, 8, 7] by b_definition ?7 ?8 ?9
9585 11936: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
9588 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9589 [1] by prove_fixed_point ?1
9596 11936: apply 16 2 3 0,2
9597 11936: f 3 1 3 0,2,2
9598 CLASH, statistics insufficient
9601 apply (apply (apply s ?3) ?4) ?5
9603 apply (apply ?3 ?5) (apply ?4 ?5)
9604 [5, 4, 3] by s_definition ?3 ?4 ?5
9606 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
9607 [9, 8, 7] by b_definition ?7 ?8 ?9
9608 11937: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
9611 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9612 [1] by prove_fixed_point ?1
9619 11937: apply 16 2 3 0,2
9620 11937: f 3 1 3 0,2,2
9621 CLASH, statistics insufficient
9624 apply (apply (apply s ?3) ?4) ?5
9626 apply (apply ?3 ?5) (apply ?4 ?5)
9627 [5, 4, 3] by s_definition ?3 ?4 ?5
9629 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
9630 [9, 8, 7] by b_definition ?7 ?8 ?9
9631 11938: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
9634 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9635 [1] by prove_fixed_point ?1
9642 11938: apply 16 2 3 0,2
9643 11938: f 3 1 3 0,2,2
9644 % SZS status Timeout for COL046-1.p
9645 CLASH, statistics insufficient
9648 apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
9649 [4, 3] by l_definition ?3 ?4
9651 apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
9652 [8, 7, 6] by q_definition ?6 ?7 ?8
9655 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9656 [1] by prove_model ?1
9662 11954: apply 12 2 3 0,2
9663 11954: f 3 1 3 0,2,2
9664 CLASH, statistics insufficient
9667 apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
9668 [4, 3] by l_definition ?3 ?4
9670 apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
9671 [8, 7, 6] by q_definition ?6 ?7 ?8
9674 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9675 [1] by prove_model ?1
9681 11955: apply 12 2 3 0,2
9682 11955: f 3 1 3 0,2,2
9683 CLASH, statistics insufficient
9686 apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
9687 [4, 3] by l_definition ?3 ?4
9689 apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
9690 [8, 7, 6] by q_definition ?6 ?7 ?8
9693 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9694 [1] by prove_model ?1
9700 11956: apply 12 2 3 0,2
9701 11956: f 3 1 3 0,2,2
9702 % SZS status Timeout for COL047-1.p
9703 CLASH, statistics insufficient
9706 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9707 [5, 4, 3] by b_definition ?3 ?4 ?5
9709 apply (apply t ?7) ?8 =>= apply ?8 ?7
9710 [8, 7] by t_definition ?7 ?8
9713 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9715 apply (g ?1) (apply (f ?1) (h ?1))
9716 [1] by prove_q_combinator ?1
9722 11983: h 2 1 2 0,2,2
9723 11983: g 2 1 2 0,2,1,2
9724 11983: apply 13 2 5 0,2
9725 11983: f 2 1 2 0,2,1,1,2
9726 CLASH, statistics insufficient
9729 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9730 [5, 4, 3] by b_definition ?3 ?4 ?5
9732 apply (apply t ?7) ?8 =>= apply ?8 ?7
9733 [8, 7] by t_definition ?7 ?8
9736 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9738 apply (g ?1) (apply (f ?1) (h ?1))
9739 [1] by prove_q_combinator ?1
9745 11984: h 2 1 2 0,2,2
9746 11984: g 2 1 2 0,2,1,2
9747 11984: apply 13 2 5 0,2
9748 11984: f 2 1 2 0,2,1,1,2
9749 CLASH, statistics insufficient
9752 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9753 [5, 4, 3] by b_definition ?3 ?4 ?5
9755 apply (apply t ?7) ?8 =?= apply ?8 ?7
9756 [8, 7] by t_definition ?7 ?8
9759 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9761 apply (g ?1) (apply (f ?1) (h ?1))
9762 [1] by prove_q_combinator ?1
9768 11985: h 2 1 2 0,2,2
9769 11985: g 2 1 2 0,2,1,2
9770 11985: apply 13 2 5 0,2
9771 11985: f 2 1 2 0,2,1,1,2
9775 Found proof, 1.436300s
9776 % SZS status Unsatisfiable for COL060-1.p
9777 % SZS output start CNFRefutation for COL060-1.p
9778 Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
9779 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
9780 Id : 447, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 445 with 2 at 2
9781 Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) [1404] by Super 277 with 3 at 1,2
9782 Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
9783 Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
9784 Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (g (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
9785 Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (g (apply (apply b ?18) ?19)) (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
9786 Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1
9787 % SZS output end CNFRefutation for COL060-1.p
9788 11983: solved COL060-1.p in 0.376023 using nrkbo
9789 11983: status Unsatisfiable for COL060-1.p
9790 CLASH, statistics insufficient
9793 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9794 [5, 4, 3] by b_definition ?3 ?4 ?5
9796 apply (apply t ?7) ?8 =>= apply ?8 ?7
9797 [8, 7] by t_definition ?7 ?8
9800 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9802 apply (f ?1) (apply (h ?1) (g ?1))
9803 [1] by prove_q1_combinator ?1
9809 11990: h 2 1 2 0,2,2
9810 11990: g 2 1 2 0,2,1,2
9811 11990: apply 13 2 5 0,2
9812 11990: f 2 1 2 0,2,1,1,2
9813 CLASH, statistics insufficient
9816 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9817 [5, 4, 3] by b_definition ?3 ?4 ?5
9819 apply (apply t ?7) ?8 =>= apply ?8 ?7
9820 [8, 7] by t_definition ?7 ?8
9823 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9825 apply (f ?1) (apply (h ?1) (g ?1))
9826 [1] by prove_q1_combinator ?1
9832 11991: h 2 1 2 0,2,2
9833 11991: g 2 1 2 0,2,1,2
9834 11991: apply 13 2 5 0,2
9835 11991: f 2 1 2 0,2,1,1,2
9836 CLASH, statistics insufficient
9839 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9840 [5, 4, 3] by b_definition ?3 ?4 ?5
9842 apply (apply t ?7) ?8 =?= apply ?8 ?7
9843 [8, 7] by t_definition ?7 ?8
9846 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9848 apply (f ?1) (apply (h ?1) (g ?1))
9849 [1] by prove_q1_combinator ?1
9855 11992: h 2 1 2 0,2,2
9856 11992: g 2 1 2 0,2,1,2
9857 11992: apply 13 2 5 0,2
9858 11992: f 2 1 2 0,2,1,1,2
9862 Found proof, 2.573692s
9863 % SZS status Unsatisfiable for COL061-1.p
9864 % SZS output start CNFRefutation for COL061-1.p
9865 Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
9866 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
9867 Id : 447, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 446 with 3 at 2,2
9868 Id : 446, {_}: apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (apply ?1406 (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) [1406] by Super 277 with 2 at 2
9869 Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
9870 Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
9871 Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
9872 Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (f (apply (apply b ?18) ?19)) (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
9873 Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1
9874 % SZS output end CNFRefutation for COL061-1.p
9875 11990: solved COL061-1.p in 0.344021 using nrkbo
9876 11990: status Unsatisfiable for COL061-1.p
9877 CLASH, statistics insufficient
9880 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9881 [5, 4, 3] by b_definition ?3 ?4 ?5
9883 apply (apply t ?7) ?8 =>= apply ?8 ?7
9884 [8, 7] by t_definition ?7 ?8
9887 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9889 apply (apply (f ?1) (h ?1)) (g ?1)
9890 [1] by prove_c_combinator ?1
9896 11997: h 2 1 2 0,2,2
9897 11997: g 2 1 2 0,2,1,2
9898 11997: apply 13 2 5 0,2
9899 11997: f 2 1 2 0,2,1,1,2
9900 CLASH, statistics insufficient
9903 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9904 [5, 4, 3] by b_definition ?3 ?4 ?5
9906 apply (apply t ?7) ?8 =>= apply ?8 ?7
9907 [8, 7] by t_definition ?7 ?8
9910 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9912 apply (apply (f ?1) (h ?1)) (g ?1)
9913 [1] by prove_c_combinator ?1
9919 11998: h 2 1 2 0,2,2
9920 11998: g 2 1 2 0,2,1,2
9921 11998: apply 13 2 5 0,2
9922 11998: f 2 1 2 0,2,1,1,2
9923 CLASH, statistics insufficient
9926 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
9927 [5, 4, 3] by b_definition ?3 ?4 ?5
9929 apply (apply t ?7) ?8 =?= apply ?8 ?7
9930 [8, 7] by t_definition ?7 ?8
9933 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
9935 apply (apply (f ?1) (h ?1)) (g ?1)
9936 [1] by prove_c_combinator ?1
9942 11999: h 2 1 2 0,2,2
9943 11999: g 2 1 2 0,2,1,2
9944 11999: apply 13 2 5 0,2
9945 11999: f 2 1 2 0,2,1,1,2
9949 Found proof, 3.178698s
9950 % SZS status Unsatisfiable for COL062-1.p
9951 % SZS output start CNFRefutation for COL062-1.p
9952 Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
9953 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
9954 Id : 1574, {_}: apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) === apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) [] by Super 1573 with 3 at 2
9955 Id : 1573, {_}: apply (apply ?5215 (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) [5215] by Super 447 with 2 at 2
9956 Id : 447, {_}: apply (apply (apply ?1408 (apply ?1409 (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) [1409, 1408] by Super 445 with 2 at 1,1,2
9957 Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) [1404] by Super 277 with 3 at 1,2
9958 Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
9959 Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
9960 Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
9961 Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
9962 Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (f ?1) (h ?1)) (g ?1) [1] by prove_c_combinator ?1
9963 % SZS output end CNFRefutation for COL062-1.p
9964 11997: solved COL062-1.p in 1.812113 using nrkbo
9965 11997: status Unsatisfiable for COL062-1.p
9966 CLASH, statistics insufficient
9969 apply (apply (apply n ?3) ?4) ?5
9971 apply (apply (apply ?3 ?5) ?4) ?5
9972 [5, 4, 3] by n_definition ?3 ?4 ?5
9973 CLASH, statistics insufficient
9976 apply (apply (apply n ?3) ?4) ?5
9978 apply (apply (apply ?3 ?5) ?4) ?5
9979 [5, 4, 3] by n_definition ?3 ?4 ?5
9981 apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
9982 [9, 8, 7] by q_definition ?7 ?8 ?9
9985 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
9986 [1] by prove_fixed_point ?1
9992 12006: apply 14 2 3 0,2
9993 12006: f 3 1 3 0,2,2
9995 apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
9996 [9, 8, 7] by q_definition ?7 ?8 ?9
9999 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
10000 [1] by prove_fixed_point ?1
10006 12004: apply 14 2 3 0,2
10007 12004: f 3 1 3 0,2,2
10008 CLASH, statistics insufficient
10010 12005: Id : 2, {_}:
10011 apply (apply (apply n ?3) ?4) ?5
10013 apply (apply (apply ?3 ?5) ?4) ?5
10014 [5, 4, 3] by n_definition ?3 ?4 ?5
10015 12005: Id : 3, {_}:
10016 apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
10017 [9, 8, 7] by q_definition ?7 ?8 ?9
10019 12005: Id : 1, {_}:
10020 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
10021 [1] by prove_fixed_point ?1
10027 12005: apply 14 2 3 0,2
10028 12005: f 3 1 3 0,2,2
10029 % SZS status Timeout for COL071-1.p
10030 CLASH, statistics insufficient
10032 12093: Id : 2, {_}:
10033 apply (apply (apply n1 ?3) ?4) ?5
10035 apply (apply (apply ?3 ?4) ?4) ?5
10036 [5, 4, 3] by n1_definition ?3 ?4 ?5
10037 12093: Id : 3, {_}:
10038 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
10039 [9, 8, 7] by b_definition ?7 ?8 ?9
10041 12093: Id : 1, {_}:
10042 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
10043 [1] by prove_strong_fixed_point ?1
10049 12093: apply 14 2 3 0,2
10050 12093: f 3 1 3 0,2,2
10051 CLASH, statistics insufficient
10053 12094: Id : 2, {_}:
10054 apply (apply (apply n1 ?3) ?4) ?5
10056 apply (apply (apply ?3 ?4) ?4) ?5
10057 [5, 4, 3] by n1_definition ?3 ?4 ?5
10058 12094: Id : 3, {_}:
10059 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
10060 [9, 8, 7] by b_definition ?7 ?8 ?9
10062 12094: Id : 1, {_}:
10063 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
10064 [1] by prove_strong_fixed_point ?1
10070 12094: apply 14 2 3 0,2
10071 12094: f 3 1 3 0,2,2
10072 CLASH, statistics insufficient
10074 12095: Id : 2, {_}:
10075 apply (apply (apply n1 ?3) ?4) ?5
10077 apply (apply (apply ?3 ?4) ?4) ?5
10078 [5, 4, 3] by n1_definition ?3 ?4 ?5
10079 12095: Id : 3, {_}:
10080 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
10081 [9, 8, 7] by b_definition ?7 ?8 ?9
10083 12095: Id : 1, {_}:
10084 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
10085 [1] by prove_strong_fixed_point ?1
10091 12095: apply 14 2 3 0,2
10092 12095: f 3 1 3 0,2,2
10093 % SZS status Timeout for COL073-1.p
10094 NO CLASH, using fixed ground order
10096 12117: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10097 12117: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10098 12117: Id : 4, {_}:
10099 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
10100 [8, 7, 6] by associativity ?6 ?7 ?8
10101 12117: Id : 5, {_}:
10104 multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
10105 [11, 10] by name ?10 ?11
10106 12117: Id : 6, {_}:
10107 commutator (commutator ?13 ?14) ?15
10109 commutator ?13 (commutator ?14 ?15)
10110 [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
10112 12117: Id : 1, {_}:
10113 multiply a (commutator b c) =<= multiply (commutator b c) a
10118 12117: inverse 3 1 0
10119 12117: identity 2 0 0
10120 12117: multiply 11 2 2 0,2
10121 12117: commutator 7 2 2 0,2,2
10122 12117: c 2 0 2 2,2,2
10123 12117: b 2 0 2 1,2,2
10125 NO CLASH, using fixed ground order
10127 12118: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10128 12118: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10129 12118: Id : 4, {_}:
10130 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10131 [8, 7, 6] by associativity ?6 ?7 ?8
10132 12118: Id : 5, {_}:
10135 multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
10136 [11, 10] by name ?10 ?11
10137 12118: Id : 6, {_}:
10138 commutator (commutator ?13 ?14) ?15
10140 commutator ?13 (commutator ?14 ?15)
10141 [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
10143 12118: Id : 1, {_}:
10144 multiply a (commutator b c) =<= multiply (commutator b c) a
10149 12118: inverse 3 1 0
10150 12118: identity 2 0 0
10151 12118: multiply 11 2 2 0,2
10152 12118: commutator 7 2 2 0,2,2
10153 12118: c 2 0 2 2,2,2
10154 12118: b 2 0 2 1,2,2
10156 NO CLASH, using fixed ground order
10158 12119: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10159 12119: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10160 12119: Id : 4, {_}:
10161 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10162 [8, 7, 6] by associativity ?6 ?7 ?8
10163 12119: Id : 5, {_}:
10166 multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
10167 [11, 10] by name ?10 ?11
10168 12119: Id : 6, {_}:
10169 commutator (commutator ?13 ?14) ?15
10171 commutator ?13 (commutator ?14 ?15)
10172 [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
10174 12119: Id : 1, {_}:
10175 multiply a (commutator b c) =<= multiply (commutator b c) a
10180 12119: inverse 3 1 0
10181 12119: identity 2 0 0
10182 12119: multiply 11 2 2 0,2
10183 12119: commutator 7 2 2 0,2,2
10184 12119: c 2 0 2 2,2,2
10185 12119: b 2 0 2 1,2,2
10187 % SZS status Timeout for GRP024-5.p
10188 CLASH, statistics insufficient
10190 12145: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10191 12145: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10192 12145: Id : 4, {_}:
10193 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10194 [8, 7, 6] by associativity ?6 ?7 ?8
10195 12145: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
10196 12145: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
10197 12145: Id : 7, {_}:
10198 inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
10199 [14, 13] by inverse_product_lemma ?13 ?14
10200 12145: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
10201 12145: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
10202 12145: Id : 10, {_}:
10203 intersection ?20 ?21 =?= intersection ?21 ?20
10204 [21, 20] by intersection_commutative ?20 ?21
10205 CLASH, statistics insufficient
10207 12146: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10208 12146: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10209 12146: Id : 4, {_}:
10210 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10211 [8, 7, 6] by associativity ?6 ?7 ?8
10212 12146: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
10213 12146: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
10214 12146: Id : 7, {_}:
10215 inverse (multiply ?13 ?14) =?= multiply (inverse ?14) (inverse ?13)
10216 [14, 13] by inverse_product_lemma ?13 ?14
10217 12146: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
10218 12146: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
10219 12146: Id : 10, {_}:
10220 intersection ?20 ?21 =?= intersection ?21 ?20
10221 [21, 20] by intersection_commutative ?20 ?21
10222 12146: Id : 11, {_}:
10223 union ?23 ?24 =?= union ?24 ?23
10224 [24, 23] by union_commutative ?23 ?24
10225 12146: Id : 12, {_}:
10226 intersection ?26 (intersection ?27 ?28)
10228 intersection (intersection ?26 ?27) ?28
10229 [28, 27, 26] by intersection_associative ?26 ?27 ?28
10230 12146: Id : 13, {_}:
10231 union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
10232 [32, 31, 30] by union_associative ?30 ?31 ?32
10233 12146: Id : 14, {_}:
10234 union (intersection ?34 ?35) ?35 =>= ?35
10235 [35, 34] by union_intersection_absorbtion ?34 ?35
10236 12146: Id : 15, {_}:
10237 intersection (union ?37 ?38) ?38 =>= ?38
10238 [38, 37] by intersection_union_absorbtion ?37 ?38
10239 12146: Id : 16, {_}:
10240 multiply ?40 (union ?41 ?42)
10242 union (multiply ?40 ?41) (multiply ?40 ?42)
10243 [42, 41, 40] by multiply_union1 ?40 ?41 ?42
10244 12146: Id : 17, {_}:
10245 multiply ?44 (intersection ?45 ?46)
10247 intersection (multiply ?44 ?45) (multiply ?44 ?46)
10248 [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
10249 12146: Id : 18, {_}:
10250 multiply (union ?48 ?49) ?50
10252 union (multiply ?48 ?50) (multiply ?49 ?50)
10253 [50, 49, 48] by multiply_union2 ?48 ?49 ?50
10254 12146: Id : 19, {_}:
10255 multiply (intersection ?52 ?53) ?54
10257 intersection (multiply ?52 ?54) (multiply ?53 ?54)
10258 [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
10259 12146: Id : 20, {_}:
10260 positive_part ?56 =>= union ?56 identity
10261 [56] by positive_part ?56
10262 12146: Id : 21, {_}:
10263 negative_part ?58 =>= intersection ?58 identity
10264 [58] by negative_part ?58
10266 12146: Id : 1, {_}:
10267 multiply (positive_part a) (negative_part a) =>= a
10268 [] by prove_product
10272 12146: union 14 2 0
10273 12146: intersection 14 2 0
10274 12146: inverse 7 1 0
10275 12146: identity 6 0 0
10276 12146: multiply 21 2 1 0,2
10277 12146: negative_part 2 1 1 0,2,2
10278 12146: positive_part 2 1 1 0,1,2
10279 12146: a 3 0 3 1,1,2
10280 12145: Id : 11, {_}:
10281 union ?23 ?24 =?= union ?24 ?23
10282 [24, 23] by union_commutative ?23 ?24
10283 12145: Id : 12, {_}:
10284 intersection ?26 (intersection ?27 ?28)
10286 intersection (intersection ?26 ?27) ?28
10287 [28, 27, 26] by intersection_associative ?26 ?27 ?28
10288 12145: Id : 13, {_}:
10289 union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
10290 [32, 31, 30] by union_associative ?30 ?31 ?32
10291 12145: Id : 14, {_}:
10292 union (intersection ?34 ?35) ?35 =>= ?35
10293 [35, 34] by union_intersection_absorbtion ?34 ?35
10294 12145: Id : 15, {_}:
10295 intersection (union ?37 ?38) ?38 =>= ?38
10296 [38, 37] by intersection_union_absorbtion ?37 ?38
10297 12145: Id : 16, {_}:
10298 multiply ?40 (union ?41 ?42)
10300 union (multiply ?40 ?41) (multiply ?40 ?42)
10301 [42, 41, 40] by multiply_union1 ?40 ?41 ?42
10302 12145: Id : 17, {_}:
10303 multiply ?44 (intersection ?45 ?46)
10305 intersection (multiply ?44 ?45) (multiply ?44 ?46)
10306 [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
10307 12145: Id : 18, {_}:
10308 multiply (union ?48 ?49) ?50
10310 union (multiply ?48 ?50) (multiply ?49 ?50)
10311 [50, 49, 48] by multiply_union2 ?48 ?49 ?50
10312 12145: Id : 19, {_}:
10313 multiply (intersection ?52 ?53) ?54
10315 intersection (multiply ?52 ?54) (multiply ?53 ?54)
10316 [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
10317 12145: Id : 20, {_}:
10318 positive_part ?56 =<= union ?56 identity
10319 [56] by positive_part ?56
10320 12145: Id : 21, {_}:
10321 negative_part ?58 =<= intersection ?58 identity
10322 [58] by negative_part ?58
10324 12145: Id : 1, {_}:
10325 multiply (positive_part a) (negative_part a) =>= a
10326 [] by prove_product
10330 12145: union 14 2 0
10331 12145: intersection 14 2 0
10332 12145: inverse 7 1 0
10333 12145: identity 6 0 0
10334 12145: multiply 21 2 1 0,2
10335 12145: negative_part 2 1 1 0,2,2
10336 12145: positive_part 2 1 1 0,1,2
10337 12145: a 3 0 3 1,1,2
10338 CLASH, statistics insufficient
10340 12144: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10341 12144: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10342 12144: Id : 4, {_}:
10343 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
10344 [8, 7, 6] by associativity ?6 ?7 ?8
10345 12144: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
10346 12144: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
10347 12144: Id : 7, {_}:
10348 inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
10349 [14, 13] by inverse_product_lemma ?13 ?14
10350 12144: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
10351 12144: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
10352 12144: Id : 10, {_}:
10353 intersection ?20 ?21 =?= intersection ?21 ?20
10354 [21, 20] by intersection_commutative ?20 ?21
10355 12144: Id : 11, {_}:
10356 union ?23 ?24 =?= union ?24 ?23
10357 [24, 23] by union_commutative ?23 ?24
10358 12144: Id : 12, {_}:
10359 intersection ?26 (intersection ?27 ?28)
10361 intersection (intersection ?26 ?27) ?28
10362 [28, 27, 26] by intersection_associative ?26 ?27 ?28
10363 12144: Id : 13, {_}:
10364 union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
10365 [32, 31, 30] by union_associative ?30 ?31 ?32
10366 12144: Id : 14, {_}:
10367 union (intersection ?34 ?35) ?35 =>= ?35
10368 [35, 34] by union_intersection_absorbtion ?34 ?35
10369 12144: Id : 15, {_}:
10370 intersection (union ?37 ?38) ?38 =>= ?38
10371 [38, 37] by intersection_union_absorbtion ?37 ?38
10372 12144: Id : 16, {_}:
10373 multiply ?40 (union ?41 ?42)
10375 union (multiply ?40 ?41) (multiply ?40 ?42)
10376 [42, 41, 40] by multiply_union1 ?40 ?41 ?42
10377 12144: Id : 17, {_}:
10378 multiply ?44 (intersection ?45 ?46)
10380 intersection (multiply ?44 ?45) (multiply ?44 ?46)
10381 [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
10382 12144: Id : 18, {_}:
10383 multiply (union ?48 ?49) ?50
10385 union (multiply ?48 ?50) (multiply ?49 ?50)
10386 [50, 49, 48] by multiply_union2 ?48 ?49 ?50
10387 12144: Id : 19, {_}:
10388 multiply (intersection ?52 ?53) ?54
10390 intersection (multiply ?52 ?54) (multiply ?53 ?54)
10391 [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
10392 12144: Id : 20, {_}:
10393 positive_part ?56 =<= union ?56 identity
10394 [56] by positive_part ?56
10395 12144: Id : 21, {_}:
10396 negative_part ?58 =<= intersection ?58 identity
10397 [58] by negative_part ?58
10399 12144: Id : 1, {_}:
10400 multiply (positive_part a) (negative_part a) =>= a
10401 [] by prove_product
10405 12144: union 14 2 0
10406 12144: intersection 14 2 0
10407 12144: inverse 7 1 0
10408 12144: identity 6 0 0
10409 12144: multiply 21 2 1 0,2
10410 12144: negative_part 2 1 1 0,2,2
10411 12144: positive_part 2 1 1 0,1,2
10412 12144: a 3 0 3 1,1,2
10415 Found proof, 17.397670s
10416 % SZS status Unsatisfiable for GRP114-1.p
10417 % SZS output start CNFRefutation for GRP114-1.p
10418 Id : 12, {_}: intersection ?26 (intersection ?27 ?28) =<= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
10419 Id : 14, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
10420 Id : 13, {_}: union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
10421 Id : 235, {_}: multiply (union ?499 ?500) ?501 =<= union (multiply ?499 ?501) (multiply ?500 ?501) [501, 500, 499] by multiply_union2 ?499 ?500 ?501
10422 Id : 15, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
10423 Id : 195, {_}: multiply ?427 (intersection ?428 ?429) =<= intersection (multiply ?427 ?428) (multiply ?427 ?429) [429, 428, 427] by multiply_intersection1 ?427 ?428 ?429
10424 Id : 10, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
10425 Id : 21, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
10426 Id : 17, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
10427 Id : 7, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14
10428 Id : 11, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
10429 Id : 20, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
10430 Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
10431 Id : 16, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
10432 Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
10433 Id : 48, {_}: inverse (multiply ?104 ?105) =<= multiply (inverse ?105) (inverse ?104) [105, 104] by inverse_product_lemma ?104 ?105
10434 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10435 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10436 Id : 26, {_}: multiply (multiply ?67 ?68) ?69 =>= multiply ?67 (multiply ?68 ?69) [69, 68, 67] by associativity ?67 ?68 ?69
10437 Id : 28, {_}: multiply identity ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Super 26 with 3 at 1,2
10438 Id : 32, {_}: ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Demod 28 with 2 at 2
10439 Id : 50, {_}: inverse (multiply (inverse ?109) ?110) =>= multiply (inverse ?110) ?109 [110, 109] by Super 48 with 6 at 2,3
10440 Id : 49, {_}: inverse (multiply identity ?107) =<= multiply (inverse ?107) identity [107] by Super 48 with 5 at 2,3
10441 Id : 835, {_}: inverse ?1371 =<= multiply (inverse ?1371) identity [1371] by Demod 49 with 2 at 1,2
10442 Id : 841, {_}: inverse (inverse ?1382) =<= multiply ?1382 identity [1382] by Super 835 with 6 at 1,3
10443 Id : 864, {_}: ?1382 =<= multiply ?1382 identity [1382] by Demod 841 with 6 at 2
10444 Id : 881, {_}: multiply ?1419 (union ?1420 identity) =?= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Super 16 with 864 at 2,3
10445 Id : 900, {_}: multiply ?1419 (positive_part ?1420) =<= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Demod 881 with 20 at 2,2
10446 Id : 2897, {_}: multiply ?3964 (positive_part ?3965) =<= union ?3964 (multiply ?3964 ?3965) [3965, 3964] by Demod 900 with 11 at 3
10447 Id : 2901, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union (inverse ?3975) identity [3975] by Super 2897 with 3 at 2,3
10448 Id : 2938, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union identity (inverse ?3975) [3975] by Demod 2901 with 11 at 3
10449 Id : 296, {_}: union identity ?627 =>= positive_part ?627 [627] by Super 11 with 20 at 3
10450 Id : 2939, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= positive_part (inverse ?3975) [3975] by Demod 2938 with 296 at 3
10451 Id : 2958, {_}: inverse (positive_part (inverse ?4028)) =<= multiply (inverse (positive_part ?4028)) ?4028 [4028] by Super 50 with 2939 at 1,2
10452 Id : 3609, {_}: ?4904 =<= multiply (inverse (inverse (positive_part ?4904))) (inverse (positive_part (inverse ?4904))) [4904] by Super 32 with 2958 at 2,3
10453 Id : 3661, {_}: ?4904 =<= inverse (multiply (positive_part (inverse ?4904)) (inverse (positive_part ?4904))) [4904] by Demod 3609 with 7 at 3
10454 Id : 52, {_}: inverse (multiply ?114 (inverse ?115)) =>= multiply ?115 (inverse ?114) [115, 114] by Super 48 with 6 at 1,3
10455 Id : 3662, {_}: ?4904 =<= multiply (positive_part ?4904) (inverse (positive_part (inverse ?4904))) [4904] by Demod 3661 with 52 at 3
10456 Id : 875, {_}: multiply ?1405 (intersection ?1406 identity) =?= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Super 17 with 864 at 2,3
10457 Id : 906, {_}: multiply ?1405 (negative_part ?1406) =<= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Demod 875 with 21 at 2,2
10458 Id : 3727, {_}: multiply ?5043 (negative_part ?5044) =<= intersection ?5043 (multiply ?5043 ?5044) [5044, 5043] by Demod 906 with 10 at 3
10459 Id : 40, {_}: multiply ?89 (inverse ?89) =>= identity [89] by Super 3 with 6 at 1,2
10460 Id : 3734, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= intersection ?5063 identity [5063] by Super 3727 with 40 at 2,3
10461 Id : 3782, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 3734 with 21 at 3
10462 Id : 201, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= intersection identity (multiply (inverse ?449) ?450) [450, 449] by Super 195 with 3 at 1,3
10463 Id : 311, {_}: intersection identity ?654 =>= negative_part ?654 [654] by Super 10 with 21 at 3
10464 Id : 8114, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= negative_part (multiply (inverse ?449) ?450) [450, 449] by Demod 201 with 311 at 3
10465 Id : 135, {_}: intersection ?38 (union ?37 ?38) =>= ?38 [37, 38] by Demod 15 with 10 at 2
10466 Id : 701, {_}: intersection ?1238 (positive_part ?1238) =>= ?1238 [1238] by Super 135 with 296 at 2,2
10467 Id : 241, {_}: multiply (union (inverse ?521) ?522) ?521 =>= union identity (multiply ?522 ?521) [522, 521] by Super 235 with 3 at 1,3
10468 Id : 8575, {_}: multiply (union (inverse ?10997) ?10998) ?10997 =>= positive_part (multiply ?10998 ?10997) [10998, 10997] by Demod 241 with 296 at 3
10469 Id : 699, {_}: union identity (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Super 13 with 296 at 1,3
10470 Id : 716, {_}: positive_part (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 699 with 296 at 2
10471 Id : 299, {_}: union ?634 (union ?635 identity) =>= positive_part (union ?634 ?635) [635, 634] by Super 13 with 20 at 3
10472 Id : 307, {_}: union ?634 (positive_part ?635) =<= positive_part (union ?634 ?635) [635, 634] by Demod 299 with 20 at 2,2
10473 Id : 1223, {_}: union ?1233 (positive_part ?1234) =<= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 716 with 307 at 2
10474 Id : 2971, {_}: multiply (inverse ?4064) (positive_part ?4064) =>= positive_part (inverse ?4064) [4064] by Demod 2938 with 296 at 3
10475 Id : 121, {_}: union ?35 (intersection ?34 ?35) =>= ?35 [34, 35] by Demod 14 with 11 at 2
10476 Id : 700, {_}: positive_part (intersection ?1236 identity) =>= identity [1236] by Super 121 with 296 at 2
10477 Id : 715, {_}: positive_part (negative_part ?1236) =>= identity [1236] by Demod 700 with 21 at 1,2
10478 Id : 2976, {_}: multiply (inverse (negative_part ?4073)) identity =>= positive_part (inverse (negative_part ?4073)) [4073] by Super 2971 with 715 at 2,2
10479 Id : 3014, {_}: inverse (negative_part ?4073) =<= positive_part (inverse (negative_part ?4073)) [4073] by Demod 2976 with 864 at 2
10480 Id : 3035, {_}: union (inverse (negative_part ?4112)) (positive_part ?4113) =>= union (inverse (negative_part ?4112)) ?4113 [4113, 4112] by Super 1223 with 3014 at 1,3
10481 Id : 8597, {_}: multiply (union (inverse (negative_part ?11063)) ?11064) (negative_part ?11063) =>= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11064, 11063] by Super 8575 with 3035 at 1,2
10482 Id : 8560, {_}: multiply (union (inverse ?521) ?522) ?521 =>= positive_part (multiply ?522 ?521) [522, 521] by Demod 241 with 296 at 3
10483 Id : 8643, {_}: positive_part (multiply ?11064 (negative_part ?11063)) =<= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11063, 11064] by Demod 8597 with 8560 at 2
10484 Id : 907, {_}: multiply ?1405 (negative_part ?1406) =<= intersection ?1405 (multiply ?1405 ?1406) [1406, 1405] by Demod 906 with 10 at 3
10485 Id : 8600, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part (multiply identity ?11072) [11072] by Super 8575 with 20 at 1,2
10486 Id : 8645, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part ?11072 [11072] by Demod 8600 with 2 at 1,3
10487 Id : 8660, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part (inverse ?11112)) (positive_part ?11112) [11112] by Super 907 with 8645 at 2,3
10488 Id : 8719, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part ?11112) (positive_part (inverse ?11112)) [11112] by Demod 8660 with 10 at 3
10489 Id : 9585, {_}: positive_part (multiply (inverse ?11973) (negative_part ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Super 8643 with 8719 at 1,3
10490 Id : 3731, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection (inverse ?5054) identity [5054] by Super 3727 with 3 at 2,3
10491 Id : 3776, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection identity (inverse ?5054) [5054] by Demod 3731 with 10 at 3
10492 Id : 3777, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= negative_part (inverse ?5054) [5054] by Demod 3776 with 311 at 3
10493 Id : 9660, {_}: positive_part (negative_part (inverse ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9585 with 3777 at 1,2
10494 Id : 9661, {_}: identity =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9660 with 715 at 2
10495 Id : 37105, {_}: intersection (intersection (positive_part ?38557) (positive_part (inverse ?38557))) identity =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Super 701 with 9661 at 2,2
10496 Id : 37338, {_}: intersection identity (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37105 with 10 at 2
10497 Id : 37339, {_}: negative_part (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37338 with 311 at 2
10498 Id : 314, {_}: intersection ?661 (intersection ?662 identity) =>= negative_part (intersection ?661 ?662) [662, 661] by Super 12 with 21 at 3
10499 Id : 321, {_}: intersection ?661 (negative_part ?662) =<= negative_part (intersection ?661 ?662) [662, 661] by Demod 314 with 21 at 2,2
10500 Id : 37340, {_}: intersection (positive_part ?38557) (negative_part (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37339 with 321 at 2
10501 Id : 743, {_}: intersection identity (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Super 12 with 311 at 1,3
10502 Id : 757, {_}: negative_part (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Demod 743 with 311 at 2
10503 Id : 1432, {_}: intersection ?2159 (negative_part ?2160) =<= intersection (negative_part ?2159) ?2160 [2160, 2159] by Demod 757 with 321 at 2
10504 Id : 738, {_}: negative_part (union ?1265 identity) =>= identity [1265] by Super 135 with 311 at 2
10505 Id : 761, {_}: negative_part (positive_part ?1265) =>= identity [1265] by Demod 738 with 20 at 1,2
10506 Id : 1437, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= intersection identity ?2174 [2174, 2173] by Super 1432 with 761 at 1,3
10507 Id : 1472, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= negative_part ?2174 [2174, 2173] by Demod 1437 with 311 at 3
10508 Id : 37341, {_}: negative_part (positive_part (inverse ?38557)) =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37340 with 1472 at 2
10509 Id : 37342, {_}: identity =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37341 with 761 at 2
10510 Id : 37637, {_}: multiply (inverse (positive_part ?38828)) identity =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Super 8114 with 37342 at 2,2
10511 Id : 37769, {_}: inverse (positive_part ?38828) =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Demod 37637 with 864 at 2
10512 Id : 8675, {_}: multiply (positive_part (inverse ?11150)) ?11150 =>= positive_part ?11150 [11150] by Demod 8600 with 2 at 1,3
10513 Id : 8679, {_}: multiply (positive_part ?11157) (inverse ?11157) =>= positive_part (inverse ?11157) [11157] by Super 8675 with 6 at 1,1,2
10514 Id : 8754, {_}: inverse ?11202 =<= multiply (inverse (positive_part ?11202)) (positive_part (inverse ?11202)) [11202] by Super 32 with 8679 at 2,3
10515 Id : 37770, {_}: inverse (positive_part ?38828) =<= negative_part (inverse ?38828) [38828] by Demod 37769 with 8754 at 1,3
10516 Id : 37939, {_}: multiply ?5063 (inverse (positive_part ?5063)) =>= negative_part ?5063 [5063] by Demod 3782 with 37770 at 2,2
10517 Id : 8672, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part (inverse (inverse ?11144)))) [11144] by Super 52 with 8645 at 1,2
10518 Id : 8705, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part ?11144)) [11144] by Demod 8672 with 6 at 1,1,2,3
10519 Id : 37967, {_}: inverse (positive_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 37939 with 8705 at 2
10520 Id : 37970, {_}: ?4904 =<= multiply (positive_part ?4904) (negative_part ?4904) [4904] by Demod 3662 with 37967 at 2,3
10521 Id : 38259, {_}: a =?= a [] by Demod 1 with 37970 at 2
10522 Id : 1, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
10523 % SZS output end CNFRefutation for GRP114-1.p
10524 12145: solved GRP114-1.p in 5.996374 using kbo
10525 12145: status Unsatisfiable for GRP114-1.p
10526 NO CLASH, using fixed ground order
10528 12157: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10529 12157: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10530 12157: Id : 4, {_}:
10531 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
10532 [8, 7, 6] by associativity ?6 ?7 ?8
10533 12157: Id : 5, {_}:
10534 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
10535 [11, 10] by symmetry_of_glb ?10 ?11
10536 12157: Id : 6, {_}:
10537 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
10538 [14, 13] by symmetry_of_lub ?13 ?14
10539 12157: Id : 7, {_}:
10540 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
10542 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
10543 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
10544 12157: Id : 8, {_}:
10545 least_upper_bound ?20 (least_upper_bound ?21 ?22)
10547 least_upper_bound (least_upper_bound ?20 ?21) ?22
10548 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
10549 12157: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
10550 12157: Id : 10, {_}:
10551 greatest_lower_bound ?26 ?26 =>= ?26
10552 [26] by idempotence_of_gld ?26
10553 12157: Id : 11, {_}:
10554 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
10555 [29, 28] by lub_absorbtion ?28 ?29
10556 12157: Id : 12, {_}:
10557 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
10558 [32, 31] by glb_absorbtion ?31 ?32
10559 12157: Id : 13, {_}:
10560 multiply ?34 (least_upper_bound ?35 ?36)
10562 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
10563 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
10564 12157: Id : 14, {_}:
10565 multiply ?38 (greatest_lower_bound ?39 ?40)
10567 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
10568 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
10569 12157: Id : 15, {_}:
10570 multiply (least_upper_bound ?42 ?43) ?44
10572 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
10573 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
10574 12157: Id : 16, {_}:
10575 multiply (greatest_lower_bound ?46 ?47) ?48
10577 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
10578 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
10579 12157: Id : 17, {_}: inverse identity =>= identity [] by p19_1
10580 12157: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
10581 12157: Id : 19, {_}:
10582 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
10583 [54, 53] by p19_3 ?53 ?54
10585 12157: Id : 1, {_}:
10588 multiply (least_upper_bound a identity)
10589 (greatest_lower_bound a identity)
10594 12157: inverse 7 1 0
10595 12157: multiply 21 2 1 0,3
10596 12157: greatest_lower_bound 14 2 1 0,2,3
10597 12157: least_upper_bound 14 2 1 0,1,3
10598 12157: identity 6 0 2 2,1,3
10600 NO CLASH, using fixed ground order
10602 12158: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10603 12158: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10604 12158: Id : 4, {_}:
10605 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10606 [8, 7, 6] by associativity ?6 ?7 ?8
10607 12158: Id : 5, {_}:
10608 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
10609 [11, 10] by symmetry_of_glb ?10 ?11
10610 12158: Id : 6, {_}:
10611 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
10612 [14, 13] by symmetry_of_lub ?13 ?14
10613 12158: Id : 7, {_}:
10614 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
10616 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
10617 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
10618 12158: Id : 8, {_}:
10619 least_upper_bound ?20 (least_upper_bound ?21 ?22)
10621 least_upper_bound (least_upper_bound ?20 ?21) ?22
10622 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
10623 12158: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
10624 12158: Id : 10, {_}:
10625 greatest_lower_bound ?26 ?26 =>= ?26
10626 [26] by idempotence_of_gld ?26
10627 12158: Id : 11, {_}:
10628 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
10629 [29, 28] by lub_absorbtion ?28 ?29
10630 12158: Id : 12, {_}:
10631 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
10632 [32, 31] by glb_absorbtion ?31 ?32
10633 12158: Id : 13, {_}:
10634 multiply ?34 (least_upper_bound ?35 ?36)
10636 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
10637 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
10638 12158: Id : 14, {_}:
10639 multiply ?38 (greatest_lower_bound ?39 ?40)
10641 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
10642 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
10643 12158: Id : 15, {_}:
10644 multiply (least_upper_bound ?42 ?43) ?44
10646 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
10647 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
10648 12158: Id : 16, {_}:
10649 multiply (greatest_lower_bound ?46 ?47) ?48
10651 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
10652 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
10653 12158: Id : 17, {_}: inverse identity =>= identity [] by p19_1
10654 12158: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
10655 12158: Id : 19, {_}:
10656 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
10657 [54, 53] by p19_3 ?53 ?54
10659 12158: Id : 1, {_}:
10662 multiply (least_upper_bound a identity)
10663 (greatest_lower_bound a identity)
10668 12158: inverse 7 1 0
10669 12158: multiply 21 2 1 0,3
10670 12158: greatest_lower_bound 14 2 1 0,2,3
10671 12158: least_upper_bound 14 2 1 0,1,3
10672 12158: identity 6 0 2 2,1,3
10674 NO CLASH, using fixed ground order
10676 12159: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10677 12159: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10678 12159: Id : 4, {_}:
10679 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10680 [8, 7, 6] by associativity ?6 ?7 ?8
10681 12159: Id : 5, {_}:
10682 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
10683 [11, 10] by symmetry_of_glb ?10 ?11
10684 12159: Id : 6, {_}:
10685 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
10686 [14, 13] by symmetry_of_lub ?13 ?14
10687 12159: Id : 7, {_}:
10688 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
10690 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
10691 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
10692 12159: Id : 8, {_}:
10693 least_upper_bound ?20 (least_upper_bound ?21 ?22)
10695 least_upper_bound (least_upper_bound ?20 ?21) ?22
10696 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
10697 12159: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
10698 12159: Id : 10, {_}:
10699 greatest_lower_bound ?26 ?26 =>= ?26
10700 [26] by idempotence_of_gld ?26
10701 12159: Id : 11, {_}:
10702 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
10703 [29, 28] by lub_absorbtion ?28 ?29
10704 12159: Id : 12, {_}:
10705 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
10706 [32, 31] by glb_absorbtion ?31 ?32
10707 12159: Id : 13, {_}:
10708 multiply ?34 (least_upper_bound ?35 ?36)
10710 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
10711 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
10712 12159: Id : 14, {_}:
10713 multiply ?38 (greatest_lower_bound ?39 ?40)
10715 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
10716 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
10717 12159: Id : 15, {_}:
10718 multiply (least_upper_bound ?42 ?43) ?44
10720 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
10721 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
10722 12159: Id : 16, {_}:
10723 multiply (greatest_lower_bound ?46 ?47) ?48
10725 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
10726 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
10727 12159: Id : 17, {_}: inverse identity =>= identity [] by p19_1
10728 12159: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
10729 12159: Id : 19, {_}:
10730 inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
10731 [54, 53] by p19_3 ?53 ?54
10733 12159: Id : 1, {_}:
10736 multiply (least_upper_bound a identity)
10737 (greatest_lower_bound a identity)
10742 12159: inverse 7 1 0
10743 12159: multiply 21 2 1 0,3
10744 12159: greatest_lower_bound 14 2 1 0,2,3
10745 12159: least_upper_bound 14 2 1 0,1,3
10746 12159: identity 6 0 2 2,1,3
10748 % SZS status Timeout for GRP167-4.p
10749 NO CLASH, using fixed ground order
10751 12195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10752 12195: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10753 12195: Id : 4, {_}:
10754 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
10755 [8, 7, 6] by associativity ?6 ?7 ?8
10756 12195: Id : 5, {_}:
10757 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
10758 [11, 10] by symmetry_of_glb ?10 ?11
10759 12195: Id : 6, {_}:
10760 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
10761 [14, 13] by symmetry_of_lub ?13 ?14
10762 12195: Id : 7, {_}:
10763 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
10765 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
10766 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
10767 12195: Id : 8, {_}:
10768 least_upper_bound ?20 (least_upper_bound ?21 ?22)
10770 least_upper_bound (least_upper_bound ?20 ?21) ?22
10771 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
10772 12195: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
10773 12195: Id : 10, {_}:
10774 greatest_lower_bound ?26 ?26 =>= ?26
10775 [26] by idempotence_of_gld ?26
10776 12195: Id : 11, {_}:
10777 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
10778 [29, 28] by lub_absorbtion ?28 ?29
10779 12195: Id : 12, {_}:
10780 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
10781 [32, 31] by glb_absorbtion ?31 ?32
10782 12195: Id : 13, {_}:
10783 multiply ?34 (least_upper_bound ?35 ?36)
10785 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
10786 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
10787 12195: Id : 14, {_}:
10788 multiply ?38 (greatest_lower_bound ?39 ?40)
10790 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
10791 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
10792 12195: Id : 15, {_}:
10793 multiply (least_upper_bound ?42 ?43) ?44
10795 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
10796 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
10797 12195: Id : 16, {_}:
10798 multiply (greatest_lower_bound ?46 ?47) ?48
10800 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
10801 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
10802 12195: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
10803 12195: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
10804 12195: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
10806 12195: Id : 1, {_}:
10807 greatest_lower_bound (greatest_lower_bound a (multiply b c))
10808 (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
10810 greatest_lower_bound a (multiply b c)
10815 12195: least_upper_bound 13 2 0
10816 12195: inverse 1 1 0
10817 12195: identity 8 0 0
10818 12195: greatest_lower_bound 21 2 5 0,2
10819 12195: multiply 21 2 3 0,2,1,2
10820 12195: c 4 0 3 2,2,1,2
10821 12195: b 4 0 3 1,2,1,2
10822 12195: a 5 0 4 1,1,2
10823 NO CLASH, using fixed ground order
10825 12196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10826 12196: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10827 12196: Id : 4, {_}:
10828 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10829 [8, 7, 6] by associativity ?6 ?7 ?8
10830 12196: Id : 5, {_}:
10831 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
10832 [11, 10] by symmetry_of_glb ?10 ?11
10833 12196: Id : 6, {_}:
10834 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
10835 [14, 13] by symmetry_of_lub ?13 ?14
10836 12196: Id : 7, {_}:
10837 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
10839 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
10840 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
10841 12196: Id : 8, {_}:
10842 least_upper_bound ?20 (least_upper_bound ?21 ?22)
10844 least_upper_bound (least_upper_bound ?20 ?21) ?22
10845 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
10846 12196: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
10847 12196: Id : 10, {_}:
10848 greatest_lower_bound ?26 ?26 =>= ?26
10849 [26] by idempotence_of_gld ?26
10850 12196: Id : 11, {_}:
10851 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
10852 [29, 28] by lub_absorbtion ?28 ?29
10853 12196: Id : 12, {_}:
10854 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
10855 [32, 31] by glb_absorbtion ?31 ?32
10856 12196: Id : 13, {_}:
10857 multiply ?34 (least_upper_bound ?35 ?36)
10859 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
10860 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
10861 12196: Id : 14, {_}:
10862 multiply ?38 (greatest_lower_bound ?39 ?40)
10864 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
10865 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
10866 12196: Id : 15, {_}:
10867 multiply (least_upper_bound ?42 ?43) ?44
10869 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
10870 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
10871 12196: Id : 16, {_}:
10872 multiply (greatest_lower_bound ?46 ?47) ?48
10874 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
10875 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
10876 12196: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
10877 12196: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
10878 12196: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
10880 12196: Id : 1, {_}:
10881 greatest_lower_bound (greatest_lower_bound a (multiply b c))
10882 (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
10884 greatest_lower_bound a (multiply b c)
10889 12196: least_upper_bound 13 2 0
10890 12196: inverse 1 1 0
10891 12196: identity 8 0 0
10892 12196: greatest_lower_bound 21 2 5 0,2
10893 12196: multiply 21 2 3 0,2,1,2
10894 12196: c 4 0 3 2,2,1,2
10895 12196: b 4 0 3 1,2,1,2
10896 12196: a 5 0 4 1,1,2
10897 NO CLASH, using fixed ground order
10899 12197: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10900 12197: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10901 12197: Id : 4, {_}:
10902 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
10903 [8, 7, 6] by associativity ?6 ?7 ?8
10904 12197: Id : 5, {_}:
10905 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
10906 [11, 10] by symmetry_of_glb ?10 ?11
10907 12197: Id : 6, {_}:
10908 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
10909 [14, 13] by symmetry_of_lub ?13 ?14
10910 12197: Id : 7, {_}:
10911 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
10913 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
10914 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
10915 12197: Id : 8, {_}:
10916 least_upper_bound ?20 (least_upper_bound ?21 ?22)
10918 least_upper_bound (least_upper_bound ?20 ?21) ?22
10919 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
10920 12197: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
10921 12197: Id : 10, {_}:
10922 greatest_lower_bound ?26 ?26 =>= ?26
10923 [26] by idempotence_of_gld ?26
10924 12197: Id : 11, {_}:
10925 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
10926 [29, 28] by lub_absorbtion ?28 ?29
10927 12197: Id : 12, {_}:
10928 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
10929 [32, 31] by glb_absorbtion ?31 ?32
10930 12197: Id : 13, {_}:
10931 multiply ?34 (least_upper_bound ?35 ?36)
10933 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
10934 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
10935 12197: Id : 14, {_}:
10936 multiply ?38 (greatest_lower_bound ?39 ?40)
10938 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
10939 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
10940 12197: Id : 15, {_}:
10941 multiply (least_upper_bound ?42 ?43) ?44
10943 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
10944 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
10945 12197: Id : 16, {_}:
10946 multiply (greatest_lower_bound ?46 ?47) ?48
10948 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
10949 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
10950 12197: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
10951 12197: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
10952 12197: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
10954 12197: Id : 1, {_}:
10955 greatest_lower_bound (greatest_lower_bound a (multiply b c))
10956 (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
10958 greatest_lower_bound a (multiply b c)
10963 12197: least_upper_bound 13 2 0
10964 12197: inverse 1 1 0
10965 12197: identity 8 0 0
10966 12197: greatest_lower_bound 21 2 5 0,2
10967 12197: multiply 21 2 3 0,2,1,2
10968 12197: c 4 0 3 2,2,1,2
10969 12197: b 4 0 3 1,2,1,2
10970 12197: a 5 0 4 1,1,2
10971 % SZS status Timeout for GRP177-2.p
10972 NO CLASH, using fixed ground order
10974 12224: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
10975 12224: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
10976 12224: Id : 4, {_}:
10977 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
10978 [8, 7, 6] by associativity ?6 ?7 ?8
10979 12224: Id : 5, {_}:
10980 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
10981 [11, 10] by symmetry_of_glb ?10 ?11
10982 12224: Id : 6, {_}:
10983 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
10984 [14, 13] by symmetry_of_lub ?13 ?14
10985 12224: Id : 7, {_}:
10986 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
10988 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
10989 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
10990 12224: Id : 8, {_}:
10991 least_upper_bound ?20 (least_upper_bound ?21 ?22)
10993 least_upper_bound (least_upper_bound ?20 ?21) ?22
10994 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
10995 12224: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
10996 12224: Id : 10, {_}:
10997 greatest_lower_bound ?26 ?26 =>= ?26
10998 [26] by idempotence_of_gld ?26
10999 12224: Id : 11, {_}:
11000 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11001 [29, 28] by lub_absorbtion ?28 ?29
11002 12224: Id : 12, {_}:
11003 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11004 [32, 31] by glb_absorbtion ?31 ?32
11005 12224: Id : 13, {_}:
11006 multiply ?34 (least_upper_bound ?35 ?36)
11008 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11009 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11010 12224: Id : 14, {_}:
11011 multiply ?38 (greatest_lower_bound ?39 ?40)
11013 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11014 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11015 12224: Id : 15, {_}:
11016 multiply (least_upper_bound ?42 ?43) ?44
11018 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11019 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11020 12224: Id : 16, {_}:
11021 multiply (greatest_lower_bound ?46 ?47) ?48
11023 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11024 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11025 12224: Id : 17, {_}: inverse identity =>= identity [] by p18_1
11026 12224: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
11027 12224: Id : 19, {_}:
11028 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
11029 [54, 53] by p18_3 ?53 ?54
11031 12224: Id : 1, {_}:
11032 least_upper_bound (inverse a) identity
11034 inverse (greatest_lower_bound a identity)
11039 12224: multiply 20 2 0
11040 12224: greatest_lower_bound 14 2 1 0,1,3
11041 12224: least_upper_bound 14 2 1 0,2
11042 12224: identity 6 0 2 2,2
11043 12224: inverse 9 1 2 0,1,2
11044 12224: a 2 0 2 1,1,2
11045 NO CLASH, using fixed ground order
11047 12225: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11048 12225: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11049 12225: Id : 4, {_}:
11050 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11051 [8, 7, 6] by associativity ?6 ?7 ?8
11052 12225: Id : 5, {_}:
11053 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11054 [11, 10] by symmetry_of_glb ?10 ?11
11055 12225: Id : 6, {_}:
11056 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11057 [14, 13] by symmetry_of_lub ?13 ?14
11058 12225: Id : 7, {_}:
11059 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11061 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11062 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11063 12225: Id : 8, {_}:
11064 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11066 least_upper_bound (least_upper_bound ?20 ?21) ?22
11067 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11068 12225: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11069 12225: Id : 10, {_}:
11070 greatest_lower_bound ?26 ?26 =>= ?26
11071 [26] by idempotence_of_gld ?26
11072 NO CLASH, using fixed ground order
11074 12226: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11075 12226: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11076 12226: Id : 4, {_}:
11077 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11078 [8, 7, 6] by associativity ?6 ?7 ?8
11079 12226: Id : 5, {_}:
11080 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11081 [11, 10] by symmetry_of_glb ?10 ?11
11082 12226: Id : 6, {_}:
11083 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11084 [14, 13] by symmetry_of_lub ?13 ?14
11085 12226: Id : 7, {_}:
11086 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11088 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11089 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11090 12226: Id : 8, {_}:
11091 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11093 least_upper_bound (least_upper_bound ?20 ?21) ?22
11094 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11095 12226: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11096 12226: Id : 10, {_}:
11097 greatest_lower_bound ?26 ?26 =>= ?26
11098 [26] by idempotence_of_gld ?26
11099 12226: Id : 11, {_}:
11100 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11101 [29, 28] by lub_absorbtion ?28 ?29
11102 12226: Id : 12, {_}:
11103 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11104 [32, 31] by glb_absorbtion ?31 ?32
11105 12226: Id : 13, {_}:
11106 multiply ?34 (least_upper_bound ?35 ?36)
11108 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11109 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11110 12226: Id : 14, {_}:
11111 multiply ?38 (greatest_lower_bound ?39 ?40)
11113 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11114 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11115 12226: Id : 15, {_}:
11116 multiply (least_upper_bound ?42 ?43) ?44
11118 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11119 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11120 12226: Id : 16, {_}:
11121 multiply (greatest_lower_bound ?46 ?47) ?48
11123 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11124 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11125 12226: Id : 17, {_}: inverse identity =>= identity [] by p18_1
11126 12226: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
11127 12226: Id : 19, {_}:
11128 inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
11129 [54, 53] by p18_3 ?53 ?54
11131 12226: Id : 1, {_}:
11132 least_upper_bound (inverse a) identity
11134 inverse (greatest_lower_bound a identity)
11139 12226: multiply 20 2 0
11140 12226: greatest_lower_bound 14 2 1 0,1,3
11141 12226: least_upper_bound 14 2 1 0,2
11142 12226: identity 6 0 2 2,2
11143 12226: inverse 9 1 2 0,1,2
11144 12226: a 2 0 2 1,1,2
11145 12225: Id : 11, {_}:
11146 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11147 [29, 28] by lub_absorbtion ?28 ?29
11148 12225: Id : 12, {_}:
11149 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11150 [32, 31] by glb_absorbtion ?31 ?32
11151 12225: Id : 13, {_}:
11152 multiply ?34 (least_upper_bound ?35 ?36)
11154 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11155 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11156 12225: Id : 14, {_}:
11157 multiply ?38 (greatest_lower_bound ?39 ?40)
11159 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11160 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11161 12225: Id : 15, {_}:
11162 multiply (least_upper_bound ?42 ?43) ?44
11164 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11165 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11166 12225: Id : 16, {_}:
11167 multiply (greatest_lower_bound ?46 ?47) ?48
11169 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11170 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11171 12225: Id : 17, {_}: inverse identity =>= identity [] by p18_1
11172 12225: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
11173 12225: Id : 19, {_}:
11174 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
11175 [54, 53] by p18_3 ?53 ?54
11177 12225: Id : 1, {_}:
11178 least_upper_bound (inverse a) identity
11180 inverse (greatest_lower_bound a identity)
11185 12225: multiply 20 2 0
11186 12225: greatest_lower_bound 14 2 1 0,1,3
11187 12225: least_upper_bound 14 2 1 0,2
11188 12225: identity 6 0 2 2,2
11189 12225: inverse 9 1 2 0,1,2
11190 12225: a 2 0 2 1,1,2
11191 % SZS status Timeout for GRP179-3.p
11192 NO CLASH, using fixed ground order
11194 12243: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11195 12243: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11196 12243: Id : 4, {_}:
11197 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
11198 [8, 7, 6] by associativity ?6 ?7 ?8
11199 12243: Id : 5, {_}:
11200 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11201 [11, 10] by symmetry_of_glb ?10 ?11
11202 12243: Id : 6, {_}:
11203 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11204 [14, 13] by symmetry_of_lub ?13 ?14
11205 12243: Id : 7, {_}:
11206 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11208 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11209 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11210 12243: Id : 8, {_}:
11211 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11213 least_upper_bound (least_upper_bound ?20 ?21) ?22
11214 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11215 12243: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11216 12243: Id : 10, {_}:
11217 greatest_lower_bound ?26 ?26 =>= ?26
11218 [26] by idempotence_of_gld ?26
11219 12243: Id : 11, {_}:
11220 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11221 [29, 28] by lub_absorbtion ?28 ?29
11222 12243: Id : 12, {_}:
11223 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11224 [32, 31] by glb_absorbtion ?31 ?32
11225 12243: Id : 13, {_}:
11226 multiply ?34 (least_upper_bound ?35 ?36)
11228 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11229 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11230 12243: Id : 14, {_}:
11231 multiply ?38 (greatest_lower_bound ?39 ?40)
11233 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11234 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11235 12243: Id : 15, {_}:
11236 multiply (least_upper_bound ?42 ?43) ?44
11238 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11239 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11240 12243: Id : 16, {_}:
11241 multiply (greatest_lower_bound ?46 ?47) ?48
11243 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11244 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11245 12243: Id : 17, {_}: inverse identity =>= identity [] by p11_1
11246 12243: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
11247 12243: Id : 19, {_}:
11248 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
11249 [54, 53] by p11_3 ?53 ?54
11251 12243: Id : 1, {_}:
11252 multiply a (multiply (inverse (greatest_lower_bound a b)) b)
11254 least_upper_bound a b
11259 12243: identity 4 0 0
11260 12243: least_upper_bound 14 2 1 0,3
11261 12243: multiply 22 2 2 0,2
11262 12243: inverse 8 1 1 0,1,2,2
11263 12243: greatest_lower_bound 14 2 1 0,1,1,2,2
11264 12243: b 3 0 3 2,1,1,2,2
11266 NO CLASH, using fixed ground order
11268 12244: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11269 12244: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11270 12244: Id : 4, {_}:
11271 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11272 [8, 7, 6] by associativity ?6 ?7 ?8
11273 12244: Id : 5, {_}:
11274 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11275 [11, 10] by symmetry_of_glb ?10 ?11
11276 12244: Id : 6, {_}:
11277 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11278 [14, 13] by symmetry_of_lub ?13 ?14
11279 12244: Id : 7, {_}:
11280 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11282 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11283 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11284 12244: Id : 8, {_}:
11285 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11287 least_upper_bound (least_upper_bound ?20 ?21) ?22
11288 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11289 12244: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11290 12244: Id : 10, {_}:
11291 greatest_lower_bound ?26 ?26 =>= ?26
11292 [26] by idempotence_of_gld ?26
11293 12244: Id : 11, {_}:
11294 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11295 [29, 28] by lub_absorbtion ?28 ?29
11296 12244: Id : 12, {_}:
11297 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11298 [32, 31] by glb_absorbtion ?31 ?32
11299 12244: Id : 13, {_}:
11300 multiply ?34 (least_upper_bound ?35 ?36)
11302 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11303 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11304 12244: Id : 14, {_}:
11305 multiply ?38 (greatest_lower_bound ?39 ?40)
11307 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11308 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11309 12244: Id : 15, {_}:
11310 multiply (least_upper_bound ?42 ?43) ?44
11312 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11313 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11314 12244: Id : 16, {_}:
11315 multiply (greatest_lower_bound ?46 ?47) ?48
11317 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11318 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11319 12244: Id : 17, {_}: inverse identity =>= identity [] by p11_1
11320 12244: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
11321 12244: Id : 19, {_}:
11322 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
11323 [54, 53] by p11_3 ?53 ?54
11325 12244: Id : 1, {_}:
11326 multiply a (multiply (inverse (greatest_lower_bound a b)) b)
11328 least_upper_bound a b
11333 12244: identity 4 0 0
11334 12244: least_upper_bound 14 2 1 0,3
11335 12244: multiply 22 2 2 0,2
11336 12244: inverse 8 1 1 0,1,2,2
11337 12244: greatest_lower_bound 14 2 1 0,1,1,2,2
11338 12244: b 3 0 3 2,1,1,2,2
11340 NO CLASH, using fixed ground order
11342 12245: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11343 12245: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11344 12245: Id : 4, {_}:
11345 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11346 [8, 7, 6] by associativity ?6 ?7 ?8
11347 12245: Id : 5, {_}:
11348 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11349 [11, 10] by symmetry_of_glb ?10 ?11
11350 12245: Id : 6, {_}:
11351 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11352 [14, 13] by symmetry_of_lub ?13 ?14
11353 12245: Id : 7, {_}:
11354 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11356 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11357 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11358 12245: Id : 8, {_}:
11359 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11361 least_upper_bound (least_upper_bound ?20 ?21) ?22
11362 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11363 12245: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11364 12245: Id : 10, {_}:
11365 greatest_lower_bound ?26 ?26 =>= ?26
11366 [26] by idempotence_of_gld ?26
11367 12245: Id : 11, {_}:
11368 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11369 [29, 28] by lub_absorbtion ?28 ?29
11370 12245: Id : 12, {_}:
11371 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11372 [32, 31] by glb_absorbtion ?31 ?32
11373 12245: Id : 13, {_}:
11374 multiply ?34 (least_upper_bound ?35 ?36)
11376 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11377 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11378 12245: Id : 14, {_}:
11379 multiply ?38 (greatest_lower_bound ?39 ?40)
11381 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11382 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11383 12245: Id : 15, {_}:
11384 multiply (least_upper_bound ?42 ?43) ?44
11386 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11387 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11388 12245: Id : 16, {_}:
11389 multiply (greatest_lower_bound ?46 ?47) ?48
11391 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11392 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11393 12245: Id : 17, {_}: inverse identity =>= identity [] by p11_1
11394 12245: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
11395 12245: Id : 19, {_}:
11396 inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
11397 [54, 53] by p11_3 ?53 ?54
11399 12245: Id : 1, {_}:
11400 multiply a (multiply (inverse (greatest_lower_bound a b)) b)
11402 least_upper_bound a b
11407 12245: identity 4 0 0
11408 12245: least_upper_bound 14 2 1 0,3
11409 12245: multiply 22 2 2 0,2
11410 12245: inverse 8 1 1 0,1,2,2
11411 12245: greatest_lower_bound 14 2 1 0,1,1,2,2
11412 12245: b 3 0 3 2,1,1,2,2
11414 % SZS status Timeout for GRP180-2.p
11415 CLASH, statistics insufficient
11417 12274: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11418 12274: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11419 12274: Id : 4, {_}:
11420 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
11421 [8, 7, 6] by associativity ?6 ?7 ?8
11422 12274: Id : 5, {_}:
11423 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11424 [11, 10] by symmetry_of_glb ?10 ?11
11425 12274: Id : 6, {_}:
11426 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11427 [14, 13] by symmetry_of_lub ?13 ?14
11428 12274: Id : 7, {_}:
11429 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11431 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11432 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11433 12274: Id : 8, {_}:
11434 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11436 least_upper_bound (least_upper_bound ?20 ?21) ?22
11437 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11438 12274: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11439 12274: Id : 10, {_}:
11440 greatest_lower_bound ?26 ?26 =>= ?26
11441 [26] by idempotence_of_gld ?26
11442 12274: Id : 11, {_}:
11443 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11444 [29, 28] by lub_absorbtion ?28 ?29
11445 12274: Id : 12, {_}:
11446 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11447 [32, 31] by glb_absorbtion ?31 ?32
11448 12274: Id : 13, {_}:
11449 multiply ?34 (least_upper_bound ?35 ?36)
11451 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11452 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11453 12274: Id : 14, {_}:
11454 multiply ?38 (greatest_lower_bound ?39 ?40)
11456 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11457 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11458 12274: Id : 15, {_}:
11459 multiply (least_upper_bound ?42 ?43) ?44
11461 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11462 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11463 12274: Id : 16, {_}:
11464 multiply (greatest_lower_bound ?46 ?47) ?48
11466 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11467 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11468 12274: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
11469 12274: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
11470 12274: Id : 19, {_}:
11471 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
11472 [54, 53] by p12x_3 ?53 ?54
11473 12274: Id : 20, {_}:
11474 greatest_lower_bound a c =>= greatest_lower_bound b c
11476 12274: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
11477 12274: Id : 22, {_}:
11478 inverse (greatest_lower_bound ?58 ?59)
11480 least_upper_bound (inverse ?58) (inverse ?59)
11481 [59, 58] by p12x_6 ?58 ?59
11482 12274: Id : 23, {_}:
11483 inverse (least_upper_bound ?61 ?62)
11485 greatest_lower_bound (inverse ?61) (inverse ?62)
11486 [62, 61] by p12x_7 ?61 ?62
11488 12274: Id : 1, {_}: a =>= b [] by prove_p12x
11493 12274: least_upper_bound 17 2 0
11494 12274: greatest_lower_bound 17 2 0
11495 12274: inverse 13 1 0
11496 12274: multiply 20 2 0
11497 12274: identity 4 0 0
11500 CLASH, statistics insufficient
11502 12275: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11503 12275: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11504 12275: Id : 4, {_}:
11505 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11506 [8, 7, 6] by associativity ?6 ?7 ?8
11507 12275: Id : 5, {_}:
11508 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11509 [11, 10] by symmetry_of_glb ?10 ?11
11510 12275: Id : 6, {_}:
11511 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11512 [14, 13] by symmetry_of_lub ?13 ?14
11513 12275: Id : 7, {_}:
11514 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11516 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11517 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11518 12275: Id : 8, {_}:
11519 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11521 least_upper_bound (least_upper_bound ?20 ?21) ?22
11522 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11523 12275: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11524 12275: Id : 10, {_}:
11525 greatest_lower_bound ?26 ?26 =>= ?26
11526 [26] by idempotence_of_gld ?26
11527 12275: Id : 11, {_}:
11528 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11529 [29, 28] by lub_absorbtion ?28 ?29
11530 12275: Id : 12, {_}:
11531 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11532 [32, 31] by glb_absorbtion ?31 ?32
11533 12275: Id : 13, {_}:
11534 multiply ?34 (least_upper_bound ?35 ?36)
11536 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11537 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11538 12275: Id : 14, {_}:
11539 multiply ?38 (greatest_lower_bound ?39 ?40)
11541 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11542 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11543 12275: Id : 15, {_}:
11544 multiply (least_upper_bound ?42 ?43) ?44
11546 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11547 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11548 12275: Id : 16, {_}:
11549 multiply (greatest_lower_bound ?46 ?47) ?48
11551 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11552 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11553 12275: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
11554 12275: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
11555 12275: Id : 19, {_}:
11556 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
11557 [54, 53] by p12x_3 ?53 ?54
11558 12275: Id : 20, {_}:
11559 greatest_lower_bound a c =>= greatest_lower_bound b c
11561 12275: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
11562 12275: Id : 22, {_}:
11563 inverse (greatest_lower_bound ?58 ?59)
11565 least_upper_bound (inverse ?58) (inverse ?59)
11566 [59, 58] by p12x_6 ?58 ?59
11567 12275: Id : 23, {_}:
11568 inverse (least_upper_bound ?61 ?62)
11570 greatest_lower_bound (inverse ?61) (inverse ?62)
11571 [62, 61] by p12x_7 ?61 ?62
11573 12275: Id : 1, {_}: a =>= b [] by prove_p12x
11578 12275: least_upper_bound 17 2 0
11579 12275: greatest_lower_bound 17 2 0
11580 12275: inverse 13 1 0
11581 12275: multiply 20 2 0
11582 12275: identity 4 0 0
11585 CLASH, statistics insufficient
11587 12276: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11588 12276: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11589 12276: Id : 4, {_}:
11590 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11591 [8, 7, 6] by associativity ?6 ?7 ?8
11592 12276: Id : 5, {_}:
11593 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11594 [11, 10] by symmetry_of_glb ?10 ?11
11595 12276: Id : 6, {_}:
11596 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11597 [14, 13] by symmetry_of_lub ?13 ?14
11598 12276: Id : 7, {_}:
11599 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11601 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11602 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11603 12276: Id : 8, {_}:
11604 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11606 least_upper_bound (least_upper_bound ?20 ?21) ?22
11607 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11608 12276: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11609 12276: Id : 10, {_}:
11610 greatest_lower_bound ?26 ?26 =>= ?26
11611 [26] by idempotence_of_gld ?26
11612 12276: Id : 11, {_}:
11613 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11614 [29, 28] by lub_absorbtion ?28 ?29
11615 12276: Id : 12, {_}:
11616 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11617 [32, 31] by glb_absorbtion ?31 ?32
11618 12276: Id : 13, {_}:
11619 multiply ?34 (least_upper_bound ?35 ?36)
11621 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11622 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11623 12276: Id : 14, {_}:
11624 multiply ?38 (greatest_lower_bound ?39 ?40)
11626 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11627 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11628 12276: Id : 15, {_}:
11629 multiply (least_upper_bound ?42 ?43) ?44
11631 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11632 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11633 12276: Id : 16, {_}:
11634 multiply (greatest_lower_bound ?46 ?47) ?48
11636 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11637 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11638 12276: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
11639 12276: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
11640 12276: Id : 19, {_}:
11641 inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
11642 [54, 53] by p12x_3 ?53 ?54
11643 12276: Id : 20, {_}:
11644 greatest_lower_bound a c =>= greatest_lower_bound b c
11646 12276: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
11647 12276: Id : 22, {_}:
11648 inverse (greatest_lower_bound ?58 ?59)
11650 least_upper_bound (inverse ?58) (inverse ?59)
11651 [59, 58] by p12x_6 ?58 ?59
11652 12276: Id : 23, {_}:
11653 inverse (least_upper_bound ?61 ?62)
11655 greatest_lower_bound (inverse ?61) (inverse ?62)
11656 [62, 61] by p12x_7 ?61 ?62
11658 12276: Id : 1, {_}: a =>= b [] by prove_p12x
11663 12276: least_upper_bound 17 2 0
11664 12276: greatest_lower_bound 17 2 0
11665 12276: inverse 13 1 0
11666 12276: multiply 20 2 0
11667 12276: identity 4 0 0
11672 Found proof, 22.107626s
11673 % SZS status Unsatisfiable for GRP181-4.p
11674 % SZS output start CNFRefutation for GRP181-4.p
11675 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
11676 Id : 20, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
11677 Id : 188, {_}: multiply ?586 (greatest_lower_bound ?587 ?588) =<= greatest_lower_bound (multiply ?586 ?587) (multiply ?586 ?588) [588, 587, 586] by monotony_glb1 ?586 ?587 ?588
11678 Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
11679 Id : 364, {_}: inverse (least_upper_bound ?929 ?930) =<= greatest_lower_bound (inverse ?929) (inverse ?930) [930, 929] by p12x_7 ?929 ?930
11680 Id : 342, {_}: inverse (greatest_lower_bound ?890 ?891) =<= least_upper_bound (inverse ?890) (inverse ?891) [891, 890] by p12x_6 ?890 ?891
11681 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
11682 Id : 158, {_}: multiply ?515 (least_upper_bound ?516 ?517) =<= least_upper_bound (multiply ?515 ?516) (multiply ?515 ?517) [517, 516, 515] by monotony_lub1 ?515 ?516 ?517
11683 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
11684 Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
11685 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11686 Id : 17, {_}: inverse identity =>= identity [] by p12x_1
11687 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11688 Id : 28, {_}: multiply (multiply ?71 ?72) ?73 =?= multiply ?71 (multiply ?72 ?73) [73, 72, 71] by associativity ?71 ?72 ?73
11689 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
11690 Id : 302, {_}: inverse (multiply ?845 ?846) =<= multiply (inverse ?846) (inverse ?845) [846, 845] by p12x_3 ?845 ?846
11691 Id : 803, {_}: inverse (multiply ?1561 (inverse ?1562)) =>= multiply ?1562 (inverse ?1561) [1562, 1561] by Super 302 with 18 at 1,3
11692 Id : 30, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= multiply ?78 identity [79, 78] by Super 28 with 3 at 2,3
11693 Id : 303, {_}: inverse (multiply identity ?848) =<= multiply (inverse ?848) identity [848] by Super 302 with 17 at 2,3
11694 Id : 394, {_}: inverse ?984 =<= multiply (inverse ?984) identity [984] by Demod 303 with 2 at 1,2
11695 Id : 396, {_}: inverse (inverse ?987) =<= multiply ?987 identity [987] by Super 394 with 18 at 1,3
11696 Id : 406, {_}: ?987 =<= multiply ?987 identity [987] by Demod 396 with 18 at 2
11697 Id : 638, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= ?78 [79, 78] by Demod 30 with 406 at 3
11698 Id : 816, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 (inverse (inverse ?1600)))) [1600, 1599] by Super 803 with 638 at 1,2
11699 Id : 306, {_}: inverse (multiply ?855 (inverse ?856)) =>= multiply ?856 (inverse ?855) [856, 855] by Super 302 with 18 at 1,3
11700 Id : 837, {_}: inverse ?1599 =<= multiply ?1600 (multiply (inverse ?1600) (inverse ?1599)) [1600, 1599] by Demod 816 with 306 at 2,3
11701 Id : 838, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 ?1600)) [1600, 1599] by Demod 837 with 19 at 2,3
11702 Id : 285, {_}: multiply ?794 (inverse ?794) =>= identity [794] by Super 3 with 18 at 1,2
11703 Id : 607, {_}: multiply (multiply ?1261 ?1262) (inverse ?1262) =>= multiply ?1261 identity [1262, 1261] by Super 4 with 285 at 2,3
11704 Id : 19344, {_}: multiply (multiply ?27523 ?27524) (inverse ?27524) =>= ?27523 [27524, 27523] by Demod 607 with 406 at 3
11705 Id : 160, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound (multiply (inverse ?522) ?523) identity [523, 522] by Super 158 with 3 at 2,3
11706 Id : 177, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound identity (multiply (inverse ?522) ?523) [523, 522] by Demod 160 with 6 at 3
11707 Id : 345, {_}: inverse (greatest_lower_bound identity ?898) =>= least_upper_bound identity (inverse ?898) [898] by Super 342 with 17 at 1,3
11708 Id : 487, {_}: inverse (multiply (greatest_lower_bound identity ?1114) ?1115) =<= multiply (inverse ?1115) (least_upper_bound identity (inverse ?1114)) [1115, 1114] by Super 19 with 345 at 2,3
11709 Id : 11534, {_}: inverse (multiply (greatest_lower_bound identity ?15482) (inverse ?15482)) =>= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Super 177 with 487 at 2
11710 Id : 11607, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =?= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Demod 11534 with 306 at 2
11711 Id : 11608, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11607 with 406 at 2,3
11712 Id : 11609, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11608 with 345 at 2,2
11713 Id : 11610, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity ?15482 [15482] by Demod 11609 with 18 at 2,3
11714 Id : 19409, {_}: multiply (least_upper_bound identity ?27743) (inverse (least_upper_bound identity (inverse ?27743))) =>= ?27743 [27743] by Super 19344 with 11610 at 1,2
11715 Id : 366, {_}: inverse (least_upper_bound ?934 (inverse ?935)) =>= greatest_lower_bound (inverse ?934) ?935 [935, 934] by Super 364 with 18 at 2,3
11716 Id : 19451, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound (inverse identity) ?27743) =>= ?27743 [27743] by Demod 19409 with 366 at 2,2
11717 Id : 44019, {_}: multiply (least_upper_bound identity ?52011) (greatest_lower_bound identity ?52011) =>= ?52011 [52011] by Demod 19451 with 17 at 1,2,2
11718 Id : 367, {_}: inverse (least_upper_bound identity ?937) =>= greatest_lower_bound identity (inverse ?937) [937] by Super 364 with 17 at 1,3
11719 Id : 8913, {_}: multiply (inverse ?11632) (least_upper_bound ?11632 ?11633) =>= least_upper_bound identity (multiply (inverse ?11632) ?11633) [11633, 11632] by Super 158 with 3 at 1,3
11720 Id : 326, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 21 with 6 at 2
11721 Id : 327, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 326 with 6 at 3
11722 Id : 8921, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 8913 with 327 at 2,2
11723 Id : 164, {_}: multiply (inverse ?538) (least_upper_bound ?538 ?539) =>= least_upper_bound identity (multiply (inverse ?538) ?539) [539, 538] by Super 158 with 3 at 1,3
11724 Id : 9001, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 8921 with 164 at 2
11725 Id : 9081, {_}: inverse (least_upper_bound identity (multiply (inverse c) b)) =>= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Super 367 with 9001 at 1,2
11726 Id : 9110, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =<= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Demod 9081 with 367 at 2
11727 Id : 304, {_}: inverse (multiply (inverse ?850) ?851) =>= multiply (inverse ?851) ?850 [851, 850] by Super 302 with 18 at 2,3
11728 Id : 9111, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =>= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9110 with 304 at 2,3
11729 Id : 9112, {_}: greatest_lower_bound identity (multiply (inverse b) c) =<= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9111 with 304 at 2,2
11730 Id : 44043, {_}: multiply (least_upper_bound identity (multiply (inverse a) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 44019 with 9112 at 2,2
11731 Id : 10178, {_}: multiply (inverse ?13641) (greatest_lower_bound ?13641 ?13642) =>= greatest_lower_bound identity (multiply (inverse ?13641) ?13642) [13642, 13641] by Super 188 with 3 at 1,3
11732 Id : 315, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 20 with 5 at 2
11733 Id : 316, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 315 with 5 at 3
11734 Id : 10190, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 10178 with 316 at 2,2
11735 Id : 194, {_}: multiply (inverse ?609) (greatest_lower_bound ?609 ?610) =>= greatest_lower_bound identity (multiply (inverse ?609) ?610) [610, 609] by Super 188 with 3 at 1,3
11736 Id : 10270, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 10190 with 194 at 2
11737 Id : 10361, {_}: inverse (greatest_lower_bound identity (multiply (inverse c) b)) =>= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Super 345 with 10270 at 1,2
11738 Id : 10393, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =<= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Demod 10361 with 345 at 2
11739 Id : 10394, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =>= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10393 with 304 at 2,3
11740 Id : 10395, {_}: least_upper_bound identity (multiply (inverse b) c) =<= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10394 with 304 at 2,2
11741 Id : 44130, {_}: multiply (least_upper_bound identity (multiply (inverse b) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 44043 with 10395 at 1,2
11742 Id : 19452, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound identity ?27743) =>= ?27743 [27743] by Demod 19451 with 17 at 1,2,2
11743 Id : 44131, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 44130 with 19452 at 2
11744 Id : 44165, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 838 with 44131 at 1,2,3
11745 Id : 44200, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 44165 with 18 at 2
11746 Id : 44201, {_}: a =<= inverse (inverse b) [] by Demod 44200 with 838 at 3
11747 Id : 44202, {_}: a =>= b [] by Demod 44201 with 18 at 3
11748 Id : 44399, {_}: b === b [] by Demod 1 with 44202 at 2
11749 Id : 1, {_}: a =>= b [] by prove_p12x
11750 % SZS output end CNFRefutation for GRP181-4.p
11751 12274: solved GRP181-4.p in 8.100505 using nrkbo
11752 12274: status Unsatisfiable for GRP181-4.p
11753 NO CLASH, using fixed ground order
11755 12282: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11756 12282: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11757 12282: Id : 4, {_}:
11758 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11759 [8, 7, 6] by associativity ?6 ?7 ?8
11760 12282: Id : 5, {_}:
11761 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11762 [11, 10] by symmetry_of_glb ?10 ?11
11763 12282: Id : 6, {_}:
11764 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11765 [14, 13] by symmetry_of_lub ?13 ?14
11766 12282: Id : 7, {_}:
11767 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11769 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11770 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11771 12282: Id : 8, {_}:
11772 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11774 least_upper_bound (least_upper_bound ?20 ?21) ?22
11775 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11776 12282: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11777 12282: Id : 10, {_}:
11778 greatest_lower_bound ?26 ?26 =>= ?26
11779 [26] by idempotence_of_gld ?26
11780 12282: Id : 11, {_}:
11781 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11782 [29, 28] by lub_absorbtion ?28 ?29
11783 12282: Id : 12, {_}:
11784 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11785 [32, 31] by glb_absorbtion ?31 ?32
11786 12282: Id : 13, {_}:
11787 multiply ?34 (least_upper_bound ?35 ?36)
11789 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11790 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11791 12282: Id : 14, {_}:
11792 multiply ?38 (greatest_lower_bound ?39 ?40)
11794 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11795 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11796 12282: Id : 15, {_}:
11797 multiply (least_upper_bound ?42 ?43) ?44
11799 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11800 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11801 12282: Id : 16, {_}:
11802 multiply (greatest_lower_bound ?46 ?47) ?48
11804 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11805 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11807 12282: Id : 1, {_}:
11808 greatest_lower_bound (least_upper_bound a identity)
11809 (inverse (greatest_lower_bound a identity))
11816 12282: multiply 18 2 0
11817 12282: inverse 2 1 1 0,2,2
11818 12282: greatest_lower_bound 15 2 2 0,2
11819 12282: least_upper_bound 14 2 1 0,1,2
11820 12282: identity 5 0 3 2,1,2
11821 12282: a 2 0 2 1,1,2
11822 NO CLASH, using fixed ground order
11824 12283: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11825 12283: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11826 12283: Id : 4, {_}:
11827 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
11828 [8, 7, 6] by associativity ?6 ?7 ?8
11829 12283: Id : 5, {_}:
11830 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11831 [11, 10] by symmetry_of_glb ?10 ?11
11832 12283: Id : 6, {_}:
11833 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11834 [14, 13] by symmetry_of_lub ?13 ?14
11835 12283: Id : 7, {_}:
11836 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11838 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11839 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11840 12283: Id : 8, {_}:
11841 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11843 least_upper_bound (least_upper_bound ?20 ?21) ?22
11844 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11845 12283: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11846 12283: Id : 10, {_}:
11847 greatest_lower_bound ?26 ?26 =>= ?26
11848 [26] by idempotence_of_gld ?26
11849 12283: Id : 11, {_}:
11850 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11851 [29, 28] by lub_absorbtion ?28 ?29
11852 12283: Id : 12, {_}:
11853 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11854 [32, 31] by glb_absorbtion ?31 ?32
11855 12283: Id : 13, {_}:
11856 multiply ?34 (least_upper_bound ?35 ?36)
11858 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11859 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11860 12283: Id : 14, {_}:
11861 multiply ?38 (greatest_lower_bound ?39 ?40)
11863 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11864 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11865 12283: Id : 15, {_}:
11866 multiply (least_upper_bound ?42 ?43) ?44
11868 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11869 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11870 12283: Id : 16, {_}:
11871 multiply (greatest_lower_bound ?46 ?47) ?48
11873 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11874 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11876 12283: Id : 1, {_}:
11877 greatest_lower_bound (least_upper_bound a identity)
11878 (inverse (greatest_lower_bound a identity))
11885 12283: multiply 18 2 0
11886 12283: inverse 2 1 1 0,2,2
11887 12283: greatest_lower_bound 15 2 2 0,2
11888 12283: least_upper_bound 14 2 1 0,1,2
11889 12283: identity 5 0 3 2,1,2
11890 12283: a 2 0 2 1,1,2
11891 NO CLASH, using fixed ground order
11893 12281: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11894 12281: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11895 12281: Id : 4, {_}:
11896 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
11897 [8, 7, 6] by associativity ?6 ?7 ?8
11898 12281: Id : 5, {_}:
11899 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11900 [11, 10] by symmetry_of_glb ?10 ?11
11901 12281: Id : 6, {_}:
11902 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11903 [14, 13] by symmetry_of_lub ?13 ?14
11904 12281: Id : 7, {_}:
11905 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11907 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11908 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11909 12281: Id : 8, {_}:
11910 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11912 least_upper_bound (least_upper_bound ?20 ?21) ?22
11913 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11914 12281: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11915 12281: Id : 10, {_}:
11916 greatest_lower_bound ?26 ?26 =>= ?26
11917 [26] by idempotence_of_gld ?26
11918 12281: Id : 11, {_}:
11919 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11920 [29, 28] by lub_absorbtion ?28 ?29
11921 12281: Id : 12, {_}:
11922 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11923 [32, 31] by glb_absorbtion ?31 ?32
11924 12281: Id : 13, {_}:
11925 multiply ?34 (least_upper_bound ?35 ?36)
11927 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11928 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11929 12281: Id : 14, {_}:
11930 multiply ?38 (greatest_lower_bound ?39 ?40)
11932 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
11933 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
11934 12281: Id : 15, {_}:
11935 multiply (least_upper_bound ?42 ?43) ?44
11937 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
11938 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
11939 12281: Id : 16, {_}:
11940 multiply (greatest_lower_bound ?46 ?47) ?48
11942 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
11943 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
11945 12281: Id : 1, {_}:
11946 greatest_lower_bound (least_upper_bound a identity)
11947 (inverse (greatest_lower_bound a identity))
11954 12281: multiply 18 2 0
11955 12281: inverse 2 1 1 0,2,2
11956 12281: greatest_lower_bound 15 2 2 0,2
11957 12281: least_upper_bound 14 2 1 0,1,2
11958 12281: identity 5 0 3 2,1,2
11959 12281: a 2 0 2 1,1,2
11960 % SZS status Timeout for GRP183-1.p
11961 NO CLASH, using fixed ground order
11963 12310: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
11964 12310: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
11965 12310: Id : 4, {_}:
11966 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
11967 [8, 7, 6] by associativity ?6 ?7 ?8
11968 12310: Id : 5, {_}:
11969 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
11970 [11, 10] by symmetry_of_glb ?10 ?11
11971 12310: Id : 6, {_}:
11972 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
11973 [14, 13] by symmetry_of_lub ?13 ?14
11974 12310: Id : 7, {_}:
11975 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
11977 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
11978 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
11979 12310: Id : 8, {_}:
11980 least_upper_bound ?20 (least_upper_bound ?21 ?22)
11982 least_upper_bound (least_upper_bound ?20 ?21) ?22
11983 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
11984 12310: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
11985 12310: Id : 10, {_}:
11986 greatest_lower_bound ?26 ?26 =>= ?26
11987 [26] by idempotence_of_gld ?26
11988 12310: Id : 11, {_}:
11989 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
11990 [29, 28] by lub_absorbtion ?28 ?29
11991 12310: Id : 12, {_}:
11992 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
11993 [32, 31] by glb_absorbtion ?31 ?32
11994 12310: Id : 13, {_}:
11995 multiply ?34 (least_upper_bound ?35 ?36)
11997 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
11998 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
11999 12310: Id : 14, {_}:
12000 multiply ?38 (greatest_lower_bound ?39 ?40)
12002 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12003 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12004 12310: Id : 15, {_}:
12005 multiply (least_upper_bound ?42 ?43) ?44
12007 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12008 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12009 12310: Id : 16, {_}:
12010 multiply (greatest_lower_bound ?46 ?47) ?48
12012 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12013 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12015 12310: Id : 1, {_}:
12016 greatest_lower_bound (least_upper_bound a identity)
12017 (least_upper_bound (inverse a) identity)
12024 12310: multiply 18 2 0
12025 12310: greatest_lower_bound 14 2 1 0,2
12026 12310: inverse 2 1 1 0,1,2,2
12027 12310: least_upper_bound 15 2 2 0,1,2
12028 12310: identity 5 0 3 2,1,2
12029 12310: a 2 0 2 1,1,2
12030 NO CLASH, using fixed ground order
12032 12311: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12033 12311: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12034 12311: Id : 4, {_}:
12035 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12036 [8, 7, 6] by associativity ?6 ?7 ?8
12037 12311: Id : 5, {_}:
12038 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12039 [11, 10] by symmetry_of_glb ?10 ?11
12040 12311: Id : 6, {_}:
12041 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12042 [14, 13] by symmetry_of_lub ?13 ?14
12043 12311: Id : 7, {_}:
12044 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12046 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12047 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12048 12311: Id : 8, {_}:
12049 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12051 least_upper_bound (least_upper_bound ?20 ?21) ?22
12052 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12053 12311: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12054 12311: Id : 10, {_}:
12055 greatest_lower_bound ?26 ?26 =>= ?26
12056 [26] by idempotence_of_gld ?26
12057 12311: Id : 11, {_}:
12058 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12059 [29, 28] by lub_absorbtion ?28 ?29
12060 12311: Id : 12, {_}:
12061 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12062 [32, 31] by glb_absorbtion ?31 ?32
12063 12311: Id : 13, {_}:
12064 multiply ?34 (least_upper_bound ?35 ?36)
12066 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12067 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12068 12311: Id : 14, {_}:
12069 multiply ?38 (greatest_lower_bound ?39 ?40)
12071 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12072 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12073 12311: Id : 15, {_}:
12074 multiply (least_upper_bound ?42 ?43) ?44
12076 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12077 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12078 12311: Id : 16, {_}:
12079 multiply (greatest_lower_bound ?46 ?47) ?48
12081 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12082 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12084 12311: Id : 1, {_}:
12085 greatest_lower_bound (least_upper_bound a identity)
12086 (least_upper_bound (inverse a) identity)
12093 12311: multiply 18 2 0
12094 12311: greatest_lower_bound 14 2 1 0,2
12095 12311: inverse 2 1 1 0,1,2,2
12096 12311: least_upper_bound 15 2 2 0,1,2
12097 12311: identity 5 0 3 2,1,2
12098 12311: a 2 0 2 1,1,2
12099 NO CLASH, using fixed ground order
12101 12312: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12102 12312: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12103 12312: Id : 4, {_}:
12104 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12105 [8, 7, 6] by associativity ?6 ?7 ?8
12106 12312: Id : 5, {_}:
12107 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12108 [11, 10] by symmetry_of_glb ?10 ?11
12109 12312: Id : 6, {_}:
12110 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12111 [14, 13] by symmetry_of_lub ?13 ?14
12112 12312: Id : 7, {_}:
12113 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12115 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12116 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12117 12312: Id : 8, {_}:
12118 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12120 least_upper_bound (least_upper_bound ?20 ?21) ?22
12121 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12122 12312: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12123 12312: Id : 10, {_}:
12124 greatest_lower_bound ?26 ?26 =>= ?26
12125 [26] by idempotence_of_gld ?26
12126 12312: Id : 11, {_}:
12127 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12128 [29, 28] by lub_absorbtion ?28 ?29
12129 12312: Id : 12, {_}:
12130 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12131 [32, 31] by glb_absorbtion ?31 ?32
12132 12312: Id : 13, {_}:
12133 multiply ?34 (least_upper_bound ?35 ?36)
12135 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12136 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12137 12312: Id : 14, {_}:
12138 multiply ?38 (greatest_lower_bound ?39 ?40)
12140 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12141 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12142 12312: Id : 15, {_}:
12143 multiply (least_upper_bound ?42 ?43) ?44
12145 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12146 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12147 12312: Id : 16, {_}:
12148 multiply (greatest_lower_bound ?46 ?47) ?48
12150 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12151 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12153 12312: Id : 1, {_}:
12154 greatest_lower_bound (least_upper_bound a identity)
12155 (least_upper_bound (inverse a) identity)
12162 12312: multiply 18 2 0
12163 12312: greatest_lower_bound 14 2 1 0,2
12164 12312: inverse 2 1 1 0,1,2,2
12165 12312: least_upper_bound 15 2 2 0,1,2
12166 12312: identity 5 0 3 2,1,2
12167 12312: a 2 0 2 1,1,2
12168 % SZS status Timeout for GRP183-3.p
12169 NO CLASH, using fixed ground order
12171 12349: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12172 12349: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12173 12349: Id : 4, {_}:
12174 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
12175 [8, 7, 6] by associativity ?6 ?7 ?8
12176 12349: Id : 5, {_}:
12177 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12178 [11, 10] by symmetry_of_glb ?10 ?11
12179 12349: Id : 6, {_}:
12180 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12181 [14, 13] by symmetry_of_lub ?13 ?14
12182 12349: Id : 7, {_}:
12183 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12185 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12186 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12187 12349: Id : 8, {_}:
12188 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12190 least_upper_bound (least_upper_bound ?20 ?21) ?22
12191 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12192 12349: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12193 12349: Id : 10, {_}:
12194 greatest_lower_bound ?26 ?26 =>= ?26
12195 [26] by idempotence_of_gld ?26
12196 12349: Id : 11, {_}:
12197 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12198 [29, 28] by lub_absorbtion ?28 ?29
12199 12349: Id : 12, {_}:
12200 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12201 [32, 31] by glb_absorbtion ?31 ?32
12202 12349: Id : 13, {_}:
12203 multiply ?34 (least_upper_bound ?35 ?36)
12205 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12206 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12207 12349: Id : 14, {_}:
12208 multiply ?38 (greatest_lower_bound ?39 ?40)
12210 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12211 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12212 12349: Id : 15, {_}:
12213 multiply (least_upper_bound ?42 ?43) ?44
12215 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12216 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12217 12349: Id : 16, {_}:
12218 multiply (greatest_lower_bound ?46 ?47) ?48
12220 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12221 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12222 12349: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
12223 12349: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
12224 12349: Id : 19, {_}:
12225 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
12226 [54, 53] by p20x_3 ?53 ?54
12228 12349: Id : 1, {_}:
12229 greatest_lower_bound (least_upper_bound a identity)
12230 (least_upper_bound (inverse a) identity)
12237 12349: multiply 20 2 0
12238 12349: greatest_lower_bound 14 2 1 0,2
12239 12349: inverse 8 1 1 0,1,2,2
12240 12349: least_upper_bound 15 2 2 0,1,2
12241 12349: identity 7 0 3 2,1,2
12242 12349: a 2 0 2 1,1,2
12243 NO CLASH, using fixed ground order
12245 12350: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12246 12350: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12247 12350: Id : 4, {_}:
12248 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12249 [8, 7, 6] by associativity ?6 ?7 ?8
12250 12350: Id : 5, {_}:
12251 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12252 [11, 10] by symmetry_of_glb ?10 ?11
12253 12350: Id : 6, {_}:
12254 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12255 [14, 13] by symmetry_of_lub ?13 ?14
12256 12350: Id : 7, {_}:
12257 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12259 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12260 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12261 12350: Id : 8, {_}:
12262 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12264 least_upper_bound (least_upper_bound ?20 ?21) ?22
12265 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12266 12350: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12267 12350: Id : 10, {_}:
12268 greatest_lower_bound ?26 ?26 =>= ?26
12269 [26] by idempotence_of_gld ?26
12270 12350: Id : 11, {_}:
12271 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12272 [29, 28] by lub_absorbtion ?28 ?29
12273 12350: Id : 12, {_}:
12274 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12275 [32, 31] by glb_absorbtion ?31 ?32
12276 12350: Id : 13, {_}:
12277 multiply ?34 (least_upper_bound ?35 ?36)
12279 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12280 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12281 12350: Id : 14, {_}:
12282 multiply ?38 (greatest_lower_bound ?39 ?40)
12284 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12285 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12286 12350: Id : 15, {_}:
12287 multiply (least_upper_bound ?42 ?43) ?44
12289 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12290 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12291 12350: Id : 16, {_}:
12292 multiply (greatest_lower_bound ?46 ?47) ?48
12294 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12295 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12296 12350: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
12297 12350: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
12298 12350: Id : 19, {_}:
12299 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
12300 [54, 53] by p20x_3 ?53 ?54
12302 12350: Id : 1, {_}:
12303 greatest_lower_bound (least_upper_bound a identity)
12304 (least_upper_bound (inverse a) identity)
12311 12350: multiply 20 2 0
12312 12350: greatest_lower_bound 14 2 1 0,2
12313 12350: inverse 8 1 1 0,1,2,2
12314 12350: least_upper_bound 15 2 2 0,1,2
12315 12350: identity 7 0 3 2,1,2
12316 12350: a 2 0 2 1,1,2
12317 NO CLASH, using fixed ground order
12319 12351: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12320 12351: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12321 12351: Id : 4, {_}:
12322 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12323 [8, 7, 6] by associativity ?6 ?7 ?8
12324 12351: Id : 5, {_}:
12325 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12326 [11, 10] by symmetry_of_glb ?10 ?11
12327 12351: Id : 6, {_}:
12328 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12329 [14, 13] by symmetry_of_lub ?13 ?14
12330 12351: Id : 7, {_}:
12331 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12333 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12334 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12335 12351: Id : 8, {_}:
12336 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12338 least_upper_bound (least_upper_bound ?20 ?21) ?22
12339 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12340 12351: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12341 12351: Id : 10, {_}:
12342 greatest_lower_bound ?26 ?26 =>= ?26
12343 [26] by idempotence_of_gld ?26
12344 12351: Id : 11, {_}:
12345 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12346 [29, 28] by lub_absorbtion ?28 ?29
12347 12351: Id : 12, {_}:
12348 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12349 [32, 31] by glb_absorbtion ?31 ?32
12350 12351: Id : 13, {_}:
12351 multiply ?34 (least_upper_bound ?35 ?36)
12353 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12354 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12355 12351: Id : 14, {_}:
12356 multiply ?38 (greatest_lower_bound ?39 ?40)
12358 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12359 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12360 12351: Id : 15, {_}:
12361 multiply (least_upper_bound ?42 ?43) ?44
12363 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12364 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12365 12351: Id : 16, {_}:
12366 multiply (greatest_lower_bound ?46 ?47) ?48
12368 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12369 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12370 12351: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
12371 12351: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
12372 12351: Id : 19, {_}:
12373 inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
12374 [54, 53] by p20x_3 ?53 ?54
12376 12351: Id : 1, {_}:
12377 greatest_lower_bound (least_upper_bound a identity)
12378 (least_upper_bound (inverse a) identity)
12385 12351: multiply 20 2 0
12386 12351: greatest_lower_bound 14 2 1 0,2
12387 12351: inverse 8 1 1 0,1,2,2
12388 12351: least_upper_bound 15 2 2 0,1,2
12389 12351: identity 7 0 3 2,1,2
12390 12351: a 2 0 2 1,1,2
12391 % SZS status Timeout for GRP183-4.p
12392 NO CLASH, using fixed ground order
12394 12378: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12395 12378: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12396 12378: Id : 4, {_}:
12397 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
12398 [8, 7, 6] by associativity ?6 ?7 ?8
12399 12378: Id : 5, {_}:
12400 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12401 [11, 10] by symmetry_of_glb ?10 ?11
12402 12378: Id : 6, {_}:
12403 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12404 [14, 13] by symmetry_of_lub ?13 ?14
12405 12378: Id : 7, {_}:
12406 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12408 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12409 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12410 12378: Id : 8, {_}:
12411 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12413 least_upper_bound (least_upper_bound ?20 ?21) ?22
12414 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12415 12378: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12416 12378: Id : 10, {_}:
12417 greatest_lower_bound ?26 ?26 =>= ?26
12418 [26] by idempotence_of_gld ?26
12419 12378: Id : 11, {_}:
12420 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12421 [29, 28] by lub_absorbtion ?28 ?29
12422 12378: Id : 12, {_}:
12423 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12424 [32, 31] by glb_absorbtion ?31 ?32
12425 12378: Id : 13, {_}:
12426 multiply ?34 (least_upper_bound ?35 ?36)
12428 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12429 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12430 12378: Id : 14, {_}:
12431 multiply ?38 (greatest_lower_bound ?39 ?40)
12433 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12434 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12435 12378: Id : 15, {_}:
12436 multiply (least_upper_bound ?42 ?43) ?44
12438 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12439 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12440 12378: Id : 16, {_}:
12441 multiply (greatest_lower_bound ?46 ?47) ?48
12443 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12444 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12446 12378: Id : 1, {_}:
12447 multiply (least_upper_bound a identity)
12448 (inverse (greatest_lower_bound a identity))
12450 multiply (inverse (greatest_lower_bound a identity))
12451 (least_upper_bound a identity)
12456 12378: multiply 20 2 2 0,2
12457 12378: inverse 3 1 2 0,2,2
12458 12378: greatest_lower_bound 15 2 2 0,1,2,2
12459 12378: least_upper_bound 15 2 2 0,1,2
12460 12378: identity 6 0 4 2,1,2
12461 12378: a 4 0 4 1,1,2
12462 NO CLASH, using fixed ground order
12464 12379: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12465 12379: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12466 12379: Id : 4, {_}:
12467 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12468 [8, 7, 6] by associativity ?6 ?7 ?8
12469 12379: Id : 5, {_}:
12470 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12471 [11, 10] by symmetry_of_glb ?10 ?11
12472 12379: Id : 6, {_}:
12473 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12474 [14, 13] by symmetry_of_lub ?13 ?14
12475 12379: Id : 7, {_}:
12476 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12478 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12479 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12480 12379: Id : 8, {_}:
12481 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12483 least_upper_bound (least_upper_bound ?20 ?21) ?22
12484 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12485 12379: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12486 12379: Id : 10, {_}:
12487 greatest_lower_bound ?26 ?26 =>= ?26
12488 [26] by idempotence_of_gld ?26
12489 12379: Id : 11, {_}:
12490 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12491 [29, 28] by lub_absorbtion ?28 ?29
12492 12379: Id : 12, {_}:
12493 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12494 [32, 31] by glb_absorbtion ?31 ?32
12495 12379: Id : 13, {_}:
12496 multiply ?34 (least_upper_bound ?35 ?36)
12498 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12499 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12500 12379: Id : 14, {_}:
12501 multiply ?38 (greatest_lower_bound ?39 ?40)
12503 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12504 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12505 12379: Id : 15, {_}:
12506 multiply (least_upper_bound ?42 ?43) ?44
12508 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12509 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12510 12379: Id : 16, {_}:
12511 multiply (greatest_lower_bound ?46 ?47) ?48
12513 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12514 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12516 12379: Id : 1, {_}:
12517 multiply (least_upper_bound a identity)
12518 (inverse (greatest_lower_bound a identity))
12520 multiply (inverse (greatest_lower_bound a identity))
12521 (least_upper_bound a identity)
12526 12379: multiply 20 2 2 0,2
12527 12379: inverse 3 1 2 0,2,2
12528 12379: greatest_lower_bound 15 2 2 0,1,2,2
12529 12379: least_upper_bound 15 2 2 0,1,2
12530 12379: identity 6 0 4 2,1,2
12531 12379: a 4 0 4 1,1,2
12532 NO CLASH, using fixed ground order
12534 12380: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12535 12380: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12536 12380: Id : 4, {_}:
12537 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12538 [8, 7, 6] by associativity ?6 ?7 ?8
12539 12380: Id : 5, {_}:
12540 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12541 [11, 10] by symmetry_of_glb ?10 ?11
12542 12380: Id : 6, {_}:
12543 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12544 [14, 13] by symmetry_of_lub ?13 ?14
12545 12380: Id : 7, {_}:
12546 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12548 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12549 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12550 12380: Id : 8, {_}:
12551 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12553 least_upper_bound (least_upper_bound ?20 ?21) ?22
12554 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12555 12380: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12556 12380: Id : 10, {_}:
12557 greatest_lower_bound ?26 ?26 =>= ?26
12558 [26] by idempotence_of_gld ?26
12559 12380: Id : 11, {_}:
12560 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12561 [29, 28] by lub_absorbtion ?28 ?29
12562 12380: Id : 12, {_}:
12563 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12564 [32, 31] by glb_absorbtion ?31 ?32
12565 12380: Id : 13, {_}:
12566 multiply ?34 (least_upper_bound ?35 ?36)
12568 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12569 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12570 12380: Id : 14, {_}:
12571 multiply ?38 (greatest_lower_bound ?39 ?40)
12573 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12574 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12575 12380: Id : 15, {_}:
12576 multiply (least_upper_bound ?42 ?43) ?44
12578 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12579 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12580 12380: Id : 16, {_}:
12581 multiply (greatest_lower_bound ?46 ?47) ?48
12583 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12584 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12586 12380: Id : 1, {_}:
12587 multiply (least_upper_bound a identity)
12588 (inverse (greatest_lower_bound a identity))
12590 multiply (inverse (greatest_lower_bound a identity))
12591 (least_upper_bound a identity)
12596 12380: multiply 20 2 2 0,2
12597 12380: inverse 3 1 2 0,2,2
12598 12380: greatest_lower_bound 15 2 2 0,1,2,2
12599 12380: least_upper_bound 15 2 2 0,1,2
12600 12380: identity 6 0 4 2,1,2
12601 12380: a 4 0 4 1,1,2
12602 % SZS status Timeout for GRP184-1.p
12603 NO CLASH, using fixed ground order
12605 12396: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12606 12396: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12607 12396: Id : 4, {_}:
12608 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
12609 [8, 7, 6] by associativity ?6 ?7 ?8
12610 12396: Id : 5, {_}:
12611 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12612 [11, 10] by symmetry_of_glb ?10 ?11
12613 12396: Id : 6, {_}:
12614 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12615 [14, 13] by symmetry_of_lub ?13 ?14
12616 12396: Id : 7, {_}:
12617 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12619 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12620 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12621 12396: Id : 8, {_}:
12622 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12624 least_upper_bound (least_upper_bound ?20 ?21) ?22
12625 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12626 12396: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12627 12396: Id : 10, {_}:
12628 greatest_lower_bound ?26 ?26 =>= ?26
12629 [26] by idempotence_of_gld ?26
12630 12396: Id : 11, {_}:
12631 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12632 [29, 28] by lub_absorbtion ?28 ?29
12633 12396: Id : 12, {_}:
12634 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12635 [32, 31] by glb_absorbtion ?31 ?32
12636 12396: Id : 13, {_}:
12637 multiply ?34 (least_upper_bound ?35 ?36)
12639 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12640 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12641 12396: Id : 14, {_}:
12642 multiply ?38 (greatest_lower_bound ?39 ?40)
12644 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12645 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12646 12396: Id : 15, {_}:
12647 multiply (least_upper_bound ?42 ?43) ?44
12649 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12650 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12651 12396: Id : 16, {_}:
12652 multiply (greatest_lower_bound ?46 ?47) ?48
12654 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12655 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12657 12396: Id : 1, {_}:
12658 multiply (least_upper_bound a identity)
12659 (inverse (greatest_lower_bound a identity))
12661 multiply (inverse (greatest_lower_bound a identity))
12662 (least_upper_bound a identity)
12667 12396: multiply 20 2 2 0,2
12668 12396: inverse 3 1 2 0,2,2
12669 12396: greatest_lower_bound 15 2 2 0,1,2,2
12670 12396: least_upper_bound 15 2 2 0,1,2
12671 12396: identity 6 0 4 2,1,2
12672 12396: a 4 0 4 1,1,2
12673 NO CLASH, using fixed ground order
12675 12397: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12676 12397: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12677 12397: Id : 4, {_}:
12678 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12679 [8, 7, 6] by associativity ?6 ?7 ?8
12680 12397: Id : 5, {_}:
12681 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12682 [11, 10] by symmetry_of_glb ?10 ?11
12683 12397: Id : 6, {_}:
12684 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12685 [14, 13] by symmetry_of_lub ?13 ?14
12686 12397: Id : 7, {_}:
12687 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12689 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12690 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12691 12397: Id : 8, {_}:
12692 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12694 least_upper_bound (least_upper_bound ?20 ?21) ?22
12695 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12696 12397: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12697 12397: Id : 10, {_}:
12698 greatest_lower_bound ?26 ?26 =>= ?26
12699 [26] by idempotence_of_gld ?26
12700 12397: Id : 11, {_}:
12701 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12702 [29, 28] by lub_absorbtion ?28 ?29
12703 12397: Id : 12, {_}:
12704 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12705 [32, 31] by glb_absorbtion ?31 ?32
12706 12397: Id : 13, {_}:
12707 multiply ?34 (least_upper_bound ?35 ?36)
12709 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12710 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12711 12397: Id : 14, {_}:
12712 multiply ?38 (greatest_lower_bound ?39 ?40)
12714 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12715 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12716 12397: Id : 15, {_}:
12717 multiply (least_upper_bound ?42 ?43) ?44
12719 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12720 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12721 12397: Id : 16, {_}:
12722 multiply (greatest_lower_bound ?46 ?47) ?48
12724 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12725 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12727 12397: Id : 1, {_}:
12728 multiply (least_upper_bound a identity)
12729 (inverse (greatest_lower_bound a identity))
12731 multiply (inverse (greatest_lower_bound a identity))
12732 (least_upper_bound a identity)
12737 12397: multiply 20 2 2 0,2
12738 12397: inverse 3 1 2 0,2,2
12739 12397: greatest_lower_bound 15 2 2 0,1,2,2
12740 12397: least_upper_bound 15 2 2 0,1,2
12741 12397: identity 6 0 4 2,1,2
12742 12397: a 4 0 4 1,1,2
12743 NO CLASH, using fixed ground order
12745 12398: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12746 12398: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12747 12398: Id : 4, {_}:
12748 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12749 [8, 7, 6] by associativity ?6 ?7 ?8
12750 12398: Id : 5, {_}:
12751 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12752 [11, 10] by symmetry_of_glb ?10 ?11
12753 12398: Id : 6, {_}:
12754 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12755 [14, 13] by symmetry_of_lub ?13 ?14
12756 12398: Id : 7, {_}:
12757 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12759 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12760 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12761 12398: Id : 8, {_}:
12762 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12764 least_upper_bound (least_upper_bound ?20 ?21) ?22
12765 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12766 12398: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12767 12398: Id : 10, {_}:
12768 greatest_lower_bound ?26 ?26 =>= ?26
12769 [26] by idempotence_of_gld ?26
12770 12398: Id : 11, {_}:
12771 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12772 [29, 28] by lub_absorbtion ?28 ?29
12773 12398: Id : 12, {_}:
12774 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12775 [32, 31] by glb_absorbtion ?31 ?32
12776 12398: Id : 13, {_}:
12777 multiply ?34 (least_upper_bound ?35 ?36)
12779 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12780 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12781 12398: Id : 14, {_}:
12782 multiply ?38 (greatest_lower_bound ?39 ?40)
12784 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12785 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12786 12398: Id : 15, {_}:
12787 multiply (least_upper_bound ?42 ?43) ?44
12789 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12790 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12791 12398: Id : 16, {_}:
12792 multiply (greatest_lower_bound ?46 ?47) ?48
12794 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12795 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12797 12398: Id : 1, {_}:
12798 multiply (least_upper_bound a identity)
12799 (inverse (greatest_lower_bound a identity))
12801 multiply (inverse (greatest_lower_bound a identity))
12802 (least_upper_bound a identity)
12807 12398: multiply 20 2 2 0,2
12808 12398: inverse 3 1 2 0,2,2
12809 12398: greatest_lower_bound 15 2 2 0,1,2,2
12810 12398: least_upper_bound 15 2 2 0,1,2
12811 12398: identity 6 0 4 2,1,2
12812 12398: a 4 0 4 1,1,2
12813 % SZS status Timeout for GRP184-3.p
12814 NO CLASH, using fixed ground order
12816 12794: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12817 12794: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12818 12794: Id : 4, {_}:
12819 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
12820 [8, 7, 6] by associativity ?6 ?7 ?8
12821 12794: Id : 5, {_}:
12822 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12823 [11, 10] by symmetry_of_glb ?10 ?11
12824 12794: Id : 6, {_}:
12825 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12826 [14, 13] by symmetry_of_lub ?13 ?14
12827 12794: Id : 7, {_}:
12828 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12830 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12831 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12832 12794: Id : 8, {_}:
12833 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12835 least_upper_bound (least_upper_bound ?20 ?21) ?22
12836 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12837 12794: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12838 12794: Id : 10, {_}:
12839 greatest_lower_bound ?26 ?26 =>= ?26
12840 [26] by idempotence_of_gld ?26
12841 12794: Id : 11, {_}:
12842 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12843 [29, 28] by lub_absorbtion ?28 ?29
12844 12794: Id : 12, {_}:
12845 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12846 [32, 31] by glb_absorbtion ?31 ?32
12847 12794: Id : 13, {_}:
12848 multiply ?34 (least_upper_bound ?35 ?36)
12850 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12851 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12852 12794: Id : 14, {_}:
12853 multiply ?38 (greatest_lower_bound ?39 ?40)
12855 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12856 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12857 12794: Id : 15, {_}:
12858 multiply (least_upper_bound ?42 ?43) ?44
12860 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12861 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12862 12794: Id : 16, {_}:
12863 multiply (greatest_lower_bound ?46 ?47) ?48
12865 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12866 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12868 12794: Id : 1, {_}:
12869 greatest_lower_bound (least_upper_bound (multiply a b) identity)
12870 (multiply (least_upper_bound a identity)
12871 (least_upper_bound b identity))
12873 least_upper_bound (multiply a b) identity
12878 12794: inverse 1 1 0
12879 12794: greatest_lower_bound 14 2 1 0,2
12880 12794: least_upper_bound 17 2 4 0,1,2
12881 12794: identity 6 0 4 2,1,2
12882 12794: multiply 21 2 3 0,1,1,2
12883 12794: b 3 0 3 2,1,1,2
12884 12794: a 3 0 3 1,1,1,2
12885 NO CLASH, using fixed ground order
12887 12795: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12888 12795: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12889 12795: Id : 4, {_}:
12890 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12891 [8, 7, 6] by associativity ?6 ?7 ?8
12892 12795: Id : 5, {_}:
12893 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12894 [11, 10] by symmetry_of_glb ?10 ?11
12895 12795: Id : 6, {_}:
12896 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12897 [14, 13] by symmetry_of_lub ?13 ?14
12898 12795: Id : 7, {_}:
12899 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12901 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12902 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12903 12795: Id : 8, {_}:
12904 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12906 least_upper_bound (least_upper_bound ?20 ?21) ?22
12907 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12908 12795: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12909 12795: Id : 10, {_}:
12910 greatest_lower_bound ?26 ?26 =>= ?26
12911 [26] by idempotence_of_gld ?26
12912 12795: Id : 11, {_}:
12913 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12914 [29, 28] by lub_absorbtion ?28 ?29
12915 NO CLASH, using fixed ground order
12917 12796: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
12918 12796: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
12919 12796: Id : 4, {_}:
12920 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
12921 [8, 7, 6] by associativity ?6 ?7 ?8
12922 12796: Id : 5, {_}:
12923 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
12924 [11, 10] by symmetry_of_glb ?10 ?11
12925 12796: Id : 6, {_}:
12926 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
12927 [14, 13] by symmetry_of_lub ?13 ?14
12928 12796: Id : 7, {_}:
12929 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
12931 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
12932 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
12933 12796: Id : 8, {_}:
12934 least_upper_bound ?20 (least_upper_bound ?21 ?22)
12936 least_upper_bound (least_upper_bound ?20 ?21) ?22
12937 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
12938 12796: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
12939 12796: Id : 10, {_}:
12940 greatest_lower_bound ?26 ?26 =>= ?26
12941 [26] by idempotence_of_gld ?26
12942 12796: Id : 11, {_}:
12943 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
12944 [29, 28] by lub_absorbtion ?28 ?29
12945 12796: Id : 12, {_}:
12946 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12947 [32, 31] by glb_absorbtion ?31 ?32
12948 12795: Id : 12, {_}:
12949 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
12950 [32, 31] by glb_absorbtion ?31 ?32
12951 12795: Id : 13, {_}:
12952 multiply ?34 (least_upper_bound ?35 ?36)
12954 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12955 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12956 12795: Id : 14, {_}:
12957 multiply ?38 (greatest_lower_bound ?39 ?40)
12959 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12960 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12961 12795: Id : 15, {_}:
12962 multiply (least_upper_bound ?42 ?43) ?44
12964 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
12965 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
12966 12795: Id : 16, {_}:
12967 multiply (greatest_lower_bound ?46 ?47) ?48
12969 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
12970 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
12972 12795: Id : 1, {_}:
12973 greatest_lower_bound (least_upper_bound (multiply a b) identity)
12974 (multiply (least_upper_bound a identity)
12975 (least_upper_bound b identity))
12977 least_upper_bound (multiply a b) identity
12982 12795: inverse 1 1 0
12983 12795: greatest_lower_bound 14 2 1 0,2
12984 12795: least_upper_bound 17 2 4 0,1,2
12985 12795: identity 6 0 4 2,1,2
12986 12795: multiply 21 2 3 0,1,1,2
12987 12795: b 3 0 3 2,1,1,2
12988 12795: a 3 0 3 1,1,1,2
12989 12796: Id : 13, {_}:
12990 multiply ?34 (least_upper_bound ?35 ?36)
12992 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
12993 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
12994 12796: Id : 14, {_}:
12995 multiply ?38 (greatest_lower_bound ?39 ?40)
12997 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
12998 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
12999 12796: Id : 15, {_}:
13000 multiply (least_upper_bound ?42 ?43) ?44
13002 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
13003 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13004 12796: Id : 16, {_}:
13005 multiply (greatest_lower_bound ?46 ?47) ?48
13007 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
13008 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
13010 12796: Id : 1, {_}:
13011 greatest_lower_bound (least_upper_bound (multiply a b) identity)
13012 (multiply (least_upper_bound a identity)
13013 (least_upper_bound b identity))
13015 least_upper_bound (multiply a b) identity
13020 12796: inverse 1 1 0
13021 12796: greatest_lower_bound 14 2 1 0,2
13022 12796: least_upper_bound 17 2 4 0,1,2
13023 12796: identity 6 0 4 2,1,2
13024 12796: multiply 21 2 3 0,1,1,2
13025 12796: b 3 0 3 2,1,1,2
13026 12796: a 3 0 3 1,1,1,2
13029 Found proof, 1.752071s
13030 % SZS status Unsatisfiable for GRP185-3.p
13031 % SZS output start CNFRefutation for GRP185-3.p
13032 Id : 120, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252
13033 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13034 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
13035 Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
13036 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13037 Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13038 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13039 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
13040 Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
13041 Id : 436, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
13042 Id : 438, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 436 with 3 at 2,3
13043 Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
13044 Id : 444, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 436 with 27 at 2,3
13045 Id : 599, {_}: ?599 =<= multiply ?599 identity [599] by Demod 438 with 444 at 3
13046 Id : 63, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
13047 Id : 894, {_}: greatest_lower_bound ?1092 (least_upper_bound ?1093 ?1092) =>= ?1092 [1093, 1092] by Super 120 with 6 at 2,2
13048 Id : 901, {_}: greatest_lower_bound ?1112 (least_upper_bound ?1113 (least_upper_bound ?1114 ?1112)) =>= ?1112 [1114, 1113, 1112] by Super 894 with 8 at 2,2
13049 Id : 2450, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 2449 with 901 at 2
13050 Id : 2449, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2448 with 2 at 1,2,2,2,2
13051 Id : 2448, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2447 with 2 at 1,2,2,2
13052 Id : 2447, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2446 with 63 at 2,2,2
13053 Id : 2446, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2445 with 599 at 1,2,2
13054 Id : 2445, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2444 with 8 at 2,2
13055 Id : 2444, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 2443 with 15 at 2,2,2
13056 Id : 2443, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2442 with 15 at 1,2,2
13057 Id : 2442, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2441 with 6 at 2,2
13058 Id : 2441, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2440 with 6 at 3
13059 Id : 2440, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 2439 with 13 at 2,2
13060 Id : 2439, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
13061 Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
13062 % SZS output end CNFRefutation for GRP185-3.p
13063 12796: solved GRP185-3.p in 0.64804 using lpo
13064 12796: status Unsatisfiable for GRP185-3.p
13065 NO CLASH, using fixed ground order
13067 12801: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13068 12801: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
13069 12801: Id : 4, {_}:
13070 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
13071 [8, 7, 6] by associativity ?6 ?7 ?8
13072 12801: Id : 5, {_}:
13073 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
13074 [11, 10] by symmetry_of_glb ?10 ?11
13075 12801: Id : 6, {_}:
13076 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
13077 [14, 13] by symmetry_of_lub ?13 ?14
13078 12801: Id : 7, {_}:
13079 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
13081 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
13082 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
13083 12801: Id : 8, {_}:
13084 least_upper_bound ?20 (least_upper_bound ?21 ?22)
13086 least_upper_bound (least_upper_bound ?20 ?21) ?22
13087 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13088 12801: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
13089 12801: Id : 10, {_}:
13090 greatest_lower_bound ?26 ?26 =>= ?26
13091 [26] by idempotence_of_gld ?26
13092 12801: Id : 11, {_}:
13093 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
13094 [29, 28] by lub_absorbtion ?28 ?29
13095 12801: Id : 12, {_}:
13096 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
13097 [32, 31] by glb_absorbtion ?31 ?32
13098 12801: Id : 13, {_}:
13099 multiply ?34 (least_upper_bound ?35 ?36)
13101 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
13102 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13103 12801: Id : 14, {_}:
13104 multiply ?38 (greatest_lower_bound ?39 ?40)
13106 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
13107 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
13108 12801: Id : 15, {_}:
13109 multiply (least_upper_bound ?42 ?43) ?44
13111 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
13112 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13113 12801: Id : 16, {_}:
13114 multiply (greatest_lower_bound ?46 ?47) ?48
13116 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
13117 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
13118 12801: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
13119 12801: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
13120 12801: Id : 19, {_}:
13121 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
13122 [54, 53] by p22b_3 ?53 ?54
13124 12801: Id : 1, {_}:
13125 greatest_lower_bound (least_upper_bound (multiply a b) identity)
13126 (multiply (least_upper_bound a identity)
13127 (least_upper_bound b identity))
13129 least_upper_bound (multiply a b) identity
13134 12801: inverse 7 1 0
13135 12801: greatest_lower_bound 14 2 1 0,2
13136 12801: least_upper_bound 17 2 4 0,1,2
13137 12801: identity 8 0 4 2,1,2
13138 12801: multiply 23 2 3 0,1,1,2
13139 12801: b 3 0 3 2,1,1,2
13140 12801: a 3 0 3 1,1,1,2
13141 NO CLASH, using fixed ground order
13143 12802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13144 12802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
13145 12802: Id : 4, {_}:
13146 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
13147 [8, 7, 6] by associativity ?6 ?7 ?8
13148 12802: Id : 5, {_}:
13149 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
13150 [11, 10] by symmetry_of_glb ?10 ?11
13151 12802: Id : 6, {_}:
13152 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
13153 [14, 13] by symmetry_of_lub ?13 ?14
13154 12802: Id : 7, {_}:
13155 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
13157 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
13158 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
13159 12802: Id : 8, {_}:
13160 least_upper_bound ?20 (least_upper_bound ?21 ?22)
13162 least_upper_bound (least_upper_bound ?20 ?21) ?22
13163 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13164 12802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
13165 12802: Id : 10, {_}:
13166 greatest_lower_bound ?26 ?26 =>= ?26
13167 [26] by idempotence_of_gld ?26
13168 12802: Id : 11, {_}:
13169 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
13170 [29, 28] by lub_absorbtion ?28 ?29
13171 12802: Id : 12, {_}:
13172 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
13173 [32, 31] by glb_absorbtion ?31 ?32
13174 12802: Id : 13, {_}:
13175 multiply ?34 (least_upper_bound ?35 ?36)
13177 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
13178 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13179 12802: Id : 14, {_}:
13180 multiply ?38 (greatest_lower_bound ?39 ?40)
13182 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
13183 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
13184 12802: Id : 15, {_}:
13185 multiply (least_upper_bound ?42 ?43) ?44
13187 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
13188 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13189 12802: Id : 16, {_}:
13190 multiply (greatest_lower_bound ?46 ?47) ?48
13192 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
13193 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
13194 12802: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
13195 12802: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
13196 12802: Id : 19, {_}:
13197 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
13198 [54, 53] by p22b_3 ?53 ?54
13200 12802: Id : 1, {_}:
13201 greatest_lower_bound (least_upper_bound (multiply a b) identity)
13202 (multiply (least_upper_bound a identity)
13203 (least_upper_bound b identity))
13205 least_upper_bound (multiply a b) identity
13210 12802: inverse 7 1 0
13211 12802: greatest_lower_bound 14 2 1 0,2
13212 12802: least_upper_bound 17 2 4 0,1,2
13213 12802: identity 8 0 4 2,1,2
13214 12802: multiply 23 2 3 0,1,1,2
13215 12802: b 3 0 3 2,1,1,2
13216 12802: a 3 0 3 1,1,1,2
13217 NO CLASH, using fixed ground order
13219 12803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13220 12803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
13221 12803: Id : 4, {_}:
13222 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
13223 [8, 7, 6] by associativity ?6 ?7 ?8
13224 12803: Id : 5, {_}:
13225 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
13226 [11, 10] by symmetry_of_glb ?10 ?11
13227 12803: Id : 6, {_}:
13228 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
13229 [14, 13] by symmetry_of_lub ?13 ?14
13230 12803: Id : 7, {_}:
13231 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
13233 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
13234 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
13235 12803: Id : 8, {_}:
13236 least_upper_bound ?20 (least_upper_bound ?21 ?22)
13238 least_upper_bound (least_upper_bound ?20 ?21) ?22
13239 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13240 12803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
13241 12803: Id : 10, {_}:
13242 greatest_lower_bound ?26 ?26 =>= ?26
13243 [26] by idempotence_of_gld ?26
13244 12803: Id : 11, {_}:
13245 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
13246 [29, 28] by lub_absorbtion ?28 ?29
13247 12803: Id : 12, {_}:
13248 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
13249 [32, 31] by glb_absorbtion ?31 ?32
13250 12803: Id : 13, {_}:
13251 multiply ?34 (least_upper_bound ?35 ?36)
13253 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
13254 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13255 12803: Id : 14, {_}:
13256 multiply ?38 (greatest_lower_bound ?39 ?40)
13258 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
13259 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
13260 12803: Id : 15, {_}:
13261 multiply (least_upper_bound ?42 ?43) ?44
13263 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
13264 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13265 12803: Id : 16, {_}:
13266 multiply (greatest_lower_bound ?46 ?47) ?48
13268 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
13269 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
13270 12803: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
13271 12803: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
13272 12803: Id : 19, {_}:
13273 inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
13274 [54, 53] by p22b_3 ?53 ?54
13276 12803: Id : 1, {_}:
13277 greatest_lower_bound (least_upper_bound (multiply a b) identity)
13278 (multiply (least_upper_bound a identity)
13279 (least_upper_bound b identity))
13281 least_upper_bound (multiply a b) identity
13286 12803: inverse 7 1 0
13287 12803: greatest_lower_bound 14 2 1 0,2
13288 12803: least_upper_bound 17 2 4 0,1,2
13289 12803: identity 8 0 4 2,1,2
13290 12803: multiply 23 2 3 0,1,1,2
13291 12803: b 3 0 3 2,1,1,2
13292 12803: a 3 0 3 1,1,1,2
13295 Found proof, 2.993705s
13296 % SZS status Unsatisfiable for GRP185-4.p
13297 % SZS output start CNFRefutation for GRP185-4.p
13298 Id : 123, {_}: greatest_lower_bound ?257 (least_upper_bound ?257 ?258) =>= ?257 [258, 257] by glb_absorbtion ?257 ?258
13299 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
13300 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13301 Id : 17, {_}: inverse identity =>= identity [] by p22b_1
13302 Id : 382, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22b_3 ?520 ?521
13303 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13304 Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13305 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13306 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
13307 Id : 383, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 382 with 17 at 2,3
13308 Id : 422, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 383 with 2 at 1,2
13309 Id : 424, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 422 with 18 at 1,3
13310 Id : 432, {_}: ?572 =<= multiply ?572 identity [572] by Demod 424 with 18 at 2
13311 Id : 66, {_}: least_upper_bound ?149 (least_upper_bound ?150 ?151) =?= least_upper_bound ?150 (least_upper_bound ?151 ?149) [151, 150, 149] by Super 6 with 8 at 3
13312 Id : 766, {_}: greatest_lower_bound ?881 (least_upper_bound ?882 ?881) =>= ?881 [882, 881] by Super 123 with 6 at 2,2
13313 Id : 773, {_}: greatest_lower_bound ?901 (least_upper_bound ?902 (least_upper_bound ?903 ?901)) =>= ?901 [903, 902, 901] by Super 766 with 8 at 2,2
13314 Id : 4003, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 4002 with 773 at 2
13315 Id : 4002, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4001 with 2 at 1,2,2,2,2
13316 Id : 4001, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4000 with 2 at 1,2,2,2
13317 Id : 4000, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3999 with 66 at 2,2,2
13318 Id : 3999, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3998 with 432 at 1,2,2
13319 Id : 3998, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3997 with 8 at 2,2
13320 Id : 3997, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 3996 with 15 at 2,2,2
13321 Id : 3996, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3995 with 15 at 1,2,2
13322 Id : 3995, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3994 with 6 at 2,2
13323 Id : 3994, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 3993 with 6 at 3
13324 Id : 3993, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 3992 with 13 at 2,2
13325 Id : 3992, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
13326 Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
13327 % SZS output end CNFRefutation for GRP185-4.p
13328 12803: solved GRP185-4.p in 0.988061 using lpo
13329 12803: status Unsatisfiable for GRP185-4.p
13330 NO CLASH, using fixed ground order
13332 12808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13333 12808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
13334 12808: Id : 4, {_}:
13335 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
13336 [8, 7, 6] by associativity ?6 ?7 ?8
13337 12808: Id : 5, {_}:
13338 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
13339 [11, 10] by symmetry_of_glb ?10 ?11
13340 12808: Id : 6, {_}:
13341 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
13342 [14, 13] by symmetry_of_lub ?13 ?14
13343 12808: Id : 7, {_}:
13344 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
13346 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
13347 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
13348 12808: Id : 8, {_}:
13349 least_upper_bound ?20 (least_upper_bound ?21 ?22)
13351 least_upper_bound (least_upper_bound ?20 ?21) ?22
13352 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13353 12808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
13354 12808: Id : 10, {_}:
13355 greatest_lower_bound ?26 ?26 =>= ?26
13356 [26] by idempotence_of_gld ?26
13357 12808: Id : 11, {_}:
13358 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
13359 [29, 28] by lub_absorbtion ?28 ?29
13360 12808: Id : 12, {_}:
13361 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
13362 [32, 31] by glb_absorbtion ?31 ?32
13363 12808: Id : 13, {_}:
13364 multiply ?34 (least_upper_bound ?35 ?36)
13366 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
13367 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13368 12808: Id : 14, {_}:
13369 multiply ?38 (greatest_lower_bound ?39 ?40)
13371 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
13372 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
13373 12808: Id : 15, {_}:
13374 multiply (least_upper_bound ?42 ?43) ?44
13376 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
13377 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13378 12808: Id : 16, {_}:
13379 multiply (greatest_lower_bound ?46 ?47) ?48
13381 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
13382 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
13383 12808: Id : 17, {_}: inverse identity =>= identity [] by p23_1
13384 12808: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
13385 12808: Id : 19, {_}:
13386 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
13387 [54, 53] by p23_3 ?53 ?54
13389 12808: Id : 1, {_}:
13390 least_upper_bound (multiply a b) identity
13392 multiply a (inverse (greatest_lower_bound a (inverse b)))
13397 12808: greatest_lower_bound 14 2 1 0,1,2,3
13398 12808: inverse 9 1 2 0,2,3
13399 12808: least_upper_bound 14 2 1 0,2
13400 12808: identity 5 0 1 2,2
13401 12808: multiply 22 2 2 0,1,2
13402 12808: b 2 0 2 2,1,2
13403 12808: a 3 0 3 1,1,2
13404 NO CLASH, using fixed ground order
13406 12809: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13407 12809: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
13408 12809: Id : 4, {_}:
13409 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
13410 [8, 7, 6] by associativity ?6 ?7 ?8
13411 12809: Id : 5, {_}:
13412 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
13413 [11, 10] by symmetry_of_glb ?10 ?11
13414 12809: Id : 6, {_}:
13415 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
13416 [14, 13] by symmetry_of_lub ?13 ?14
13417 12809: Id : 7, {_}:
13418 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
13420 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
13421 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
13422 12809: Id : 8, {_}:
13423 least_upper_bound ?20 (least_upper_bound ?21 ?22)
13425 least_upper_bound (least_upper_bound ?20 ?21) ?22
13426 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13427 12809: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
13428 12809: Id : 10, {_}:
13429 greatest_lower_bound ?26 ?26 =>= ?26
13430 [26] by idempotence_of_gld ?26
13431 12809: Id : 11, {_}:
13432 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
13433 [29, 28] by lub_absorbtion ?28 ?29
13434 12809: Id : 12, {_}:
13435 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
13436 [32, 31] by glb_absorbtion ?31 ?32
13437 12809: Id : 13, {_}:
13438 multiply ?34 (least_upper_bound ?35 ?36)
13440 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
13441 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13442 12809: Id : 14, {_}:
13443 multiply ?38 (greatest_lower_bound ?39 ?40)
13445 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
13446 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
13447 12809: Id : 15, {_}:
13448 multiply (least_upper_bound ?42 ?43) ?44
13450 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
13451 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13452 12809: Id : 16, {_}:
13453 multiply (greatest_lower_bound ?46 ?47) ?48
13455 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
13456 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
13457 12809: Id : 17, {_}: inverse identity =>= identity [] by p23_1
13458 12809: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
13459 12809: Id : 19, {_}:
13460 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
13461 [54, 53] by p23_3 ?53 ?54
13463 12809: Id : 1, {_}:
13464 least_upper_bound (multiply a b) identity
13466 multiply a (inverse (greatest_lower_bound a (inverse b)))
13471 12809: greatest_lower_bound 14 2 1 0,1,2,3
13472 12809: inverse 9 1 2 0,2,3
13473 12809: least_upper_bound 14 2 1 0,2
13474 12809: identity 5 0 1 2,2
13475 12809: multiply 22 2 2 0,1,2
13476 12809: b 2 0 2 2,1,2
13477 12809: a 3 0 3 1,1,2
13478 NO CLASH, using fixed ground order
13480 12810: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13481 12810: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
13482 12810: Id : 4, {_}:
13483 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
13484 [8, 7, 6] by associativity ?6 ?7 ?8
13485 12810: Id : 5, {_}:
13486 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
13487 [11, 10] by symmetry_of_glb ?10 ?11
13488 12810: Id : 6, {_}:
13489 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
13490 [14, 13] by symmetry_of_lub ?13 ?14
13491 12810: Id : 7, {_}:
13492 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
13494 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
13495 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
13496 12810: Id : 8, {_}:
13497 least_upper_bound ?20 (least_upper_bound ?21 ?22)
13499 least_upper_bound (least_upper_bound ?20 ?21) ?22
13500 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
13501 12810: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
13502 12810: Id : 10, {_}:
13503 greatest_lower_bound ?26 ?26 =>= ?26
13504 [26] by idempotence_of_gld ?26
13505 12810: Id : 11, {_}:
13506 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
13507 [29, 28] by lub_absorbtion ?28 ?29
13508 12810: Id : 12, {_}:
13509 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
13510 [32, 31] by glb_absorbtion ?31 ?32
13511 12810: Id : 13, {_}:
13512 multiply ?34 (least_upper_bound ?35 ?36)
13514 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
13515 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
13516 12810: Id : 14, {_}:
13517 multiply ?38 (greatest_lower_bound ?39 ?40)
13519 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
13520 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
13521 12810: Id : 15, {_}:
13522 multiply (least_upper_bound ?42 ?43) ?44
13524 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
13525 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
13526 12810: Id : 16, {_}:
13527 multiply (greatest_lower_bound ?46 ?47) ?48
13529 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
13530 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
13531 12810: Id : 17, {_}: inverse identity =>= identity [] by p23_1
13532 12810: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
13533 12810: Id : 19, {_}:
13534 inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
13535 [54, 53] by p23_3 ?53 ?54
13537 12810: Id : 1, {_}:
13538 least_upper_bound (multiply a b) identity
13540 multiply a (inverse (greatest_lower_bound a (inverse b)))
13545 12810: greatest_lower_bound 14 2 1 0,1,2,3
13546 12810: inverse 9 1 2 0,2,3
13547 12810: least_upper_bound 14 2 1 0,2
13548 12810: identity 5 0 1 2,2
13549 12810: multiply 22 2 2 0,1,2
13550 12810: b 2 0 2 2,1,2
13551 12810: a 3 0 3 1,1,2
13552 % SZS status Timeout for GRP186-2.p
13553 NO CLASH, using fixed ground order
13555 12831: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13556 12831: Id : 3, {_}:
13557 multiply (left_inverse ?4) ?4 =>= identity
13558 [4] by left_inverse ?4
13559 12831: Id : 4, {_}:
13560 multiply (multiply ?6 (multiply ?7 ?8)) ?6
13562 multiply (multiply ?6 ?7) (multiply ?8 ?6)
13563 [8, 7, 6] by moufang1 ?6 ?7 ?8
13565 12831: Id : 1, {_}:
13566 multiply (multiply (multiply a b) c) b
13568 multiply a (multiply b (multiply c b))
13569 [] by prove_moufang2
13573 12831: left_inverse 1 1 0
13574 12831: identity 2 0 0
13575 12831: c 2 0 2 2,1,2
13576 12831: multiply 14 2 6 0,2
13577 12831: b 4 0 4 2,1,1,2
13578 12831: a 2 0 2 1,1,1,2
13579 NO CLASH, using fixed ground order
13581 12833: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13582 12833: Id : 3, {_}:
13583 multiply (left_inverse ?4) ?4 =>= identity
13584 [4] by left_inverse ?4
13585 12833: Id : 4, {_}:
13586 multiply (multiply ?6 (multiply ?7 ?8)) ?6
13588 multiply (multiply ?6 ?7) (multiply ?8 ?6)
13589 [8, 7, 6] by moufang1 ?6 ?7 ?8
13591 12833: Id : 1, {_}:
13592 multiply (multiply (multiply a b) c) b
13594 multiply a (multiply b (multiply c b))
13595 [] by prove_moufang2
13599 12833: left_inverse 1 1 0
13600 12833: identity 2 0 0
13601 12833: c 2 0 2 2,1,2
13602 12833: multiply 14 2 6 0,2
13603 12833: b 4 0 4 2,1,1,2
13604 12833: a 2 0 2 1,1,1,2
13605 NO CLASH, using fixed ground order
13607 12832: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13608 12832: Id : 3, {_}:
13609 multiply (left_inverse ?4) ?4 =>= identity
13610 [4] by left_inverse ?4
13611 12832: Id : 4, {_}:
13612 multiply (multiply ?6 (multiply ?7 ?8)) ?6
13614 multiply (multiply ?6 ?7) (multiply ?8 ?6)
13615 [8, 7, 6] by moufang1 ?6 ?7 ?8
13617 12832: Id : 1, {_}:
13618 multiply (multiply (multiply a b) c) b
13620 multiply a (multiply b (multiply c b))
13621 [] by prove_moufang2
13625 12832: left_inverse 1 1 0
13626 12832: identity 2 0 0
13627 12832: c 2 0 2 2,1,2
13628 12832: multiply 14 2 6 0,2
13629 12832: b 4 0 4 2,1,1,2
13630 12832: a 2 0 2 1,1,1,2
13631 % SZS status Timeout for GRP204-1.p
13632 CLASH, statistics insufficient
13634 12860: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13635 12860: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
13636 12860: Id : 4, {_}:
13637 multiply ?6 (left_division ?6 ?7) =>= ?7
13638 [7, 6] by multiply_left_division ?6 ?7
13639 12860: Id : 5, {_}:
13640 left_division ?9 (multiply ?9 ?10) =>= ?10
13641 [10, 9] by left_division_multiply ?9 ?10
13642 12860: Id : 6, {_}:
13643 multiply (right_division ?12 ?13) ?13 =>= ?12
13644 [13, 12] by multiply_right_division ?12 ?13
13645 12860: Id : 7, {_}:
13646 right_division (multiply ?15 ?16) ?16 =>= ?15
13647 [16, 15] by right_division_multiply ?15 ?16
13648 12860: Id : 8, {_}:
13649 multiply ?18 (right_inverse ?18) =>= identity
13650 [18] by right_inverse ?18
13651 12860: Id : 9, {_}:
13652 multiply (left_inverse ?20) ?20 =>= identity
13653 [20] by left_inverse ?20
13654 12860: Id : 10, {_}:
13655 multiply (multiply (multiply ?22 ?23) ?22) ?24
13657 multiply ?22 (multiply ?23 (multiply ?22 ?24))
13658 [24, 23, 22] by moufang3 ?22 ?23 ?24
13660 12860: Id : 1, {_}:
13661 multiply x (multiply (multiply y z) x)
13663 multiply (multiply x y) (multiply z x)
13664 [] by prove_moufang4
13668 12860: left_inverse 1 1 0
13669 12860: right_inverse 1 1 0
13670 12860: right_division 2 2 0
13671 12860: left_division 2 2 0
13672 12860: identity 4 0 0
13673 12860: multiply 20 2 6 0,2
13674 12860: z 2 0 2 2,1,2,2
13675 12860: y 2 0 2 1,1,2,2
13677 CLASH, statistics insufficient
13679 12861: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13680 12861: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
13681 12861: Id : 4, {_}:
13682 multiply ?6 (left_division ?6 ?7) =>= ?7
13683 [7, 6] by multiply_left_division ?6 ?7
13684 12861: Id : 5, {_}:
13685 left_division ?9 (multiply ?9 ?10) =>= ?10
13686 [10, 9] by left_division_multiply ?9 ?10
13687 12861: Id : 6, {_}:
13688 multiply (right_division ?12 ?13) ?13 =>= ?12
13689 [13, 12] by multiply_right_division ?12 ?13
13690 12861: Id : 7, {_}:
13691 right_division (multiply ?15 ?16) ?16 =>= ?15
13692 [16, 15] by right_division_multiply ?15 ?16
13693 12861: Id : 8, {_}:
13694 multiply ?18 (right_inverse ?18) =>= identity
13695 [18] by right_inverse ?18
13696 12861: Id : 9, {_}:
13697 multiply (left_inverse ?20) ?20 =>= identity
13698 [20] by left_inverse ?20
13699 12861: Id : 10, {_}:
13700 multiply (multiply (multiply ?22 ?23) ?22) ?24
13702 multiply ?22 (multiply ?23 (multiply ?22 ?24))
13703 [24, 23, 22] by moufang3 ?22 ?23 ?24
13705 12861: Id : 1, {_}:
13706 multiply x (multiply (multiply y z) x)
13708 multiply (multiply x y) (multiply z x)
13709 [] by prove_moufang4
13713 12861: left_inverse 1 1 0
13714 12861: right_inverse 1 1 0
13715 12861: right_division 2 2 0
13716 12861: left_division 2 2 0
13717 12861: identity 4 0 0
13718 12861: multiply 20 2 6 0,2
13719 12861: z 2 0 2 2,1,2,2
13720 12861: y 2 0 2 1,1,2,2
13722 CLASH, statistics insufficient
13724 12862: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13725 12862: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
13726 12862: Id : 4, {_}:
13727 multiply ?6 (left_division ?6 ?7) =>= ?7
13728 [7, 6] by multiply_left_division ?6 ?7
13729 12862: Id : 5, {_}:
13730 left_division ?9 (multiply ?9 ?10) =>= ?10
13731 [10, 9] by left_division_multiply ?9 ?10
13732 12862: Id : 6, {_}:
13733 multiply (right_division ?12 ?13) ?13 =>= ?12
13734 [13, 12] by multiply_right_division ?12 ?13
13735 12862: Id : 7, {_}:
13736 right_division (multiply ?15 ?16) ?16 =>= ?15
13737 [16, 15] by right_division_multiply ?15 ?16
13738 12862: Id : 8, {_}:
13739 multiply ?18 (right_inverse ?18) =>= identity
13740 [18] by right_inverse ?18
13741 12862: Id : 9, {_}:
13742 multiply (left_inverse ?20) ?20 =>= identity
13743 [20] by left_inverse ?20
13744 12862: Id : 10, {_}:
13745 multiply (multiply (multiply ?22 ?23) ?22) ?24
13747 multiply ?22 (multiply ?23 (multiply ?22 ?24))
13748 [24, 23, 22] by moufang3 ?22 ?23 ?24
13750 12862: Id : 1, {_}:
13751 multiply x (multiply (multiply y z) x)
13753 multiply (multiply x y) (multiply z x)
13754 [] by prove_moufang4
13758 12862: left_inverse 1 1 0
13759 12862: right_inverse 1 1 0
13760 12862: right_division 2 2 0
13761 12862: left_division 2 2 0
13762 12862: identity 4 0 0
13763 12862: multiply 20 2 6 0,2
13764 12862: z 2 0 2 2,1,2,2
13765 12862: y 2 0 2 1,1,2,2
13769 Found proof, 29.150598s
13770 % SZS status Unsatisfiable for GRP205-1.p
13771 % SZS output start CNFRefutation for GRP205-1.p
13772 Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
13773 Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
13774 Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
13775 Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
13776 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
13777 Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
13778 Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
13779 Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
13780 Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
13781 Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
13782 Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
13783 Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
13784 Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
13785 Id : 889, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
13786 Id : 895, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 889 with 6 at 2,1,2
13787 Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
13788 Id : 2553, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
13789 Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
13790 Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
13791 Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
13792 Id : 763, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
13793 Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
13794 Id : 789, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 763 with 24 at 2
13795 Id : 816, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 789 at 1,2
13796 Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
13797 Id : 843, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 816 with 45 at 2
13798 Id : 857, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 843 at 2,2
13799 Id : 2562, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2553 with 857 at 2,2,1,2
13800 Id : 2621, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2562 with 3 at 2,1,2
13801 Id : 2806, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 895 with 2621 at 2,3
13802 Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
13803 Id : 963, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
13804 Id : 970, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 963 with 9 at 2,1,2,2,2,2
13805 Id : 1030, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 970 with 3 at 1,2,2,2,2
13806 Id : 1031, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1030 with 4 at 2,2,2
13807 Id : 1164, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1031 at 2,2
13808 Id : 2852, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2806 with 1164 at 1,2
13809 Id : 2853, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2852 with 1164 at 3
13810 Id : 2854, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2853 with 5 at 1,2
13811 Id : 2855, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2854 with 5 at 3
13812 Id : 1378, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1164 at 1,2
13813 Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
13814 Id : 1384, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1378 with 28 at 1,2
13815 Id : 3643, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
13816 Id : 3648, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3643 with 4 at 2,2,3
13817 Id : 2922, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1384 with 2855 at 1,3
13818 Id : 3008, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2855 with 2922 at 2
13819 Id : 3027, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3008 with 1164 at 1,2
13820 Id : 3028, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3027 with 1164 at 3
13821 Id : 3191, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2855 with 3028 at 2,2
13822 Id : 8019, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3648 with 3191 at 2
13823 Id : 3187, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1164 with 3028 at 1,3
13824 Id : 8020, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8019 with 3187 at 2,3
13825 Id : 8021, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8020 with 3191 at 3
13826 Id : 8034, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1384 with 8021 at 1,3
13827 Id : 8099, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8034 with 1384 at 3
13828 Id : 23672, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2855 with 8099 at 2
13829 Id : 2932, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2854 with 5 at 3
13830 Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
13831 Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
13832 Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
13833 Id : 860, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 843 at 2
13834 Id : 2936, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2932 with 860 at 2,2
13835 Id : 3077, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1164 with 2936 at 3
13836 Id : 3115, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3077 with 2922 at 3
13837 Id : 23819, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23672 with 3115 at 1,2
13838 Id : 23820, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23819 with 2936 at 2,2
13839 Id : 23821, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23820 with 3187 at 3
13840 Id : 23822, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23821 with 2922 at 2
13841 Id : 23823, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23822 with 3115 at 1,1,3
13842 Id : 1167, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1030 with 4 at 2,2,2
13843 Id : 1177, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1167 with 4 at 2,2
13844 Id : 1414, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1177 with 1384 at 1,3
13845 Id : 23824, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23823 with 1414 at 1,2
13846 Id : 23825, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23824 with 1177 at 1,3
13847 Id : 37248, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23825 with 3028 at 2
13848 Id : 37265, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37248 with 2936 at 1,1,3
13849 Id : 37472, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37265 with 2855 at 2,2
13850 Id : 37473, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37472 with 1414 at 1,3
13851 Id : 8041, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8020 with 3191 at 3
13852 Id : 8054, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8041 with 3115 at 2,2
13853 Id : 8126, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8054 with 2855 at 2
13854 Id : 8127, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8126 with 2922 at 3
13855 Id : 8128, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8127 with 2936 at 1,2
13856 Id : 8129, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8128 with 3187 at 1,3
13857 Id : 8130, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8129 with 1414 at 2
13858 Id : 8131, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8130 with 3028 at 3
13859 Id : 8132, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8131 with 3115 at 1,2,3
13860 Id : 24031, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8132 with 1177 at 2,3
13861 Id : 24068, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24031 with 2855 at 1,2
13862 Id : 24287, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24068 with 2936 at 1,2,3
13863 Id : 24288, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24287 with 1414 at 2,3
13864 Id : 47819, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37473 with 24288 at 2
13865 Id : 1246, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1164 at 1,3
13866 Id : 1310, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1246 with 1164 at 2
13867 Id : 3056, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1310 with 2936 at 2,2
13868 Id : 3057, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3056 with 2936 at 3
13869 Id : 47887, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47819 with 3057 at 1,3
13870 Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
13871 Id : 3632, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
13872 Id : 7833, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3632 with 3187 at 3
13873 Id : 7841, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3028 with 7833 at 1,2
13874 Id : 7910, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7841 with 3028 at 2
13875 Id : 22545, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3115 with 7910 at 2
13876 Id : 22628, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22545 with 1164 at 1,2
13877 Id : 22629, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22628 with 3115 at 2,2
13878 Id : 22630, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22629 with 2936 at 1,2,1,3
13879 Id : 22631, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22630 with 3115 at 2
13880 Id : 22632, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22631 with 1414 at 2,1,3
13881 Id : 22633, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22632 with 3191 at 1,2
13882 Id : 22634, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22633 with 3191 at 1,3
13883 Id : 22635, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22634 with 1384 at 2
13884 Id : 33282, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22635 with 1384 at 3
13885 Id : 33363, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33282 with 1177 at 1,3
13886 Id : 33649, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33363 with 1177 at 1,2
13887 Id : 2939, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2932 with 1384 at 2,2
13888 Id : 33650, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33649 with 2939 at 1,3
13889 Id : 48257, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 47887 with 33650 at 1,2,2
13890 Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
13891 Id : 1251, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1164 at 2,1,2
13892 Id : 1306, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1251 with 1164 at 2,3
13893 Id : 5008, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1306 with 3191 at 1,2
13894 Id : 5009, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5008 with 3191 at 3
13895 Id : 5010, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5009 with 1414 at 2
13896 Id : 48258, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48257 with 5010 at 3
13897 Id : 3070, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2936 at 2,1,2
13898 Id : 3126, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3070 with 1164 at 1,2
13899 Id : 3127, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3126 with 1164 at 3
13900 Id : 3128, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3127 with 3057 at 1,2
13901 Id : 3129, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3128 with 1164 at 2,2,3
13902 Id : 3130, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3129 with 1414 at 2
13903 Id : 7047, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3130 with 3191 at 2,3
13904 Id : 7063, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3115 with 7047 at 2
13905 Id : 7165, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7063 with 1177 at 2,2,2
13906 Id : 7166, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7165 with 2939 at 1,3
13907 Id : 7167, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7166 with 1384 at 3
13908 Id : 21426, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3028 with 7167 at 1,2
13909 Id : 21547, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21426 with 1384 at 2
13910 Id : 48259, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48258 with 21547 at 2,2
13911 Id : 48260, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48259 with 1414 at 1,2,3
13912 Id : 3073, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2936 at 2,2
13913 Id : 48261, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48260 with 3073 at 2
13914 Id : 48262, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48261 with 28 at 1,2,3
13915 Id : 48263, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48262 with 1384 at 2
13916 Id : 52424, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1384 with 48263 at 1,3
13917 Id : 52654, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52424 with 1384 at 3
13918 Id : 54963, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2855 with 52654 at 2
13919 Id : 55156, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 54963 with 1177 at 1,2
13920 Id : 55157, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55156 with 2922 at 2,2
13921 Id : 55158, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55157 with 3187 at 3
13922 Id : 55159, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55158 with 2855 at 2
13923 Id : 55160, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55159 with 3115 at 1,3
13924 Id : 55161, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55160 with 1177 at 3
13925 Id : 55162, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55161 with 70 at 3
13926 Id : 56911, {_}: multiply x (multiply (multiply y z) x) =?= multiply x (multiply (multiply y z) x) [] by Demod 1 with 55162 at 3
13927 Id : 1, {_}: multiply x (multiply (multiply y z) x) =<= multiply (multiply x y) (multiply z x) [] by prove_moufang4
13928 % SZS output end CNFRefutation for GRP205-1.p
13929 12861: solved GRP205-1.p in 14.652915 using kbo
13930 12861: status Unsatisfiable for GRP205-1.p
13931 NO CLASH, using fixed ground order
13933 12867: Id : 2, {_}:
13938 (multiply (multiply ?4 (inverse ?4))
13939 (inverse (multiply ?2 ?3))) ?2)))
13942 [4, 3, 2] by single_non_axiom ?2 ?3 ?4
13944 12867: Id : 1, {_}:
13949 (multiply (multiply z (inverse z)) (inverse (multiply u y)))
13953 [] by try_prove_this_axiom
13957 12867: u 2 0 2 1,1,2,1,2,1,2,2
13958 12867: multiply 12 2 6 0,2
13959 12867: inverse 6 1 3 0,2,2
13960 12867: z 2 0 2 1,1,1,2,1,2,2
13961 12867: y 2 0 2 1,1,2,2
13963 NO CLASH, using fixed ground order
13965 12868: Id : 2, {_}:
13970 (multiply (multiply ?4 (inverse ?4))
13971 (inverse (multiply ?2 ?3))) ?2)))
13974 [4, 3, 2] by single_non_axiom ?2 ?3 ?4
13976 12868: Id : 1, {_}:
13981 (multiply (multiply z (inverse z)) (inverse (multiply u y)))
13985 [] by try_prove_this_axiom
13989 12868: u 2 0 2 1,1,2,1,2,1,2,2
13990 12868: multiply 12 2 6 0,2
13991 12868: inverse 6 1 3 0,2,2
13992 12868: z 2 0 2 1,1,1,2,1,2,2
13993 12868: y 2 0 2 1,1,2,2
13995 NO CLASH, using fixed ground order
13997 12869: Id : 2, {_}:
14002 (multiply (multiply ?4 (inverse ?4))
14003 (inverse (multiply ?2 ?3))) ?2)))
14006 [4, 3, 2] by single_non_axiom ?2 ?3 ?4
14008 12869: Id : 1, {_}:
14013 (multiply (multiply z (inverse z)) (inverse (multiply u y)))
14017 [] by try_prove_this_axiom
14021 12869: u 2 0 2 1,1,2,1,2,1,2,2
14022 12869: multiply 12 2 6 0,2
14023 12869: inverse 6 1 3 0,2,2
14024 12869: z 2 0 2 1,1,1,2,1,2,2
14025 12869: y 2 0 2 1,1,2,2
14027 % SZS status Timeout for GRP207-1.p
14028 Fatal error: exception Assert_failure("matitaprover.ml", 265, 46)
14029 NO CLASH, using fixed ground order
14031 12900: Id : 2, {_}:
14037 (multiply (inverse ?3)
14039 (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
14043 [4, 3, 2] by single_axiom ?2 ?3 ?4
14045 12900: Id : 1, {_}:
14046 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
14047 [] by prove_these_axioms_3
14051 12900: inverse 7 1 0
14052 12900: c3 2 0 2 2,2
14053 12900: multiply 10 2 4 0,2
14054 12900: b3 2 0 2 2,1,2
14055 12900: a3 2 0 2 1,1,2
14056 NO CLASH, using fixed ground order
14058 12901: Id : 2, {_}:
14064 (multiply (inverse ?3)
14066 (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
14070 [4, 3, 2] by single_axiom ?2 ?3 ?4
14072 12901: Id : 1, {_}:
14073 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
14074 [] by prove_these_axioms_3
14078 12901: inverse 7 1 0
14079 12901: c3 2 0 2 2,2
14080 12901: multiply 10 2 4 0,2
14081 12901: b3 2 0 2 2,1,2
14082 12901: a3 2 0 2 1,1,2
14083 NO CLASH, using fixed ground order
14085 12902: Id : 2, {_}:
14091 (multiply (inverse ?3)
14093 (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
14097 [4, 3, 2] by single_axiom ?2 ?3 ?4
14099 12902: Id : 1, {_}:
14100 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
14101 [] by prove_these_axioms_3
14105 12902: inverse 7 1 0
14106 12902: c3 2 0 2 2,2
14107 12902: multiply 10 2 4 0,2
14108 12902: b3 2 0 2 2,1,2
14109 12902: a3 2 0 2 1,1,2
14110 % SZS status Timeout for GRP420-1.p
14111 NO CLASH, using fixed ground order
14113 12949: Id : 2, {_}:
14115 (divide (divide ?2 ?2)
14116 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
14120 [4, 3, 2] by single_axiom ?2 ?3 ?4
14121 12949: Id : 3, {_}:
14122 multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
14123 [8, 7, 6] by multiply ?6 ?7 ?8
14124 12949: Id : 4, {_}:
14125 inverse ?10 =<= divide (divide ?11 ?11) ?10
14126 [11, 10] by inverse ?10 ?11
14128 12949: Id : 1, {_}:
14129 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
14130 [] by prove_these_axioms_3
14134 12949: inverse 1 1 0
14135 12949: divide 13 2 0
14136 12949: c3 2 0 2 2,2
14137 12949: multiply 5 2 4 0,2
14138 12949: b3 2 0 2 2,1,2
14139 12949: a3 2 0 2 1,1,2
14140 NO CLASH, using fixed ground order
14142 12950: Id : 2, {_}:
14144 (divide (divide ?2 ?2)
14145 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
14149 [4, 3, 2] by single_axiom ?2 ?3 ?4
14150 12950: Id : 3, {_}:
14151 multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
14152 [8, 7, 6] by multiply ?6 ?7 ?8
14153 12950: Id : 4, {_}:
14154 inverse ?10 =<= divide (divide ?11 ?11) ?10
14155 [11, 10] by inverse ?10 ?11
14157 12950: Id : 1, {_}:
14158 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
14159 [] by prove_these_axioms_3
14163 12950: inverse 1 1 0
14164 12950: divide 13 2 0
14165 12950: c3 2 0 2 2,2
14166 12950: multiply 5 2 4 0,2
14167 12950: b3 2 0 2 2,1,2
14168 12950: a3 2 0 2 1,1,2
14169 NO CLASH, using fixed ground order
14171 12951: Id : 2, {_}:
14173 (divide (divide ?2 ?2)
14174 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
14178 [4, 3, 2] by single_axiom ?2 ?3 ?4
14179 12951: Id : 3, {_}:
14180 multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7)
14181 [8, 7, 6] by multiply ?6 ?7 ?8
14182 12951: Id : 4, {_}:
14183 inverse ?10 =<= divide (divide ?11 ?11) ?10
14184 [11, 10] by inverse ?10 ?11
14186 12951: Id : 1, {_}:
14187 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
14188 [] by prove_these_axioms_3
14192 12951: inverse 1 1 0
14193 12951: divide 13 2 0
14194 12951: c3 2 0 2 2,2
14195 12951: multiply 5 2 4 0,2
14196 12951: b3 2 0 2 2,1,2
14197 12951: a3 2 0 2 1,1,2
14200 Found proof, 2.410071s
14201 % SZS status Unsatisfiable for GRP453-1.p
14202 % SZS output start CNFRefutation for GRP453-1.p
14203 Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
14204 Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
14205 Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
14206 Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
14207 Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
14208 Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
14209 Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
14210 Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
14211 Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
14212 Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
14213 Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
14214 Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
14215 Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
14216 Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
14217 Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
14218 Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
14219 Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
14220 Id : 479, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
14221 Id : 480, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 479 with 4 at 1,2,1,1,1,2
14222 Id : 481, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 480 with 36 at 2,1,1,1,2
14223 Id : 482, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 481 with 29 at 1,1,1,2
14224 Id : 888, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
14225 Id : 903, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 888 with 36 at 2,1,1,3
14226 Id : 936, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 903 with 4 at 1,1,2
14227 Id : 969, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 903 with 4 at 1,1,2
14228 Id : 980, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =>= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 969 with 32 at 1,1,3
14229 Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
14230 Id : 1009, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 980 with 223 at 2
14231 Id : 1026, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1009 at 2,3
14232 Id : 1064, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1026 with 29 at 3
14233 Id : 1096, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 936 with 1064 at 1,1,3
14234 Id : 1169, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1096 with 29 at 2
14235 Id : 1211, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 936 with 1169 at 1,1,3
14236 Id : 1253, {_}: multiply (inverse (inverse (inverse (inverse ?2471)))) ?2472 =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Demod 1211 with 29 at 2
14237 Id : 1506, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?3181 ?3182))))))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Super 482 with 1253 at 1,1,1,2
14238 Id : 1558, {_}: divide (inverse (inverse (multiply ?3181 ?3182))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Demod 1506 with 1009 at 1,2
14239 Id : 1559, {_}: ?3181 =<= inverse (inverse (inverse (inverse ?3181))) [3181] by Demod 1558 with 482 at 2
14240 Id : 1611, {_}: multiply ?3343 (inverse (inverse (inverse ?3344))) =>= divide ?3343 ?3344 [3344, 3343] by Super 29 with 1559 at 2,3
14241 Id : 1683, {_}: divide (inverse (inverse ?3483)) (inverse (inverse ?3484)) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Super 936 with 1611 at 1,1,3
14242 Id : 1717, {_}: multiply (inverse (inverse ?3483)) (inverse ?3484) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Demod 1683 with 29 at 2
14243 Id : 1782, {_}: divide (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) (inverse ?3606) =>= inverse (inverse ?3605) [3606, 3605] by Super 482 with 1717 at 1,1,1,2
14244 Id : 1824, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1782 with 29 at 2
14245 Id : 1825, {_}: multiply (divide ?3605 ?3606) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1824 with 1559 at 1,2
14246 Id : 1854, {_}: inverse (inverse ?3731) =<= divide (divide ?3731 (inverse (inverse (inverse ?3732)))) ?3732 [3732, 3731] by Super 1611 with 1825 at 2
14247 Id : 2653, {_}: inverse (inverse ?5844) =<= divide (multiply ?5844 (inverse (inverse ?5845))) ?5845 [5845, 5844] by Demod 1854 with 29 at 1,3
14248 Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
14249 Id : 2679, {_}: inverse (inverse (inverse (inverse (divide ?5935 ?5935)))) =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Super 2653 with 224 at 1,3
14250 Id : 2732, {_}: divide ?5935 ?5935 =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Demod 2679 with 1559 at 2
14251 Id : 2733, {_}: divide ?5935 ?5935 =?= divide ?5936 ?5936 [5936, 5935] by Demod 2732 with 1559 at 1,3
14252 Id : 2794, {_}: divide (inverse (divide ?6115 (divide (inverse ?6116) (divide (inverse ?6115) ?6117)))) ?6117 =?= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6117, 6116, 6115] by Super 145 with 2733 at 2,1,3
14253 Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
14254 Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
14255 Id : 2869, {_}: inverse ?6116 =<= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6116] by Demod 2794 with 31 at 2
14256 Id : 2925, {_}: divide ?6471 (divide ?6472 ?6472) =>= inverse (inverse (inverse (inverse ?6471))) [6472, 6471] by Super 1559 with 2869 at 1,1,1,3
14257 Id : 2977, {_}: divide ?6471 (divide ?6472 ?6472) =>= ?6471 [6472, 6471] by Demod 2925 with 1559 at 3
14258 Id : 3050, {_}: divide (inverse (divide ?6728 ?6729)) (divide ?6730 ?6730) =>= inverse (inverse (multiply ?6729 (inverse ?6728))) [6730, 6729, 6728] by Super 250 with 2977 at 2,1,1,3
14259 Id : 3110, {_}: inverse (divide ?6728 ?6729) =<= inverse (inverse (multiply ?6729 (inverse ?6728))) [6729, 6728] by Demod 3050 with 2977 at 2
14260 Id : 3383, {_}: inverse (divide ?7439 ?7440) =<= divide (inverse (inverse ?7440)) ?7439 [7440, 7439] by Demod 3110 with 936 at 3
14261 Id : 1622, {_}: ?3381 =<= inverse (inverse (inverse (inverse ?3381))) [3381] by Demod 1558 with 482 at 2
14262 Id : 1636, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (divide (inverse (inverse ?3417)) ?3418)) [3418, 3417] by Super 1622 with 936 at 1,1,3
14263 Id : 3111, {_}: inverse (divide ?6728 ?6729) =<= divide (inverse (inverse ?6729)) ?6728 [6729, 6728] by Demod 3110 with 936 at 3
14264 Id : 3340, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (inverse (divide ?3418 ?3417))) [3418, 3417] by Demod 1636 with 3111 at 1,1,3
14265 Id : 3404, {_}: inverse (divide ?7516 (inverse (divide ?7517 ?7518))) =>= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Super 3383 with 3340 at 1,3
14266 Id : 3497, {_}: inverse (multiply ?7516 (divide ?7517 ?7518)) =<= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Demod 3404 with 29 at 1,2
14267 Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
14268 Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
14269 Id : 3338, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3111 at 3
14270 Id : 3343, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3338 with 29 at 1,3
14271 Id : 3051, {_}: multiply ?6732 (divide ?6733 ?6733) =>= inverse (inverse ?6732) [6733, 6732] by Super 1825 with 2977 at 1,2
14272 Id : 3711, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3343 with 3051 at 1,3
14273 Id : 3714, {_}: multiply ?3343 (inverse ?3344) =>= divide ?3343 ?3344 [3344, 3343] by Demod 1611 with 3711 at 2,2
14274 Id : 4200, {_}: inverse (multiply ?8647 (divide ?8648 ?8649)) =>= divide (divide ?8649 ?8648) ?8647 [8649, 8648, 8647] by Demod 3497 with 3714 at 1,3
14275 Id : 3401, {_}: inverse (divide ?7505 (inverse (inverse ?7506))) =>= divide ?7506 ?7505 [7506, 7505] by Super 3383 with 1559 at 1,3
14276 Id : 3496, {_}: inverse (multiply ?7505 (inverse ?7506)) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3401 with 29 at 1,2
14277 Id : 3715, {_}: inverse (divide ?7505 ?7506) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3496 with 3714 at 1,2
14278 Id : 3725, {_}: divide (divide ?527 ?526) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 526, 527] by Demod 250 with 3715 at 1,2
14279 Id : 3337, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 482 with 3111 at 2
14280 Id : 3721, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3337 with 3715 at 2
14281 Id : 1860, {_}: multiply (divide ?3752 ?3753) ?3753 =>= inverse (inverse ?3752) [3753, 3752] by Demod 1824 with 1559 at 1,2
14282 Id : 1869, {_}: multiply (multiply ?3781 ?3782) (inverse ?3782) =>= inverse (inverse ?3781) [3782, 3781] by Super 1860 with 29 at 1,2
14283 Id : 3717, {_}: divide (multiply ?3781 ?3782) ?3782 =>= inverse (inverse ?3781) [3782, 3781] by Demod 1869 with 3714 at 2
14284 Id : 3737, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3721 with 3717 at 2
14285 Id : 3738, {_}: divide (divide ?527 ?526) ?528 =<= multiply ?527 (divide (inverse ?526) ?528) [528, 526, 527] by Demod 3725 with 3737 at 3
14286 Id : 4230, {_}: inverse (divide (divide ?8777 ?8778) ?8779) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8779, 8778, 8777] by Super 4200 with 3738 at 1,2
14287 Id : 4280, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8778, 8777, 8779] by Demod 4230 with 3715 at 2
14288 Id : 4281, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (multiply ?8779 ?8778) ?8777 [8778, 8777, 8779] by Demod 4280 with 29 at 1,3
14289 Id : 4962, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (divide (inverse ?10175) ?10174) [10175, 10174, 10173] by Super 29 with 4281 at 3
14290 Id : 4205, {_}: inverse (multiply ?8667 ?8668) =<= divide (divide (divide ?8669 ?8669) ?8668) ?8667 [8669, 8668, 8667] by Super 4200 with 2977 at 2,1,2
14291 Id : 4245, {_}: inverse (multiply ?8667 ?8668) =<= divide (inverse ?8668) ?8667 [8668, 8667] by Demod 4205 with 4 at 1,3
14292 Id : 5005, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (inverse (multiply ?10174 ?10175)) [10175, 10174, 10173] by Demod 4962 with 4245 at 2,3
14293 Id : 5006, {_}: multiply (multiply ?10173 ?10174) ?10175 =>= multiply ?10173 (multiply ?10174 ?10175) [10175, 10174, 10173] by Demod 5005 with 29 at 3
14294 Id : 5130, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 5006 at 2
14295 Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
14296 % SZS output end CNFRefutation for GRP453-1.p
14297 12950: solved GRP453-1.p in 1.216075 using kbo
14298 12950: status Unsatisfiable for GRP453-1.p
14299 Fatal error: exception Assert_failure("matitaprover.ml", 265, 46)
14300 NO CLASH, using fixed ground order
14302 12960: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
14303 12960: Id : 3, {_}:
14304 meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
14305 [7, 6, 5] by distribution ?5 ?6 ?7
14307 12960: Id : 1, {_}:
14308 join (join a b) c =>= join a (join b c)
14309 [] by prove_associativity_of_join
14315 12960: join 7 2 4 0,2
14316 12960: b 2 0 2 2,1,2
14317 12960: a 2 0 2 1,1,2
14318 NO CLASH, using fixed ground order
14319 NO CLASH, using fixed ground order
14321 12962: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
14322 12962: Id : 3, {_}:
14323 meet ?5 (join ?6 ?7) =?= join (meet ?7 ?5) (meet ?6 ?5)
14324 [7, 6, 5] by distribution ?5 ?6 ?7
14326 12962: Id : 1, {_}:
14327 join (join a b) c =>= join a (join b c)
14328 [] by prove_associativity_of_join
14334 12962: join 7 2 4 0,2
14335 12962: b 2 0 2 2,1,2
14336 12962: a 2 0 2 1,1,2
14338 12961: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
14339 12961: Id : 3, {_}:
14340 meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
14341 [7, 6, 5] by distribution ?5 ?6 ?7
14343 12961: Id : 1, {_}:
14344 join (join a b) c =>= join a (join b c)
14345 [] by prove_associativity_of_join
14351 12961: join 7 2 4 0,2
14352 12961: b 2 0 2 2,1,2
14353 12961: a 2 0 2 1,1,2
14356 Found proof, 37.088774s
14357 % SZS status Unsatisfiable for LAT007-1.p
14358 % SZS output start CNFRefutation for LAT007-1.p
14359 Id : 3, {_}: meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) [7, 6, 5] by distribution ?5 ?6 ?7
14360 Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
14361 Id : 7, {_}: meet ?18 (join ?19 ?20) =<= join (meet ?20 ?18) (meet ?19 ?18) [20, 19, 18] by distribution ?18 ?19 ?20
14362 Id : 8, {_}: meet (join ?22 ?23) (join ?22 ?24) =<= join (meet ?24 (join ?22 ?23)) ?22 [24, 23, 22] by Super 7 with 2 at 2,3
14363 Id : 122, {_}: meet (meet ?274 ?275) (meet ?275 (join ?276 ?274)) =>= meet ?274 ?275 [276, 275, 274] by Super 2 with 3 at 2,2
14364 Id : 132, {_}: meet (meet ?317 ?318) ?318 =>= meet ?317 ?318 [318, 317] by Super 122 with 2 at 2,2
14365 Id : 166, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =<= join (meet ?382 ?380) (meet ?381 ?380) [382, 381, 380] by Super 3 with 132 at 1,3
14366 Id : 405, {_}: meet ?915 (join ?916 (meet ?917 ?915)) =>= meet ?915 (join ?916 ?917) [917, 916, 915] by Demod 166 with 3 at 3
14367 Id : 419, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =?= meet ?974 (join (meet ?976 ?974) ?975) [976, 975, 974] by Super 405 with 3 at 2,2
14368 Id : 165, {_}: meet ?376 (join (meet ?377 ?376) ?378) =<= join (meet ?378 ?376) (meet ?377 ?376) [378, 377, 376] by Super 3 with 132 at 2,3
14369 Id : 187, {_}: meet ?376 (join (meet ?377 ?376) ?378) =>= meet ?376 (join ?377 ?378) [378, 377, 376] by Demod 165 with 3 at 3
14370 Id : 473, {_}: meet ?1062 (meet ?1062 (join ?1063 ?1064)) =>= meet ?1062 (join ?1064 ?1063) [1064, 1063, 1062] by Demod 419 with 187 at 3
14371 Id : 484, {_}: meet ?1111 ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Super 473 with 2 at 2,2
14372 Id : 590, {_}: meet (join ?1333 ?1334) (join ?1333 ?1334) =>= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Super 8 with 484 at 1,3
14373 Id : 593, {_}: meet ?1344 ?1344 =>= ?1344 [1344] by Super 2 with 484 at 2
14374 Id : 2478, {_}: join ?1333 ?1334 =<= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Demod 590 with 593 at 2
14375 Id : 2479, {_}: join ?1333 ?1334 =?= join ?1334 ?1333 [1334, 1333] by Demod 2478 with 593 at 1,3
14376 Id : 639, {_}: meet ?1436 (join ?1437 ?1436) =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Super 3 with 593 at 1,3
14377 Id : 631, {_}: ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Demod 484 with 593 at 2
14378 Id : 669, {_}: ?1436 =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Demod 639 with 631 at 2
14379 Id : 53, {_}: meet (join ?112 ?113) (join ?112 ?114) =<= join (meet ?114 (join ?112 ?113)) ?112 [114, 113, 112] by Super 7 with 2 at 2,3
14380 Id : 62, {_}: meet (join ?150 ?151) (join ?150 ?150) =>= join ?150 ?150 [151, 150] by Super 53 with 2 at 1,3
14381 Id : 57, {_}: meet (join (meet ?128 ?129) (meet ?130 ?129)) (join (meet ?128 ?129) ?131) =>= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 130, 129, 128] by Super 53 with 3 at 2,1,3
14382 Id : 73, {_}: meet (meet ?129 (join ?130 ?128)) (join (meet ?128 ?129) ?131) =<= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 128, 130, 129] by Demod 57 with 3 at 1,2
14383 Id : 642, {_}: meet (meet ?1444 (join ?1445 ?1444)) (join (meet ?1444 ?1444) ?1446) =>= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1446, 1445, 1444] by Super 73 with 593 at 2,3
14384 Id : 657, {_}: meet ?1444 (join (meet ?1444 ?1444) ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 642 with 631 at 1,2
14385 Id : 658, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 657 with 593 at 1,2,2
14386 Id : 659, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 658 with 631 at 2,1,3
14387 Id : 699, {_}: ?1517 =<= join (meet ?1518 ?1517) ?1517 [1518, 1517] by Demod 659 with 2 at 2
14388 Id : 711, {_}: ?1557 =<= join ?1557 ?1557 [1557] by Super 699 with 593 at 1,3
14389 Id : 744, {_}: meet (join ?150 ?151) ?150 =>= join ?150 ?150 [151, 150] by Demod 62 with 711 at 2,2
14390 Id : 745, {_}: meet (join ?150 ?151) ?150 =>= ?150 [151, 150] by Demod 744 with 711 at 3
14391 Id : 713, {_}: join ?1562 ?1563 =<= join ?1563 (join ?1562 ?1563) [1563, 1562] by Super 699 with 631 at 1,3
14392 Id : 1157, {_}: meet (join ?2329 ?2330) ?2330 =>= ?2330 [2330, 2329] by Super 745 with 713 at 1,2
14393 Id : 1688, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= join (meet ?3264 ?3262) ?3262 [3264, 3263, 3262] by Super 3 with 1157 at 2,3
14394 Id : 660, {_}: ?1444 =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 659 with 2 at 2
14395 Id : 1738, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= ?3262 [3264, 3263, 3262] by Demod 1688 with 660 at 3
14396 Id : 4104, {_}: join (join ?7363 ?7364) ?7365 =<= join (join (join ?7363 ?7364) ?7365) ?7364 [7365, 7364, 7363] by Super 669 with 1738 at 2,3
14397 Id : 9885, {_}: join (join ?18104 ?18105) ?18106 =<= join ?18105 (join (join ?18104 ?18105) ?18106) [18106, 18105, 18104] by Demod 4104 with 2479 at 3
14398 Id : 9889, {_}: join (join ?18120 ?18121) ?18122 =<= join ?18121 (join (join ?18121 ?18120) ?18122) [18122, 18121, 18120] by Super 9885 with 2479 at 1,2,3
14399 Id : 4118, {_}: meet ?7422 (join (join ?7423 ?7422) ?7424) =>= ?7422 [7424, 7423, 7422] by Demod 1688 with 660 at 3
14400 Id : 4122, {_}: meet ?7438 (join (join ?7438 ?7439) ?7440) =>= ?7438 [7440, 7439, 7438] by Super 4118 with 2479 at 1,2,2
14401 Id : 9604, {_}: join (join ?17475 ?17476) ?17477 =<= join (join (join ?17475 ?17476) ?17477) ?17475 [17477, 17476, 17475] by Super 669 with 4122 at 2,3
14402 Id : 9740, {_}: join (join ?17475 ?17476) ?17477 =<= join ?17475 (join (join ?17475 ?17476) ?17477) [17477, 17476, 17475] by Demod 9604 with 2479 at 3
14403 Id : 16688, {_}: join (join ?18120 ?18121) ?18122 =?= join (join ?18121 ?18120) ?18122 [18122, 18121, 18120] by Demod 9889 with 9740 at 3
14404 Id : 9, {_}: meet (join ?26 ?27) (join ?28 ?26) =<= join ?26 (meet ?28 (join ?26 ?27)) [28, 27, 26] by Super 7 with 2 at 1,3
14405 Id : 753, {_}: meet ?1599 (join ?1600 ?1600) =>= meet ?1600 ?1599 [1600, 1599] by Super 3 with 711 at 3
14406 Id : 773, {_}: meet ?1599 ?1600 =?= meet ?1600 ?1599 [1600, 1599] by Demod 753 with 711 at 2,2
14407 Id : 2380, {_}: meet (join ?4513 ?4514) (join ?4515 ?4513) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4515, 4514, 4513] by Super 9 with 773 at 2,3
14408 Id : 2506, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =<= join ?4784 (meet ?4786 (join ?4785 ?4784)) [4786, 4785, 4784] by Super 9 with 2479 at 2,2,3
14409 Id : 1153, {_}: meet (join ?2312 (join ?2313 ?2312)) (join ?2314 ?2312) =>= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2313, 2312] by Super 9 with 713 at 2,2,3
14410 Id : 1191, {_}: meet (join ?2313 ?2312) (join ?2314 ?2312) =<= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2312, 2313] by Demod 1153 with 713 at 1,2
14411 Id : 5434, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =?= meet (join ?4785 ?4784) (join ?4786 ?4784) [4786, 4785, 4784] by Demod 2506 with 1191 at 3
14412 Id : 455, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =>= meet ?974 (join ?976 ?975) [976, 975, 974] by Demod 419 with 187 at 3
14413 Id : 757, {_}: meet ?1611 (meet ?1611 ?1612) =?= meet ?1611 (join ?1612 ?1612) [1612, 1611] by Super 455 with 711 at 2,2,2
14414 Id : 767, {_}: meet ?1611 (meet ?1611 ?1612) =>= meet ?1611 ?1612 [1612, 1611] by Demod 757 with 711 at 2,3
14415 Id : 1239, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =<= join (meet ?2428 (meet ?2426 ?2427)) (meet ?2426 ?2427) [2428, 2427, 2426] by Super 3 with 767 at 2,3
14416 Id : 1275, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =>= meet ?2426 ?2427 [2428, 2427, 2426] by Demod 1239 with 660 at 3
14417 Id : 30976, {_}: meet (join ?55510 ?55511) (join (meet ?55510 ?55512) ?55511) =>= join ?55511 (meet ?55510 ?55512) [55512, 55511, 55510] by Super 1191 with 1275 at 2,3
14418 Id : 30986, {_}: meet (join ?55551 ?55552) (join (meet ?55553 ?55551) ?55552) =>= join ?55552 (meet ?55551 ?55553) [55553, 55552, 55551] by Super 30976 with 773 at 1,2,2
14419 Id : 3010, {_}: meet (join ?5441 ?5442) (join ?5443 ?5442) =<= join ?5442 (meet ?5443 (join ?5441 ?5442)) [5443, 5442, 5441] by Demod 1153 with 713 at 1,2
14420 Id : 3031, {_}: meet (join (meet ?5530 ?5531) ?5532) (join ?5531 ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5532, 5531, 5530] by Super 3010 with 187 at 2,3
14421 Id : 3109, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5530, 5532, 5531] by Demod 3031 with 773 at 2
14422 Id : 3110, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= meet (join ?5530 ?5532) (join ?5531 ?5532) [5530, 5532, 5531] by Demod 3109 with 1191 at 3
14423 Id : 31246, {_}: meet (join ?55553 ?55552) (join ?55551 ?55552) =>= join ?55552 (meet ?55551 ?55553) [55551, 55552, 55553] by Demod 30986 with 3110 at 2
14424 Id : 31561, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =>= join ?4784 (meet ?4786 ?4785) [4786, 4785, 4784] by Demod 5434 with 31246 at 3
14425 Id : 31569, {_}: join ?4513 (meet ?4515 ?4514) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4514, 4515, 4513] by Demod 2380 with 31561 at 2
14426 Id : 31659, {_}: join ?56550 (meet (join ?56551 ?56552) ?56552) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56552, 56551, 56550] by Super 31569 with 31246 at 2,3
14427 Id : 31781, {_}: join ?56550 (meet ?56552 (join ?56551 ?56552)) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31659 with 773 at 2,2
14428 Id : 32533, {_}: join ?58368 ?58369 =<= join ?58368 (join ?58369 (meet ?58370 ?58368)) [58370, 58369, 58368] by Demod 31781 with 631 at 2,2
14429 Id : 32536, {_}: join (join ?58380 ?58381) ?58382 =<= join (join ?58380 ?58381) (join ?58382 ?58380) [58382, 58381, 58380] by Super 32533 with 2 at 2,2,3
14430 Id : 35660, {_}: join (join ?62824 ?62825) (join ?62825 ?62826) =>= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Super 2479 with 32536 at 3
14431 Id : 188, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =>= meet ?380 (join ?381 ?382) [382, 381, 380] by Demod 166 with 3 at 3
14432 Id : 1695, {_}: meet ?3292 (join ?3293 ?3292) =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Super 188 with 1157 at 2,2,2
14433 Id : 1732, {_}: ?3292 =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Demod 1695 with 631 at 2
14434 Id : 3955, {_}: join ?7063 (join ?7064 ?7065) =<= join (join ?7063 (join ?7064 ?7065)) ?7065 [7065, 7064, 7063] by Super 669 with 1732 at 2,3
14435 Id : 9413, {_}: join ?17183 (join ?17184 ?17185) =<= join ?17185 (join ?17183 (join ?17184 ?17185)) [17185, 17184, 17183] by Demod 3955 with 2479 at 3
14436 Id : 9417, {_}: join ?17199 (join ?17200 ?17201) =<= join ?17201 (join ?17199 (join ?17201 ?17200)) [17201, 17200, 17199] by Super 9413 with 2479 at 2,2,3
14437 Id : 3974, {_}: ?7142 =<= meet ?7142 (join ?7143 (join ?7144 ?7142)) [7144, 7143, 7142] by Demod 1695 with 631 at 2
14438 Id : 3978, {_}: ?7158 =<= meet ?7158 (join ?7159 (join ?7158 ?7160)) [7160, 7159, 7158] by Super 3974 with 2479 at 2,2,3
14439 Id : 8662, {_}: join ?15620 (join ?15621 ?15622) =<= join (join ?15620 (join ?15621 ?15622)) ?15621 [15622, 15621, 15620] by Super 669 with 3978 at 2,3
14440 Id : 8767, {_}: join ?15620 (join ?15621 ?15622) =<= join ?15621 (join ?15620 (join ?15621 ?15622)) [15622, 15621, 15620] by Demod 8662 with 2479 at 3
14441 Id : 15553, {_}: join ?17199 (join ?17200 ?17201) =?= join ?17199 (join ?17201 ?17200) [17201, 17200, 17199] by Demod 9417 with 8767 at 3
14442 Id : 31782, {_}: join ?56550 ?56552 =<= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31781 with 631 at 2,2
14443 Id : 35263, {_}: join ?62192 (join (meet ?62193 ?62192) ?62194) =>= join ?62192 ?62194 [62194, 62193, 62192] by Super 15553 with 31782 at 3
14444 Id : 35296, {_}: join (join ?62350 ?62351) (join ?62351 ?62352) =>= join (join ?62350 ?62351) ?62352 [62352, 62351, 62350] by Super 35263 with 631 at 1,2,2
14445 Id : 38052, {_}: join (join ?62824 ?62825) ?62826 =?= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Demod 35660 with 35296 at 2
14446 Id : 38125, {_}: join ?67897 (join ?67898 ?67899) =<= join (join ?67899 ?67897) ?67898 [67899, 67898, 67897] by Super 2479 with 38052 at 3
14447 Id : 38567, {_}: join ?18121 (join ?18122 ?18120) =<= join (join ?18121 ?18120) ?18122 [18120, 18122, 18121] by Demod 16688 with 38125 at 2
14448 Id : 38568, {_}: join ?18121 (join ?18122 ?18120) =?= join ?18120 (join ?18122 ?18121) [18120, 18122, 18121] by Demod 38567 with 38125 at 3
14449 Id : 39014, {_}: join c (join b a) =?= join c (join b a) [] by Demod 39013 with 2479 at 2,2
14450 Id : 39013, {_}: join c (join a b) =?= join c (join b a) [] by Demod 39012 with 38568 at 3
14451 Id : 39012, {_}: join c (join a b) =<= join a (join b c) [] by Demod 1 with 2479 at 2
14452 Id : 1, {_}: join (join a b) c =>= join a (join b c) [] by prove_associativity_of_join
14453 % SZS output end CNFRefutation for LAT007-1.p
14454 12961: solved LAT007-1.p in 17.645102 using kbo
14455 12961: status Unsatisfiable for LAT007-1.p
14456 NO CLASH, using fixed ground order
14458 12978: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
14459 12978: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
14460 12978: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
14461 12978: Id : 5, {_}:
14462 meet ?9 ?10 =?= meet ?10 ?9
14463 [10, 9] by commutativity_of_meet ?9 ?10
14464 12978: Id : 6, {_}:
14465 join ?12 ?13 =?= join ?13 ?12
14466 [13, 12] by commutativity_of_join ?12 ?13
14467 12978: Id : 7, {_}:
14468 meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
14469 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
14470 12978: Id : 8, {_}:
14471 join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
14472 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
14473 12978: Id : 9, {_}:
14474 complement (complement ?23) =>= ?23
14475 [23] by complement_involution ?23
14476 12978: Id : 10, {_}:
14477 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
14478 [26, 25] by join_complement ?25 ?26
14479 12978: Id : 11, {_}:
14480 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
14481 [29, 28] by meet_complement ?28 ?29
14483 12978: Id : 1, {_}:
14484 join (complement (join (meet a (complement b)) (complement a)))
14485 (join (meet a (complement b))
14487 (meet (complement a) (meet (join a (complement b)) (join a b)))
14488 (meet (complement a)
14489 (complement (meet (join a (complement b)) (join a b))))))
14498 12978: join 20 2 8 0,2
14499 12978: meet 15 2 6 0,1,1,1,2
14500 12978: complement 18 1 9 0,1,2
14501 12978: b 6 0 6 1,2,1,1,1,2
14502 12978: a 9 0 9 1,1,1,1,2
14503 NO CLASH, using fixed ground order
14505 12979: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
14506 12979: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
14507 12979: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
14508 12979: Id : 5, {_}:
14509 meet ?9 ?10 =?= meet ?10 ?9
14510 [10, 9] by commutativity_of_meet ?9 ?10
14511 12979: Id : 6, {_}:
14512 join ?12 ?13 =?= join ?13 ?12
14513 [13, 12] by commutativity_of_join ?12 ?13
14514 12979: Id : 7, {_}:
14515 meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
14516 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
14517 12979: Id : 8, {_}:
14518 join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
14519 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
14520 12979: Id : 9, {_}:
14521 complement (complement ?23) =>= ?23
14522 [23] by complement_involution ?23
14523 12979: Id : 10, {_}:
14524 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
14525 [26, 25] by join_complement ?25 ?26
14526 12979: Id : 11, {_}:
14527 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
14528 [29, 28] by meet_complement ?28 ?29
14530 12979: Id : 1, {_}:
14531 join (complement (join (meet a (complement b)) (complement a)))
14532 (join (meet a (complement b))
14534 (meet (complement a) (meet (join a (complement b)) (join a b)))
14535 (meet (complement a)
14536 (complement (meet (join a (complement b)) (join a b))))))
14545 12979: join 20 2 8 0,2
14546 12979: meet 15 2 6 0,1,1,1,2
14547 12979: complement 18 1 9 0,1,2
14548 12979: b 6 0 6 1,2,1,1,1,2
14549 12979: a 9 0 9 1,1,1,1,2
14550 NO CLASH, using fixed ground order
14552 12980: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
14553 12980: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
14554 12980: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
14555 12980: Id : 5, {_}:
14556 meet ?9 ?10 =?= meet ?10 ?9
14557 [10, 9] by commutativity_of_meet ?9 ?10
14558 12980: Id : 6, {_}:
14559 join ?12 ?13 =?= join ?13 ?12
14560 [13, 12] by commutativity_of_join ?12 ?13
14561 12980: Id : 7, {_}:
14562 meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
14563 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
14564 12980: Id : 8, {_}:
14565 join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
14566 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
14567 12980: Id : 9, {_}:
14568 complement (complement ?23) =>= ?23
14569 [23] by complement_involution ?23
14570 12980: Id : 10, {_}:
14571 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
14572 [26, 25] by join_complement ?25 ?26
14573 12980: Id : 11, {_}:
14574 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
14575 [29, 28] by meet_complement ?28 ?29
14577 12980: Id : 1, {_}:
14578 join (complement (join (meet a (complement b)) (complement a)))
14579 (join (meet a (complement b))
14581 (meet (complement a) (meet (join a (complement b)) (join a b)))
14582 (meet (complement a)
14583 (complement (meet (join a (complement b)) (join a b))))))
14592 12980: join 20 2 8 0,2
14593 12980: meet 15 2 6 0,1,1,1,2
14594 12980: complement 18 1 9 0,1,2
14595 12980: b 6 0 6 1,2,1,1,1,2
14596 12980: a 9 0 9 1,1,1,1,2
14597 % SZS status Timeout for LAT016-1.p
14598 NO CLASH, using fixed ground order
14600 12998: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14601 12998: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14602 NO CLASH, using fixed ground order
14604 12999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14605 12999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14606 12999: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
14607 12999: Id : 5, {_}:
14608 join ?9 ?10 =?= join ?10 ?9
14609 [10, 9] by commutativity_of_join ?9 ?10
14610 12999: Id : 6, {_}:
14611 meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
14612 [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
14613 12999: Id : 7, {_}:
14614 join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
14615 [18, 17, 16] by associativity_of_join ?16 ?17 ?18
14616 12999: Id : 8, {_}:
14617 join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
14619 meet ?20 (join ?21 ?22)
14620 [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
14621 NO CLASH, using fixed ground order
14623 13000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14624 13000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14625 13000: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
14626 13000: Id : 5, {_}:
14627 join ?9 ?10 =?= join ?10 ?9
14628 [10, 9] by commutativity_of_join ?9 ?10
14629 13000: Id : 6, {_}:
14630 meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
14631 [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
14632 13000: Id : 7, {_}:
14633 join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
14634 [18, 17, 16] by associativity_of_join ?16 ?17 ?18
14635 13000: Id : 8, {_}:
14636 join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
14638 meet ?20 (join ?21 ?22)
14639 [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
14640 13000: Id : 9, {_}:
14641 meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
14643 join ?24 (meet ?25 ?26)
14644 [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
14645 13000: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
14646 13000: Id : 11, {_}:
14647 meet2 ?30 ?31 =?= meet2 ?31 ?30
14648 [31, 30] by commutativity_of_meet2 ?30 ?31
14649 13000: Id : 12, {_}:
14650 meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
14651 [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
14652 12998: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
14653 12999: Id : 9, {_}:
14654 meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
14656 join ?24 (meet ?25 ?26)
14657 [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
14658 12998: Id : 5, {_}:
14659 join ?9 ?10 =?= join ?10 ?9
14660 [10, 9] by commutativity_of_join ?9 ?10
14661 13000: Id : 13, {_}:
14662 join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
14664 meet2 ?37 (join ?38 ?39)
14665 [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
14666 13000: Id : 14, {_}:
14667 meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
14669 join ?41 (meet2 ?42 ?43)
14670 [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
14672 13000: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
14677 13000: meet2 14 2 1 0,3
14678 13000: meet 14 2 1 0,2
14681 12998: Id : 6, {_}:
14682 meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
14683 [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
14684 12998: Id : 7, {_}:
14685 join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
14686 [18, 17, 16] by associativity_of_join ?16 ?17 ?18
14687 12998: Id : 8, {_}:
14688 join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
14690 meet ?20 (join ?21 ?22)
14691 [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
14692 12998: Id : 9, {_}:
14693 meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
14695 join ?24 (meet ?25 ?26)
14696 [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
14697 12998: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
14698 12998: Id : 11, {_}:
14699 meet2 ?30 ?31 =?= meet2 ?31 ?30
14700 [31, 30] by commutativity_of_meet2 ?30 ?31
14701 12998: Id : 12, {_}:
14702 meet2 (meet2 ?33 ?34) ?35 =?= meet2 ?33 (meet2 ?34 ?35)
14703 [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
14704 12998: Id : 13, {_}:
14705 join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
14707 meet2 ?37 (join ?38 ?39)
14708 [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
14709 12998: Id : 14, {_}:
14710 meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
14712 join ?41 (meet2 ?42 ?43)
14713 [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
14715 12998: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
14720 12998: meet2 14 2 1 0,3
14721 12998: meet 14 2 1 0,2
14724 12999: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
14725 12999: Id : 11, {_}:
14726 meet2 ?30 ?31 =?= meet2 ?31 ?30
14727 [31, 30] by commutativity_of_meet2 ?30 ?31
14728 12999: Id : 12, {_}:
14729 meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
14730 [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
14731 12999: Id : 13, {_}:
14732 join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
14734 meet2 ?37 (join ?38 ?39)
14735 [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
14736 12999: Id : 14, {_}:
14737 meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
14739 join ?41 (meet2 ?42 ?43)
14740 [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
14742 12999: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
14747 12999: meet2 14 2 1 0,3
14748 12999: meet 14 2 1 0,2
14751 % SZS status Timeout for LAT024-1.p
14752 NO CLASH, using fixed ground order
14754 13029: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14755 13029: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14756 13029: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
14757 13029: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
14758 13029: Id : 6, {_}:
14759 meet ?12 ?13 =?= meet ?13 ?12
14760 [13, 12] by commutativity_of_meet ?12 ?13
14761 13029: Id : 7, {_}:
14762 join ?15 ?16 =?= join ?16 ?15
14763 [16, 15] by commutativity_of_join ?15 ?16
14764 13029: Id : 8, {_}:
14765 join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
14766 [20, 19, 18] by tnl_1 ?18 ?19 ?20
14767 13029: Id : 9, {_}:
14768 meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
14769 [24, 23, 22] by tnl_2 ?22 ?23 ?24
14770 13029: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
14771 13029: Id : 11, {_}:
14772 meet2 ?28 (join ?28 ?29) =>= ?28
14773 [29, 28] by absorption1_2 ?28 ?29
14774 13029: Id : 12, {_}:
14775 join ?31 (meet2 ?31 ?32) =>= ?31
14776 [32, 31] by absorption2_2 ?31 ?32
14777 13029: Id : 13, {_}:
14778 meet2 ?34 ?35 =?= meet2 ?35 ?34
14779 [35, 34] by commutativity_of_meet2 ?34 ?35
14780 13029: Id : 14, {_}:
14781 join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
14782 [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
14783 13029: Id : 15, {_}:
14784 meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
14785 [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
14787 13029: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
14792 13029: meet2 9 2 1 0,3
14793 13029: meet 9 2 1 0,2
14796 NO CLASH, using fixed ground order
14798 13030: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14799 13030: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14800 13030: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
14801 13030: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
14802 13030: Id : 6, {_}:
14803 meet ?12 ?13 =?= meet ?13 ?12
14804 [13, 12] by commutativity_of_meet ?12 ?13
14805 13030: Id : 7, {_}:
14806 join ?15 ?16 =?= join ?16 ?15
14807 [16, 15] by commutativity_of_join ?15 ?16
14808 13030: Id : 8, {_}:
14809 join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
14810 [20, 19, 18] by tnl_1 ?18 ?19 ?20
14811 13030: Id : 9, {_}:
14812 meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
14813 [24, 23, 22] by tnl_2 ?22 ?23 ?24
14814 13030: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
14815 13030: Id : 11, {_}:
14816 meet2 ?28 (join ?28 ?29) =>= ?28
14817 [29, 28] by absorption1_2 ?28 ?29
14818 13030: Id : 12, {_}:
14819 join ?31 (meet2 ?31 ?32) =>= ?31
14820 [32, 31] by absorption2_2 ?31 ?32
14821 13030: Id : 13, {_}:
14822 meet2 ?34 ?35 =?= meet2 ?35 ?34
14823 [35, 34] by commutativity_of_meet2 ?34 ?35
14824 13030: Id : 14, {_}:
14825 join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
14826 [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
14827 13030: Id : 15, {_}:
14828 meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
14829 [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
14831 13030: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
14836 13030: meet2 9 2 1 0,3
14837 13030: meet 9 2 1 0,2
14840 NO CLASH, using fixed ground order
14842 13031: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14843 13031: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14844 13031: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
14845 13031: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
14846 13031: Id : 6, {_}:
14847 meet ?12 ?13 =?= meet ?13 ?12
14848 [13, 12] by commutativity_of_meet ?12 ?13
14849 13031: Id : 7, {_}:
14850 join ?15 ?16 =?= join ?16 ?15
14851 [16, 15] by commutativity_of_join ?15 ?16
14852 13031: Id : 8, {_}:
14853 join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
14854 [20, 19, 18] by tnl_1 ?18 ?19 ?20
14855 13031: Id : 9, {_}:
14856 meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
14857 [24, 23, 22] by tnl_2 ?22 ?23 ?24
14858 13031: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
14859 13031: Id : 11, {_}:
14860 meet2 ?28 (join ?28 ?29) =>= ?28
14861 [29, 28] by absorption1_2 ?28 ?29
14862 13031: Id : 12, {_}:
14863 join ?31 (meet2 ?31 ?32) =>= ?31
14864 [32, 31] by absorption2_2 ?31 ?32
14865 13031: Id : 13, {_}:
14866 meet2 ?34 ?35 =?= meet2 ?35 ?34
14867 [35, 34] by commutativity_of_meet2 ?34 ?35
14868 13031: Id : 14, {_}:
14869 join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
14870 [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
14871 13031: Id : 15, {_}:
14872 meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
14873 [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
14875 13031: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
14880 13031: meet2 9 2 1 0,3
14881 13031: meet 9 2 1 0,2
14884 % SZS status Timeout for LAT025-1.p
14885 CLASH, statistics insufficient
14887 13057: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14888 13057: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14889 13057: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
14890 13057: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
14891 13057: Id : 6, {_}:
14892 meet ?12 ?13 =?= meet ?13 ?12
14893 [13, 12] by commutativity_of_meet ?12 ?13
14894 13057: Id : 7, {_}:
14895 join ?15 ?16 =?= join ?16 ?15
14896 [16, 15] by commutativity_of_join ?15 ?16
14897 13057: Id : 8, {_}:
14898 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
14899 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
14900 13057: Id : 9, {_}:
14901 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
14902 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
14903 13057: Id : 10, {_}:
14904 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
14905 [27, 26] by compatibility1 ?26 ?27
14906 13057: Id : 11, {_}:
14907 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
14908 [30, 29] by compatibility2 ?29 ?30
14909 13057: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
14910 13057: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
14911 13057: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
14912 13057: Id : 15, {_}:
14913 join ?38 (meet ?39 (join ?38 ?40))
14915 meet (join ?38 ?39) (join ?38 ?40)
14916 [40, 39, 38] by modular_law ?38 ?39 ?40
14918 13057: Id : 1, {_}:
14919 meet a (join b c) =<= join (meet a b) (meet a c)
14920 [] by prove_distributivity
14926 13057: complement 10 1 0
14927 13057: meet 17 2 3 0,2
14928 13057: join 18 2 2 0,2,2
14929 13057: c 2 0 2 2,2,2
14930 13057: b 2 0 2 1,2,2
14932 CLASH, statistics insufficient
14934 13058: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14935 13058: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14936 13058: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
14937 13058: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
14938 13058: Id : 6, {_}:
14939 meet ?12 ?13 =?= meet ?13 ?12
14940 [13, 12] by commutativity_of_meet ?12 ?13
14941 13058: Id : 7, {_}:
14942 join ?15 ?16 =?= join ?16 ?15
14943 [16, 15] by commutativity_of_join ?15 ?16
14944 13058: Id : 8, {_}:
14945 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
14946 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
14947 13058: Id : 9, {_}:
14948 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
14949 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
14950 13058: Id : 10, {_}:
14951 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
14952 [27, 26] by compatibility1 ?26 ?27
14953 13058: Id : 11, {_}:
14954 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
14955 [30, 29] by compatibility2 ?29 ?30
14956 13058: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
14957 13058: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
14958 13058: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
14959 13058: Id : 15, {_}:
14960 join ?38 (meet ?39 (join ?38 ?40))
14962 meet (join ?38 ?39) (join ?38 ?40)
14963 [40, 39, 38] by modular_law ?38 ?39 ?40
14965 13058: Id : 1, {_}:
14966 meet a (join b c) =<= join (meet a b) (meet a c)
14967 [] by prove_distributivity
14973 13058: complement 10 1 0
14974 13058: meet 17 2 3 0,2
14975 13058: join 18 2 2 0,2,2
14976 13058: c 2 0 2 2,2,2
14977 13058: b 2 0 2 1,2,2
14979 CLASH, statistics insufficient
14981 13059: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
14982 13059: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
14983 13059: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
14984 13059: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
14985 13059: Id : 6, {_}:
14986 meet ?12 ?13 =?= meet ?13 ?12
14987 [13, 12] by commutativity_of_meet ?12 ?13
14988 13059: Id : 7, {_}:
14989 join ?15 ?16 =?= join ?16 ?15
14990 [16, 15] by commutativity_of_join ?15 ?16
14991 13059: Id : 8, {_}:
14992 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
14993 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
14994 13059: Id : 9, {_}:
14995 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
14996 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
14997 13059: Id : 10, {_}:
14998 complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
14999 [27, 26] by compatibility1 ?26 ?27
15000 13059: Id : 11, {_}:
15001 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15002 [30, 29] by compatibility2 ?29 ?30
15003 13059: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15004 13059: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15005 13059: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15006 13059: Id : 15, {_}:
15007 join ?38 (meet ?39 (join ?38 ?40))
15009 meet (join ?38 ?39) (join ?38 ?40)
15010 [40, 39, 38] by modular_law ?38 ?39 ?40
15012 13059: Id : 1, {_}:
15013 meet a (join b c) =<= join (meet a b) (meet a c)
15014 [] by prove_distributivity
15020 13059: complement 10 1 0
15021 13059: meet 17 2 3 0,2
15022 13059: join 18 2 2 0,2,2
15023 13059: c 2 0 2 2,2,2
15024 13059: b 2 0 2 1,2,2
15026 % SZS status Timeout for LAT046-1.p
15027 NO CLASH, using fixed ground order
15029 NO CLASH, using fixed ground order
15031 13088: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15032 13088: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15033 13088: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15034 13088: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15035 13088: Id : 6, {_}:
15036 meet ?12 ?13 =?= meet ?13 ?12
15037 [13, 12] by commutativity_of_meet ?12 ?13
15038 13088: Id : 7, {_}:
15039 join ?15 ?16 =?= join ?16 ?15
15040 [16, 15] by commutativity_of_join ?15 ?16
15041 13088: Id : 8, {_}:
15042 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15043 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15044 13088: Id : 9, {_}:
15045 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15046 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15048 13088: Id : 1, {_}:
15049 join a (meet b (join a c)) =>= meet (join a b) (join a c)
15050 [] by prove_modularity
15054 13088: meet 11 2 2 0,2,2
15055 13088: join 13 2 4 0,2
15056 13088: c 2 0 2 2,2,2,2
15057 13088: b 2 0 2 1,2,2
15059 13087: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15060 13087: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15061 13087: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15062 13087: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15063 13087: Id : 6, {_}:
15064 meet ?12 ?13 =?= meet ?13 ?12
15065 [13, 12] by commutativity_of_meet ?12 ?13
15066 13087: Id : 7, {_}:
15067 join ?15 ?16 =?= join ?16 ?15
15068 [16, 15] by commutativity_of_join ?15 ?16
15069 13087: Id : 8, {_}:
15070 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15071 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15072 13087: Id : 9, {_}:
15073 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15074 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15076 13087: Id : 1, {_}:
15077 join a (meet b (join a c)) =>= meet (join a b) (join a c)
15078 [] by prove_modularity
15082 13087: meet 11 2 2 0,2,2
15083 13087: join 13 2 4 0,2
15084 13087: c 2 0 2 2,2,2,2
15085 13087: b 2 0 2 1,2,2
15087 NO CLASH, using fixed ground order
15089 13089: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15090 13089: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15091 13089: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15092 13089: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15093 13089: Id : 6, {_}:
15094 meet ?12 ?13 =?= meet ?13 ?12
15095 [13, 12] by commutativity_of_meet ?12 ?13
15096 13089: Id : 7, {_}:
15097 join ?15 ?16 =?= join ?16 ?15
15098 [16, 15] by commutativity_of_join ?15 ?16
15099 13089: Id : 8, {_}:
15100 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15101 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15102 13089: Id : 9, {_}:
15103 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15104 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15106 13089: Id : 1, {_}:
15107 join a (meet b (join a c)) =>= meet (join a b) (join a c)
15108 [] by prove_modularity
15112 13089: meet 11 2 2 0,2,2
15113 13089: join 13 2 4 0,2
15114 13089: c 2 0 2 2,2,2,2
15115 13089: b 2 0 2 1,2,2
15117 % SZS status Timeout for LAT047-1.p
15118 NO CLASH, using fixed ground order
15120 13105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15121 13105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15122 13105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15123 13105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15124 13105: Id : 6, {_}:
15125 meet ?12 ?13 =?= meet ?13 ?12
15126 [13, 12] by commutativity_of_meet ?12 ?13
15127 13105: Id : 7, {_}:
15128 join ?15 ?16 =?= join ?16 ?15
15129 [16, 15] by commutativity_of_join ?15 ?16
15130 13105: Id : 8, {_}:
15131 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15132 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15133 13105: Id : 9, {_}:
15134 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15135 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15136 13105: Id : 10, {_}:
15137 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15138 [27, 26] by compatibility1 ?26 ?27
15139 13105: Id : 11, {_}:
15140 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15141 [30, 29] by compatibility2 ?29 ?30
15142 13105: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15143 13105: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15144 13105: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15145 13105: Id : 15, {_}:
15146 join (meet (complement ?38) (join ?38 ?39))
15147 (join (complement ?39) (meet ?38 ?39))
15150 [39, 38] by weak_orthomodular_law ?38 ?39
15152 13105: Id : 1, {_}:
15153 join a (meet (complement a) (join a b)) =>= join a b
15154 [] by prove_orthomodular_law
15160 13105: meet 15 2 1 0,2,2
15161 13105: join 18 2 3 0,2
15162 13105: b 2 0 2 2,2,2,2
15163 13105: complement 13 1 1 0,1,2,2
15165 NO CLASH, using fixed ground order
15167 13106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15168 13106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15169 13106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15170 13106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15171 13106: Id : 6, {_}:
15172 meet ?12 ?13 =?= meet ?13 ?12
15173 [13, 12] by commutativity_of_meet ?12 ?13
15174 13106: Id : 7, {_}:
15175 join ?15 ?16 =?= join ?16 ?15
15176 [16, 15] by commutativity_of_join ?15 ?16
15177 13106: Id : 8, {_}:
15178 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15179 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15180 13106: Id : 9, {_}:
15181 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15182 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15183 13106: Id : 10, {_}:
15184 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15185 [27, 26] by compatibility1 ?26 ?27
15186 13106: Id : 11, {_}:
15187 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15188 [30, 29] by compatibility2 ?29 ?30
15189 13106: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15190 13106: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15191 13106: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15192 13106: Id : 15, {_}:
15193 join (meet (complement ?38) (join ?38 ?39))
15194 (join (complement ?39) (meet ?38 ?39))
15197 [39, 38] by weak_orthomodular_law ?38 ?39
15199 13106: Id : 1, {_}:
15200 join a (meet (complement a) (join a b)) =>= join a b
15201 [] by prove_orthomodular_law
15207 13106: meet 15 2 1 0,2,2
15208 13106: join 18 2 3 0,2
15209 13106: b 2 0 2 2,2,2,2
15210 13106: complement 13 1 1 0,1,2,2
15212 NO CLASH, using fixed ground order
15214 13107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15215 13107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15216 13107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15217 13107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15218 13107: Id : 6, {_}:
15219 meet ?12 ?13 =?= meet ?13 ?12
15220 [13, 12] by commutativity_of_meet ?12 ?13
15221 13107: Id : 7, {_}:
15222 join ?15 ?16 =?= join ?16 ?15
15223 [16, 15] by commutativity_of_join ?15 ?16
15224 13107: Id : 8, {_}:
15225 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15226 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15227 13107: Id : 9, {_}:
15228 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15229 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15230 13107: Id : 10, {_}:
15231 complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
15232 [27, 26] by compatibility1 ?26 ?27
15233 13107: Id : 11, {_}:
15234 complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
15235 [30, 29] by compatibility2 ?29 ?30
15236 13107: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15237 13107: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15238 13107: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15239 13107: Id : 15, {_}:
15240 join (meet (complement ?38) (join ?38 ?39))
15241 (join (complement ?39) (meet ?38 ?39))
15244 [39, 38] by weak_orthomodular_law ?38 ?39
15246 13107: Id : 1, {_}:
15247 join a (meet (complement a) (join a b)) =>= join a b
15248 [] by prove_orthomodular_law
15254 13107: meet 15 2 1 0,2,2
15255 13107: join 18 2 3 0,2
15256 13107: b 2 0 2 2,2,2,2
15257 13107: complement 13 1 1 0,1,2,2
15259 % SZS status Timeout for LAT048-1.p
15260 NO CLASH, using fixed ground order
15262 13228: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15263 13228: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15264 13228: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15265 13228: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15266 13228: Id : 6, {_}:
15267 meet ?12 ?13 =?= meet ?13 ?12
15268 [13, 12] by commutativity_of_meet ?12 ?13
15269 13228: Id : 7, {_}:
15270 join ?15 ?16 =?= join ?16 ?15
15271 [16, 15] by commutativity_of_join ?15 ?16
15272 13228: Id : 8, {_}:
15273 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15274 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15275 13228: Id : 9, {_}:
15276 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15277 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15278 13228: Id : 10, {_}:
15279 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15280 [27, 26] by compatibility1 ?26 ?27
15281 13228: Id : 11, {_}:
15282 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15283 [30, 29] by compatibility2 ?29 ?30
15284 13228: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15285 13228: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15286 13228: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15288 13228: Id : 1, {_}:
15289 join (meet (complement a) (join a b))
15290 (join (complement b) (meet a b))
15293 [] by prove_weak_orthomodular_law
15299 13228: meet 14 2 2 0,1,2
15300 13228: join 15 2 3 0,2
15301 13228: b 3 0 3 2,2,1,2
15302 13228: complement 12 1 2 0,1,1,2
15303 13228: a 3 0 3 1,1,1,2
15304 NO CLASH, using fixed ground order
15306 13229: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15307 13229: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15308 13229: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15309 13229: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15310 13229: Id : 6, {_}:
15311 meet ?12 ?13 =?= meet ?13 ?12
15312 [13, 12] by commutativity_of_meet ?12 ?13
15313 13229: Id : 7, {_}:
15314 join ?15 ?16 =?= join ?16 ?15
15315 [16, 15] by commutativity_of_join ?15 ?16
15316 13229: Id : 8, {_}:
15317 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15318 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15319 13229: Id : 9, {_}:
15320 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15321 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15322 13229: Id : 10, {_}:
15323 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15324 [27, 26] by compatibility1 ?26 ?27
15325 13229: Id : 11, {_}:
15326 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15327 [30, 29] by compatibility2 ?29 ?30
15328 13229: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15329 13229: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15330 13229: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15332 13229: Id : 1, {_}:
15333 join (meet (complement a) (join a b))
15334 (join (complement b) (meet a b))
15337 [] by prove_weak_orthomodular_law
15343 13229: meet 14 2 2 0,1,2
15344 13229: join 15 2 3 0,2
15345 13229: b 3 0 3 2,2,1,2
15346 13229: complement 12 1 2 0,1,1,2
15347 13229: a 3 0 3 1,1,1,2
15348 NO CLASH, using fixed ground order
15350 13230: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15351 13230: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15352 13230: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15353 13230: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15354 13230: Id : 6, {_}:
15355 meet ?12 ?13 =?= meet ?13 ?12
15356 [13, 12] by commutativity_of_meet ?12 ?13
15357 13230: Id : 7, {_}:
15358 join ?15 ?16 =?= join ?16 ?15
15359 [16, 15] by commutativity_of_join ?15 ?16
15360 13230: Id : 8, {_}:
15361 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15362 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15363 13230: Id : 9, {_}:
15364 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15365 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15366 13230: Id : 10, {_}:
15367 complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
15368 [27, 26] by compatibility1 ?26 ?27
15369 13230: Id : 11, {_}:
15370 complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
15371 [30, 29] by compatibility2 ?29 ?30
15372 13230: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15373 13230: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15374 13230: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15376 13230: Id : 1, {_}:
15377 join (meet (complement a) (join a b))
15378 (join (complement b) (meet a b))
15381 [] by prove_weak_orthomodular_law
15387 13230: meet 14 2 2 0,1,2
15388 13230: join 15 2 3 0,2
15389 13230: b 3 0 3 2,2,1,2
15390 13230: complement 12 1 2 0,1,1,2
15391 13230: a 3 0 3 1,1,1,2
15392 % SZS status Timeout for LAT049-1.p
15393 CLASH, statistics insufficient
15395 13579: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15396 13579: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15397 13579: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15398 13579: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15399 13579: Id : 6, {_}:
15400 meet ?12 ?13 =?= meet ?13 ?12
15401 [13, 12] by commutativity_of_meet ?12 ?13
15402 13579: Id : 7, {_}:
15403 join ?15 ?16 =?= join ?16 ?15
15404 [16, 15] by commutativity_of_join ?15 ?16
15405 13579: Id : 8, {_}:
15406 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15407 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15408 13579: Id : 9, {_}:
15409 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15410 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15411 13579: Id : 10, {_}:
15412 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15413 [27, 26] by compatibility1 ?26 ?27
15414 13579: Id : 11, {_}:
15415 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15416 [30, 29] by compatibility2 ?29 ?30
15417 13579: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15418 13579: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15419 13579: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15420 13579: Id : 15, {_}:
15421 join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
15422 [39, 38] by orthomodular_law ?38 ?39
15424 13579: Id : 1, {_}:
15425 join a (meet b (join a c)) =>= meet (join a b) (join a c)
15426 [] by prove_modular_law
15432 13579: complement 11 1 0
15433 13579: meet 15 2 2 0,2,2
15434 13579: join 19 2 4 0,2
15435 13579: c 2 0 2 2,2,2,2
15436 13579: b 2 0 2 1,2,2
15438 CLASH, statistics insufficient
15440 13580: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15441 13580: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15442 13580: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15443 13580: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15444 13580: Id : 6, {_}:
15445 meet ?12 ?13 =?= meet ?13 ?12
15446 [13, 12] by commutativity_of_meet ?12 ?13
15447 13580: Id : 7, {_}:
15448 join ?15 ?16 =?= join ?16 ?15
15449 [16, 15] by commutativity_of_join ?15 ?16
15450 13580: Id : 8, {_}:
15451 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15452 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15453 13580: Id : 9, {_}:
15454 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15455 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15456 13580: Id : 10, {_}:
15457 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15458 [27, 26] by compatibility1 ?26 ?27
15459 13580: Id : 11, {_}:
15460 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15461 [30, 29] by compatibility2 ?29 ?30
15462 13580: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15463 13580: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15464 13580: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15465 13580: Id : 15, {_}:
15466 join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
15467 [39, 38] by orthomodular_law ?38 ?39
15469 13580: Id : 1, {_}:
15470 join a (meet b (join a c)) =>= meet (join a b) (join a c)
15471 [] by prove_modular_law
15477 13580: complement 11 1 0
15478 13580: meet 15 2 2 0,2,2
15479 13580: join 19 2 4 0,2
15480 13580: c 2 0 2 2,2,2,2
15481 13580: b 2 0 2 1,2,2
15483 CLASH, statistics insufficient
15485 13582: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15486 13582: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15487 13582: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15488 13582: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15489 13582: Id : 6, {_}:
15490 meet ?12 ?13 =?= meet ?13 ?12
15491 [13, 12] by commutativity_of_meet ?12 ?13
15492 13582: Id : 7, {_}:
15493 join ?15 ?16 =?= join ?16 ?15
15494 [16, 15] by commutativity_of_join ?15 ?16
15495 13582: Id : 8, {_}:
15496 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15497 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15498 13582: Id : 9, {_}:
15499 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15500 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15501 13582: Id : 10, {_}:
15502 complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
15503 [27, 26] by compatibility1 ?26 ?27
15504 13582: Id : 11, {_}:
15505 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15506 [30, 29] by compatibility2 ?29 ?30
15507 13582: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15508 13582: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15509 13582: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15510 13582: Id : 15, {_}:
15511 join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
15512 [39, 38] by orthomodular_law ?38 ?39
15514 13582: Id : 1, {_}:
15515 join a (meet b (join a c)) =>= meet (join a b) (join a c)
15516 [] by prove_modular_law
15522 13582: complement 11 1 0
15523 13582: meet 15 2 2 0,2,2
15524 13582: join 19 2 4 0,2
15525 13582: c 2 0 2 2,2,2,2
15526 13582: b 2 0 2 1,2,2
15528 % SZS status Timeout for LAT050-1.p
15529 CLASH, statistics insufficient
15531 13811: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15532 13811: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15533 13811: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15534 13811: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15535 13811: Id : 6, {_}:
15536 meet ?12 ?13 =?= meet ?13 ?12
15537 [13, 12] by commutativity_of_meet ?12 ?13
15538 13811: Id : 7, {_}:
15539 join ?15 ?16 =?= join ?16 ?15
15540 [16, 15] by commutativity_of_join ?15 ?16
15541 13811: Id : 8, {_}:
15542 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15543 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15544 13811: Id : 9, {_}:
15545 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15546 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15547 13811: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
15548 13811: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
15549 13811: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
15551 13811: Id : 1, {_}:
15552 complement (join a b) =<= meet (complement a) (complement b)
15553 [] by prove_compatibility_law
15559 13811: meet 11 2 1 0,3
15560 13811: complement 7 1 3 0,2
15561 13811: join 11 2 1 0,1,2
15562 13811: b 2 0 2 2,1,2
15563 13811: a 2 0 2 1,1,2
15564 CLASH, statistics insufficient
15566 13812: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15567 13812: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15568 13812: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15569 13812: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15570 13812: Id : 6, {_}:
15571 meet ?12 ?13 =?= meet ?13 ?12
15572 [13, 12] by commutativity_of_meet ?12 ?13
15573 13812: Id : 7, {_}:
15574 join ?15 ?16 =?= join ?16 ?15
15575 [16, 15] by commutativity_of_join ?15 ?16
15576 13812: Id : 8, {_}:
15577 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15578 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15579 13812: Id : 9, {_}:
15580 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15581 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15582 13812: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
15583 13812: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
15584 13812: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
15586 13812: Id : 1, {_}:
15587 complement (join a b) =<= meet (complement a) (complement b)
15588 [] by prove_compatibility_law
15594 13812: meet 11 2 1 0,3
15595 13812: complement 7 1 3 0,2
15596 13812: join 11 2 1 0,1,2
15597 13812: b 2 0 2 2,1,2
15598 13812: a 2 0 2 1,1,2
15599 CLASH, statistics insufficient
15601 13813: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15602 13813: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15603 13813: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15604 13813: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15605 13813: Id : 6, {_}:
15606 meet ?12 ?13 =?= meet ?13 ?12
15607 [13, 12] by commutativity_of_meet ?12 ?13
15608 13813: Id : 7, {_}:
15609 join ?15 ?16 =?= join ?16 ?15
15610 [16, 15] by commutativity_of_join ?15 ?16
15611 13813: Id : 8, {_}:
15612 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15613 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15614 13813: Id : 9, {_}:
15615 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15616 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15617 13813: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
15618 13813: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
15619 13813: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
15621 13813: Id : 1, {_}:
15622 complement (join a b) =>= meet (complement a) (complement b)
15623 [] by prove_compatibility_law
15629 13813: meet 11 2 1 0,3
15630 13813: complement 7 1 3 0,2
15631 13813: join 11 2 1 0,1,2
15632 13813: b 2 0 2 2,1,2
15633 13813: a 2 0 2 1,1,2
15634 % SZS status Timeout for LAT051-1.p
15635 CLASH, statistics insufficient
15637 13839: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15638 13839: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15639 13839: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15640 13839: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15641 13839: Id : 6, {_}:
15642 meet ?12 ?13 =?= meet ?13 ?12
15643 [13, 12] by commutativity_of_meet ?12 ?13
15644 13839: Id : 7, {_}:
15645 join ?15 ?16 =?= join ?16 ?15
15646 [16, 15] by commutativity_of_join ?15 ?16
15647 13839: Id : 8, {_}:
15648 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15649 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15650 13839: Id : 9, {_}:
15651 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15652 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15653 13839: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
15654 13839: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
15655 13839: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
15656 13839: Id : 13, {_}:
15657 join ?32 (meet ?33 (join ?32 ?34))
15659 meet (join ?32 ?33) (join ?32 ?34)
15660 [34, 33, 32] by modular_law ?32 ?33 ?34
15662 13839: Id : 1, {_}:
15663 complement (join a b) =<= meet (complement a) (complement b)
15664 [] by prove_compatibility_law
15670 13839: meet 13 2 1 0,3
15671 13839: complement 7 1 3 0,2
15672 13839: join 15 2 1 0,1,2
15673 13839: b 2 0 2 2,1,2
15674 13839: a 2 0 2 1,1,2
15675 CLASH, statistics insufficient
15677 13840: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15678 13840: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15679 13840: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15680 13840: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15681 13840: Id : 6, {_}:
15682 meet ?12 ?13 =?= meet ?13 ?12
15683 [13, 12] by commutativity_of_meet ?12 ?13
15684 13840: Id : 7, {_}:
15685 join ?15 ?16 =?= join ?16 ?15
15686 [16, 15] by commutativity_of_join ?15 ?16
15687 13840: Id : 8, {_}:
15688 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15689 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15690 13840: Id : 9, {_}:
15691 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15692 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15693 13840: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
15694 13840: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
15695 13840: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
15696 13840: Id : 13, {_}:
15697 join ?32 (meet ?33 (join ?32 ?34))
15699 meet (join ?32 ?33) (join ?32 ?34)
15700 [34, 33, 32] by modular_law ?32 ?33 ?34
15702 13840: Id : 1, {_}:
15703 complement (join a b) =<= meet (complement a) (complement b)
15704 [] by prove_compatibility_law
15710 13840: meet 13 2 1 0,3
15711 13840: complement 7 1 3 0,2
15712 13840: join 15 2 1 0,1,2
15713 13840: b 2 0 2 2,1,2
15714 13840: a 2 0 2 1,1,2
15715 CLASH, statistics insufficient
15717 13841: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15718 13841: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15719 13841: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15720 13841: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15721 13841: Id : 6, {_}:
15722 meet ?12 ?13 =?= meet ?13 ?12
15723 [13, 12] by commutativity_of_meet ?12 ?13
15724 13841: Id : 7, {_}:
15725 join ?15 ?16 =?= join ?16 ?15
15726 [16, 15] by commutativity_of_join ?15 ?16
15727 13841: Id : 8, {_}:
15728 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15729 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15730 13841: Id : 9, {_}:
15731 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15732 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15733 13841: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
15734 13841: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
15735 13841: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
15736 13841: Id : 13, {_}:
15737 join ?32 (meet ?33 (join ?32 ?34))
15739 meet (join ?32 ?33) (join ?32 ?34)
15740 [34, 33, 32] by modular_law ?32 ?33 ?34
15742 13841: Id : 1, {_}:
15743 complement (join a b) =>= meet (complement a) (complement b)
15744 [] by prove_compatibility_law
15750 13841: meet 13 2 1 0,3
15751 13841: complement 7 1 3 0,2
15752 13841: join 15 2 1 0,1,2
15753 13841: b 2 0 2 2,1,2
15754 13841: a 2 0 2 1,1,2
15755 % SZS status Timeout for LAT052-1.p
15756 CLASH, statistics insufficient
15758 13871: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15759 13871: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15760 13871: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15761 13871: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15762 13871: Id : 6, {_}:
15763 meet ?12 ?13 =?= meet ?13 ?12
15764 [13, 12] by commutativity_of_meet ?12 ?13
15765 13871: Id : 7, {_}:
15766 join ?15 ?16 =?= join ?16 ?15
15767 [16, 15] by commutativity_of_join ?15 ?16
15768 13871: Id : 8, {_}:
15769 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15770 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15771 13871: Id : 9, {_}:
15772 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15773 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15774 13871: Id : 10, {_}:
15775 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15776 [27, 26] by compatibility1 ?26 ?27
15777 13871: Id : 11, {_}:
15778 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15779 [30, 29] by compatibility2 ?29 ?30
15780 13871: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15781 13871: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15782 13871: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15784 13871: Id : 1, {_}:
15786 (meet (complement b)
15787 (join (complement a)
15788 (meet (complement b)
15789 (join a (meet (complement b) (complement a))))))
15792 (meet (complement b)
15793 (join (complement a)
15794 (meet (complement b)
15796 (meet (complement b)
15797 (join (complement a) (meet (complement b) a)))))))
15804 13871: join 19 2 7 0,2
15805 13871: meet 19 2 7 0,2,2
15806 13871: complement 21 1 11 0,1,2,2
15807 13871: b 7 0 7 1,1,2,2
15809 CLASH, statistics insufficient
15811 13872: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15812 13872: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15813 13872: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15814 13872: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15815 13872: Id : 6, {_}:
15816 meet ?12 ?13 =?= meet ?13 ?12
15817 [13, 12] by commutativity_of_meet ?12 ?13
15818 13872: Id : 7, {_}:
15819 join ?15 ?16 =?= join ?16 ?15
15820 [16, 15] by commutativity_of_join ?15 ?16
15821 13872: Id : 8, {_}:
15822 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15823 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15824 13872: Id : 9, {_}:
15825 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15826 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15827 13872: Id : 10, {_}:
15828 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
15829 [27, 26] by compatibility1 ?26 ?27
15830 13872: Id : 11, {_}:
15831 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
15832 [30, 29] by compatibility2 ?29 ?30
15833 13872: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15834 13872: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15835 13872: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15837 13872: Id : 1, {_}:
15839 (meet (complement b)
15840 (join (complement a)
15841 (meet (complement b)
15842 (join a (meet (complement b) (complement a))))))
15845 (meet (complement b)
15846 (join (complement a)
15847 (meet (complement b)
15849 (meet (complement b)
15850 (join (complement a) (meet (complement b) a)))))))
15857 13872: join 19 2 7 0,2
15858 13872: meet 19 2 7 0,2,2
15859 13872: complement 21 1 11 0,1,2,2
15860 13872: b 7 0 7 1,1,2,2
15862 CLASH, statistics insufficient
15864 13873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15865 13873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15866 13873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15867 13873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15868 13873: Id : 6, {_}:
15869 meet ?12 ?13 =?= meet ?13 ?12
15870 [13, 12] by commutativity_of_meet ?12 ?13
15871 13873: Id : 7, {_}:
15872 join ?15 ?16 =?= join ?16 ?15
15873 [16, 15] by commutativity_of_join ?15 ?16
15874 13873: Id : 8, {_}:
15875 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15876 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15877 13873: Id : 9, {_}:
15878 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15879 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15880 13873: Id : 10, {_}:
15881 complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
15882 [27, 26] by compatibility1 ?26 ?27
15883 13873: Id : 11, {_}:
15884 complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
15885 [30, 29] by compatibility2 ?29 ?30
15886 13873: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
15887 13873: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
15888 13873: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
15890 13873: Id : 1, {_}:
15892 (meet (complement b)
15893 (join (complement a)
15894 (meet (complement b)
15895 (join a (meet (complement b) (complement a))))))
15898 (meet (complement b)
15899 (join (complement a)
15900 (meet (complement b)
15902 (meet (complement b)
15903 (join (complement a) (meet (complement b) a)))))))
15910 13873: join 19 2 7 0,2
15911 13873: meet 19 2 7 0,2,2
15912 13873: complement 21 1 11 0,1,2,2
15913 13873: b 7 0 7 1,1,2,2
15915 % SZS status Timeout for LAT054-1.p
15916 CLASH, statistics insufficient
15918 13890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15919 13890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15920 13890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15921 13890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15922 13890: Id : 6, {_}:
15923 meet ?12 ?13 =?= meet ?13 ?12
15924 [13, 12] by commutativity_of_meet ?12 ?13
15925 13890: Id : 7, {_}:
15926 join ?15 ?16 =?= join ?16 ?15
15927 [16, 15] by commutativity_of_join ?15 ?16
15928 13890: Id : 8, {_}:
15929 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
15930 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15931 13890: Id : 9, {_}:
15932 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
15933 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15934 13890: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
15935 13890: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
15936 13890: Id : 12, {_}:
15937 meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
15938 [31, 30] by compatibility ?30 ?31
15940 13890: Id : 1, {_}:
15941 meet (join a (complement b))
15942 (join (join (meet a b) (meet (complement a) b))
15943 (meet (complement a) (complement b)))
15945 join (meet a b) (meet (complement a) (complement b))
15952 13890: meet 17 2 6 0,2
15953 13890: join 15 2 4 0,1,2
15954 13890: complement 11 1 6 0,2,1,2
15955 13890: b 6 0 6 1,2,1,2
15956 13890: a 6 0 6 1,1,2
15957 CLASH, statistics insufficient
15959 13891: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
15960 13891: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
15961 13891: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
15962 13891: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
15963 13891: Id : 6, {_}:
15964 meet ?12 ?13 =?= meet ?13 ?12
15965 [13, 12] by commutativity_of_meet ?12 ?13
15966 13891: Id : 7, {_}:
15967 join ?15 ?16 =?= join ?16 ?15
15968 [16, 15] by commutativity_of_join ?15 ?16
15969 13891: Id : 8, {_}:
15970 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
15971 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
15972 13891: Id : 9, {_}:
15973 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
15974 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
15975 13891: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
15976 13891: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
15977 13891: Id : 12, {_}:
15978 meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
15979 [31, 30] by compatibility ?30 ?31
15981 13891: Id : 1, {_}:
15982 meet (join a (complement b))
15983 (join (join (meet a b) (meet (complement a) b))
15984 (meet (complement a) (complement b)))
15986 join (meet a b) (meet (complement a) (complement b))
15993 13891: meet 17 2 6 0,2
15994 13891: join 15 2 4 0,1,2
15995 13891: complement 11 1 6 0,2,1,2
15996 13891: b 6 0 6 1,2,1,2
15997 13891: a 6 0 6 1,1,2
15998 CLASH, statistics insufficient
16000 13892: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16001 13892: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16002 13892: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16003 13892: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16004 13892: Id : 6, {_}:
16005 meet ?12 ?13 =?= meet ?13 ?12
16006 [13, 12] by commutativity_of_meet ?12 ?13
16007 13892: Id : 7, {_}:
16008 join ?15 ?16 =?= join ?16 ?15
16009 [16, 15] by commutativity_of_join ?15 ?16
16010 13892: Id : 8, {_}:
16011 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16012 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16013 13892: Id : 9, {_}:
16014 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16015 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16016 13892: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
16017 13892: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
16018 13892: Id : 12, {_}:
16019 meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
16020 [31, 30] by compatibility ?30 ?31
16022 13892: Id : 1, {_}:
16023 meet (join a (complement b))
16024 (join (join (meet a b) (meet (complement a) b))
16025 (meet (complement a) (complement b)))
16027 join (meet a b) (meet (complement a) (complement b))
16034 13892: meet 17 2 6 0,2
16035 13892: join 15 2 4 0,1,2
16036 13892: complement 11 1 6 0,2,1,2
16037 13892: b 6 0 6 1,2,1,2
16038 13892: a 6 0 6 1,1,2
16039 % SZS status Timeout for LAT062-1.p
16040 CLASH, statistics insufficient
16042 13921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16043 13921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16044 13921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16045 13921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16046 13921: Id : 6, {_}:
16047 meet ?12 ?13 =?= meet ?13 ?12
16048 [13, 12] by commutativity_of_meet ?12 ?13
16049 13921: Id : 7, {_}:
16050 join ?15 ?16 =?= join ?16 ?15
16051 [16, 15] by commutativity_of_join ?15 ?16
16052 13921: Id : 8, {_}:
16053 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16054 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16055 13921: Id : 9, {_}:
16056 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16057 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16058 13921: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
16059 13921: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
16060 13921: Id : 12, {_}:
16061 meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
16062 [31, 30] by compatibility ?30 ?31
16064 CLASH, statistics insufficient
16065 CLASH, statistics insufficient
16066 13921: Id : 1, {_}:
16067 meet a (join b (meet a (join (complement a) (meet a b))))
16069 meet a (join (complement a) (meet a b))
16076 13921: join 14 2 3 0,2,2
16077 13921: meet 16 2 5 0,2
16078 13921: complement 7 1 2 0,1,2,2,2,2
16079 13921: b 3 0 3 1,2,2
16082 13923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16083 13923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16084 13923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16085 13923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16086 13923: Id : 6, {_}:
16087 meet ?12 ?13 =?= meet ?13 ?12
16088 [13, 12] by commutativity_of_meet ?12 ?13
16089 13923: Id : 7, {_}:
16090 join ?15 ?16 =?= join ?16 ?15
16091 [16, 15] by commutativity_of_join ?15 ?16
16092 13923: Id : 8, {_}:
16093 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16094 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16095 13923: Id : 9, {_}:
16096 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16097 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16098 13923: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
16099 13923: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
16100 13923: Id : 12, {_}:
16101 meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
16102 [31, 30] by compatibility ?30 ?31
16104 13923: Id : 1, {_}:
16105 meet a (join b (meet a (join (complement a) (meet a b))))
16107 meet a (join (complement a) (meet a b))
16114 13923: join 14 2 3 0,2,2
16115 13923: meet 16 2 5 0,2
16116 13923: complement 7 1 2 0,1,2,2,2,2
16117 13923: b 3 0 3 1,2,2
16120 13922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16121 13922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16122 13922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16123 13922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16124 13922: Id : 6, {_}:
16125 meet ?12 ?13 =?= meet ?13 ?12
16126 [13, 12] by commutativity_of_meet ?12 ?13
16127 13922: Id : 7, {_}:
16128 join ?15 ?16 =?= join ?16 ?15
16129 [16, 15] by commutativity_of_join ?15 ?16
16130 13922: Id : 8, {_}:
16131 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16132 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16133 13922: Id : 9, {_}:
16134 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16135 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16136 13922: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
16137 13922: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
16138 13922: Id : 12, {_}:
16139 meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
16140 [31, 30] by compatibility ?30 ?31
16142 13922: Id : 1, {_}:
16143 meet a (join b (meet a (join (complement a) (meet a b))))
16145 meet a (join (complement a) (meet a b))
16152 13922: join 14 2 3 0,2,2
16153 13922: meet 16 2 5 0,2
16154 13922: complement 7 1 2 0,1,2,2,2,2
16155 13922: b 3 0 3 1,2,2
16157 % SZS status Timeout for LAT063-1.p
16158 NO CLASH, using fixed ground order
16160 13955: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16161 13955: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16162 13955: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16163 13955: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16164 13955: Id : 6, {_}:
16165 meet ?12 ?13 =?= meet ?13 ?12
16166 [13, 12] by commutativity_of_meet ?12 ?13
16167 13955: Id : 7, {_}:
16168 join ?15 ?16 =?= join ?16 ?15
16169 [16, 15] by commutativity_of_join ?15 ?16
16170 13955: Id : 8, {_}:
16171 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16172 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16173 13955: Id : 9, {_}:
16174 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16175 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16176 13955: Id : 10, {_}:
16177 meet ?26 (join ?27 (meet ?26 ?28))
16181 (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
16182 [28, 27, 26] by equation_H2 ?26 ?27 ?28
16184 13955: Id : 1, {_}:
16185 meet a (join b (meet a c))
16187 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
16192 13955: join 17 2 4 0,2,2
16193 13955: meet 21 2 6 0,2
16194 13955: c 3 0 3 2,2,2,2
16195 13955: b 4 0 4 1,2,2
16197 NO CLASH, using fixed ground order
16199 13956: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16200 13956: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16201 13956: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16202 13956: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16203 13956: Id : 6, {_}:
16204 meet ?12 ?13 =?= meet ?13 ?12
16205 [13, 12] by commutativity_of_meet ?12 ?13
16206 13956: Id : 7, {_}:
16207 join ?15 ?16 =?= join ?16 ?15
16208 [16, 15] by commutativity_of_join ?15 ?16
16209 13956: Id : 8, {_}:
16210 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16211 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16212 13956: Id : 9, {_}:
16213 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16214 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16215 13956: Id : 10, {_}:
16216 meet ?26 (join ?27 (meet ?26 ?28))
16220 (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
16221 [28, 27, 26] by equation_H2 ?26 ?27 ?28
16223 13956: Id : 1, {_}:
16224 meet a (join b (meet a c))
16226 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
16231 13956: join 17 2 4 0,2,2
16232 13956: meet 21 2 6 0,2
16233 13956: c 3 0 3 2,2,2,2
16234 13956: b 4 0 4 1,2,2
16236 NO CLASH, using fixed ground order
16238 13957: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16239 13957: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16240 13957: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16241 13957: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16242 13957: Id : 6, {_}:
16243 meet ?12 ?13 =?= meet ?13 ?12
16244 [13, 12] by commutativity_of_meet ?12 ?13
16245 13957: Id : 7, {_}:
16246 join ?15 ?16 =?= join ?16 ?15
16247 [16, 15] by commutativity_of_join ?15 ?16
16248 13957: Id : 8, {_}:
16249 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16250 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16251 13957: Id : 9, {_}:
16252 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16253 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16254 13957: Id : 10, {_}:
16255 meet ?26 (join ?27 (meet ?26 ?28))
16259 (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
16260 [28, 27, 26] by equation_H2 ?26 ?27 ?28
16262 13957: Id : 1, {_}:
16263 meet a (join b (meet a c))
16265 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
16270 13957: join 17 2 4 0,2,2
16271 13957: meet 21 2 6 0,2
16272 13957: c 3 0 3 2,2,2,2
16273 13957: b 4 0 4 1,2,2
16275 % SZS status Timeout for LAT098-1.p
16276 NO CLASH, using fixed ground order
16278 13999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16279 13999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16280 13999: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16281 13999: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16282 13999: Id : 6, {_}:
16283 meet ?12 ?13 =?= meet ?13 ?12
16284 [13, 12] by commutativity_of_meet ?12 ?13
16285 13999: Id : 7, {_}:
16286 join ?15 ?16 =?= join ?16 ?15
16287 [16, 15] by commutativity_of_join ?15 ?16
16288 13999: Id : 8, {_}:
16289 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16290 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16291 13999: Id : 9, {_}:
16292 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16293 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16294 13999: Id : 10, {_}:
16295 meet ?26 (join ?27 (meet ?26 ?28))
16298 (join (meet ?26 (join ?27 (meet ?26 ?28)))
16299 (meet ?28 (join ?26 ?27)))
16300 [28, 27, 26] by equation_H6 ?26 ?27 ?28
16302 13999: Id : 1, {_}:
16303 meet a (join b (meet a (join c d)))
16305 meet a (join b (meet (join a (meet b d)) (join c d)))
16310 13999: meet 20 2 5 0,2
16311 13999: join 18 2 5 0,2,2
16312 13999: d 3 0 3 2,2,2,2,2
16313 13999: c 2 0 2 1,2,2,2,2
16314 13999: b 3 0 3 1,2,2
16316 NO CLASH, using fixed ground order
16318 14000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16319 14000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16320 14000: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16321 14000: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16322 14000: Id : 6, {_}:
16323 meet ?12 ?13 =?= meet ?13 ?12
16324 [13, 12] by commutativity_of_meet ?12 ?13
16325 14000: Id : 7, {_}:
16326 join ?15 ?16 =?= join ?16 ?15
16327 [16, 15] by commutativity_of_join ?15 ?16
16328 14000: Id : 8, {_}:
16329 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16330 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16331 14000: Id : 9, {_}:
16332 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16333 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16334 14000: Id : 10, {_}:
16335 meet ?26 (join ?27 (meet ?26 ?28))
16338 (join (meet ?26 (join ?27 (meet ?26 ?28)))
16339 (meet ?28 (join ?26 ?27)))
16340 [28, 27, 26] by equation_H6 ?26 ?27 ?28
16342 14000: Id : 1, {_}:
16343 meet a (join b (meet a (join c d)))
16345 meet a (join b (meet (join a (meet b d)) (join c d)))
16350 14000: meet 20 2 5 0,2
16351 14000: join 18 2 5 0,2,2
16352 14000: d 3 0 3 2,2,2,2,2
16353 14000: c 2 0 2 1,2,2,2,2
16354 14000: b 3 0 3 1,2,2
16356 NO CLASH, using fixed ground order
16358 14001: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16359 14001: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16360 14001: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16361 14001: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16362 14001: Id : 6, {_}:
16363 meet ?12 ?13 =?= meet ?13 ?12
16364 [13, 12] by commutativity_of_meet ?12 ?13
16365 14001: Id : 7, {_}:
16366 join ?15 ?16 =?= join ?16 ?15
16367 [16, 15] by commutativity_of_join ?15 ?16
16368 14001: Id : 8, {_}:
16369 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16370 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16371 14001: Id : 9, {_}:
16372 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16373 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16374 14001: Id : 10, {_}:
16375 meet ?26 (join ?27 (meet ?26 ?28))
16378 (join (meet ?26 (join ?27 (meet ?26 ?28)))
16379 (meet ?28 (join ?26 ?27)))
16380 [28, 27, 26] by equation_H6 ?26 ?27 ?28
16382 14001: Id : 1, {_}:
16383 meet a (join b (meet a (join c d)))
16385 meet a (join b (meet (join a (meet b d)) (join c d)))
16390 14001: meet 20 2 5 0,2
16391 14001: join 18 2 5 0,2,2
16392 14001: d 3 0 3 2,2,2,2,2
16393 14001: c 2 0 2 1,2,2,2,2
16394 14001: b 3 0 3 1,2,2
16396 % SZS status Timeout for LAT100-1.p
16397 NO CLASH, using fixed ground order
16399 14017: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16400 14017: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16401 14017: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16402 14017: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16403 14017: Id : 6, {_}:
16404 meet ?12 ?13 =?= meet ?13 ?12
16405 [13, 12] by commutativity_of_meet ?12 ?13
16406 14017: Id : 7, {_}:
16407 join ?15 ?16 =?= join ?16 ?15
16408 [16, 15] by commutativity_of_join ?15 ?16
16409 14017: Id : 8, {_}:
16410 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16411 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16412 14017: Id : 9, {_}:
16413 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16414 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16415 14017: Id : 10, {_}:
16416 meet ?26 (join ?27 (meet ?26 ?28))
16419 (join (meet ?26 (join ?27 (meet ?26 ?28)))
16420 (meet ?28 (join ?26 ?27)))
16421 [28, 27, 26] by equation_H6 ?26 ?27 ?28
16423 14017: Id : 1, {_}:
16424 meet a (join b (meet a c))
16426 meet a (join b (meet c (join a (meet b c))))
16431 14017: join 16 2 3 0,2,2
16432 14017: meet 20 2 5 0,2
16433 14017: c 3 0 3 2,2,2,2
16434 14017: b 3 0 3 1,2,2
16436 NO CLASH, using fixed ground order
16438 14018: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16439 14018: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16440 14018: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16441 14018: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16442 14018: Id : 6, {_}:
16443 meet ?12 ?13 =?= meet ?13 ?12
16444 [13, 12] by commutativity_of_meet ?12 ?13
16445 14018: Id : 7, {_}:
16446 join ?15 ?16 =?= join ?16 ?15
16447 [16, 15] by commutativity_of_join ?15 ?16
16448 14018: Id : 8, {_}:
16449 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16450 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16451 14018: Id : 9, {_}:
16452 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16453 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16454 14018: Id : 10, {_}:
16455 meet ?26 (join ?27 (meet ?26 ?28))
16458 (join (meet ?26 (join ?27 (meet ?26 ?28)))
16459 (meet ?28 (join ?26 ?27)))
16460 [28, 27, 26] by equation_H6 ?26 ?27 ?28
16462 14018: Id : 1, {_}:
16463 meet a (join b (meet a c))
16465 meet a (join b (meet c (join a (meet b c))))
16470 14018: join 16 2 3 0,2,2
16471 14018: meet 20 2 5 0,2
16472 14018: c 3 0 3 2,2,2,2
16473 14018: b 3 0 3 1,2,2
16475 NO CLASH, using fixed ground order
16477 14019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16478 14019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16479 14019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16480 14019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16481 14019: Id : 6, {_}:
16482 meet ?12 ?13 =?= meet ?13 ?12
16483 [13, 12] by commutativity_of_meet ?12 ?13
16484 14019: Id : 7, {_}:
16485 join ?15 ?16 =?= join ?16 ?15
16486 [16, 15] by commutativity_of_join ?15 ?16
16487 14019: Id : 8, {_}:
16488 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16489 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16490 14019: Id : 9, {_}:
16491 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16492 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16493 14019: Id : 10, {_}:
16494 meet ?26 (join ?27 (meet ?26 ?28))
16497 (join (meet ?26 (join ?27 (meet ?26 ?28)))
16498 (meet ?28 (join ?26 ?27)))
16499 [28, 27, 26] by equation_H6 ?26 ?27 ?28
16501 14019: Id : 1, {_}:
16502 meet a (join b (meet a c))
16504 meet a (join b (meet c (join a (meet b c))))
16509 14019: join 16 2 3 0,2,2
16510 14019: meet 20 2 5 0,2
16511 14019: c 3 0 3 2,2,2,2
16512 14019: b 3 0 3 1,2,2
16514 % SZS status Timeout for LAT101-1.p
16515 NO CLASH, using fixed ground order
16517 14050: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16518 14050: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16519 14050: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16520 14050: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16521 14050: Id : 6, {_}:
16522 meet ?12 ?13 =?= meet ?13 ?12
16523 [13, 12] by commutativity_of_meet ?12 ?13
16524 14050: Id : 7, {_}:
16525 join ?15 ?16 =?= join ?16 ?15
16526 [16, 15] by commutativity_of_join ?15 ?16
16527 14050: Id : 8, {_}:
16528 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16529 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16530 14050: Id : 9, {_}:
16531 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16532 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16533 14050: Id : 10, {_}:
16534 meet ?26 (join ?27 (meet ?26 ?28))
16538 (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
16539 [28, 27, 26] by equation_H7 ?26 ?27 ?28
16541 14050: Id : 1, {_}:
16542 meet a (join b (meet a (join c d)))
16544 meet a (join b (meet (join a (meet b d)) (join c d)))
16549 14050: meet 20 2 5 0,2
16550 14050: join 18 2 5 0,2,2
16551 14050: d 3 0 3 2,2,2,2,2
16552 14050: c 2 0 2 1,2,2,2,2
16553 14050: b 3 0 3 1,2,2
16555 NO CLASH, using fixed ground order
16557 14051: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16558 14051: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16559 14051: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16560 14051: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16561 14051: Id : 6, {_}:
16562 meet ?12 ?13 =?= meet ?13 ?12
16563 [13, 12] by commutativity_of_meet ?12 ?13
16564 14051: Id : 7, {_}:
16565 join ?15 ?16 =?= join ?16 ?15
16566 [16, 15] by commutativity_of_join ?15 ?16
16567 14051: Id : 8, {_}:
16568 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16569 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16570 14051: Id : 9, {_}:
16571 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16572 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16573 14051: Id : 10, {_}:
16574 meet ?26 (join ?27 (meet ?26 ?28))
16578 (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
16579 [28, 27, 26] by equation_H7 ?26 ?27 ?28
16581 14051: Id : 1, {_}:
16582 meet a (join b (meet a (join c d)))
16584 meet a (join b (meet (join a (meet b d)) (join c d)))
16589 14051: meet 20 2 5 0,2
16590 14051: join 18 2 5 0,2,2
16591 14051: d 3 0 3 2,2,2,2,2
16592 14051: c 2 0 2 1,2,2,2,2
16593 14051: b 3 0 3 1,2,2
16595 NO CLASH, using fixed ground order
16597 14052: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16598 14052: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16599 14052: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16600 14052: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16601 14052: Id : 6, {_}:
16602 meet ?12 ?13 =?= meet ?13 ?12
16603 [13, 12] by commutativity_of_meet ?12 ?13
16604 14052: Id : 7, {_}:
16605 join ?15 ?16 =?= join ?16 ?15
16606 [16, 15] by commutativity_of_join ?15 ?16
16607 14052: Id : 8, {_}:
16608 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16609 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16610 14052: Id : 9, {_}:
16611 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16612 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16613 14052: Id : 10, {_}:
16614 meet ?26 (join ?27 (meet ?26 ?28))
16618 (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
16619 [28, 27, 26] by equation_H7 ?26 ?27 ?28
16621 14052: Id : 1, {_}:
16622 meet a (join b (meet a (join c d)))
16624 meet a (join b (meet (join a (meet b d)) (join c d)))
16629 14052: meet 20 2 5 0,2
16630 14052: join 18 2 5 0,2,2
16631 14052: d 3 0 3 2,2,2,2,2
16632 14052: c 2 0 2 1,2,2,2,2
16633 14052: b 3 0 3 1,2,2
16635 % SZS status Timeout for LAT102-1.p
16636 NO CLASH, using fixed ground order
16638 14140: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16639 14140: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16640 14140: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16641 14140: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16642 14140: Id : 6, {_}:
16643 meet ?12 ?13 =?= meet ?13 ?12
16644 [13, 12] by commutativity_of_meet ?12 ?13
16645 14140: Id : 7, {_}:
16646 join ?15 ?16 =?= join ?16 ?15
16647 [16, 15] by commutativity_of_join ?15 ?16
16648 14140: Id : 8, {_}:
16649 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16650 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16651 14140: Id : 9, {_}:
16652 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16653 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16654 14140: Id : 10, {_}:
16655 meet ?26 (join ?27 (meet ?26 ?28))
16657 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
16658 [28, 27, 26] by equation_H10 ?26 ?27 ?28
16660 14140: Id : 1, {_}:
16661 meet a (join b (meet a c))
16663 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
16668 14140: join 16 2 4 0,2,2
16669 14140: meet 20 2 6 0,2
16670 14140: c 3 0 3 2,2,2,2
16671 14140: b 3 0 3 1,2,2
16673 NO CLASH, using fixed ground order
16675 14141: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16676 14141: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16677 14141: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16678 14141: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16679 14141: Id : 6, {_}:
16680 meet ?12 ?13 =?= meet ?13 ?12
16681 [13, 12] by commutativity_of_meet ?12 ?13
16682 14141: Id : 7, {_}:
16683 join ?15 ?16 =?= join ?16 ?15
16684 [16, 15] by commutativity_of_join ?15 ?16
16685 14141: Id : 8, {_}:
16686 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16687 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16688 14141: Id : 9, {_}:
16689 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16690 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16691 14141: Id : 10, {_}:
16692 meet ?26 (join ?27 (meet ?26 ?28))
16694 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
16695 [28, 27, 26] by equation_H10 ?26 ?27 ?28
16697 14141: Id : 1, {_}:
16698 meet a (join b (meet a c))
16700 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
16705 14141: join 16 2 4 0,2,2
16706 14141: meet 20 2 6 0,2
16707 14141: c 3 0 3 2,2,2,2
16708 14141: b 3 0 3 1,2,2
16710 NO CLASH, using fixed ground order
16712 14142: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16713 14142: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16714 14142: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16715 14142: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16716 14142: Id : 6, {_}:
16717 meet ?12 ?13 =?= meet ?13 ?12
16718 [13, 12] by commutativity_of_meet ?12 ?13
16719 14142: Id : 7, {_}:
16720 join ?15 ?16 =?= join ?16 ?15
16721 [16, 15] by commutativity_of_join ?15 ?16
16722 14142: Id : 8, {_}:
16723 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16724 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16725 14142: Id : 9, {_}:
16726 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16727 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16728 14142: Id : 10, {_}:
16729 meet ?26 (join ?27 (meet ?26 ?28))
16731 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
16732 [28, 27, 26] by equation_H10 ?26 ?27 ?28
16734 14142: Id : 1, {_}:
16735 meet a (join b (meet a c))
16737 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
16742 14142: join 16 2 4 0,2,2
16743 14142: meet 20 2 6 0,2
16744 14142: c 3 0 3 2,2,2,2
16745 14142: b 3 0 3 1,2,2
16747 % SZS status Timeout for LAT103-1.p
16748 NO CLASH, using fixed ground order
16750 14175: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16751 14175: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16752 14175: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16753 14175: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16754 14175: Id : 6, {_}:
16755 meet ?12 ?13 =?= meet ?13 ?12
16756 [13, 12] by commutativity_of_meet ?12 ?13
16757 14175: Id : 7, {_}:
16758 join ?15 ?16 =?= join ?16 ?15
16759 [16, 15] by commutativity_of_join ?15 ?16
16760 14175: Id : 8, {_}:
16761 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16762 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16763 14175: Id : 9, {_}:
16764 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16765 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16766 14175: Id : 10, {_}:
16767 join (meet ?26 ?27) (meet ?26 ?28)
16770 (join (meet ?27 (join ?26 (meet ?27 ?28)))
16771 (meet ?28 (join ?26 ?27)))
16772 [28, 27, 26] by equation_H21 ?26 ?27 ?28
16774 14175: Id : 1, {_}:
16775 meet a (join b (meet a c))
16777 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
16782 14175: join 17 2 4 0,2,2
16783 14175: meet 21 2 6 0,2
16784 14175: c 3 0 3 2,2,2,2
16785 14175: b 4 0 4 1,2,2
16787 NO CLASH, using fixed ground order
16789 14176: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16790 14176: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16791 14176: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16792 14176: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16793 14176: Id : 6, {_}:
16794 meet ?12 ?13 =?= meet ?13 ?12
16795 [13, 12] by commutativity_of_meet ?12 ?13
16796 14176: Id : 7, {_}:
16797 join ?15 ?16 =?= join ?16 ?15
16798 [16, 15] by commutativity_of_join ?15 ?16
16799 14176: Id : 8, {_}:
16800 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16801 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16802 14176: Id : 9, {_}:
16803 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16804 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16805 14176: Id : 10, {_}:
16806 join (meet ?26 ?27) (meet ?26 ?28)
16809 (join (meet ?27 (join ?26 (meet ?27 ?28)))
16810 (meet ?28 (join ?26 ?27)))
16811 [28, 27, 26] by equation_H21 ?26 ?27 ?28
16813 14176: Id : 1, {_}:
16814 meet a (join b (meet a c))
16816 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
16821 14176: join 17 2 4 0,2,2
16822 14176: meet 21 2 6 0,2
16823 14176: c 3 0 3 2,2,2,2
16824 14176: b 4 0 4 1,2,2
16826 NO CLASH, using fixed ground order
16828 14174: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16829 14174: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16830 14174: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16831 14174: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16832 14174: Id : 6, {_}:
16833 meet ?12 ?13 =?= meet ?13 ?12
16834 [13, 12] by commutativity_of_meet ?12 ?13
16835 14174: Id : 7, {_}:
16836 join ?15 ?16 =?= join ?16 ?15
16837 [16, 15] by commutativity_of_join ?15 ?16
16838 14174: Id : 8, {_}:
16839 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16840 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16841 14174: Id : 9, {_}:
16842 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16843 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16844 14174: Id : 10, {_}:
16845 join (meet ?26 ?27) (meet ?26 ?28)
16848 (join (meet ?27 (join ?26 (meet ?27 ?28)))
16849 (meet ?28 (join ?26 ?27)))
16850 [28, 27, 26] by equation_H21 ?26 ?27 ?28
16852 14174: Id : 1, {_}:
16853 meet a (join b (meet a c))
16855 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
16860 14174: join 17 2 4 0,2,2
16861 14174: meet 21 2 6 0,2
16862 14174: c 3 0 3 2,2,2,2
16863 14174: b 4 0 4 1,2,2
16865 % SZS status Timeout for LAT104-1.p
16866 NO CLASH, using fixed ground order
16868 14193: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16869 14193: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16870 14193: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16871 14193: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16872 14193: Id : 6, {_}:
16873 meet ?12 ?13 =?= meet ?13 ?12
16874 [13, 12] by commutativity_of_meet ?12 ?13
16875 14193: Id : 7, {_}:
16876 join ?15 ?16 =?= join ?16 ?15
16877 [16, 15] by commutativity_of_join ?15 ?16
16878 14193: Id : 8, {_}:
16879 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16880 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16881 14193: Id : 9, {_}:
16882 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
16883 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16884 14193: Id : 10, {_}:
16885 join (meet ?26 ?27) (meet ?26 ?28)
16888 (join (meet ?27 (join ?26 (meet ?27 ?28)))
16889 (meet ?28 (join ?26 ?27)))
16890 [28, 27, 26] by equation_H21 ?26 ?27 ?28
16892 14193: Id : 1, {_}:
16893 meet a (join b (meet a c))
16895 meet a (join b (meet c (join a (meet b c))))
16900 14193: join 16 2 3 0,2,2
16901 14193: meet 20 2 5 0,2
16902 14193: c 3 0 3 2,2,2,2
16903 14193: b 3 0 3 1,2,2
16905 NO CLASH, using fixed ground order
16907 14194: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16908 14194: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16909 14194: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16910 14194: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16911 14194: Id : 6, {_}:
16912 meet ?12 ?13 =?= meet ?13 ?12
16913 [13, 12] by commutativity_of_meet ?12 ?13
16914 14194: Id : 7, {_}:
16915 join ?15 ?16 =?= join ?16 ?15
16916 [16, 15] by commutativity_of_join ?15 ?16
16917 14194: Id : 8, {_}:
16918 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16919 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16920 14194: Id : 9, {_}:
16921 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16922 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16923 14194: Id : 10, {_}:
16924 join (meet ?26 ?27) (meet ?26 ?28)
16927 (join (meet ?27 (join ?26 (meet ?27 ?28)))
16928 (meet ?28 (join ?26 ?27)))
16929 [28, 27, 26] by equation_H21 ?26 ?27 ?28
16931 14194: Id : 1, {_}:
16932 meet a (join b (meet a c))
16934 meet a (join b (meet c (join a (meet b c))))
16939 14194: join 16 2 3 0,2,2
16940 14194: meet 20 2 5 0,2
16941 14194: c 3 0 3 2,2,2,2
16942 14194: b 3 0 3 1,2,2
16944 NO CLASH, using fixed ground order
16946 14195: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16947 14195: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16948 14195: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16949 14195: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16950 14195: Id : 6, {_}:
16951 meet ?12 ?13 =?= meet ?13 ?12
16952 [13, 12] by commutativity_of_meet ?12 ?13
16953 14195: Id : 7, {_}:
16954 join ?15 ?16 =?= join ?16 ?15
16955 [16, 15] by commutativity_of_join ?15 ?16
16956 14195: Id : 8, {_}:
16957 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
16958 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16959 14195: Id : 9, {_}:
16960 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
16961 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
16962 14195: Id : 10, {_}:
16963 join (meet ?26 ?27) (meet ?26 ?28)
16966 (join (meet ?27 (join ?26 (meet ?27 ?28)))
16967 (meet ?28 (join ?26 ?27)))
16968 [28, 27, 26] by equation_H21 ?26 ?27 ?28
16970 14195: Id : 1, {_}:
16971 meet a (join b (meet a c))
16973 meet a (join b (meet c (join a (meet b c))))
16978 14195: join 16 2 3 0,2,2
16979 14195: meet 20 2 5 0,2
16980 14195: c 3 0 3 2,2,2,2
16981 14195: b 3 0 3 1,2,2
16983 % SZS status Timeout for LAT105-1.p
16984 NO CLASH, using fixed ground order
16986 14223: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
16987 14223: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
16988 14223: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
16989 14223: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
16990 14223: Id : 6, {_}:
16991 meet ?12 ?13 =?= meet ?13 ?12
16992 [13, 12] by commutativity_of_meet ?12 ?13
16993 14223: Id : 7, {_}:
16994 join ?15 ?16 =?= join ?16 ?15
16995 [16, 15] by commutativity_of_join ?15 ?16
16996 14223: Id : 8, {_}:
16997 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
16998 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
16999 14223: Id : 9, {_}:
17000 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17001 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17002 14223: Id : 10, {_}:
17003 join (meet ?26 ?27) (meet ?26 ?28)
17006 (join (meet ?27 (join ?28 (meet ?26 ?27)))
17007 (meet ?28 (join ?26 ?27)))
17008 [28, 27, 26] by equation_H22 ?26 ?27 ?28
17010 14223: Id : 1, {_}:
17011 meet a (join b (meet a c))
17013 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
17018 14223: join 17 2 4 0,2,2
17019 14223: meet 21 2 6 0,2
17020 14223: c 3 0 3 2,2,2,2
17021 14223: b 4 0 4 1,2,2
17023 NO CLASH, using fixed ground order
17025 14224: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17026 14224: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17027 14224: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17028 14224: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17029 14224: Id : 6, {_}:
17030 meet ?12 ?13 =?= meet ?13 ?12
17031 [13, 12] by commutativity_of_meet ?12 ?13
17032 14224: Id : 7, {_}:
17033 join ?15 ?16 =?= join ?16 ?15
17034 [16, 15] by commutativity_of_join ?15 ?16
17035 14224: Id : 8, {_}:
17036 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17037 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17038 14224: Id : 9, {_}:
17039 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17040 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17041 14224: Id : 10, {_}:
17042 join (meet ?26 ?27) (meet ?26 ?28)
17045 (join (meet ?27 (join ?28 (meet ?26 ?27)))
17046 (meet ?28 (join ?26 ?27)))
17047 [28, 27, 26] by equation_H22 ?26 ?27 ?28
17049 14224: Id : 1, {_}:
17050 meet a (join b (meet a c))
17052 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
17057 NO CLASH, using fixed ground order
17059 14225: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17060 14225: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17061 14225: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17062 14225: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17063 14225: Id : 6, {_}:
17064 meet ?12 ?13 =?= meet ?13 ?12
17065 [13, 12] by commutativity_of_meet ?12 ?13
17066 14225: Id : 7, {_}:
17067 join ?15 ?16 =?= join ?16 ?15
17068 [16, 15] by commutativity_of_join ?15 ?16
17069 14225: Id : 8, {_}:
17070 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17071 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17072 14225: Id : 9, {_}:
17073 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17074 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17075 14225: Id : 10, {_}:
17076 join (meet ?26 ?27) (meet ?26 ?28)
17079 (join (meet ?27 (join ?28 (meet ?26 ?27)))
17080 (meet ?28 (join ?26 ?27)))
17081 [28, 27, 26] by equation_H22 ?26 ?27 ?28
17083 14225: Id : 1, {_}:
17084 meet a (join b (meet a c))
17086 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
17091 14225: join 17 2 4 0,2,2
17092 14225: meet 21 2 6 0,2
17093 14225: c 3 0 3 2,2,2,2
17094 14225: b 4 0 4 1,2,2
17096 14224: join 17 2 4 0,2,2
17097 14224: meet 21 2 6 0,2
17098 14224: c 3 0 3 2,2,2,2
17099 14224: b 4 0 4 1,2,2
17101 % SZS status Timeout for LAT106-1.p
17102 NO CLASH, using fixed ground order
17104 14371: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17105 14371: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17106 14371: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17107 14371: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17108 14371: Id : 6, {_}:
17109 meet ?12 ?13 =?= meet ?13 ?12
17110 [13, 12] by commutativity_of_meet ?12 ?13
17111 14371: Id : 7, {_}:
17112 join ?15 ?16 =?= join ?16 ?15
17113 [16, 15] by commutativity_of_join ?15 ?16
17114 14371: Id : 8, {_}:
17115 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17116 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17117 14371: Id : 9, {_}:
17118 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17119 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17120 14371: Id : 10, {_}:
17121 join (meet ?26 ?27) (meet ?26 ?28)
17124 (join (meet ?27 (join ?28 (meet ?26 ?27)))
17125 (meet ?28 (join ?26 ?27)))
17126 [28, 27, 26] by equation_H22 ?26 ?27 ?28
17128 14371: Id : 1, {_}:
17129 meet a (join (meet a b) (meet a c))
17131 meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
17136 14371: join 17 2 4 0,2,2
17137 14371: c 3 0 3 2,2,2,2
17138 14371: meet 22 2 7 0,2
17139 14371: b 4 0 4 2,1,2,2
17141 NO CLASH, using fixed ground order
17143 14372: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17144 14372: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17145 14372: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17146 14372: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17147 14372: Id : 6, {_}:
17148 meet ?12 ?13 =?= meet ?13 ?12
17149 [13, 12] by commutativity_of_meet ?12 ?13
17150 14372: Id : 7, {_}:
17151 join ?15 ?16 =?= join ?16 ?15
17152 [16, 15] by commutativity_of_join ?15 ?16
17153 14372: Id : 8, {_}:
17154 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17155 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17156 14372: Id : 9, {_}:
17157 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17158 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17159 14372: Id : 10, {_}:
17160 join (meet ?26 ?27) (meet ?26 ?28)
17163 (join (meet ?27 (join ?28 (meet ?26 ?27)))
17164 (meet ?28 (join ?26 ?27)))
17165 [28, 27, 26] by equation_H22 ?26 ?27 ?28
17167 14372: Id : 1, {_}:
17168 meet a (join (meet a b) (meet a c))
17170 meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
17175 14372: join 17 2 4 0,2,2
17176 14372: c 3 0 3 2,2,2,2
17177 14372: meet 22 2 7 0,2
17178 14372: b 4 0 4 2,1,2,2
17180 NO CLASH, using fixed ground order
17182 14373: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17183 14373: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17184 14373: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17185 14373: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17186 14373: Id : 6, {_}:
17187 meet ?12 ?13 =?= meet ?13 ?12
17188 [13, 12] by commutativity_of_meet ?12 ?13
17189 14373: Id : 7, {_}:
17190 join ?15 ?16 =?= join ?16 ?15
17191 [16, 15] by commutativity_of_join ?15 ?16
17192 14373: Id : 8, {_}:
17193 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17194 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17195 14373: Id : 9, {_}:
17196 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17197 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17198 14373: Id : 10, {_}:
17199 join (meet ?26 ?27) (meet ?26 ?28)
17202 (join (meet ?27 (join ?28 (meet ?26 ?27)))
17203 (meet ?28 (join ?26 ?27)))
17204 [28, 27, 26] by equation_H22 ?26 ?27 ?28
17206 14373: Id : 1, {_}:
17207 meet a (join (meet a b) (meet a c))
17209 meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
17214 14373: join 17 2 4 0,2,2
17215 14373: c 3 0 3 2,2,2,2
17216 14373: meet 22 2 7 0,2
17217 14373: b 4 0 4 2,1,2,2
17219 % SZS status Timeout for LAT107-1.p
17220 NO CLASH, using fixed ground order
17222 15801: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17223 15801: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17224 15801: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17225 15801: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17226 15801: Id : 6, {_}:
17227 meet ?12 ?13 =?= meet ?13 ?12
17228 [13, 12] by commutativity_of_meet ?12 ?13
17229 15801: Id : 7, {_}:
17230 join ?15 ?16 =?= join ?16 ?15
17231 [16, 15] by commutativity_of_join ?15 ?16
17232 15801: Id : 8, {_}:
17233 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17234 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17235 15801: Id : 9, {_}:
17236 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17237 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17238 15801: Id : 10, {_}:
17239 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
17241 meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
17242 [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
17244 15801: Id : 1, {_}:
17245 meet a (join b (meet c (join a d)))
17247 meet a (join b (meet c (join b (join d (meet a c)))))
17252 15801: meet 21 2 5 0,2
17253 15801: join 17 2 5 0,2,2
17254 15801: d 2 0 2 2,2,2,2,2
17255 15801: c 3 0 3 1,2,2,2
17256 15801: b 3 0 3 1,2,2
17258 NO CLASH, using fixed ground order
17260 15804: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17261 15804: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17262 15804: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17263 15804: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17264 15804: Id : 6, {_}:
17265 meet ?12 ?13 =?= meet ?13 ?12
17266 [13, 12] by commutativity_of_meet ?12 ?13
17267 15804: Id : 7, {_}:
17268 join ?15 ?16 =?= join ?16 ?15
17269 [16, 15] by commutativity_of_join ?15 ?16
17270 15804: Id : 8, {_}:
17271 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17272 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17273 15804: Id : 9, {_}:
17274 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17275 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17276 15804: Id : 10, {_}:
17277 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
17279 meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
17280 [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
17282 15804: Id : 1, {_}:
17283 meet a (join b (meet c (join a d)))
17285 meet a (join b (meet c (join b (join d (meet a c)))))
17290 15804: meet 21 2 5 0,2
17291 15804: join 17 2 5 0,2,2
17292 15804: d 2 0 2 2,2,2,2,2
17293 15804: c 3 0 3 1,2,2,2
17294 15804: b 3 0 3 1,2,2
17296 NO CLASH, using fixed ground order
17298 15805: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17299 15805: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17300 15805: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17301 15805: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17302 15805: Id : 6, {_}:
17303 meet ?12 ?13 =?= meet ?13 ?12
17304 [13, 12] by commutativity_of_meet ?12 ?13
17305 15805: Id : 7, {_}:
17306 join ?15 ?16 =?= join ?16 ?15
17307 [16, 15] by commutativity_of_join ?15 ?16
17308 15805: Id : 8, {_}:
17309 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17310 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17311 15805: Id : 9, {_}:
17312 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17313 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17314 15805: Id : 10, {_}:
17315 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
17317 meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
17318 [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
17320 15805: Id : 1, {_}:
17321 meet a (join b (meet c (join a d)))
17323 meet a (join b (meet c (join b (join d (meet a c)))))
17328 15805: meet 21 2 5 0,2
17329 15805: join 17 2 5 0,2,2
17330 15805: d 2 0 2 2,2,2,2,2
17331 15805: c 3 0 3 1,2,2,2
17332 15805: b 3 0 3 1,2,2
17334 % SZS status Timeout for LAT108-1.p
17335 NO CLASH, using fixed ground order
17337 17324: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17338 17324: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17339 17324: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17340 17324: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17341 17324: Id : 6, {_}:
17342 meet ?12 ?13 =?= meet ?13 ?12
17343 [13, 12] by commutativity_of_meet ?12 ?13
17344 17324: Id : 7, {_}:
17345 join ?15 ?16 =?= join ?16 ?15
17346 [16, 15] by commutativity_of_join ?15 ?16
17347 17324: Id : 8, {_}:
17348 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17349 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17350 17324: Id : 9, {_}:
17351 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17352 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17353 17324: Id : 10, {_}:
17354 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
17356 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
17357 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
17359 17324: Id : 1, {_}:
17360 meet a (join b (meet c (join a d)))
17362 meet a (join b (meet c (join d (meet c (join a b)))))
17367 17324: meet 19 2 5 0,2
17368 17324: join 19 2 5 0,2,2
17369 17324: d 2 0 2 2,2,2,2,2
17370 17324: c 3 0 3 1,2,2,2
17371 17324: b 3 0 3 1,2,2
17373 NO CLASH, using fixed ground order
17375 17322: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17376 17322: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17377 17322: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17378 17322: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17379 17322: Id : 6, {_}:
17380 meet ?12 ?13 =?= meet ?13 ?12
17381 [13, 12] by commutativity_of_meet ?12 ?13
17382 17322: Id : 7, {_}:
17383 join ?15 ?16 =?= join ?16 ?15
17384 [16, 15] by commutativity_of_join ?15 ?16
17385 17322: Id : 8, {_}:
17386 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17387 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17388 17322: Id : 9, {_}:
17389 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17390 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17391 17322: Id : 10, {_}:
17392 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
17394 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
17395 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
17397 17322: Id : 1, {_}:
17398 meet a (join b (meet c (join a d)))
17400 meet a (join b (meet c (join d (meet c (join a b)))))
17405 17322: meet 19 2 5 0,2
17406 17322: join 19 2 5 0,2,2
17407 17322: d 2 0 2 2,2,2,2,2
17408 17322: c 3 0 3 1,2,2,2
17409 17322: b 3 0 3 1,2,2
17411 NO CLASH, using fixed ground order
17413 17323: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17414 17323: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17415 17323: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17416 17323: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17417 17323: Id : 6, {_}:
17418 meet ?12 ?13 =?= meet ?13 ?12
17419 [13, 12] by commutativity_of_meet ?12 ?13
17420 17323: Id : 7, {_}:
17421 join ?15 ?16 =?= join ?16 ?15
17422 [16, 15] by commutativity_of_join ?15 ?16
17423 17323: Id : 8, {_}:
17424 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17425 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17426 17323: Id : 9, {_}:
17427 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17428 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17429 17323: Id : 10, {_}:
17430 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
17432 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
17433 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
17435 17323: Id : 1, {_}:
17436 meet a (join b (meet c (join a d)))
17438 meet a (join b (meet c (join d (meet c (join a b)))))
17443 17323: meet 19 2 5 0,2
17444 17323: join 19 2 5 0,2,2
17445 17323: d 2 0 2 2,2,2,2,2
17446 17323: c 3 0 3 1,2,2,2
17447 17323: b 3 0 3 1,2,2
17449 % SZS status Timeout for LAT109-1.p
17450 NO CLASH, using fixed ground order
17452 19002: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17453 19002: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17454 19002: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17455 19002: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17456 19002: Id : 6, {_}:
17457 meet ?12 ?13 =?= meet ?13 ?12
17458 [13, 12] by commutativity_of_meet ?12 ?13
17459 19002: Id : 7, {_}:
17460 join ?15 ?16 =?= join ?16 ?15
17461 [16, 15] by commutativity_of_join ?15 ?16
17462 19002: Id : 8, {_}:
17463 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17464 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17465 19002: Id : 9, {_}:
17466 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17467 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17468 19002: Id : 10, {_}:
17469 meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
17471 meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
17472 [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
17474 19002: Id : 1, {_}:
17475 meet a (join b (meet c (join a d)))
17477 meet a (join b (meet c (join d (meet c (join a b)))))
17482 19002: meet 21 2 5 0,2
17483 19002: join 17 2 5 0,2,2
17484 19002: d 2 0 2 2,2,2,2,2
17485 19002: c 3 0 3 1,2,2,2
17486 19002: b 3 0 3 1,2,2
17488 NO CLASH, using fixed ground order
17490 19008: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17491 19008: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17492 19008: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17493 19008: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17494 19008: Id : 6, {_}:
17495 meet ?12 ?13 =?= meet ?13 ?12
17496 [13, 12] by commutativity_of_meet ?12 ?13
17497 19008: Id : 7, {_}:
17498 join ?15 ?16 =?= join ?16 ?15
17499 [16, 15] by commutativity_of_join ?15 ?16
17500 19008: Id : 8, {_}:
17501 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17502 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17503 19008: Id : 9, {_}:
17504 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17505 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17506 19008: Id : 10, {_}:
17507 meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
17509 meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
17510 [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
17512 19008: Id : 1, {_}:
17513 meet a (join b (meet c (join a d)))
17515 meet a (join b (meet c (join d (meet c (join a b)))))
17520 19008: meet 21 2 5 0,2
17521 19008: join 17 2 5 0,2,2
17522 19008: d 2 0 2 2,2,2,2,2
17523 19008: c 3 0 3 1,2,2,2
17524 19008: b 3 0 3 1,2,2
17526 NO CLASH, using fixed ground order
17528 19009: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17529 19009: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17530 19009: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17531 19009: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17532 19009: Id : 6, {_}:
17533 meet ?12 ?13 =?= meet ?13 ?12
17534 [13, 12] by commutativity_of_meet ?12 ?13
17535 19009: Id : 7, {_}:
17536 join ?15 ?16 =?= join ?16 ?15
17537 [16, 15] by commutativity_of_join ?15 ?16
17538 19009: Id : 8, {_}:
17539 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17540 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17541 19009: Id : 9, {_}:
17542 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17543 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17544 19009: Id : 10, {_}:
17545 meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
17547 meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
17548 [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
17550 19009: Id : 1, {_}:
17551 meet a (join b (meet c (join a d)))
17553 meet a (join b (meet c (join d (meet c (join a b)))))
17558 19009: meet 21 2 5 0,2
17559 19009: join 17 2 5 0,2,2
17560 19009: d 2 0 2 2,2,2,2,2
17561 19009: c 3 0 3 1,2,2,2
17562 19009: b 3 0 3 1,2,2
17564 % SZS status Timeout for LAT111-1.p
17565 NO CLASH, using fixed ground order
17567 19496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17568 19496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17569 19496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17570 19496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17571 19496: Id : 6, {_}:
17572 meet ?12 ?13 =?= meet ?13 ?12
17573 [13, 12] by commutativity_of_meet ?12 ?13
17574 19496: Id : 7, {_}:
17575 join ?15 ?16 =?= join ?16 ?15
17576 [16, 15] by commutativity_of_join ?15 ?16
17577 19496: Id : 8, {_}:
17578 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17579 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17580 19496: Id : 9, {_}:
17581 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17582 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17583 19496: Id : 10, {_}:
17584 meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
17586 meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
17587 [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
17589 19496: Id : 1, {_}:
17590 meet a (join b (meet c (join a d)))
17592 meet a (join b (meet c (join b (join d (meet a c)))))
17597 19496: meet 21 2 5 0,2
17598 19496: join 17 2 5 0,2,2
17599 19496: d 2 0 2 2,2,2,2,2
17600 19496: c 3 0 3 1,2,2,2
17601 19496: b 3 0 3 1,2,2
17603 NO CLASH, using fixed ground order
17605 19497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17606 19497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17607 19497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17608 19497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17609 19497: Id : 6, {_}:
17610 meet ?12 ?13 =?= meet ?13 ?12
17611 [13, 12] by commutativity_of_meet ?12 ?13
17612 19497: Id : 7, {_}:
17613 join ?15 ?16 =?= join ?16 ?15
17614 [16, 15] by commutativity_of_join ?15 ?16
17615 19497: Id : 8, {_}:
17616 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17617 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17618 19497: Id : 9, {_}:
17619 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17620 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17621 19497: Id : 10, {_}:
17622 meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
17624 meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
17625 [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
17627 19497: Id : 1, {_}:
17628 meet a (join b (meet c (join a d)))
17630 meet a (join b (meet c (join b (join d (meet a c)))))
17635 19497: meet 21 2 5 0,2
17636 19497: join 17 2 5 0,2,2
17637 19497: d 2 0 2 2,2,2,2,2
17638 19497: c 3 0 3 1,2,2,2
17639 19497: b 3 0 3 1,2,2
17641 NO CLASH, using fixed ground order
17643 19498: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17644 19498: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17645 19498: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17646 19498: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17647 19498: Id : 6, {_}:
17648 meet ?12 ?13 =?= meet ?13 ?12
17649 [13, 12] by commutativity_of_meet ?12 ?13
17650 19498: Id : 7, {_}:
17651 join ?15 ?16 =?= join ?16 ?15
17652 [16, 15] by commutativity_of_join ?15 ?16
17653 19498: Id : 8, {_}:
17654 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17655 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17656 19498: Id : 9, {_}:
17657 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17658 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17659 19498: Id : 10, {_}:
17660 meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
17662 meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
17663 [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
17665 19498: Id : 1, {_}:
17666 meet a (join b (meet c (join a d)))
17668 meet a (join b (meet c (join b (join d (meet a c)))))
17673 19498: meet 21 2 5 0,2
17674 19498: join 17 2 5 0,2,2
17675 19498: d 2 0 2 2,2,2,2,2
17676 19498: c 3 0 3 1,2,2,2
17677 19498: b 3 0 3 1,2,2
17679 % SZS status Timeout for LAT112-1.p
17680 NO CLASH, using fixed ground order
17682 19529: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17683 19529: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17684 19529: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17685 19529: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17686 19529: Id : 6, {_}:
17687 meet ?12 ?13 =?= meet ?13 ?12
17688 [13, 12] by commutativity_of_meet ?12 ?13
17689 19529: Id : 7, {_}:
17690 join ?15 ?16 =?= join ?16 ?15
17691 [16, 15] by commutativity_of_join ?15 ?16
17692 19529: Id : 8, {_}:
17693 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17694 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17695 19529: Id : 9, {_}:
17696 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17697 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17698 19529: Id : 10, {_}:
17699 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
17701 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
17702 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
17704 19529: Id : 1, {_}:
17705 meet a (join b (meet c (join a d)))
17707 meet a (join b (meet c (join d (meet c (join a b)))))
17712 19529: meet 19 2 5 0,2
17713 19529: join 19 2 5 0,2,2
17714 19529: d 2 0 2 2,2,2,2,2
17715 19529: c 3 0 3 1,2,2,2
17716 19529: b 3 0 3 1,2,2
17718 NO CLASH, using fixed ground order
17720 19530: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17721 19530: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17722 19530: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17723 19530: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17724 19530: Id : 6, {_}:
17725 meet ?12 ?13 =?= meet ?13 ?12
17726 [13, 12] by commutativity_of_meet ?12 ?13
17727 19530: Id : 7, {_}:
17728 join ?15 ?16 =?= join ?16 ?15
17729 [16, 15] by commutativity_of_join ?15 ?16
17730 19530: Id : 8, {_}:
17731 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17732 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17733 19530: Id : 9, {_}:
17734 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17735 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17736 19530: Id : 10, {_}:
17737 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
17739 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
17740 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
17742 19530: Id : 1, {_}:
17743 meet a (join b (meet c (join a d)))
17745 meet a (join b (meet c (join d (meet c (join a b)))))
17750 19530: meet 19 2 5 0,2
17751 19530: join 19 2 5 0,2,2
17752 19530: d 2 0 2 2,2,2,2,2
17753 19530: c 3 0 3 1,2,2,2
17754 19530: b 3 0 3 1,2,2
17756 NO CLASH, using fixed ground order
17758 19531: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17759 19531: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17760 19531: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17761 19531: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17762 19531: Id : 6, {_}:
17763 meet ?12 ?13 =?= meet ?13 ?12
17764 [13, 12] by commutativity_of_meet ?12 ?13
17765 19531: Id : 7, {_}:
17766 join ?15 ?16 =?= join ?16 ?15
17767 [16, 15] by commutativity_of_join ?15 ?16
17768 19531: Id : 8, {_}:
17769 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17770 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17771 19531: Id : 9, {_}:
17772 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17773 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17774 19531: Id : 10, {_}:
17775 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
17777 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
17778 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
17780 19531: Id : 1, {_}:
17781 meet a (join b (meet c (join a d)))
17783 meet a (join b (meet c (join d (meet c (join a b)))))
17788 19531: meet 19 2 5 0,2
17789 19531: join 19 2 5 0,2,2
17790 19531: d 2 0 2 2,2,2,2,2
17791 19531: c 3 0 3 1,2,2,2
17792 19531: b 3 0 3 1,2,2
17794 % SZS status Timeout for LAT113-1.p
17795 NO CLASH, using fixed ground order
17797 19568: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17798 19568: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17799 19568: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17800 19568: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17801 19568: Id : 6, {_}:
17802 meet ?12 ?13 =?= meet ?13 ?12
17803 [13, 12] by commutativity_of_meet ?12 ?13
17804 19568: Id : 7, {_}:
17805 join ?15 ?16 =?= join ?16 ?15
17806 [16, 15] by commutativity_of_join ?15 ?16
17807 19568: Id : 8, {_}:
17808 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17809 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17810 19568: Id : 9, {_}:
17811 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17812 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17813 19568: Id : 10, {_}:
17814 join ?26 (meet ?27 (join ?26 ?28))
17816 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
17817 [28, 27, 26] by equation_H55 ?26 ?27 ?28
17819 19568: Id : 1, {_}:
17820 join (meet a b) (meet a (join b c))
17822 meet a (join b (meet (join a b) (join c (meet a b))))
17827 19568: join 19 2 5 0,2
17828 19568: c 2 0 2 2,2,2,2
17829 19568: meet 17 2 5 0,1,2
17830 19568: b 5 0 5 2,1,2
17831 19568: a 5 0 5 1,1,2
17832 NO CLASH, using fixed ground order
17834 19567: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17835 19567: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17836 19567: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17837 19567: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17838 19567: Id : 6, {_}:
17839 meet ?12 ?13 =?= meet ?13 ?12
17840 [13, 12] by commutativity_of_meet ?12 ?13
17841 19567: Id : 7, {_}:
17842 join ?15 ?16 =?= join ?16 ?15
17843 [16, 15] by commutativity_of_join ?15 ?16
17844 19567: Id : 8, {_}:
17845 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17846 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17847 19567: Id : 9, {_}:
17848 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17849 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17850 19567: Id : 10, {_}:
17851 join ?26 (meet ?27 (join ?26 ?28))
17853 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
17854 [28, 27, 26] by equation_H55 ?26 ?27 ?28
17856 19567: Id : 1, {_}:
17857 join (meet a b) (meet a (join b c))
17859 meet a (join b (meet (join a b) (join c (meet a b))))
17864 19567: join 19 2 5 0,2
17865 19567: c 2 0 2 2,2,2,2
17866 19567: meet 17 2 5 0,1,2
17867 19567: b 5 0 5 2,1,2
17868 19567: a 5 0 5 1,1,2
17869 NO CLASH, using fixed ground order
17871 19569: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17872 19569: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17873 19569: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17874 19569: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17875 19569: Id : 6, {_}:
17876 meet ?12 ?13 =?= meet ?13 ?12
17877 [13, 12] by commutativity_of_meet ?12 ?13
17878 19569: Id : 7, {_}:
17879 join ?15 ?16 =?= join ?16 ?15
17880 [16, 15] by commutativity_of_join ?15 ?16
17881 19569: Id : 8, {_}:
17882 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17883 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17884 19569: Id : 9, {_}:
17885 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17886 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17887 19569: Id : 10, {_}:
17888 join ?26 (meet ?27 (join ?26 ?28))
17890 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
17891 [28, 27, 26] by equation_H55 ?26 ?27 ?28
17893 19569: Id : 1, {_}:
17894 join (meet a b) (meet a (join b c))
17896 meet a (join b (meet (join a b) (join c (meet a b))))
17901 19569: join 19 2 5 0,2
17902 19569: c 2 0 2 2,2,2,2
17903 19569: meet 17 2 5 0,1,2
17904 19569: b 5 0 5 2,1,2
17905 19569: a 5 0 5 1,1,2
17906 % SZS status Timeout for LAT114-1.p
17907 NO CLASH, using fixed ground order
17909 19631: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17910 19631: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17911 19631: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17912 19631: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17913 19631: Id : 6, {_}:
17914 meet ?12 ?13 =?= meet ?13 ?12
17915 [13, 12] by commutativity_of_meet ?12 ?13
17916 19631: Id : 7, {_}:
17917 join ?15 ?16 =?= join ?16 ?15
17918 [16, 15] by commutativity_of_join ?15 ?16
17919 19631: Id : 8, {_}:
17920 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
17921 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17922 19631: Id : 9, {_}:
17923 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
17924 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17925 19631: Id : 10, {_}:
17926 join ?26 (meet ?27 (join ?26 ?28))
17928 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
17929 [28, 27, 26] by equation_H55 ?26 ?27 ?28
17931 19631: Id : 1, {_}:
17932 meet a (meet (join b c) (join b d))
17934 meet a (join b (meet (join b d) (join c (meet a b))))
17939 19631: meet 17 2 5 0,2
17940 19631: d 2 0 2 2,2,2,2
17941 19631: join 19 2 5 0,1,2,2
17942 19631: c 2 0 2 2,1,2,2
17943 19631: b 5 0 5 1,1,2,2
17945 NO CLASH, using fixed ground order
17947 19632: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17948 19632: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17949 19632: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17950 19632: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17951 19632: Id : 6, {_}:
17952 meet ?12 ?13 =?= meet ?13 ?12
17953 [13, 12] by commutativity_of_meet ?12 ?13
17954 19632: Id : 7, {_}:
17955 join ?15 ?16 =?= join ?16 ?15
17956 [16, 15] by commutativity_of_join ?15 ?16
17957 19632: Id : 8, {_}:
17958 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17959 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17960 19632: Id : 9, {_}:
17961 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
17962 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
17963 19632: Id : 10, {_}:
17964 join ?26 (meet ?27 (join ?26 ?28))
17966 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
17967 [28, 27, 26] by equation_H55 ?26 ?27 ?28
17969 19632: Id : 1, {_}:
17970 meet a (meet (join b c) (join b d))
17972 meet a (join b (meet (join b d) (join c (meet a b))))
17977 19632: meet 17 2 5 0,2
17978 19632: d 2 0 2 2,2,2,2
17979 19632: join 19 2 5 0,1,2,2
17980 19632: c 2 0 2 2,1,2,2
17981 19632: b 5 0 5 1,1,2,2
17983 NO CLASH, using fixed ground order
17985 19633: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
17986 19633: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
17987 19633: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
17988 19633: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
17989 19633: Id : 6, {_}:
17990 meet ?12 ?13 =?= meet ?13 ?12
17991 [13, 12] by commutativity_of_meet ?12 ?13
17992 19633: Id : 7, {_}:
17993 join ?15 ?16 =?= join ?16 ?15
17994 [16, 15] by commutativity_of_join ?15 ?16
17995 19633: Id : 8, {_}:
17996 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
17997 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
17998 19633: Id : 9, {_}:
17999 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18000 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18001 19633: Id : 10, {_}:
18002 join ?26 (meet ?27 (join ?26 ?28))
18004 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
18005 [28, 27, 26] by equation_H55 ?26 ?27 ?28
18007 19633: Id : 1, {_}:
18008 meet a (meet (join b c) (join b d))
18010 meet a (join b (meet (join b d) (join c (meet a b))))
18015 19633: meet 17 2 5 0,2
18016 19633: d 2 0 2 2,2,2,2
18017 19633: join 19 2 5 0,1,2,2
18018 19633: c 2 0 2 2,1,2,2
18019 19633: b 5 0 5 1,1,2,2
18021 % SZS status Timeout for LAT115-1.p
18022 NO CLASH, using fixed ground order
18024 19650: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18025 19650: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18026 19650: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18027 19650: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18028 19650: Id : 6, {_}:
18029 meet ?12 ?13 =?= meet ?13 ?12
18030 [13, 12] by commutativity_of_meet ?12 ?13
18031 19650: Id : 7, {_}:
18032 join ?15 ?16 =?= join ?16 ?15
18033 [16, 15] by commutativity_of_join ?15 ?16
18034 NO CLASH, using fixed ground order
18036 19651: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18037 19651: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18038 19651: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18039 19651: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18040 19651: Id : 6, {_}:
18041 meet ?12 ?13 =?= meet ?13 ?12
18042 [13, 12] by commutativity_of_meet ?12 ?13
18043 19651: Id : 7, {_}:
18044 join ?15 ?16 =?= join ?16 ?15
18045 [16, 15] by commutativity_of_join ?15 ?16
18046 19651: Id : 8, {_}:
18047 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18048 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18049 19651: Id : 9, {_}:
18050 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18051 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18052 19651: Id : 10, {_}:
18053 join ?26 (meet ?27 (join ?26 ?28))
18055 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
18056 [28, 27, 26] by equation_H55 ?26 ?27 ?28
18058 19651: Id : 1, {_}:
18059 meet a (meet (join b c) (join b d))
18061 meet a (join b (meet (join b c) (join d (meet a b))))
18066 19651: meet 17 2 5 0,2
18067 19651: d 2 0 2 2,2,2,2
18068 19651: join 19 2 5 0,1,2,2
18069 19651: c 2 0 2 2,1,2,2
18070 19651: b 5 0 5 1,1,2,2
18072 19650: Id : 8, {_}:
18073 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18074 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18075 19650: Id : 9, {_}:
18076 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18077 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18078 19650: Id : 10, {_}:
18079 join ?26 (meet ?27 (join ?26 ?28))
18081 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
18082 [28, 27, 26] by equation_H55 ?26 ?27 ?28
18084 19650: Id : 1, {_}:
18085 meet a (meet (join b c) (join b d))
18087 meet a (join b (meet (join b c) (join d (meet a b))))
18092 19650: meet 17 2 5 0,2
18093 19650: d 2 0 2 2,2,2,2
18094 19650: join 19 2 5 0,1,2,2
18095 19650: c 2 0 2 2,1,2,2
18096 19650: b 5 0 5 1,1,2,2
18098 NO CLASH, using fixed ground order
18100 19652: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18101 19652: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18102 19652: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18103 19652: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18104 19652: Id : 6, {_}:
18105 meet ?12 ?13 =?= meet ?13 ?12
18106 [13, 12] by commutativity_of_meet ?12 ?13
18107 19652: Id : 7, {_}:
18108 join ?15 ?16 =?= join ?16 ?15
18109 [16, 15] by commutativity_of_join ?15 ?16
18110 19652: Id : 8, {_}:
18111 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18112 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18113 19652: Id : 9, {_}:
18114 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18115 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18116 19652: Id : 10, {_}:
18117 join ?26 (meet ?27 (join ?26 ?28))
18119 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
18120 [28, 27, 26] by equation_H55 ?26 ?27 ?28
18122 19652: Id : 1, {_}:
18123 meet a (meet (join b c) (join b d))
18125 meet a (join b (meet (join b c) (join d (meet a b))))
18130 19652: meet 17 2 5 0,2
18131 19652: d 2 0 2 2,2,2,2
18132 19652: join 19 2 5 0,1,2,2
18133 19652: c 2 0 2 2,1,2,2
18134 19652: b 5 0 5 1,1,2,2
18136 % SZS status Timeout for LAT116-1.p
18137 NO CLASH, using fixed ground order
18139 19680: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18140 19680: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18141 19680: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18142 19680: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18143 19680: Id : 6, {_}:
18144 meet ?12 ?13 =?= meet ?13 ?12
18145 [13, 12] by commutativity_of_meet ?12 ?13
18146 19680: Id : 7, {_}:
18147 join ?15 ?16 =?= join ?16 ?15
18148 [16, 15] by commutativity_of_join ?15 ?16
18149 19680: Id : 8, {_}:
18150 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18151 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18152 19680: Id : 9, {_}:
18153 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18154 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18155 19680: Id : 10, {_}:
18156 meet ?26 (join ?27 (meet ?28 ?29))
18158 meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
18159 [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
18161 19680: Id : 1, {_}:
18164 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
18169 19680: meet 20 2 5 0,2
18170 19680: join 16 2 4 0,2,2
18171 19680: c 3 0 3 2,2,2
18172 19680: b 3 0 3 1,2,2
18174 NO CLASH, using fixed ground order
18176 19681: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18177 19681: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18178 19681: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18179 19681: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18180 19681: Id : 6, {_}:
18181 meet ?12 ?13 =?= meet ?13 ?12
18182 [13, 12] by commutativity_of_meet ?12 ?13
18183 19681: Id : 7, {_}:
18184 join ?15 ?16 =?= join ?16 ?15
18185 [16, 15] by commutativity_of_join ?15 ?16
18186 19681: Id : 8, {_}:
18187 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18188 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18189 19681: Id : 9, {_}:
18190 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18191 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18192 19681: Id : 10, {_}:
18193 meet ?26 (join ?27 (meet ?28 ?29))
18195 meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
18196 [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
18198 19681: Id : 1, {_}:
18201 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
18206 19681: meet 20 2 5 0,2
18207 19681: join 16 2 4 0,2,2
18208 19681: c 3 0 3 2,2,2
18209 19681: b 3 0 3 1,2,2
18211 NO CLASH, using fixed ground order
18213 19682: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18214 19682: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18215 19682: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18216 19682: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18217 19682: Id : 6, {_}:
18218 meet ?12 ?13 =?= meet ?13 ?12
18219 [13, 12] by commutativity_of_meet ?12 ?13
18220 19682: Id : 7, {_}:
18221 join ?15 ?16 =?= join ?16 ?15
18222 [16, 15] by commutativity_of_join ?15 ?16
18223 19682: Id : 8, {_}:
18224 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18225 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18226 19682: Id : 9, {_}:
18227 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18228 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18229 19682: Id : 10, {_}:
18230 meet ?26 (join ?27 (meet ?28 ?29))
18232 meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
18233 [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
18235 19682: Id : 1, {_}:
18238 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
18243 19682: meet 20 2 5 0,2
18244 19682: join 16 2 4 0,2,2
18245 19682: c 3 0 3 2,2,2
18246 19682: b 3 0 3 1,2,2
18248 % SZS status Timeout for LAT117-1.p
18249 NO CLASH, using fixed ground order
18251 19698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18252 19698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18253 19698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18254 19698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18255 19698: Id : 6, {_}:
18256 meet ?12 ?13 =?= meet ?13 ?12
18257 [13, 12] by commutativity_of_meet ?12 ?13
18258 19698: Id : 7, {_}:
18259 join ?15 ?16 =?= join ?16 ?15
18260 [16, 15] by commutativity_of_join ?15 ?16
18261 19698: Id : 8, {_}:
18262 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18263 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18264 19698: Id : 9, {_}:
18265 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18266 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18267 19698: Id : 10, {_}:
18268 meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
18270 join (meet ?26 ?27) (meet ?26 ?28)
18271 [28, 27, 26] by equation_H82 ?26 ?27 ?28
18273 19698: Id : 1, {_}:
18274 meet a (join b (meet a c))
18276 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
18281 19698: join 17 2 4 0,2,2
18282 19698: meet 20 2 6 0,2
18283 19698: c 3 0 3 2,2,2,2
18284 19698: b 4 0 4 1,2,2
18286 NO CLASH, using fixed ground order
18288 19699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18289 19699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18290 19699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18291 19699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18292 19699: Id : 6, {_}:
18293 meet ?12 ?13 =?= meet ?13 ?12
18294 [13, 12] by commutativity_of_meet ?12 ?13
18295 19699: Id : 7, {_}:
18296 join ?15 ?16 =?= join ?16 ?15
18297 [16, 15] by commutativity_of_join ?15 ?16
18298 19699: Id : 8, {_}:
18299 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18300 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18301 19699: Id : 9, {_}:
18302 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18303 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18304 19699: Id : 10, {_}:
18305 meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
18307 join (meet ?26 ?27) (meet ?26 ?28)
18308 [28, 27, 26] by equation_H82 ?26 ?27 ?28
18310 19699: Id : 1, {_}:
18311 meet a (join b (meet a c))
18313 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
18318 19699: join 17 2 4 0,2,2
18319 19699: meet 20 2 6 0,2
18320 19699: c 3 0 3 2,2,2,2
18321 19699: b 4 0 4 1,2,2
18323 NO CLASH, using fixed ground order
18325 19700: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18326 19700: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18327 19700: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18328 19700: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18329 19700: Id : 6, {_}:
18330 meet ?12 ?13 =?= meet ?13 ?12
18331 [13, 12] by commutativity_of_meet ?12 ?13
18332 19700: Id : 7, {_}:
18333 join ?15 ?16 =?= join ?16 ?15
18334 [16, 15] by commutativity_of_join ?15 ?16
18335 19700: Id : 8, {_}:
18336 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18337 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18338 19700: Id : 9, {_}:
18339 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18340 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18341 19700: Id : 10, {_}:
18342 meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
18344 join (meet ?26 ?27) (meet ?26 ?28)
18345 [28, 27, 26] by equation_H82 ?26 ?27 ?28
18347 19700: Id : 1, {_}:
18348 meet a (join b (meet a c))
18350 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
18355 19700: join 17 2 4 0,2,2
18356 19700: meet 20 2 6 0,2
18357 19700: c 3 0 3 2,2,2,2
18358 19700: b 4 0 4 1,2,2
18360 % SZS status Timeout for LAT119-1.p
18361 NO CLASH, using fixed ground order
18363 19732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18364 19732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18365 19732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18366 19732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18367 19732: Id : 6, {_}:
18368 meet ?12 ?13 =?= meet ?13 ?12
18369 [13, 12] by commutativity_of_meet ?12 ?13
18370 19732: Id : 7, {_}:
18371 join ?15 ?16 =?= join ?16 ?15
18372 [16, 15] by commutativity_of_join ?15 ?16
18373 19732: Id : 8, {_}:
18374 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18375 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18376 19732: Id : 9, {_}:
18377 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18378 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18379 19732: Id : 10, {_}:
18380 join ?26 (meet ?27 (join ?26 ?28))
18382 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
18383 [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
18385 19732: Id : 1, {_}:
18388 meet a (join b (meet (join a b) (join c (meet a b))))
18393 19732: meet 16 2 4 0,2
18394 19732: join 18 2 4 0,2,2
18395 19732: c 2 0 2 2,2,2
18396 19732: b 4 0 4 1,2,2
18398 NO CLASH, using fixed ground order
18400 19733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18401 19733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18402 19733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18403 19733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18404 19733: Id : 6, {_}:
18405 meet ?12 ?13 =?= meet ?13 ?12
18406 [13, 12] by commutativity_of_meet ?12 ?13
18407 19733: Id : 7, {_}:
18408 join ?15 ?16 =?= join ?16 ?15
18409 [16, 15] by commutativity_of_join ?15 ?16
18410 19733: Id : 8, {_}:
18411 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18412 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18413 19733: Id : 9, {_}:
18414 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18415 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18416 19733: Id : 10, {_}:
18417 join ?26 (meet ?27 (join ?26 ?28))
18419 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
18420 [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
18422 19733: Id : 1, {_}:
18425 meet a (join b (meet (join a b) (join c (meet a b))))
18430 19733: meet 16 2 4 0,2
18431 19733: join 18 2 4 0,2,2
18432 19733: c 2 0 2 2,2,2
18433 19733: b 4 0 4 1,2,2
18435 NO CLASH, using fixed ground order
18437 19734: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18438 19734: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18439 19734: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18440 19734: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18441 19734: Id : 6, {_}:
18442 meet ?12 ?13 =?= meet ?13 ?12
18443 [13, 12] by commutativity_of_meet ?12 ?13
18444 19734: Id : 7, {_}:
18445 join ?15 ?16 =?= join ?16 ?15
18446 [16, 15] by commutativity_of_join ?15 ?16
18447 19734: Id : 8, {_}:
18448 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18449 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18450 19734: Id : 9, {_}:
18451 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18452 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18453 19734: Id : 10, {_}:
18454 join ?26 (meet ?27 (join ?26 ?28))
18456 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
18457 [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
18459 19734: Id : 1, {_}:
18462 meet a (join b (meet (join a b) (join c (meet a b))))
18467 19734: meet 16 2 4 0,2
18468 19734: join 18 2 4 0,2,2
18469 19734: c 2 0 2 2,2,2
18470 19734: b 4 0 4 1,2,2
18472 % SZS status Timeout for LAT120-1.p
18473 NO CLASH, using fixed ground order
18475 19750: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18476 19750: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18477 19750: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18478 19750: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18479 19750: Id : 6, {_}:
18480 meet ?12 ?13 =?= meet ?13 ?12
18481 [13, 12] by commutativity_of_meet ?12 ?13
18482 19750: Id : 7, {_}:
18483 join ?15 ?16 =?= join ?16 ?15
18484 [16, 15] by commutativity_of_join ?15 ?16
18485 19750: Id : 8, {_}:
18486 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18487 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18488 19750: Id : 9, {_}:
18489 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18490 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18491 19750: Id : 10, {_}:
18492 meet (join ?26 ?27) (join ?26 ?28)
18495 (meet (join ?26 ?27)
18496 (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
18497 [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
18499 19750: Id : 1, {_}:
18500 join a (meet b (join a c))
18502 join a (meet b (join c (meet a (join c b))))
18507 19750: meet 16 2 3 0,2,2
18508 19750: join 20 2 5 0,2
18509 19750: c 3 0 3 2,2,2,2
18510 19750: b 3 0 3 1,2,2
18512 NO CLASH, using fixed ground order
18514 19751: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18515 19751: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18516 19751: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18517 19751: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18518 19751: Id : 6, {_}:
18519 meet ?12 ?13 =?= meet ?13 ?12
18520 [13, 12] by commutativity_of_meet ?12 ?13
18521 19751: Id : 7, {_}:
18522 join ?15 ?16 =?= join ?16 ?15
18523 [16, 15] by commutativity_of_join ?15 ?16
18524 19751: Id : 8, {_}:
18525 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18526 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18527 19751: Id : 9, {_}:
18528 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18529 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18530 19751: Id : 10, {_}:
18531 meet (join ?26 ?27) (join ?26 ?28)
18534 (meet (join ?26 ?27)
18535 (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
18536 [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
18538 19751: Id : 1, {_}:
18539 join a (meet b (join a c))
18541 join a (meet b (join c (meet a (join c b))))
18546 19751: meet 16 2 3 0,2,2
18547 19751: join 20 2 5 0,2
18548 19751: c 3 0 3 2,2,2,2
18549 19751: b 3 0 3 1,2,2
18551 NO CLASH, using fixed ground order
18553 19752: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18554 19752: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18555 19752: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18556 19752: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18557 19752: Id : 6, {_}:
18558 meet ?12 ?13 =?= meet ?13 ?12
18559 [13, 12] by commutativity_of_meet ?12 ?13
18560 19752: Id : 7, {_}:
18561 join ?15 ?16 =?= join ?16 ?15
18562 [16, 15] by commutativity_of_join ?15 ?16
18563 19752: Id : 8, {_}:
18564 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18565 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18566 19752: Id : 9, {_}:
18567 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18568 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18569 19752: Id : 10, {_}:
18570 meet (join ?26 ?27) (join ?26 ?28)
18573 (meet (join ?26 ?27)
18574 (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
18575 [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
18577 19752: Id : 1, {_}:
18578 join a (meet b (join a c))
18580 join a (meet b (join c (meet a (join c b))))
18585 19752: meet 16 2 3 0,2,2
18586 19752: join 20 2 5 0,2
18587 19752: c 3 0 3 2,2,2,2
18588 19752: b 3 0 3 1,2,2
18590 % SZS status Timeout for LAT121-1.p
18591 NO CLASH, using fixed ground order
18593 19779: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18594 19779: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18595 19779: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18596 19779: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18597 19779: Id : 6, {_}:
18598 meet ?12 ?13 =?= meet ?13 ?12
18599 [13, 12] by commutativity_of_meet ?12 ?13
18600 19779: Id : 7, {_}:
18601 join ?15 ?16 =?= join ?16 ?15
18602 [16, 15] by commutativity_of_join ?15 ?16
18603 19779: Id : 8, {_}:
18604 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18605 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18606 19779: Id : 9, {_}:
18607 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18608 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18609 19779: Id : 10, {_}:
18610 meet (join ?26 ?27) (join ?26 ?28)
18613 (meet (join ?27 (meet ?26 (join ?27 ?28)))
18614 (join ?28 (meet ?26 ?27)))
18615 [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
18617 19779: Id : 1, {_}:
18618 join a (meet b (join a c))
18620 join a (meet b (join c (meet a (join c b))))
18625 19779: meet 16 2 3 0,2,2
18626 19779: join 20 2 5 0,2
18627 19779: c 3 0 3 2,2,2,2
18628 19779: b 3 0 3 1,2,2
18630 NO CLASH, using fixed ground order
18632 19780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18633 19780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18634 19780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18635 19780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18636 19780: Id : 6, {_}:
18637 meet ?12 ?13 =?= meet ?13 ?12
18638 [13, 12] by commutativity_of_meet ?12 ?13
18639 19780: Id : 7, {_}:
18640 join ?15 ?16 =?= join ?16 ?15
18641 [16, 15] by commutativity_of_join ?15 ?16
18642 19780: Id : 8, {_}:
18643 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18644 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18645 19780: Id : 9, {_}:
18646 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18647 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18648 19780: Id : 10, {_}:
18649 meet (join ?26 ?27) (join ?26 ?28)
18652 (meet (join ?27 (meet ?26 (join ?27 ?28)))
18653 (join ?28 (meet ?26 ?27)))
18654 [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
18656 19780: Id : 1, {_}:
18657 join a (meet b (join a c))
18659 join a (meet b (join c (meet a (join c b))))
18664 19780: meet 16 2 3 0,2,2
18665 19780: join 20 2 5 0,2
18666 19780: c 3 0 3 2,2,2,2
18667 19780: b 3 0 3 1,2,2
18669 NO CLASH, using fixed ground order
18671 19781: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18672 19781: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18673 19781: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18674 19781: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18675 19781: Id : 6, {_}:
18676 meet ?12 ?13 =?= meet ?13 ?12
18677 [13, 12] by commutativity_of_meet ?12 ?13
18678 19781: Id : 7, {_}:
18679 join ?15 ?16 =?= join ?16 ?15
18680 [16, 15] by commutativity_of_join ?15 ?16
18681 19781: Id : 8, {_}:
18682 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18683 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18684 19781: Id : 9, {_}:
18685 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18686 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18687 19781: Id : 10, {_}:
18688 meet (join ?26 ?27) (join ?26 ?28)
18691 (meet (join ?27 (meet ?26 (join ?27 ?28)))
18692 (join ?28 (meet ?26 ?27)))
18693 [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
18695 19781: Id : 1, {_}:
18696 join a (meet b (join a c))
18698 join a (meet b (join c (meet a (join c b))))
18703 19781: meet 16 2 3 0,2,2
18704 19781: join 20 2 5 0,2
18705 19781: c 3 0 3 2,2,2,2
18706 19781: b 3 0 3 1,2,2
18708 % SZS status Timeout for LAT122-1.p
18709 NO CLASH, using fixed ground order
18711 19798: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18712 19798: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18713 19798: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18714 19798: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18715 19798: Id : 6, {_}:
18716 meet ?12 ?13 =?= meet ?13 ?12
18717 [13, 12] by commutativity_of_meet ?12 ?13
18718 19798: Id : 7, {_}:
18719 join ?15 ?16 =?= join ?16 ?15
18720 [16, 15] by commutativity_of_join ?15 ?16
18721 19798: Id : 8, {_}:
18722 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18723 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18724 19798: Id : 9, {_}:
18725 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18726 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18727 19798: Id : 10, {_}:
18728 meet (join ?26 ?27) (join ?26 ?28)
18731 (meet (join ?27 (meet ?28 (join ?26 ?27)))
18732 (join ?28 (meet ?26 ?27)))
18733 [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
18735 19798: Id : 1, {_}:
18736 join a (meet b (join a c))
18738 join a (meet b (join c (meet a (join c b))))
18743 19798: meet 16 2 3 0,2,2
18744 19798: join 20 2 5 0,2
18745 19798: c 3 0 3 2,2,2,2
18746 19798: b 3 0 3 1,2,2
18748 NO CLASH, using fixed ground order
18750 19799: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18751 19799: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18752 19799: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18753 19799: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18754 19799: Id : 6, {_}:
18755 meet ?12 ?13 =?= meet ?13 ?12
18756 [13, 12] by commutativity_of_meet ?12 ?13
18757 19799: Id : 7, {_}:
18758 join ?15 ?16 =?= join ?16 ?15
18759 [16, 15] by commutativity_of_join ?15 ?16
18760 19799: Id : 8, {_}:
18761 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18762 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18763 19799: Id : 9, {_}:
18764 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18765 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18766 19799: Id : 10, {_}:
18767 meet (join ?26 ?27) (join ?26 ?28)
18770 (meet (join ?27 (meet ?28 (join ?26 ?27)))
18771 (join ?28 (meet ?26 ?27)))
18772 [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
18774 19799: Id : 1, {_}:
18775 join a (meet b (join a c))
18777 join a (meet b (join c (meet a (join c b))))
18782 19799: meet 16 2 3 0,2,2
18783 19799: join 20 2 5 0,2
18784 19799: c 3 0 3 2,2,2,2
18785 19799: b 3 0 3 1,2,2
18787 NO CLASH, using fixed ground order
18789 19800: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18790 19800: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18791 19800: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18792 19800: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18793 19800: Id : 6, {_}:
18794 meet ?12 ?13 =?= meet ?13 ?12
18795 [13, 12] by commutativity_of_meet ?12 ?13
18796 19800: Id : 7, {_}:
18797 join ?15 ?16 =?= join ?16 ?15
18798 [16, 15] by commutativity_of_join ?15 ?16
18799 19800: Id : 8, {_}:
18800 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18801 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18802 19800: Id : 9, {_}:
18803 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18804 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18805 19800: Id : 10, {_}:
18806 meet (join ?26 ?27) (join ?26 ?28)
18809 (meet (join ?27 (meet ?28 (join ?26 ?27)))
18810 (join ?28 (meet ?26 ?27)))
18811 [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
18813 19800: Id : 1, {_}:
18814 join a (meet b (join a c))
18816 join a (meet b (join c (meet a (join c b))))
18821 19800: meet 16 2 3 0,2,2
18822 19800: join 20 2 5 0,2
18823 19800: c 3 0 3 2,2,2,2
18824 19800: b 3 0 3 1,2,2
18826 % SZS status Timeout for LAT123-1.p
18827 NO CLASH, using fixed ground order
18829 19842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18830 19842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18831 19842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18832 19842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18833 19842: Id : 6, {_}:
18834 meet ?12 ?13 =?= meet ?13 ?12
18835 [13, 12] by commutativity_of_meet ?12 ?13
18836 19842: Id : 7, {_}:
18837 join ?15 ?16 =?= join ?16 ?15
18838 [16, 15] by commutativity_of_join ?15 ?16
18839 19842: Id : 8, {_}:
18840 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18841 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18842 19842: Id : 9, {_}:
18843 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18844 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18845 19842: Id : 10, {_}:
18846 join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
18848 join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
18849 [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
18851 19842: Id : 1, {_}:
18854 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
18859 19842: meet 17 2 5 0,2
18860 19842: join 20 2 4 0,2,2
18861 19842: c 3 0 3 2,2,2
18862 19842: b 3 0 3 1,2,2
18864 NO CLASH, using fixed ground order
18866 19843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18867 19843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18868 19843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18869 19843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18870 19843: Id : 6, {_}:
18871 meet ?12 ?13 =?= meet ?13 ?12
18872 [13, 12] by commutativity_of_meet ?12 ?13
18873 19843: Id : 7, {_}:
18874 join ?15 ?16 =?= join ?16 ?15
18875 [16, 15] by commutativity_of_join ?15 ?16
18876 19843: Id : 8, {_}:
18877 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18878 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18879 19843: Id : 9, {_}:
18880 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18881 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18882 19843: Id : 10, {_}:
18883 join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
18885 join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
18886 [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
18888 19843: Id : 1, {_}:
18891 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
18896 19843: meet 17 2 5 0,2
18897 19843: join 20 2 4 0,2,2
18898 19843: c 3 0 3 2,2,2
18899 19843: b 3 0 3 1,2,2
18901 NO CLASH, using fixed ground order
18903 19844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18904 19844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18905 19844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18906 19844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18907 19844: Id : 6, {_}:
18908 meet ?12 ?13 =?= meet ?13 ?12
18909 [13, 12] by commutativity_of_meet ?12 ?13
18910 19844: Id : 7, {_}:
18911 join ?15 ?16 =?= join ?16 ?15
18912 [16, 15] by commutativity_of_join ?15 ?16
18913 19844: Id : 8, {_}:
18914 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18915 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18916 19844: Id : 9, {_}:
18917 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18918 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18919 19844: Id : 10, {_}:
18920 join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
18922 join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
18923 [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
18925 19844: Id : 1, {_}:
18928 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
18933 19844: meet 17 2 5 0,2
18934 19844: join 20 2 4 0,2,2
18935 19844: c 3 0 3 2,2,2
18936 19844: b 3 0 3 1,2,2
18938 % SZS status Timeout for LAT124-1.p
18939 NO CLASH, using fixed ground order
18941 19863: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18942 19863: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18943 19863: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18944 19863: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18945 19863: Id : 6, {_}:
18946 meet ?12 ?13 =?= meet ?13 ?12
18947 [13, 12] by commutativity_of_meet ?12 ?13
18948 19863: Id : 7, {_}:
18949 join ?15 ?16 =?= join ?16 ?15
18950 [16, 15] by commutativity_of_join ?15 ?16
18951 19863: Id : 8, {_}:
18952 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
18953 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18954 19863: Id : 9, {_}:
18955 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
18956 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18957 19863: Id : 10, {_}:
18958 join ?26 (meet ?27 (join ?28 ?29))
18960 join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
18961 [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
18963 19863: Id : 1, {_}:
18966 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
18971 19863: meet 18 2 5 0,2
18972 19863: join 18 2 4 0,2,2
18973 19863: c 3 0 3 2,2,2
18974 19863: b 3 0 3 1,2,2
18976 NO CLASH, using fixed ground order
18978 19864: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
18979 19864: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
18980 19864: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
18981 19864: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
18982 19864: Id : 6, {_}:
18983 meet ?12 ?13 =?= meet ?13 ?12
18984 [13, 12] by commutativity_of_meet ?12 ?13
18985 19864: Id : 7, {_}:
18986 join ?15 ?16 =?= join ?16 ?15
18987 [16, 15] by commutativity_of_join ?15 ?16
18988 19864: Id : 8, {_}:
18989 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
18990 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
18991 19864: Id : 9, {_}:
18992 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
18993 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
18994 19864: Id : 10, {_}:
18995 join ?26 (meet ?27 (join ?28 ?29))
18997 join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
18998 [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
19000 19864: Id : 1, {_}:
19003 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
19008 19864: meet 18 2 5 0,2
19009 19864: join 18 2 4 0,2,2
19010 19864: c 3 0 3 2,2,2
19011 19864: b 3 0 3 1,2,2
19013 NO CLASH, using fixed ground order
19015 19865: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19016 19865: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19017 19865: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19018 19865: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19019 19865: Id : 6, {_}:
19020 meet ?12 ?13 =?= meet ?13 ?12
19021 [13, 12] by commutativity_of_meet ?12 ?13
19022 19865: Id : 7, {_}:
19023 join ?15 ?16 =?= join ?16 ?15
19024 [16, 15] by commutativity_of_join ?15 ?16
19025 19865: Id : 8, {_}:
19026 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19027 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19028 19865: Id : 9, {_}:
19029 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19030 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19031 19865: Id : 10, {_}:
19032 join ?26 (meet ?27 (join ?28 ?29))
19034 join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
19035 [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
19037 19865: Id : 1, {_}:
19040 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
19045 19865: meet 18 2 5 0,2
19046 19865: join 18 2 4 0,2,2
19047 19865: c 3 0 3 2,2,2
19048 19865: b 3 0 3 1,2,2
19050 % SZS status Timeout for LAT125-1.p
19051 NO CLASH, using fixed ground order
19053 19895: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19054 19895: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19055 19895: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19056 19895: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19057 19895: Id : 6, {_}:
19058 meet ?12 ?13 =?= meet ?13 ?12
19059 [13, 12] by commutativity_of_meet ?12 ?13
19060 19895: Id : 7, {_}:
19061 join ?15 ?16 =?= join ?16 ?15
19062 [16, 15] by commutativity_of_join ?15 ?16
19063 19895: Id : 8, {_}:
19064 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19065 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19066 19895: Id : 9, {_}:
19067 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19068 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19069 19895: Id : 10, {_}:
19070 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
19072 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
19073 [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
19075 19895: Id : 1, {_}:
19078 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
19083 19895: meet 18 2 5 0,2
19084 19895: join 18 2 4 0,2,2
19085 19895: c 3 0 3 2,2,2
19086 19895: b 3 0 3 1,2,2
19088 NO CLASH, using fixed ground order
19090 19894: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19091 19894: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19092 19894: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19093 19894: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19094 19894: Id : 6, {_}:
19095 meet ?12 ?13 =?= meet ?13 ?12
19096 [13, 12] by commutativity_of_meet ?12 ?13
19097 19894: Id : 7, {_}:
19098 join ?15 ?16 =?= join ?16 ?15
19099 [16, 15] by commutativity_of_join ?15 ?16
19100 19894: Id : 8, {_}:
19101 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19102 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19103 19894: Id : 9, {_}:
19104 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19105 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19106 19894: Id : 10, {_}:
19107 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
19109 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
19110 [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
19112 19894: Id : 1, {_}:
19115 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
19120 19894: meet 18 2 5 0,2
19121 19894: join 18 2 4 0,2,2
19122 19894: c 3 0 3 2,2,2
19123 19894: b 3 0 3 1,2,2
19125 NO CLASH, using fixed ground order
19127 19896: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19128 19896: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19129 19896: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19130 19896: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19131 19896: Id : 6, {_}:
19132 meet ?12 ?13 =?= meet ?13 ?12
19133 [13, 12] by commutativity_of_meet ?12 ?13
19134 19896: Id : 7, {_}:
19135 join ?15 ?16 =?= join ?16 ?15
19136 [16, 15] by commutativity_of_join ?15 ?16
19137 19896: Id : 8, {_}:
19138 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19139 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19140 19896: Id : 9, {_}:
19141 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19142 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19143 19896: Id : 10, {_}:
19144 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
19146 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
19147 [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
19149 19896: Id : 1, {_}:
19152 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
19157 19896: meet 18 2 5 0,2
19158 19896: join 18 2 4 0,2,2
19159 19896: c 3 0 3 2,2,2
19160 19896: b 3 0 3 1,2,2
19162 % SZS status Timeout for LAT126-1.p
19163 NO CLASH, using fixed ground order
19165 19924: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19166 19924: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19167 19924: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19168 19924: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19169 19924: Id : 6, {_}:
19170 meet ?12 ?13 =?= meet ?13 ?12
19171 [13, 12] by commutativity_of_meet ?12 ?13
19172 19924: Id : 7, {_}:
19173 join ?15 ?16 =?= join ?16 ?15
19174 [16, 15] by commutativity_of_join ?15 ?16
19175 19924: Id : 8, {_}:
19176 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19177 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19178 19924: Id : 9, {_}:
19179 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19180 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19181 19924: Id : 10, {_}:
19182 meet ?26 (join ?27 (meet ?26 ?28))
19184 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
19185 [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
19187 19924: Id : 1, {_}:
19188 meet a (join b (meet a c))
19190 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
19195 19924: join 16 2 4 0,2,2
19196 19924: meet 20 2 6 0,2
19197 19924: c 3 0 3 2,2,2,2
19198 19924: b 3 0 3 1,2,2
19200 NO CLASH, using fixed ground order
19202 19925: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19203 19925: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19204 19925: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19205 19925: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19206 19925: Id : 6, {_}:
19207 meet ?12 ?13 =?= meet ?13 ?12
19208 [13, 12] by commutativity_of_meet ?12 ?13
19209 19925: Id : 7, {_}:
19210 join ?15 ?16 =?= join ?16 ?15
19211 [16, 15] by commutativity_of_join ?15 ?16
19212 19925: Id : 8, {_}:
19213 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19214 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19215 19925: Id : 9, {_}:
19216 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19217 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19218 19925: Id : 10, {_}:
19219 meet ?26 (join ?27 (meet ?26 ?28))
19221 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
19222 [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
19224 19925: Id : 1, {_}:
19225 meet a (join b (meet a c))
19227 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
19232 19925: join 16 2 4 0,2,2
19233 19925: meet 20 2 6 0,2
19234 19925: c 3 0 3 2,2,2,2
19235 19925: b 3 0 3 1,2,2
19237 NO CLASH, using fixed ground order
19239 19926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19240 19926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19241 19926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19242 19926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19243 19926: Id : 6, {_}:
19244 meet ?12 ?13 =?= meet ?13 ?12
19245 [13, 12] by commutativity_of_meet ?12 ?13
19246 19926: Id : 7, {_}:
19247 join ?15 ?16 =?= join ?16 ?15
19248 [16, 15] by commutativity_of_join ?15 ?16
19249 19926: Id : 8, {_}:
19250 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19251 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19252 19926: Id : 9, {_}:
19253 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19254 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19255 19926: Id : 10, {_}:
19256 meet ?26 (join ?27 (meet ?26 ?28))
19258 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
19259 [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
19261 19926: Id : 1, {_}:
19262 meet a (join b (meet a c))
19264 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
19269 19926: join 16 2 4 0,2,2
19270 19926: meet 20 2 6 0,2
19271 19926: c 3 0 3 2,2,2,2
19272 19926: b 3 0 3 1,2,2
19274 % SZS status Timeout for LAT127-1.p
19275 NO CLASH, using fixed ground order
19277 20053: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19278 20053: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19279 20053: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19280 20053: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19281 20053: Id : 6, {_}:
19282 meet ?12 ?13 =?= meet ?13 ?12
19283 [13, 12] by commutativity_of_meet ?12 ?13
19284 20053: Id : 7, {_}:
19285 join ?15 ?16 =?= join ?16 ?15
19286 [16, 15] by commutativity_of_join ?15 ?16
19287 20053: Id : 8, {_}:
19288 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19289 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19290 20053: Id : 9, {_}:
19291 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19292 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19293 20053: Id : 10, {_}:
19294 join ?26 (meet ?27 ?28)
19296 join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
19297 [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
19299 20053: Id : 1, {_}:
19300 meet a (join b (meet a c))
19302 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
19307 20053: join 17 2 4 0,2,2
19308 20053: meet 19 2 6 0,2
19309 20053: c 3 0 3 2,2,2,2
19310 20053: b 4 0 4 1,2,2
19312 NO CLASH, using fixed ground order
19314 20054: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19315 20054: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19316 20054: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19317 20054: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19318 20054: Id : 6, {_}:
19319 meet ?12 ?13 =?= meet ?13 ?12
19320 [13, 12] by commutativity_of_meet ?12 ?13
19321 20054: Id : 7, {_}:
19322 join ?15 ?16 =?= join ?16 ?15
19323 [16, 15] by commutativity_of_join ?15 ?16
19324 20054: Id : 8, {_}:
19325 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19326 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19327 20054: Id : 9, {_}:
19328 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19329 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19330 20054: Id : 10, {_}:
19331 join ?26 (meet ?27 ?28)
19333 join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
19334 [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
19336 20054: Id : 1, {_}:
19337 meet a (join b (meet a c))
19339 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
19344 20054: join 17 2 4 0,2,2
19345 20054: meet 19 2 6 0,2
19346 20054: c 3 0 3 2,2,2,2
19347 20054: b 4 0 4 1,2,2
19349 NO CLASH, using fixed ground order
19351 20055: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19352 20055: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19353 20055: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19354 20055: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19355 20055: Id : 6, {_}:
19356 meet ?12 ?13 =?= meet ?13 ?12
19357 [13, 12] by commutativity_of_meet ?12 ?13
19358 20055: Id : 7, {_}:
19359 join ?15 ?16 =?= join ?16 ?15
19360 [16, 15] by commutativity_of_join ?15 ?16
19361 20055: Id : 8, {_}:
19362 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19363 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19364 20055: Id : 9, {_}:
19365 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19366 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19367 20055: Id : 10, {_}:
19368 join ?26 (meet ?27 ?28)
19370 join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
19371 [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
19373 20055: Id : 1, {_}:
19374 meet a (join b (meet a c))
19376 meet a (join b (meet c (join b (meet a (join c (meet a b))))))
19381 20055: join 17 2 4 0,2,2
19382 20055: meet 19 2 6 0,2
19383 20055: c 3 0 3 2,2,2,2
19384 20055: b 4 0 4 1,2,2
19386 % SZS status Timeout for LAT128-1.p
19387 NO CLASH, using fixed ground order
19389 20071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19390 20071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19391 20071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19392 20071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19393 20071: Id : 6, {_}:
19394 meet ?12 ?13 =?= meet ?13 ?12
19395 [13, 12] by commutativity_of_meet ?12 ?13
19396 20071: Id : 7, {_}:
19397 join ?15 ?16 =?= join ?16 ?15
19398 [16, 15] by commutativity_of_join ?15 ?16
19399 20071: Id : 8, {_}:
19400 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19401 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19402 20071: Id : 9, {_}:
19403 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19404 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19405 20071: Id : 10, {_}:
19406 join ?26 (meet ?27 ?28)
19408 join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
19409 [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
19411 20071: Id : 1, {_}:
19412 meet a (join b (meet a c))
19414 meet a (join b (meet c (join a (meet b c))))
19419 20071: join 16 2 3 0,2,2
19420 20071: meet 18 2 5 0,2
19421 20071: c 3 0 3 2,2,2,2
19422 20071: b 3 0 3 1,2,2
19424 NO CLASH, using fixed ground order
19426 20072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19427 20072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19428 20072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19429 20072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19430 20072: Id : 6, {_}:
19431 meet ?12 ?13 =?= meet ?13 ?12
19432 [13, 12] by commutativity_of_meet ?12 ?13
19433 20072: Id : 7, {_}:
19434 join ?15 ?16 =?= join ?16 ?15
19435 [16, 15] by commutativity_of_join ?15 ?16
19436 20072: Id : 8, {_}:
19437 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19438 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19439 20072: Id : 9, {_}:
19440 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19441 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19442 20072: Id : 10, {_}:
19443 join ?26 (meet ?27 ?28)
19445 join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
19446 [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
19448 20072: Id : 1, {_}:
19449 meet a (join b (meet a c))
19451 meet a (join b (meet c (join a (meet b c))))
19456 20072: join 16 2 3 0,2,2
19457 20072: meet 18 2 5 0,2
19458 20072: c 3 0 3 2,2,2,2
19459 20072: b 3 0 3 1,2,2
19461 NO CLASH, using fixed ground order
19463 20073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19464 20073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19465 20073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19466 20073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19467 20073: Id : 6, {_}:
19468 meet ?12 ?13 =?= meet ?13 ?12
19469 [13, 12] by commutativity_of_meet ?12 ?13
19470 20073: Id : 7, {_}:
19471 join ?15 ?16 =?= join ?16 ?15
19472 [16, 15] by commutativity_of_join ?15 ?16
19473 20073: Id : 8, {_}:
19474 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19475 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19476 20073: Id : 9, {_}:
19477 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19478 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19479 20073: Id : 10, {_}:
19480 join ?26 (meet ?27 ?28)
19482 join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
19483 [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
19485 20073: Id : 1, {_}:
19486 meet a (join b (meet a c))
19488 meet a (join b (meet c (join a (meet b c))))
19493 20073: join 16 2 3 0,2,2
19494 20073: meet 18 2 5 0,2
19495 20073: c 3 0 3 2,2,2,2
19496 20073: b 3 0 3 1,2,2
19498 % SZS status Timeout for LAT129-1.p
19499 NO CLASH, using fixed ground order
19501 20105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19502 20105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19503 20105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19504 20105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19505 20105: Id : 6, {_}:
19506 meet ?12 ?13 =?= meet ?13 ?12
19507 [13, 12] by commutativity_of_meet ?12 ?13
19508 20105: Id : 7, {_}:
19509 join ?15 ?16 =?= join ?16 ?15
19510 [16, 15] by commutativity_of_join ?15 ?16
19511 20105: Id : 8, {_}:
19512 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19513 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19514 20105: Id : 9, {_}:
19515 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19516 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19517 20105: Id : 10, {_}:
19518 join ?26 (meet ?27 ?28)
19520 join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
19521 [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
19523 20105: Id : 1, {_}:
19524 meet a (join b (meet c (join a d)))
19526 meet a (join b (meet c (join d (meet a c))))
19531 20105: meet 17 2 5 0,2
19532 20105: join 17 2 4 0,2,2
19533 20105: d 2 0 2 2,2,2,2,2
19534 20105: c 3 0 3 1,2,2,2
19535 20105: b 2 0 2 1,2,2
19537 NO CLASH, using fixed ground order
19539 20106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19540 20106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19541 20106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19542 20106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19543 20106: Id : 6, {_}:
19544 meet ?12 ?13 =?= meet ?13 ?12
19545 [13, 12] by commutativity_of_meet ?12 ?13
19546 20106: Id : 7, {_}:
19547 join ?15 ?16 =?= join ?16 ?15
19548 [16, 15] by commutativity_of_join ?15 ?16
19549 20106: Id : 8, {_}:
19550 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19551 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19552 20106: Id : 9, {_}:
19553 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19554 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19555 20106: Id : 10, {_}:
19556 join ?26 (meet ?27 ?28)
19558 join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
19559 [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
19561 20106: Id : 1, {_}:
19562 meet a (join b (meet c (join a d)))
19564 meet a (join b (meet c (join d (meet a c))))
19569 20106: meet 17 2 5 0,2
19570 20106: join 17 2 4 0,2,2
19571 20106: d 2 0 2 2,2,2,2,2
19572 20106: c 3 0 3 1,2,2,2
19573 20106: b 2 0 2 1,2,2
19575 NO CLASH, using fixed ground order
19577 20107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19578 20107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19579 20107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19580 20107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19581 20107: Id : 6, {_}:
19582 meet ?12 ?13 =?= meet ?13 ?12
19583 [13, 12] by commutativity_of_meet ?12 ?13
19584 20107: Id : 7, {_}:
19585 join ?15 ?16 =?= join ?16 ?15
19586 [16, 15] by commutativity_of_join ?15 ?16
19587 20107: Id : 8, {_}:
19588 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19589 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19590 20107: Id : 9, {_}:
19591 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19592 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19593 20107: Id : 10, {_}:
19594 join ?26 (meet ?27 ?28)
19596 join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
19597 [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
19599 20107: Id : 1, {_}:
19600 meet a (join b (meet c (join a d)))
19602 meet a (join b (meet c (join d (meet a c))))
19607 20107: meet 17 2 5 0,2
19608 20107: join 17 2 4 0,2,2
19609 20107: d 2 0 2 2,2,2,2,2
19610 20107: c 3 0 3 1,2,2,2
19611 20107: b 2 0 2 1,2,2
19613 % SZS status Timeout for LAT130-1.p
19614 NO CLASH, using fixed ground order
19616 20123: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19617 20123: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19618 20123: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19619 20123: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19620 20123: Id : 6, {_}:
19621 meet ?12 ?13 =?= meet ?13 ?12
19622 [13, 12] by commutativity_of_meet ?12 ?13
19623 20123: Id : 7, {_}:
19624 join ?15 ?16 =?= join ?16 ?15
19625 [16, 15] by commutativity_of_join ?15 ?16
19626 20123: Id : 8, {_}:
19627 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19628 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19629 20123: Id : 9, {_}:
19630 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19631 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19632 20123: Id : 10, {_}:
19633 join ?26 (meet ?27 ?28)
19635 join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
19636 [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
19638 20123: Id : 1, {_}:
19639 meet a (join b (meet c (join a d)))
19641 meet a (join b (meet c (join b (join d (meet a c)))))
19646 20123: meet 17 2 5 0,2
19647 20123: join 18 2 5 0,2,2
19648 20123: d 2 0 2 2,2,2,2,2
19649 20123: c 3 0 3 1,2,2,2
19650 20123: b 3 0 3 1,2,2
19652 NO CLASH, using fixed ground order
19654 20124: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19655 20124: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19656 20124: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19657 20124: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19658 20124: Id : 6, {_}:
19659 meet ?12 ?13 =?= meet ?13 ?12
19660 [13, 12] by commutativity_of_meet ?12 ?13
19661 20124: Id : 7, {_}:
19662 join ?15 ?16 =?= join ?16 ?15
19663 [16, 15] by commutativity_of_join ?15 ?16
19664 20124: Id : 8, {_}:
19665 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19666 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19667 20124: Id : 9, {_}:
19668 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19669 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19670 20124: Id : 10, {_}:
19671 join ?26 (meet ?27 ?28)
19673 join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
19674 [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
19676 20124: Id : 1, {_}:
19677 meet a (join b (meet c (join a d)))
19679 meet a (join b (meet c (join b (join d (meet a c)))))
19684 20124: meet 17 2 5 0,2
19685 20124: join 18 2 5 0,2,2
19686 20124: d 2 0 2 2,2,2,2,2
19687 20124: c 3 0 3 1,2,2,2
19688 20124: b 3 0 3 1,2,2
19690 NO CLASH, using fixed ground order
19692 20125: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19693 20125: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19694 20125: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19695 20125: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19696 20125: Id : 6, {_}:
19697 meet ?12 ?13 =?= meet ?13 ?12
19698 [13, 12] by commutativity_of_meet ?12 ?13
19699 20125: Id : 7, {_}:
19700 join ?15 ?16 =?= join ?16 ?15
19701 [16, 15] by commutativity_of_join ?15 ?16
19702 20125: Id : 8, {_}:
19703 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19704 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19705 20125: Id : 9, {_}:
19706 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19707 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19708 20125: Id : 10, {_}:
19709 join ?26 (meet ?27 ?28)
19711 join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
19712 [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
19714 20125: Id : 1, {_}:
19715 meet a (join b (meet c (join a d)))
19717 meet a (join b (meet c (join b (join d (meet a c)))))
19722 20125: meet 17 2 5 0,2
19723 20125: join 18 2 5 0,2,2
19724 20125: d 2 0 2 2,2,2,2,2
19725 20125: c 3 0 3 1,2,2,2
19726 20125: b 3 0 3 1,2,2
19728 % SZS status Timeout for LAT131-1.p
19729 NO CLASH, using fixed ground order
19731 20152: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19732 20152: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19733 20152: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19734 20152: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19735 20152: Id : 6, {_}:
19736 meet ?12 ?13 =?= meet ?13 ?12
19737 [13, 12] by commutativity_of_meet ?12 ?13
19738 20152: Id : 7, {_}:
19739 join ?15 ?16 =?= join ?16 ?15
19740 [16, 15] by commutativity_of_join ?15 ?16
19741 20152: Id : 8, {_}:
19742 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19743 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19744 20152: Id : 9, {_}:
19745 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19746 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19747 20152: Id : 10, {_}:
19748 join ?26 (meet ?27 ?28)
19750 meet (join ?26 (meet ?28 (join ?26 ?27)))
19751 (join ?26 (meet ?27 (join ?26 ?28)))
19752 [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
19754 20152: Id : 1, {_}:
19755 meet a (join b (meet c (join a d)))
19757 meet a (join b (meet c (join b (join d (meet a c)))))
19762 20152: meet 18 2 5 0,2
19763 20152: join 19 2 5 0,2,2
19764 20152: d 2 0 2 2,2,2,2,2
19765 20152: c 3 0 3 1,2,2,2
19766 20152: b 3 0 3 1,2,2
19768 NO CLASH, using fixed ground order
19770 20153: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19771 20153: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19772 20153: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19773 20153: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19774 20153: Id : 6, {_}:
19775 meet ?12 ?13 =?= meet ?13 ?12
19776 [13, 12] by commutativity_of_meet ?12 ?13
19777 20153: Id : 7, {_}:
19778 join ?15 ?16 =?= join ?16 ?15
19779 [16, 15] by commutativity_of_join ?15 ?16
19780 20153: Id : 8, {_}:
19781 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19782 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19783 20153: Id : 9, {_}:
19784 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19785 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19786 20153: Id : 10, {_}:
19787 join ?26 (meet ?27 ?28)
19789 meet (join ?26 (meet ?28 (join ?26 ?27)))
19790 (join ?26 (meet ?27 (join ?26 ?28)))
19791 [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
19793 20153: Id : 1, {_}:
19794 meet a (join b (meet c (join a d)))
19796 meet a (join b (meet c (join b (join d (meet a c)))))
19801 20153: meet 18 2 5 0,2
19802 20153: join 19 2 5 0,2,2
19803 20153: d 2 0 2 2,2,2,2,2
19804 20153: c 3 0 3 1,2,2,2
19805 20153: b 3 0 3 1,2,2
19807 NO CLASH, using fixed ground order
19809 20154: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19810 20154: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19811 20154: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19812 20154: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19813 20154: Id : 6, {_}:
19814 meet ?12 ?13 =?= meet ?13 ?12
19815 [13, 12] by commutativity_of_meet ?12 ?13
19816 20154: Id : 7, {_}:
19817 join ?15 ?16 =?= join ?16 ?15
19818 [16, 15] by commutativity_of_join ?15 ?16
19819 20154: Id : 8, {_}:
19820 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19821 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19822 20154: Id : 9, {_}:
19823 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19824 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19825 20154: Id : 10, {_}:
19826 join ?26 (meet ?27 ?28)
19828 meet (join ?26 (meet ?28 (join ?26 ?27)))
19829 (join ?26 (meet ?27 (join ?26 ?28)))
19830 [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
19832 20154: Id : 1, {_}:
19833 meet a (join b (meet c (join a d)))
19835 meet a (join b (meet c (join b (join d (meet a c)))))
19840 20154: meet 18 2 5 0,2
19841 20154: join 19 2 5 0,2,2
19842 20154: d 2 0 2 2,2,2,2,2
19843 20154: c 3 0 3 1,2,2,2
19844 20154: b 3 0 3 1,2,2
19846 % SZS status Timeout for LAT132-1.p
19847 NO CLASH, using fixed ground order
19849 20170: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19850 20170: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19851 20170: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19852 20170: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19853 20170: Id : 6, {_}:
19854 meet ?12 ?13 =?= meet ?13 ?12
19855 [13, 12] by commutativity_of_meet ?12 ?13
19856 20170: Id : 7, {_}:
19857 join ?15 ?16 =?= join ?16 ?15
19858 [16, 15] by commutativity_of_join ?15 ?16
19859 20170: Id : 8, {_}:
19860 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
19861 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19862 20170: Id : 9, {_}:
19863 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
19864 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19865 20170: Id : 10, {_}:
19866 join ?26 (meet ?27 (join ?26 ?28))
19868 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
19869 [28, 27, 26] by equation_H55 ?26 ?27 ?28
19871 20170: Id : 1, {_}:
19872 join a (meet b (join a c))
19874 join a (meet (join a (meet b (join a c))) (join c (meet a b)))
19875 [] by prove_H6_dual
19879 20170: meet 16 2 4 0,2,2
19880 20170: join 20 2 6 0,2
19881 20170: c 3 0 3 2,2,2,2
19882 20170: b 3 0 3 1,2,2
19884 NO CLASH, using fixed ground order
19886 20171: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19887 20171: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19888 20171: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19889 20171: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19890 20171: Id : 6, {_}:
19891 meet ?12 ?13 =?= meet ?13 ?12
19892 [13, 12] by commutativity_of_meet ?12 ?13
19893 20171: Id : 7, {_}:
19894 join ?15 ?16 =?= join ?16 ?15
19895 [16, 15] by commutativity_of_join ?15 ?16
19896 20171: Id : 8, {_}:
19897 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19898 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19899 20171: Id : 9, {_}:
19900 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19901 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19902 20171: Id : 10, {_}:
19903 join ?26 (meet ?27 (join ?26 ?28))
19905 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
19906 [28, 27, 26] by equation_H55 ?26 ?27 ?28
19908 20171: Id : 1, {_}:
19909 join a (meet b (join a c))
19911 join a (meet (join a (meet b (join a c))) (join c (meet a b)))
19912 [] by prove_H6_dual
19916 20171: meet 16 2 4 0,2,2
19917 20171: join 20 2 6 0,2
19918 20171: c 3 0 3 2,2,2,2
19919 20171: b 3 0 3 1,2,2
19921 NO CLASH, using fixed ground order
19923 20172: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19924 20172: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19925 20172: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19926 20172: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19927 20172: Id : 6, {_}:
19928 meet ?12 ?13 =?= meet ?13 ?12
19929 [13, 12] by commutativity_of_meet ?12 ?13
19930 20172: Id : 7, {_}:
19931 join ?15 ?16 =?= join ?16 ?15
19932 [16, 15] by commutativity_of_join ?15 ?16
19933 20172: Id : 8, {_}:
19934 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19935 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19936 20172: Id : 9, {_}:
19937 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19938 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19939 20172: Id : 10, {_}:
19940 join ?26 (meet ?27 (join ?26 ?28))
19942 join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
19943 [28, 27, 26] by equation_H55 ?26 ?27 ?28
19945 20172: Id : 1, {_}:
19946 join a (meet b (join a c))
19948 join a (meet (join a (meet b (join a c))) (join c (meet a b)))
19949 [] by prove_H6_dual
19953 20172: meet 16 2 4 0,2,2
19954 20172: join 20 2 6 0,2
19955 20172: c 3 0 3 2,2,2,2
19956 20172: b 3 0 3 1,2,2
19958 % SZS status Timeout for LAT133-1.p
19959 NO CLASH, using fixed ground order
19961 20205: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19962 20205: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
19963 20205: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
19964 20205: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
19965 20205: Id : 6, {_}:
19966 meet ?12 ?13 =?= meet ?13 ?12
19967 [13, 12] by commutativity_of_meet ?12 ?13
19968 20205: Id : 7, {_}:
19969 join ?15 ?16 =?= join ?16 ?15
19970 [16, 15] by commutativity_of_join ?15 ?16
19971 20205: Id : 8, {_}:
19972 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
19973 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
19974 20205: Id : 9, {_}:
19975 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
19976 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
19977 20205: Id : 10, {_}:
19978 meet (join ?26 ?27) (join ?26 ?28)
19980 join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
19981 [28, 27, 26] by equation_H61 ?26 ?27 ?28
19983 20205: Id : 1, {_}:
19984 meet (join a b) (join a c)
19986 join a (meet (join b (meet c (join a b))) (join c (meet a b)))
19987 [] by prove_H22_dual
19991 20205: meet 16 2 4 0,2
19992 20205: c 3 0 3 2,2,2
19993 20205: join 20 2 6 0,1,2
19994 20205: b 4 0 4 2,1,2
19995 20205: a 5 0 5 1,1,2
19996 NO CLASH, using fixed ground order
19998 20204: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
19999 20204: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20000 20204: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20001 20204: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20002 20204: Id : 6, {_}:
20003 meet ?12 ?13 =?= meet ?13 ?12
20004 [13, 12] by commutativity_of_meet ?12 ?13
20005 20204: Id : 7, {_}:
20006 join ?15 ?16 =?= join ?16 ?15
20007 [16, 15] by commutativity_of_join ?15 ?16
20008 20204: Id : 8, {_}:
20009 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
20010 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20011 20204: Id : 9, {_}:
20012 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
20013 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20014 20204: Id : 10, {_}:
20015 meet (join ?26 ?27) (join ?26 ?28)
20017 join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
20018 [28, 27, 26] by equation_H61 ?26 ?27 ?28
20020 20204: Id : 1, {_}:
20021 meet (join a b) (join a c)
20023 join a (meet (join b (meet c (join a b))) (join c (meet a b)))
20024 [] by prove_H22_dual
20028 20204: meet 16 2 4 0,2
20029 20204: c 3 0 3 2,2,2
20030 20204: join 20 2 6 0,1,2
20031 20204: b 4 0 4 2,1,2
20032 20204: a 5 0 5 1,1,2
20033 NO CLASH, using fixed ground order
20035 20206: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20036 20206: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20037 20206: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20038 20206: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20039 20206: Id : 6, {_}:
20040 meet ?12 ?13 =?= meet ?13 ?12
20041 [13, 12] by commutativity_of_meet ?12 ?13
20042 20206: Id : 7, {_}:
20043 join ?15 ?16 =?= join ?16 ?15
20044 [16, 15] by commutativity_of_join ?15 ?16
20045 20206: Id : 8, {_}:
20046 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20047 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20048 20206: Id : 9, {_}:
20049 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20050 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20051 20206: Id : 10, {_}:
20052 meet (join ?26 ?27) (join ?26 ?28)
20054 join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
20055 [28, 27, 26] by equation_H61 ?26 ?27 ?28
20057 20206: Id : 1, {_}:
20058 meet (join a b) (join a c)
20060 join a (meet (join b (meet c (join a b))) (join c (meet a b)))
20061 [] by prove_H22_dual
20065 20206: meet 16 2 4 0,2
20066 20206: c 3 0 3 2,2,2
20067 20206: join 20 2 6 0,1,2
20068 20206: b 4 0 4 2,1,2
20069 20206: a 5 0 5 1,1,2
20070 % SZS status Timeout for LAT134-1.p
20071 NO CLASH, using fixed ground order
20073 20243: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20074 20243: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20075 20243: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20076 20243: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20077 20243: Id : 6, {_}:
20078 meet ?12 ?13 =?= meet ?13 ?12
20079 [13, 12] by commutativity_of_meet ?12 ?13
20080 20243: Id : 7, {_}:
20081 join ?15 ?16 =?= join ?16 ?15
20082 [16, 15] by commutativity_of_join ?15 ?16
20083 20243: Id : 8, {_}:
20084 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
20085 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20086 20243: Id : 9, {_}:
20087 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
20088 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20089 20243: Id : 10, {_}:
20090 meet ?26 (join ?27 ?28)
20092 meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
20093 [28, 27, 26] by equation_H68 ?26 ?27 ?28
20095 20243: Id : 1, {_}:
20096 join a (meet b (join c (meet a d)))
20098 join a (meet b (join c (meet d (join a c))))
20099 [] by prove_H39_dual
20103 20243: join 17 2 5 0,2
20104 20243: meet 17 2 4 0,2,2
20105 20243: d 2 0 2 2,2,2,2,2
20106 20243: c 3 0 3 1,2,2,2
20107 20243: b 2 0 2 1,2,2
20109 NO CLASH, using fixed ground order
20111 20244: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20112 20244: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20113 20244: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20114 20244: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20115 20244: Id : 6, {_}:
20116 meet ?12 ?13 =?= meet ?13 ?12
20117 [13, 12] by commutativity_of_meet ?12 ?13
20118 20244: Id : 7, {_}:
20119 join ?15 ?16 =?= join ?16 ?15
20120 [16, 15] by commutativity_of_join ?15 ?16
20121 20244: Id : 8, {_}:
20122 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20123 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20124 20244: Id : 9, {_}:
20125 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20126 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20127 20244: Id : 10, {_}:
20128 meet ?26 (join ?27 ?28)
20130 meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
20131 [28, 27, 26] by equation_H68 ?26 ?27 ?28
20133 20244: Id : 1, {_}:
20134 join a (meet b (join c (meet a d)))
20136 join a (meet b (join c (meet d (join a c))))
20137 [] by prove_H39_dual
20141 20244: join 17 2 5 0,2
20142 20244: meet 17 2 4 0,2,2
20143 20244: d 2 0 2 2,2,2,2,2
20144 20244: c 3 0 3 1,2,2,2
20145 20244: b 2 0 2 1,2,2
20147 NO CLASH, using fixed ground order
20149 20245: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20150 20245: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20151 20245: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20152 20245: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20153 20245: Id : 6, {_}:
20154 meet ?12 ?13 =?= meet ?13 ?12
20155 [13, 12] by commutativity_of_meet ?12 ?13
20156 20245: Id : 7, {_}:
20157 join ?15 ?16 =?= join ?16 ?15
20158 [16, 15] by commutativity_of_join ?15 ?16
20159 20245: Id : 8, {_}:
20160 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20161 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20162 20245: Id : 9, {_}:
20163 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20164 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20165 20245: Id : 10, {_}:
20166 meet ?26 (join ?27 ?28)
20168 meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
20169 [28, 27, 26] by equation_H68 ?26 ?27 ?28
20171 20245: Id : 1, {_}:
20172 join a (meet b (join c (meet a d)))
20174 join a (meet b (join c (meet d (join a c))))
20175 [] by prove_H39_dual
20179 20245: join 17 2 5 0,2
20180 20245: meet 17 2 4 0,2,2
20181 20245: d 2 0 2 2,2,2,2,2
20182 20245: c 3 0 3 1,2,2,2
20183 20245: b 2 0 2 1,2,2
20185 % SZS status Timeout for LAT135-1.p
20186 NO CLASH, using fixed ground order
20188 20272: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20189 20272: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20190 20272: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20191 20272: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20192 20272: Id : 6, {_}:
20193 meet ?12 ?13 =?= meet ?13 ?12
20194 [13, 12] by commutativity_of_meet ?12 ?13
20195 20272: Id : 7, {_}:
20196 join ?15 ?16 =?= join ?16 ?15
20197 [16, 15] by commutativity_of_join ?15 ?16
20198 20272: Id : 8, {_}:
20199 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
20200 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20201 20272: Id : 9, {_}:
20202 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
20203 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20204 20272: Id : 10, {_}:
20205 meet ?26 (join ?27 ?28)
20207 join (meet ?26 (join ?28 (meet ?26 ?27)))
20208 (meet ?26 (join ?27 (meet ?26 ?28)))
20209 [28, 27, 26] by equation_H69 ?26 ?27 ?28
20211 20272: Id : 1, {_}:
20212 join a (meet b (join c (meet a d)))
20214 join a (meet b (join c (meet d (join a c))))
20215 [] by prove_H39_dual
20219 20272: join 18 2 5 0,2
20220 20272: meet 18 2 4 0,2,2
20221 20272: d 2 0 2 2,2,2,2,2
20222 20272: c 3 0 3 1,2,2,2
20223 20272: b 2 0 2 1,2,2
20225 NO CLASH, using fixed ground order
20227 20273: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20228 20273: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20229 20273: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20230 20273: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20231 20273: Id : 6, {_}:
20232 meet ?12 ?13 =?= meet ?13 ?12
20233 [13, 12] by commutativity_of_meet ?12 ?13
20234 20273: Id : 7, {_}:
20235 join ?15 ?16 =?= join ?16 ?15
20236 [16, 15] by commutativity_of_join ?15 ?16
20237 20273: Id : 8, {_}:
20238 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20239 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20240 20273: Id : 9, {_}:
20241 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20242 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20243 20273: Id : 10, {_}:
20244 meet ?26 (join ?27 ?28)
20246 join (meet ?26 (join ?28 (meet ?26 ?27)))
20247 (meet ?26 (join ?27 (meet ?26 ?28)))
20248 [28, 27, 26] by equation_H69 ?26 ?27 ?28
20250 20273: Id : 1, {_}:
20251 join a (meet b (join c (meet a d)))
20253 join a (meet b (join c (meet d (join a c))))
20254 [] by prove_H39_dual
20258 20273: join 18 2 5 0,2
20259 20273: meet 18 2 4 0,2,2
20260 20273: d 2 0 2 2,2,2,2,2
20261 20273: c 3 0 3 1,2,2,2
20262 20273: b 2 0 2 1,2,2
20264 NO CLASH, using fixed ground order
20266 20274: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20267 20274: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20268 20274: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20269 20274: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20270 20274: Id : 6, {_}:
20271 meet ?12 ?13 =?= meet ?13 ?12
20272 [13, 12] by commutativity_of_meet ?12 ?13
20273 20274: Id : 7, {_}:
20274 join ?15 ?16 =?= join ?16 ?15
20275 [16, 15] by commutativity_of_join ?15 ?16
20276 20274: Id : 8, {_}:
20277 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20278 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20279 20274: Id : 9, {_}:
20280 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20281 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20282 20274: Id : 10, {_}:
20283 meet ?26 (join ?27 ?28)
20285 join (meet ?26 (join ?28 (meet ?26 ?27)))
20286 (meet ?26 (join ?27 (meet ?26 ?28)))
20287 [28, 27, 26] by equation_H69 ?26 ?27 ?28
20289 20274: Id : 1, {_}:
20290 join a (meet b (join c (meet a d)))
20292 join a (meet b (join c (meet d (join a c))))
20293 [] by prove_H39_dual
20297 20274: join 18 2 5 0,2
20298 20274: meet 18 2 4 0,2,2
20299 20274: d 2 0 2 2,2,2,2,2
20300 20274: c 3 0 3 1,2,2,2
20301 20274: b 2 0 2 1,2,2
20303 % SZS status Timeout for LAT136-1.p
20304 NO CLASH, using fixed ground order
20306 20301: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20307 20301: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20308 20301: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20309 20301: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20310 20301: Id : 6, {_}:
20311 meet ?12 ?13 =?= meet ?13 ?12
20312 [13, 12] by commutativity_of_meet ?12 ?13
20313 20301: Id : 7, {_}:
20314 join ?15 ?16 =?= join ?16 ?15
20315 [16, 15] by commutativity_of_join ?15 ?16
20316 20301: Id : 8, {_}:
20317 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
20318 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20319 20301: Id : 9, {_}:
20320 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
20321 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20322 20301: Id : 10, {_}:
20323 meet ?26 (join ?27 ?28)
20325 join (meet ?26 (join ?28 (meet ?26 ?27)))
20326 (meet ?26 (join ?27 (meet ?26 ?28)))
20327 [28, 27, 26] by equation_H69 ?26 ?27 ?28
20329 20301: Id : 1, {_}:
20330 join a (meet b (join c (meet a d)))
20332 join a (meet b (join c (meet d (join c (meet a b)))))
20333 [] by prove_H40_dual
20337 20301: join 18 2 5 0,2
20338 20301: meet 19 2 5 0,2,2
20339 20301: d 2 0 2 2,2,2,2,2
20340 20301: c 3 0 3 1,2,2,2
20341 20301: b 3 0 3 1,2,2
20343 NO CLASH, using fixed ground order
20345 20302: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20346 20302: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20347 20302: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20348 20302: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20349 20302: Id : 6, {_}:
20350 meet ?12 ?13 =?= meet ?13 ?12
20351 [13, 12] by commutativity_of_meet ?12 ?13
20352 20302: Id : 7, {_}:
20353 join ?15 ?16 =?= join ?16 ?15
20354 [16, 15] by commutativity_of_join ?15 ?16
20355 20302: Id : 8, {_}:
20356 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20357 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20358 20302: Id : 9, {_}:
20359 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20360 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20361 20302: Id : 10, {_}:
20362 meet ?26 (join ?27 ?28)
20364 join (meet ?26 (join ?28 (meet ?26 ?27)))
20365 (meet ?26 (join ?27 (meet ?26 ?28)))
20366 [28, 27, 26] by equation_H69 ?26 ?27 ?28
20368 20302: Id : 1, {_}:
20369 join a (meet b (join c (meet a d)))
20371 join a (meet b (join c (meet d (join c (meet a b)))))
20372 [] by prove_H40_dual
20376 20302: join 18 2 5 0,2
20377 20302: meet 19 2 5 0,2,2
20378 20302: d 2 0 2 2,2,2,2,2
20379 20302: c 3 0 3 1,2,2,2
20380 20302: b 3 0 3 1,2,2
20382 NO CLASH, using fixed ground order
20384 20303: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20385 20303: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20386 20303: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20387 20303: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20388 20303: Id : 6, {_}:
20389 meet ?12 ?13 =?= meet ?13 ?12
20390 [13, 12] by commutativity_of_meet ?12 ?13
20391 20303: Id : 7, {_}:
20392 join ?15 ?16 =?= join ?16 ?15
20393 [16, 15] by commutativity_of_join ?15 ?16
20394 20303: Id : 8, {_}:
20395 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20396 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20397 20303: Id : 9, {_}:
20398 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20399 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20400 20303: Id : 10, {_}:
20401 meet ?26 (join ?27 ?28)
20403 join (meet ?26 (join ?28 (meet ?26 ?27)))
20404 (meet ?26 (join ?27 (meet ?26 ?28)))
20405 [28, 27, 26] by equation_H69 ?26 ?27 ?28
20407 20303: Id : 1, {_}:
20408 join a (meet b (join c (meet a d)))
20410 join a (meet b (join c (meet d (join c (meet a b)))))
20411 [] by prove_H40_dual
20415 20303: join 18 2 5 0,2
20416 20303: meet 19 2 5 0,2,2
20417 20303: d 2 0 2 2,2,2,2,2
20418 20303: c 3 0 3 1,2,2,2
20419 20303: b 3 0 3 1,2,2
20421 % SZS status Timeout for LAT137-1.p
20422 NO CLASH, using fixed ground order
20424 20331: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20425 20331: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20426 20331: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20427 20331: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20428 20331: Id : 6, {_}:
20429 meet ?12 ?13 =?= meet ?13 ?12
20430 [13, 12] by commutativity_of_meet ?12 ?13
20431 20331: Id : 7, {_}:
20432 join ?15 ?16 =?= join ?16 ?15
20433 [16, 15] by commutativity_of_join ?15 ?16
20434 20331: Id : 8, {_}:
20435 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
20436 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20437 20331: Id : 9, {_}:
20438 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
20439 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20440 20331: Id : 10, {_}:
20441 join (meet ?26 ?27) (meet ?26 ?28)
20443 meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
20444 [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
20446 20331: Id : 1, {_}:
20447 meet a (join b (meet a c))
20449 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
20454 20331: join 16 2 4 0,2,2
20455 20331: meet 20 2 6 0,2
20456 20331: c 3 0 3 2,2,2,2
20457 20331: b 3 0 3 1,2,2
20459 NO CLASH, using fixed ground order
20461 20332: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20462 20332: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20463 20332: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20464 20332: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20465 20332: Id : 6, {_}:
20466 meet ?12 ?13 =?= meet ?13 ?12
20467 [13, 12] by commutativity_of_meet ?12 ?13
20468 20332: Id : 7, {_}:
20469 join ?15 ?16 =?= join ?16 ?15
20470 [16, 15] by commutativity_of_join ?15 ?16
20471 20332: Id : 8, {_}:
20472 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20473 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20474 20332: Id : 9, {_}:
20475 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20476 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20477 20332: Id : 10, {_}:
20478 join (meet ?26 ?27) (meet ?26 ?28)
20480 meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
20481 [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
20483 20332: Id : 1, {_}:
20484 meet a (join b (meet a c))
20486 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
20491 20332: join 16 2 4 0,2,2
20492 20332: meet 20 2 6 0,2
20493 20332: c 3 0 3 2,2,2,2
20494 20332: b 3 0 3 1,2,2
20496 NO CLASH, using fixed ground order
20498 20333: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
20499 20333: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
20500 20333: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
20501 20333: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
20502 20333: Id : 6, {_}:
20503 meet ?12 ?13 =?= meet ?13 ?12
20504 [13, 12] by commutativity_of_meet ?12 ?13
20505 20333: Id : 7, {_}:
20506 join ?15 ?16 =?= join ?16 ?15
20507 [16, 15] by commutativity_of_join ?15 ?16
20508 20333: Id : 8, {_}:
20509 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
20510 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
20511 20333: Id : 9, {_}:
20512 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
20513 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
20514 20333: Id : 10, {_}:
20515 join (meet ?26 ?27) (meet ?26 ?28)
20517 meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
20518 [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
20520 20333: Id : 1, {_}:
20521 meet a (join b (meet a c))
20523 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
20528 20333: join 16 2 4 0,2,2
20529 20333: meet 20 2 6 0,2
20530 20333: c 3 0 3 2,2,2,2
20531 20333: b 3 0 3 1,2,2
20533 % SZS status Timeout for LAT171-1.p
20534 NO CLASH, using fixed ground order
20536 20686: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20537 20686: Id : 3, {_}:
20538 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20541 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20542 20686: Id : 4, {_}:
20543 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20544 [9, 8] by wajsberg_3 ?8 ?9
20545 20686: Id : 5, {_}:
20546 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20547 [12, 11] by wajsberg_4 ?11 ?12
20548 20686: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
20550 20686: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
20556 20686: truth 4 0 1 3
20557 20686: implies 16 2 1 0,2
20560 NO CLASH, using fixed ground order
20562 20687: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20563 20687: Id : 3, {_}:
20564 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20567 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20568 20687: Id : 4, {_}:
20569 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20570 [9, 8] by wajsberg_3 ?8 ?9
20571 20687: Id : 5, {_}:
20572 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20573 [12, 11] by wajsberg_4 ?11 ?12
20574 20687: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
20576 20687: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
20582 20687: truth 4 0 1 3
20583 20687: implies 16 2 1 0,2
20586 NO CLASH, using fixed ground order
20588 20688: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20589 20688: Id : 3, {_}:
20590 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20593 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20594 20688: Id : 4, {_}:
20595 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20596 [9, 8] by wajsberg_3 ?8 ?9
20597 20688: Id : 5, {_}:
20598 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20599 [12, 11] by wajsberg_4 ?11 ?12
20600 20688: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
20602 20688: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
20608 20688: truth 4 0 1 3
20609 20688: implies 16 2 1 0,2
20612 % SZS status Timeout for LCL136-1.p
20613 NO CLASH, using fixed ground order
20615 20715: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20616 20715: Id : 3, {_}:
20617 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20620 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20621 20715: Id : 4, {_}:
20622 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20623 [9, 8] by wajsberg_3 ?8 ?9
20624 20715: Id : 5, {_}:
20625 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20626 [12, 11] by wajsberg_4 ?11 ?12
20628 20715: Id : 1, {_}:
20629 implies (implies (implies x y) y)
20630 (implies (implies y z) (implies x z))
20633 [] by prove_wajsberg_lemma
20638 20715: truth 4 0 1 3
20639 20715: z 2 0 2 2,1,2,2
20640 20715: implies 19 2 6 0,2
20641 20715: y 3 0 3 2,1,1,2
20642 20715: x 2 0 2 1,1,1,2
20643 NO CLASH, using fixed ground order
20645 20716: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20646 20716: Id : 3, {_}:
20647 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20650 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20651 20716: Id : 4, {_}:
20652 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20653 [9, 8] by wajsberg_3 ?8 ?9
20654 20716: Id : 5, {_}:
20655 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20656 [12, 11] by wajsberg_4 ?11 ?12
20658 20716: Id : 1, {_}:
20659 implies (implies (implies x y) y)
20660 (implies (implies y z) (implies x z))
20663 [] by prove_wajsberg_lemma
20668 20716: truth 4 0 1 3
20669 20716: z 2 0 2 2,1,2,2
20670 20716: implies 19 2 6 0,2
20671 20716: y 3 0 3 2,1,1,2
20672 20716: x 2 0 2 1,1,1,2
20673 NO CLASH, using fixed ground order
20675 20717: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20676 20717: Id : 3, {_}:
20677 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20680 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20681 20717: Id : 4, {_}:
20682 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20683 [9, 8] by wajsberg_3 ?8 ?9
20684 20717: Id : 5, {_}:
20685 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20686 [12, 11] by wajsberg_4 ?11 ?12
20688 20717: Id : 1, {_}:
20689 implies (implies (implies x y) y)
20690 (implies (implies y z) (implies x z))
20693 [] by prove_wajsberg_lemma
20698 20717: truth 4 0 1 3
20699 20717: z 2 0 2 2,1,2,2
20700 20717: implies 19 2 6 0,2
20701 20717: y 3 0 3 2,1,1,2
20702 20717: x 2 0 2 1,1,1,2
20703 % SZS status Timeout for LCL137-1.p
20704 NO CLASH, using fixed ground order
20706 20733: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20707 20733: Id : 3, {_}:
20708 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20711 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20712 20733: Id : 4, {_}:
20713 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20714 [9, 8] by wajsberg_3 ?8 ?9
20715 20733: Id : 5, {_}:
20716 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20717 [12, 11] by wajsberg_4 ?11 ?12
20718 20733: Id : 6, {_}:
20719 or ?14 ?15 =<= implies (not ?14) ?15
20720 [15, 14] by or_definition ?14 ?15
20721 20733: Id : 7, {_}:
20722 or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
20723 [19, 18, 17] by or_associativity ?17 ?18 ?19
20724 20733: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
20725 20733: Id : 9, {_}:
20726 and ?24 ?25 =<= not (or (not ?24) (not ?25))
20727 [25, 24] by and_definition ?24 ?25
20728 20733: Id : 10, {_}:
20729 and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
20730 [29, 28, 27] by and_associativity ?27 ?28 ?29
20731 20733: Id : 11, {_}:
20732 and ?31 ?32 =?= and ?32 ?31
20733 [32, 31] by and_commutativity ?31 ?32
20735 20733: Id : 1, {_}:
20736 not (or (and x (or x x)) (and x x))
20738 and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
20739 [] by prove_wajsberg_theorem
20743 20733: implies 14 2 0
20745 20733: not 12 1 6 0,2
20746 20733: and 11 2 4 0,1,1,2
20747 20733: or 12 2 4 0,1,2
20748 20733: x 10 0 10 1,1,1,2
20749 NO CLASH, using fixed ground order
20751 20734: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20752 20734: Id : 3, {_}:
20753 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20756 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20757 20734: Id : 4, {_}:
20758 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20759 [9, 8] by wajsberg_3 ?8 ?9
20760 20734: Id : 5, {_}:
20761 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20762 [12, 11] by wajsberg_4 ?11 ?12
20763 20734: Id : 6, {_}:
20764 or ?14 ?15 =<= implies (not ?14) ?15
20765 [15, 14] by or_definition ?14 ?15
20766 20734: Id : 7, {_}:
20767 or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
20768 [19, 18, 17] by or_associativity ?17 ?18 ?19
20769 20734: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
20770 20734: Id : 9, {_}:
20771 and ?24 ?25 =<= not (or (not ?24) (not ?25))
20772 [25, 24] by and_definition ?24 ?25
20773 20734: Id : 10, {_}:
20774 and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
20775 [29, 28, 27] by and_associativity ?27 ?28 ?29
20776 20734: Id : 11, {_}:
20777 and ?31 ?32 =?= and ?32 ?31
20778 [32, 31] by and_commutativity ?31 ?32
20780 NO CLASH, using fixed ground order
20782 20735: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
20783 20735: Id : 3, {_}:
20784 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
20787 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
20788 20735: Id : 4, {_}:
20789 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
20790 [9, 8] by wajsberg_3 ?8 ?9
20791 20735: Id : 5, {_}:
20792 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
20793 [12, 11] by wajsberg_4 ?11 ?12
20794 20735: Id : 6, {_}:
20795 or ?14 ?15 =>= implies (not ?14) ?15
20796 [15, 14] by or_definition ?14 ?15
20797 20735: Id : 7, {_}:
20798 or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
20799 [19, 18, 17] by or_associativity ?17 ?18 ?19
20800 20735: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
20801 20735: Id : 9, {_}:
20802 and ?24 ?25 =<= not (or (not ?24) (not ?25))
20803 [25, 24] by and_definition ?24 ?25
20804 20735: Id : 10, {_}:
20805 and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
20806 [29, 28, 27] by and_associativity ?27 ?28 ?29
20807 20735: Id : 11, {_}:
20808 and ?31 ?32 =?= and ?32 ?31
20809 [32, 31] by and_commutativity ?31 ?32
20811 20735: Id : 1, {_}:
20812 not (or (and x (or x x)) (and x x))
20814 and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
20815 [] by prove_wajsberg_theorem
20819 20735: implies 14 2 0
20821 20735: not 12 1 6 0,2
20822 20735: and 11 2 4 0,1,1,2
20823 20735: or 12 2 4 0,1,2
20824 20735: x 10 0 10 1,1,1,2
20825 20734: Id : 1, {_}:
20826 not (or (and x (or x x)) (and x x))
20828 and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
20829 [] by prove_wajsberg_theorem
20833 20734: implies 14 2 0
20835 20734: not 12 1 6 0,2
20836 20734: and 11 2 4 0,1,1,2
20837 20734: or 12 2 4 0,1,2
20838 20734: x 10 0 10 1,1,1,2
20839 % SZS status Timeout for LCL165-1.p
20840 NO CLASH, using fixed ground order
20842 20763: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
20843 20763: Id : 3, {_}:
20844 add ?4 additive_identity =>= ?4
20845 [4] by right_additive_identity ?4
20846 20763: Id : 4, {_}:
20847 multiply additive_identity ?6 =>= additive_identity
20848 [6] by left_multiplicative_zero ?6
20849 20763: Id : 5, {_}:
20850 multiply ?8 additive_identity =>= additive_identity
20851 [8] by right_multiplicative_zero ?8
20852 20763: Id : 6, {_}:
20853 add (additive_inverse ?10) ?10 =>= additive_identity
20854 [10] by left_additive_inverse ?10
20855 20763: Id : 7, {_}:
20856 add ?12 (additive_inverse ?12) =>= additive_identity
20857 [12] by right_additive_inverse ?12
20858 20763: Id : 8, {_}:
20859 additive_inverse (additive_inverse ?14) =>= ?14
20860 [14] by additive_inverse_additive_inverse ?14
20861 20763: Id : 9, {_}:
20862 multiply ?16 (add ?17 ?18)
20864 add (multiply ?16 ?17) (multiply ?16 ?18)
20865 [18, 17, 16] by distribute1 ?16 ?17 ?18
20866 20763: Id : 10, {_}:
20867 multiply (add ?20 ?21) ?22
20869 add (multiply ?20 ?22) (multiply ?21 ?22)
20870 [22, 21, 20] by distribute2 ?20 ?21 ?22
20871 20763: Id : 11, {_}:
20872 add ?24 ?25 =?= add ?25 ?24
20873 [25, 24] by commutativity_for_addition ?24 ?25
20874 20763: Id : 12, {_}:
20875 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
20876 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
20877 20763: Id : 13, {_}:
20878 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
20879 [32, 31] by right_alternative ?31 ?32
20880 20763: Id : 14, {_}:
20881 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
20882 [35, 34] by left_alternative ?34 ?35
20883 20763: Id : 15, {_}:
20884 associator ?37 ?38 ?39
20886 add (multiply (multiply ?37 ?38) ?39)
20887 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
20888 [39, 38, 37] by associator ?37 ?38 ?39
20889 20763: Id : 16, {_}:
20892 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
20893 [42, 41] by commutator ?41 ?42
20894 20763: Id : 17, {_}:
20895 multiply (additive_inverse ?44) (additive_inverse ?45)
20898 [45, 44] by product_of_inverses ?44 ?45
20899 20763: Id : 18, {_}:
20900 multiply (additive_inverse ?47) ?48
20902 additive_inverse (multiply ?47 ?48)
20903 [48, 47] by inverse_product1 ?47 ?48
20904 20763: Id : 19, {_}:
20905 multiply ?50 (additive_inverse ?51)
20907 additive_inverse (multiply ?50 ?51)
20908 [51, 50] by inverse_product2 ?50 ?51
20909 20763: Id : 20, {_}:
20910 multiply ?53 (add ?54 (additive_inverse ?55))
20912 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
20913 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
20914 20763: Id : 21, {_}:
20915 multiply (add ?57 (additive_inverse ?58)) ?59
20917 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
20918 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
20919 20763: Id : 22, {_}:
20920 multiply (additive_inverse ?61) (add ?62 ?63)
20922 add (additive_inverse (multiply ?61 ?62))
20923 (additive_inverse (multiply ?61 ?63))
20924 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
20925 20763: Id : 23, {_}:
20926 multiply (add ?65 ?66) (additive_inverse ?67)
20928 add (additive_inverse (multiply ?65 ?67))
20929 (additive_inverse (multiply ?66 ?67))
20930 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
20932 20763: Id : 1, {_}:
20933 associator x y (add u v)
20935 add (associator x y u) (associator x y v)
20936 [] by prove_linearised_form1
20940 20763: commutator 1 2 0
20941 20763: additive_inverse 22 1 0
20942 20763: multiply 40 2 0
20943 20763: additive_identity 8 0 0
20944 20763: associator 4 3 3 0,2
20945 20763: add 26 2 2 0,3,2
20946 20763: v 2 0 2 2,3,2
20947 20763: u 2 0 2 1,3,2
20950 NO CLASH, using fixed ground order
20952 20762: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
20953 20762: Id : 3, {_}:
20954 add ?4 additive_identity =>= ?4
20955 [4] by right_additive_identity ?4
20956 20762: Id : 4, {_}:
20957 multiply additive_identity ?6 =>= additive_identity
20958 [6] by left_multiplicative_zero ?6
20959 20762: Id : 5, {_}:
20960 multiply ?8 additive_identity =>= additive_identity
20961 [8] by right_multiplicative_zero ?8
20962 20762: Id : 6, {_}:
20963 add (additive_inverse ?10) ?10 =>= additive_identity
20964 [10] by left_additive_inverse ?10
20965 20762: Id : 7, {_}:
20966 add ?12 (additive_inverse ?12) =>= additive_identity
20967 [12] by right_additive_inverse ?12
20968 20762: Id : 8, {_}:
20969 additive_inverse (additive_inverse ?14) =>= ?14
20970 [14] by additive_inverse_additive_inverse ?14
20971 20762: Id : 9, {_}:
20972 multiply ?16 (add ?17 ?18)
20974 add (multiply ?16 ?17) (multiply ?16 ?18)
20975 [18, 17, 16] by distribute1 ?16 ?17 ?18
20976 20762: Id : 10, {_}:
20977 multiply (add ?20 ?21) ?22
20979 add (multiply ?20 ?22) (multiply ?21 ?22)
20980 [22, 21, 20] by distribute2 ?20 ?21 ?22
20981 20762: Id : 11, {_}:
20982 add ?24 ?25 =?= add ?25 ?24
20983 [25, 24] by commutativity_for_addition ?24 ?25
20984 20762: Id : 12, {_}:
20985 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
20986 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
20987 20762: Id : 13, {_}:
20988 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
20989 [32, 31] by right_alternative ?31 ?32
20990 20762: Id : 14, {_}:
20991 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
20992 [35, 34] by left_alternative ?34 ?35
20993 20762: Id : 15, {_}:
20994 associator ?37 ?38 ?39
20996 add (multiply (multiply ?37 ?38) ?39)
20997 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
20998 [39, 38, 37] by associator ?37 ?38 ?39
20999 20762: Id : 16, {_}:
21002 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21003 [42, 41] by commutator ?41 ?42
21004 20762: Id : 17, {_}:
21005 multiply (additive_inverse ?44) (additive_inverse ?45)
21008 [45, 44] by product_of_inverses ?44 ?45
21009 20762: Id : 18, {_}:
21010 multiply (additive_inverse ?47) ?48
21012 additive_inverse (multiply ?47 ?48)
21013 [48, 47] by inverse_product1 ?47 ?48
21014 20762: Id : 19, {_}:
21015 multiply ?50 (additive_inverse ?51)
21017 additive_inverse (multiply ?50 ?51)
21018 [51, 50] by inverse_product2 ?50 ?51
21019 20762: Id : 20, {_}:
21020 multiply ?53 (add ?54 (additive_inverse ?55))
21022 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
21023 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
21024 20762: Id : 21, {_}:
21025 multiply (add ?57 (additive_inverse ?58)) ?59
21027 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
21028 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
21029 20762: Id : 22, {_}:
21030 multiply (additive_inverse ?61) (add ?62 ?63)
21032 add (additive_inverse (multiply ?61 ?62))
21033 (additive_inverse (multiply ?61 ?63))
21034 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
21035 20762: Id : 23, {_}:
21036 multiply (add ?65 ?66) (additive_inverse ?67)
21038 add (additive_inverse (multiply ?65 ?67))
21039 (additive_inverse (multiply ?66 ?67))
21040 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
21042 20762: Id : 1, {_}:
21043 associator x y (add u v)
21045 add (associator x y u) (associator x y v)
21046 [] by prove_linearised_form1
21050 20762: commutator 1 2 0
21051 20762: additive_inverse 22 1 0
21052 20762: multiply 40 2 0
21053 20762: additive_identity 8 0 0
21054 20762: associator 4 3 3 0,2
21055 20762: add 26 2 2 0,3,2
21056 20762: v 2 0 2 2,3,2
21057 20762: u 2 0 2 1,3,2
21060 NO CLASH, using fixed ground order
21062 20764: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21063 20764: Id : 3, {_}:
21064 add ?4 additive_identity =>= ?4
21065 [4] by right_additive_identity ?4
21066 20764: Id : 4, {_}:
21067 multiply additive_identity ?6 =>= additive_identity
21068 [6] by left_multiplicative_zero ?6
21069 20764: Id : 5, {_}:
21070 multiply ?8 additive_identity =>= additive_identity
21071 [8] by right_multiplicative_zero ?8
21072 20764: Id : 6, {_}:
21073 add (additive_inverse ?10) ?10 =>= additive_identity
21074 [10] by left_additive_inverse ?10
21075 20764: Id : 7, {_}:
21076 add ?12 (additive_inverse ?12) =>= additive_identity
21077 [12] by right_additive_inverse ?12
21078 20764: Id : 8, {_}:
21079 additive_inverse (additive_inverse ?14) =>= ?14
21080 [14] by additive_inverse_additive_inverse ?14
21081 20764: Id : 9, {_}:
21082 multiply ?16 (add ?17 ?18)
21084 add (multiply ?16 ?17) (multiply ?16 ?18)
21085 [18, 17, 16] by distribute1 ?16 ?17 ?18
21086 20764: Id : 10, {_}:
21087 multiply (add ?20 ?21) ?22
21089 add (multiply ?20 ?22) (multiply ?21 ?22)
21090 [22, 21, 20] by distribute2 ?20 ?21 ?22
21091 20764: Id : 11, {_}:
21092 add ?24 ?25 =?= add ?25 ?24
21093 [25, 24] by commutativity_for_addition ?24 ?25
21094 20764: Id : 12, {_}:
21095 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
21096 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21097 20764: Id : 13, {_}:
21098 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
21099 [32, 31] by right_alternative ?31 ?32
21100 20764: Id : 14, {_}:
21101 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
21102 [35, 34] by left_alternative ?34 ?35
21103 20764: Id : 15, {_}:
21104 associator ?37 ?38 ?39
21106 add (multiply (multiply ?37 ?38) ?39)
21107 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21108 [39, 38, 37] by associator ?37 ?38 ?39
21109 20764: Id : 16, {_}:
21112 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21113 [42, 41] by commutator ?41 ?42
21114 20764: Id : 17, {_}:
21115 multiply (additive_inverse ?44) (additive_inverse ?45)
21118 [45, 44] by product_of_inverses ?44 ?45
21119 20764: Id : 18, {_}:
21120 multiply (additive_inverse ?47) ?48
21122 additive_inverse (multiply ?47 ?48)
21123 [48, 47] by inverse_product1 ?47 ?48
21124 20764: Id : 19, {_}:
21125 multiply ?50 (additive_inverse ?51)
21127 additive_inverse (multiply ?50 ?51)
21128 [51, 50] by inverse_product2 ?50 ?51
21129 20764: Id : 20, {_}:
21130 multiply ?53 (add ?54 (additive_inverse ?55))
21132 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
21133 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
21134 20764: Id : 21, {_}:
21135 multiply (add ?57 (additive_inverse ?58)) ?59
21137 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
21138 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
21139 20764: Id : 22, {_}:
21140 multiply (additive_inverse ?61) (add ?62 ?63)
21142 add (additive_inverse (multiply ?61 ?62))
21143 (additive_inverse (multiply ?61 ?63))
21144 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
21145 20764: Id : 23, {_}:
21146 multiply (add ?65 ?66) (additive_inverse ?67)
21148 add (additive_inverse (multiply ?65 ?67))
21149 (additive_inverse (multiply ?66 ?67))
21150 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
21152 20764: Id : 1, {_}:
21153 associator x y (add u v)
21155 add (associator x y u) (associator x y v)
21156 [] by prove_linearised_form1
21160 20764: commutator 1 2 0
21161 20764: additive_inverse 22 1 0
21162 20764: multiply 40 2 0
21163 20764: additive_identity 8 0 0
21164 20764: associator 4 3 3 0,2
21165 20764: add 26 2 2 0,3,2
21166 20764: v 2 0 2 2,3,2
21167 20764: u 2 0 2 1,3,2
21170 % SZS status Timeout for RNG019-7.p
21171 NO CLASH, using fixed ground order
21173 20780: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21174 20780: Id : 3, {_}:
21175 add ?4 additive_identity =>= ?4
21176 [4] by right_additive_identity ?4
21177 20780: Id : 4, {_}:
21178 multiply additive_identity ?6 =>= additive_identity
21179 [6] by left_multiplicative_zero ?6
21180 20780: Id : 5, {_}:
21181 multiply ?8 additive_identity =>= additive_identity
21182 [8] by right_multiplicative_zero ?8
21183 20780: Id : 6, {_}:
21184 add (additive_inverse ?10) ?10 =>= additive_identity
21185 [10] by left_additive_inverse ?10
21186 20780: Id : 7, {_}:
21187 add ?12 (additive_inverse ?12) =>= additive_identity
21188 [12] by right_additive_inverse ?12
21189 20780: Id : 8, {_}:
21190 additive_inverse (additive_inverse ?14) =>= ?14
21191 [14] by additive_inverse_additive_inverse ?14
21192 20780: Id : 9, {_}:
21193 multiply ?16 (add ?17 ?18)
21195 add (multiply ?16 ?17) (multiply ?16 ?18)
21196 [18, 17, 16] by distribute1 ?16 ?17 ?18
21197 20780: Id : 10, {_}:
21198 multiply (add ?20 ?21) ?22
21200 add (multiply ?20 ?22) (multiply ?21 ?22)
21201 [22, 21, 20] by distribute2 ?20 ?21 ?22
21202 20780: Id : 11, {_}:
21203 add ?24 ?25 =?= add ?25 ?24
21204 [25, 24] by commutativity_for_addition ?24 ?25
21205 20780: Id : 12, {_}:
21206 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
21207 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21208 20780: Id : 13, {_}:
21209 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
21210 [32, 31] by right_alternative ?31 ?32
21211 20780: Id : 14, {_}:
21212 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
21213 [35, 34] by left_alternative ?34 ?35
21214 20780: Id : 15, {_}:
21215 associator ?37 ?38 ?39
21217 add (multiply (multiply ?37 ?38) ?39)
21218 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21219 [39, 38, 37] by associator ?37 ?38 ?39
21220 20780: Id : 16, {_}:
21223 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21224 [42, 41] by commutator ?41 ?42
21226 20780: Id : 1, {_}:
21227 associator x (add u v) y
21229 add (associator x u y) (associator x v y)
21230 [] by prove_linearised_form2
21234 20780: commutator 1 2 0
21235 20780: additive_inverse 6 1 0
21236 20780: multiply 22 2 0
21237 20780: additive_identity 8 0 0
21238 20780: associator 4 3 3 0,2
21240 20780: add 18 2 2 0,2,2
21241 20780: v 2 0 2 2,2,2
21242 20780: u 2 0 2 1,2,2
21244 NO CLASH, using fixed ground order
21246 20781: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21247 20781: Id : 3, {_}:
21248 add ?4 additive_identity =>= ?4
21249 [4] by right_additive_identity ?4
21250 20781: Id : 4, {_}:
21251 multiply additive_identity ?6 =>= additive_identity
21252 [6] by left_multiplicative_zero ?6
21253 20781: Id : 5, {_}:
21254 multiply ?8 additive_identity =>= additive_identity
21255 [8] by right_multiplicative_zero ?8
21256 20781: Id : 6, {_}:
21257 add (additive_inverse ?10) ?10 =>= additive_identity
21258 [10] by left_additive_inverse ?10
21259 20781: Id : 7, {_}:
21260 add ?12 (additive_inverse ?12) =>= additive_identity
21261 [12] by right_additive_inverse ?12
21262 20781: Id : 8, {_}:
21263 additive_inverse (additive_inverse ?14) =>= ?14
21264 [14] by additive_inverse_additive_inverse ?14
21265 20781: Id : 9, {_}:
21266 multiply ?16 (add ?17 ?18)
21268 add (multiply ?16 ?17) (multiply ?16 ?18)
21269 [18, 17, 16] by distribute1 ?16 ?17 ?18
21270 20781: Id : 10, {_}:
21271 multiply (add ?20 ?21) ?22
21273 add (multiply ?20 ?22) (multiply ?21 ?22)
21274 [22, 21, 20] by distribute2 ?20 ?21 ?22
21275 20781: Id : 11, {_}:
21276 add ?24 ?25 =?= add ?25 ?24
21277 [25, 24] by commutativity_for_addition ?24 ?25
21278 20781: Id : 12, {_}:
21279 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
21280 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21281 20781: Id : 13, {_}:
21282 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
21283 [32, 31] by right_alternative ?31 ?32
21284 20781: Id : 14, {_}:
21285 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
21286 [35, 34] by left_alternative ?34 ?35
21287 20781: Id : 15, {_}:
21288 associator ?37 ?38 ?39
21290 add (multiply (multiply ?37 ?38) ?39)
21291 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21292 [39, 38, 37] by associator ?37 ?38 ?39
21293 20781: Id : 16, {_}:
21296 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21297 [42, 41] by commutator ?41 ?42
21299 20781: Id : 1, {_}:
21300 associator x (add u v) y
21302 add (associator x u y) (associator x v y)
21303 [] by prove_linearised_form2
21307 20781: commutator 1 2 0
21308 20781: additive_inverse 6 1 0
21309 20781: multiply 22 2 0
21310 20781: additive_identity 8 0 0
21311 20781: associator 4 3 3 0,2
21313 20781: add 18 2 2 0,2,2
21314 20781: v 2 0 2 2,2,2
21315 20781: u 2 0 2 1,2,2
21317 NO CLASH, using fixed ground order
21319 20782: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21320 20782: Id : 3, {_}:
21321 add ?4 additive_identity =>= ?4
21322 [4] by right_additive_identity ?4
21323 20782: Id : 4, {_}:
21324 multiply additive_identity ?6 =>= additive_identity
21325 [6] by left_multiplicative_zero ?6
21326 20782: Id : 5, {_}:
21327 multiply ?8 additive_identity =>= additive_identity
21328 [8] by right_multiplicative_zero ?8
21329 20782: Id : 6, {_}:
21330 add (additive_inverse ?10) ?10 =>= additive_identity
21331 [10] by left_additive_inverse ?10
21332 20782: Id : 7, {_}:
21333 add ?12 (additive_inverse ?12) =>= additive_identity
21334 [12] by right_additive_inverse ?12
21335 20782: Id : 8, {_}:
21336 additive_inverse (additive_inverse ?14) =>= ?14
21337 [14] by additive_inverse_additive_inverse ?14
21338 20782: Id : 9, {_}:
21339 multiply ?16 (add ?17 ?18)
21341 add (multiply ?16 ?17) (multiply ?16 ?18)
21342 [18, 17, 16] by distribute1 ?16 ?17 ?18
21343 20782: Id : 10, {_}:
21344 multiply (add ?20 ?21) ?22
21346 add (multiply ?20 ?22) (multiply ?21 ?22)
21347 [22, 21, 20] by distribute2 ?20 ?21 ?22
21348 20782: Id : 11, {_}:
21349 add ?24 ?25 =?= add ?25 ?24
21350 [25, 24] by commutativity_for_addition ?24 ?25
21351 20782: Id : 12, {_}:
21352 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
21353 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21354 20782: Id : 13, {_}:
21355 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
21356 [32, 31] by right_alternative ?31 ?32
21357 20782: Id : 14, {_}:
21358 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
21359 [35, 34] by left_alternative ?34 ?35
21360 20782: Id : 15, {_}:
21361 associator ?37 ?38 ?39
21363 add (multiply (multiply ?37 ?38) ?39)
21364 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21365 [39, 38, 37] by associator ?37 ?38 ?39
21366 20782: Id : 16, {_}:
21369 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21370 [42, 41] by commutator ?41 ?42
21372 20782: Id : 1, {_}:
21373 associator x (add u v) y
21375 add (associator x u y) (associator x v y)
21376 [] by prove_linearised_form2
21380 20782: commutator 1 2 0
21381 20782: additive_inverse 6 1 0
21382 20782: multiply 22 2 0
21383 20782: additive_identity 8 0 0
21384 20782: associator 4 3 3 0,2
21386 20782: add 18 2 2 0,2,2
21387 20782: v 2 0 2 2,2,2
21388 20782: u 2 0 2 1,2,2
21390 % SZS status Timeout for RNG020-6.p
21391 NO CLASH, using fixed ground order
21393 20815: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21394 20815: Id : 3, {_}:
21395 add ?4 additive_identity =>= ?4
21396 [4] by right_additive_identity ?4
21397 20815: Id : 4, {_}:
21398 multiply additive_identity ?6 =>= additive_identity
21399 [6] by left_multiplicative_zero ?6
21400 20815: Id : 5, {_}:
21401 multiply ?8 additive_identity =>= additive_identity
21402 [8] by right_multiplicative_zero ?8
21403 20815: Id : 6, {_}:
21404 add (additive_inverse ?10) ?10 =>= additive_identity
21405 [10] by left_additive_inverse ?10
21406 20815: Id : 7, {_}:
21407 add ?12 (additive_inverse ?12) =>= additive_identity
21408 [12] by right_additive_inverse ?12
21409 20815: Id : 8, {_}:
21410 additive_inverse (additive_inverse ?14) =>= ?14
21411 [14] by additive_inverse_additive_inverse ?14
21412 20815: Id : 9, {_}:
21413 multiply ?16 (add ?17 ?18)
21415 add (multiply ?16 ?17) (multiply ?16 ?18)
21416 [18, 17, 16] by distribute1 ?16 ?17 ?18
21417 20815: Id : 10, {_}:
21418 multiply (add ?20 ?21) ?22
21420 add (multiply ?20 ?22) (multiply ?21 ?22)
21421 [22, 21, 20] by distribute2 ?20 ?21 ?22
21422 20815: Id : 11, {_}:
21423 add ?24 ?25 =?= add ?25 ?24
21424 [25, 24] by commutativity_for_addition ?24 ?25
21425 20815: Id : 12, {_}:
21426 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
21427 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21428 20815: Id : 13, {_}:
21429 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
21430 [32, 31] by right_alternative ?31 ?32
21431 20815: Id : 14, {_}:
21432 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
21433 [35, 34] by left_alternative ?34 ?35
21434 NO CLASH, using fixed ground order
21436 20816: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21437 20816: Id : 3, {_}:
21438 add ?4 additive_identity =>= ?4
21439 [4] by right_additive_identity ?4
21440 20816: Id : 4, {_}:
21441 multiply additive_identity ?6 =>= additive_identity
21442 [6] by left_multiplicative_zero ?6
21443 20816: Id : 5, {_}:
21444 multiply ?8 additive_identity =>= additive_identity
21445 [8] by right_multiplicative_zero ?8
21446 NO CLASH, using fixed ground order
21448 20817: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21449 20817: Id : 3, {_}:
21450 add ?4 additive_identity =>= ?4
21451 [4] by right_additive_identity ?4
21452 20816: Id : 6, {_}:
21453 add (additive_inverse ?10) ?10 =>= additive_identity
21454 [10] by left_additive_inverse ?10
21455 20817: Id : 4, {_}:
21456 multiply additive_identity ?6 =>= additive_identity
21457 [6] by left_multiplicative_zero ?6
21458 20816: Id : 7, {_}:
21459 add ?12 (additive_inverse ?12) =>= additive_identity
21460 [12] by right_additive_inverse ?12
21461 20817: Id : 5, {_}:
21462 multiply ?8 additive_identity =>= additive_identity
21463 [8] by right_multiplicative_zero ?8
21464 20817: Id : 6, {_}:
21465 add (additive_inverse ?10) ?10 =>= additive_identity
21466 [10] by left_additive_inverse ?10
21467 20816: Id : 8, {_}:
21468 additive_inverse (additive_inverse ?14) =>= ?14
21469 [14] by additive_inverse_additive_inverse ?14
21470 20817: Id : 7, {_}:
21471 add ?12 (additive_inverse ?12) =>= additive_identity
21472 [12] by right_additive_inverse ?12
21473 20817: Id : 8, {_}:
21474 additive_inverse (additive_inverse ?14) =>= ?14
21475 [14] by additive_inverse_additive_inverse ?14
21476 20816: Id : 9, {_}:
21477 multiply ?16 (add ?17 ?18)
21479 add (multiply ?16 ?17) (multiply ?16 ?18)
21480 [18, 17, 16] by distribute1 ?16 ?17 ?18
21481 20817: Id : 9, {_}:
21482 multiply ?16 (add ?17 ?18)
21484 add (multiply ?16 ?17) (multiply ?16 ?18)
21485 [18, 17, 16] by distribute1 ?16 ?17 ?18
21486 20816: Id : 10, {_}:
21487 multiply (add ?20 ?21) ?22
21489 add (multiply ?20 ?22) (multiply ?21 ?22)
21490 [22, 21, 20] by distribute2 ?20 ?21 ?22
21491 20815: Id : 15, {_}:
21492 associator ?37 ?38 ?39
21494 add (multiply (multiply ?37 ?38) ?39)
21495 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21496 [39, 38, 37] by associator ?37 ?38 ?39
21497 20816: Id : 11, {_}:
21498 add ?24 ?25 =?= add ?25 ?24
21499 [25, 24] by commutativity_for_addition ?24 ?25
21500 20815: Id : 16, {_}:
21503 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21504 [42, 41] by commutator ?41 ?42
21505 20816: Id : 12, {_}:
21506 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
21507 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21508 20816: Id : 13, {_}:
21509 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
21510 [32, 31] by right_alternative ?31 ?32
21511 20815: Id : 17, {_}:
21512 multiply (additive_inverse ?44) (additive_inverse ?45)
21515 [45, 44] by product_of_inverses ?44 ?45
21516 20816: Id : 14, {_}:
21517 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
21518 [35, 34] by left_alternative ?34 ?35
21519 20815: Id : 18, {_}:
21520 multiply (additive_inverse ?47) ?48
21522 additive_inverse (multiply ?47 ?48)
21523 [48, 47] by inverse_product1 ?47 ?48
21524 20816: Id : 15, {_}:
21525 associator ?37 ?38 ?39
21527 add (multiply (multiply ?37 ?38) ?39)
21528 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21529 [39, 38, 37] by associator ?37 ?38 ?39
21530 20815: Id : 19, {_}:
21531 multiply ?50 (additive_inverse ?51)
21533 additive_inverse (multiply ?50 ?51)
21534 [51, 50] by inverse_product2 ?50 ?51
21535 20816: Id : 16, {_}:
21538 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21539 [42, 41] by commutator ?41 ?42
21540 20815: Id : 20, {_}:
21541 multiply ?53 (add ?54 (additive_inverse ?55))
21543 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
21544 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
21545 20816: Id : 17, {_}:
21546 multiply (additive_inverse ?44) (additive_inverse ?45)
21549 [45, 44] by product_of_inverses ?44 ?45
21550 20815: Id : 21, {_}:
21551 multiply (add ?57 (additive_inverse ?58)) ?59
21553 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
21554 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
21555 20815: Id : 22, {_}:
21556 multiply (additive_inverse ?61) (add ?62 ?63)
21558 add (additive_inverse (multiply ?61 ?62))
21559 (additive_inverse (multiply ?61 ?63))
21560 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
21561 20815: Id : 23, {_}:
21562 multiply (add ?65 ?66) (additive_inverse ?67)
21564 add (additive_inverse (multiply ?65 ?67))
21565 (additive_inverse (multiply ?66 ?67))
21566 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
21568 20815: Id : 1, {_}:
21569 associator x (add u v) y
21571 add (associator x u y) (associator x v y)
21572 [] by prove_linearised_form2
21576 20815: commutator 1 2 0
21577 20815: additive_inverse 22 1 0
21578 20815: multiply 40 2 0
21579 20815: additive_identity 8 0 0
21580 20815: associator 4 3 3 0,2
21582 20815: add 26 2 2 0,2,2
21583 20815: v 2 0 2 2,2,2
21584 20815: u 2 0 2 1,2,2
21586 20817: Id : 10, {_}:
21587 multiply (add ?20 ?21) ?22
21589 add (multiply ?20 ?22) (multiply ?21 ?22)
21590 [22, 21, 20] by distribute2 ?20 ?21 ?22
21591 20816: Id : 18, {_}:
21592 multiply (additive_inverse ?47) ?48
21594 additive_inverse (multiply ?47 ?48)
21595 [48, 47] by inverse_product1 ?47 ?48
21596 20816: Id : 19, {_}:
21597 multiply ?50 (additive_inverse ?51)
21599 additive_inverse (multiply ?50 ?51)
21600 [51, 50] by inverse_product2 ?50 ?51
21601 20816: Id : 20, {_}:
21602 multiply ?53 (add ?54 (additive_inverse ?55))
21604 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
21605 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
21606 20816: Id : 21, {_}:
21607 multiply (add ?57 (additive_inverse ?58)) ?59
21609 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
21610 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
21611 20816: Id : 22, {_}:
21612 multiply (additive_inverse ?61) (add ?62 ?63)
21614 add (additive_inverse (multiply ?61 ?62))
21615 (additive_inverse (multiply ?61 ?63))
21616 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
21617 20816: Id : 23, {_}:
21618 multiply (add ?65 ?66) (additive_inverse ?67)
21620 add (additive_inverse (multiply ?65 ?67))
21621 (additive_inverse (multiply ?66 ?67))
21622 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
21624 20816: Id : 1, {_}:
21625 associator x (add u v) y
21627 add (associator x u y) (associator x v y)
21628 [] by prove_linearised_form2
21632 20816: commutator 1 2 0
21633 20816: additive_inverse 22 1 0
21634 20816: multiply 40 2 0
21635 20816: additive_identity 8 0 0
21636 20816: associator 4 3 3 0,2
21638 20816: add 26 2 2 0,2,2
21639 20816: v 2 0 2 2,2,2
21640 20816: u 2 0 2 1,2,2
21642 20817: Id : 11, {_}:
21643 add ?24 ?25 =?= add ?25 ?24
21644 [25, 24] by commutativity_for_addition ?24 ?25
21645 20817: Id : 12, {_}:
21646 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
21647 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21648 20817: Id : 13, {_}:
21649 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
21650 [32, 31] by right_alternative ?31 ?32
21651 20817: Id : 14, {_}:
21652 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
21653 [35, 34] by left_alternative ?34 ?35
21654 20817: Id : 15, {_}:
21655 associator ?37 ?38 ?39
21657 add (multiply (multiply ?37 ?38) ?39)
21658 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21659 [39, 38, 37] by associator ?37 ?38 ?39
21660 20817: Id : 16, {_}:
21663 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21664 [42, 41] by commutator ?41 ?42
21665 20817: Id : 17, {_}:
21666 multiply (additive_inverse ?44) (additive_inverse ?45)
21669 [45, 44] by product_of_inverses ?44 ?45
21670 20817: Id : 18, {_}:
21671 multiply (additive_inverse ?47) ?48
21673 additive_inverse (multiply ?47 ?48)
21674 [48, 47] by inverse_product1 ?47 ?48
21675 20817: Id : 19, {_}:
21676 multiply ?50 (additive_inverse ?51)
21678 additive_inverse (multiply ?50 ?51)
21679 [51, 50] by inverse_product2 ?50 ?51
21680 20817: Id : 20, {_}:
21681 multiply ?53 (add ?54 (additive_inverse ?55))
21683 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
21684 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
21685 20817: Id : 21, {_}:
21686 multiply (add ?57 (additive_inverse ?58)) ?59
21688 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
21689 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
21690 20817: Id : 22, {_}:
21691 multiply (additive_inverse ?61) (add ?62 ?63)
21693 add (additive_inverse (multiply ?61 ?62))
21694 (additive_inverse (multiply ?61 ?63))
21695 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
21696 20817: Id : 23, {_}:
21697 multiply (add ?65 ?66) (additive_inverse ?67)
21699 add (additive_inverse (multiply ?65 ?67))
21700 (additive_inverse (multiply ?66 ?67))
21701 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
21703 20817: Id : 1, {_}:
21704 associator x (add u v) y
21706 add (associator x u y) (associator x v y)
21707 [] by prove_linearised_form2
21711 20817: commutator 1 2 0
21712 20817: additive_inverse 22 1 0
21713 20817: multiply 40 2 0
21714 20817: additive_identity 8 0 0
21715 20817: associator 4 3 3 0,2
21717 20817: add 26 2 2 0,2,2
21718 20817: v 2 0 2 2,2,2
21719 20817: u 2 0 2 1,2,2
21721 % SZS status Timeout for RNG020-7.p
21722 NO CLASH, using fixed ground order
21724 20843: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21725 20843: Id : 3, {_}:
21726 add ?4 additive_identity =>= ?4
21727 [4] by right_additive_identity ?4
21728 20843: Id : 4, {_}:
21729 multiply additive_identity ?6 =>= additive_identity
21730 [6] by left_multiplicative_zero ?6
21731 20843: Id : 5, {_}:
21732 multiply ?8 additive_identity =>= additive_identity
21733 [8] by right_multiplicative_zero ?8
21734 20843: Id : 6, {_}:
21735 add (additive_inverse ?10) ?10 =>= additive_identity
21736 [10] by left_additive_inverse ?10
21737 20843: Id : 7, {_}:
21738 add ?12 (additive_inverse ?12) =>= additive_identity
21739 [12] by right_additive_inverse ?12
21740 20843: Id : 8, {_}:
21741 additive_inverse (additive_inverse ?14) =>= ?14
21742 [14] by additive_inverse_additive_inverse ?14
21743 20843: Id : 9, {_}:
21744 multiply ?16 (add ?17 ?18)
21746 add (multiply ?16 ?17) (multiply ?16 ?18)
21747 [18, 17, 16] by distribute1 ?16 ?17 ?18
21748 20843: Id : 10, {_}:
21749 multiply (add ?20 ?21) ?22
21751 add (multiply ?20 ?22) (multiply ?21 ?22)
21752 [22, 21, 20] by distribute2 ?20 ?21 ?22
21753 20843: Id : 11, {_}:
21754 add ?24 ?25 =?= add ?25 ?24
21755 [25, 24] by commutativity_for_addition ?24 ?25
21756 20843: Id : 12, {_}:
21757 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
21758 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21759 20843: Id : 13, {_}:
21760 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
21761 [32, 31] by right_alternative ?31 ?32
21762 20843: Id : 14, {_}:
21763 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
21764 [35, 34] by left_alternative ?34 ?35
21765 20843: Id : 15, {_}:
21766 associator ?37 ?38 ?39
21768 add (multiply (multiply ?37 ?38) ?39)
21769 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21770 [39, 38, 37] by associator ?37 ?38 ?39
21771 20843: Id : 16, {_}:
21774 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21775 [42, 41] by commutator ?41 ?42
21776 20843: Id : 17, {_}:
21777 multiply (additive_inverse ?44) (additive_inverse ?45)
21780 [45, 44] by product_of_inverses ?44 ?45
21781 20843: Id : 18, {_}:
21782 multiply (additive_inverse ?47) ?48
21784 additive_inverse (multiply ?47 ?48)
21785 [48, 47] by inverse_product1 ?47 ?48
21786 20843: Id : 19, {_}:
21787 multiply ?50 (additive_inverse ?51)
21789 additive_inverse (multiply ?50 ?51)
21790 [51, 50] by inverse_product2 ?50 ?51
21791 20843: Id : 20, {_}:
21792 multiply ?53 (add ?54 (additive_inverse ?55))
21794 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
21795 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
21796 20843: Id : 21, {_}:
21797 multiply (add ?57 (additive_inverse ?58)) ?59
21799 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
21800 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
21801 20843: Id : 22, {_}:
21802 multiply (additive_inverse ?61) (add ?62 ?63)
21804 add (additive_inverse (multiply ?61 ?62))
21805 (additive_inverse (multiply ?61 ?63))
21806 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
21807 20843: Id : 23, {_}:
21808 multiply (add ?65 ?66) (additive_inverse ?67)
21810 add (additive_inverse (multiply ?65 ?67))
21811 (additive_inverse (multiply ?66 ?67))
21812 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
21814 20843: Id : 1, {_}:
21815 associator (add u v) x y
21817 add (associator u x y) (associator v x y)
21818 [] by prove_linearised_form3
21822 20843: commutator 1 2 0
21823 20843: additive_inverse 22 1 0
21824 20843: multiply 40 2 0
21825 20843: additive_identity 8 0 0
21826 20843: associator 4 3 3 0,2
21829 20843: add 26 2 2 0,1,2
21830 20843: v 2 0 2 2,1,2
21831 20843: u 2 0 2 1,1,2
21832 NO CLASH, using fixed ground order
21834 20842: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21835 20842: Id : 3, {_}:
21836 add ?4 additive_identity =>= ?4
21837 [4] by right_additive_identity ?4
21838 20842: Id : 4, {_}:
21839 multiply additive_identity ?6 =>= additive_identity
21840 [6] by left_multiplicative_zero ?6
21841 20842: Id : 5, {_}:
21842 multiply ?8 additive_identity =>= additive_identity
21843 [8] by right_multiplicative_zero ?8
21844 20842: Id : 6, {_}:
21845 add (additive_inverse ?10) ?10 =>= additive_identity
21846 [10] by left_additive_inverse ?10
21847 20842: Id : 7, {_}:
21848 add ?12 (additive_inverse ?12) =>= additive_identity
21849 [12] by right_additive_inverse ?12
21850 20842: Id : 8, {_}:
21851 additive_inverse (additive_inverse ?14) =>= ?14
21852 [14] by additive_inverse_additive_inverse ?14
21853 20842: Id : 9, {_}:
21854 multiply ?16 (add ?17 ?18)
21856 add (multiply ?16 ?17) (multiply ?16 ?18)
21857 [18, 17, 16] by distribute1 ?16 ?17 ?18
21858 20842: Id : 10, {_}:
21859 multiply (add ?20 ?21) ?22
21861 add (multiply ?20 ?22) (multiply ?21 ?22)
21862 [22, 21, 20] by distribute2 ?20 ?21 ?22
21863 20842: Id : 11, {_}:
21864 add ?24 ?25 =?= add ?25 ?24
21865 [25, 24] by commutativity_for_addition ?24 ?25
21866 20842: Id : 12, {_}:
21867 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
21868 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21869 20842: Id : 13, {_}:
21870 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
21871 [32, 31] by right_alternative ?31 ?32
21872 20842: Id : 14, {_}:
21873 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
21874 [35, 34] by left_alternative ?34 ?35
21875 20842: Id : 15, {_}:
21876 associator ?37 ?38 ?39
21878 add (multiply (multiply ?37 ?38) ?39)
21879 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21880 [39, 38, 37] by associator ?37 ?38 ?39
21881 20842: Id : 16, {_}:
21884 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21885 [42, 41] by commutator ?41 ?42
21886 20842: Id : 17, {_}:
21887 multiply (additive_inverse ?44) (additive_inverse ?45)
21890 [45, 44] by product_of_inverses ?44 ?45
21891 20842: Id : 18, {_}:
21892 multiply (additive_inverse ?47) ?48
21894 additive_inverse (multiply ?47 ?48)
21895 [48, 47] by inverse_product1 ?47 ?48
21896 20842: Id : 19, {_}:
21897 multiply ?50 (additive_inverse ?51)
21899 additive_inverse (multiply ?50 ?51)
21900 [51, 50] by inverse_product2 ?50 ?51
21901 20842: Id : 20, {_}:
21902 multiply ?53 (add ?54 (additive_inverse ?55))
21904 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
21905 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
21906 20842: Id : 21, {_}:
21907 multiply (add ?57 (additive_inverse ?58)) ?59
21909 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
21910 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
21911 20842: Id : 22, {_}:
21912 multiply (additive_inverse ?61) (add ?62 ?63)
21914 add (additive_inverse (multiply ?61 ?62))
21915 (additive_inverse (multiply ?61 ?63))
21916 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
21917 20842: Id : 23, {_}:
21918 multiply (add ?65 ?66) (additive_inverse ?67)
21920 add (additive_inverse (multiply ?65 ?67))
21921 (additive_inverse (multiply ?66 ?67))
21922 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
21924 20842: Id : 1, {_}:
21925 associator (add u v) x y
21927 add (associator u x y) (associator v x y)
21928 [] by prove_linearised_form3
21932 20842: commutator 1 2 0
21933 20842: additive_inverse 22 1 0
21934 20842: multiply 40 2 0
21935 20842: additive_identity 8 0 0
21936 20842: associator 4 3 3 0,2
21939 20842: add 26 2 2 0,1,2
21940 20842: v 2 0 2 2,1,2
21941 20842: u 2 0 2 1,1,2
21942 NO CLASH, using fixed ground order
21944 20844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
21945 20844: Id : 3, {_}:
21946 add ?4 additive_identity =>= ?4
21947 [4] by right_additive_identity ?4
21948 20844: Id : 4, {_}:
21949 multiply additive_identity ?6 =>= additive_identity
21950 [6] by left_multiplicative_zero ?6
21951 20844: Id : 5, {_}:
21952 multiply ?8 additive_identity =>= additive_identity
21953 [8] by right_multiplicative_zero ?8
21954 20844: Id : 6, {_}:
21955 add (additive_inverse ?10) ?10 =>= additive_identity
21956 [10] by left_additive_inverse ?10
21957 20844: Id : 7, {_}:
21958 add ?12 (additive_inverse ?12) =>= additive_identity
21959 [12] by right_additive_inverse ?12
21960 20844: Id : 8, {_}:
21961 additive_inverse (additive_inverse ?14) =>= ?14
21962 [14] by additive_inverse_additive_inverse ?14
21963 20844: Id : 9, {_}:
21964 multiply ?16 (add ?17 ?18)
21966 add (multiply ?16 ?17) (multiply ?16 ?18)
21967 [18, 17, 16] by distribute1 ?16 ?17 ?18
21968 20844: Id : 10, {_}:
21969 multiply (add ?20 ?21) ?22
21971 add (multiply ?20 ?22) (multiply ?21 ?22)
21972 [22, 21, 20] by distribute2 ?20 ?21 ?22
21973 20844: Id : 11, {_}:
21974 add ?24 ?25 =?= add ?25 ?24
21975 [25, 24] by commutativity_for_addition ?24 ?25
21976 20844: Id : 12, {_}:
21977 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
21978 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
21979 20844: Id : 13, {_}:
21980 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
21981 [32, 31] by right_alternative ?31 ?32
21982 20844: Id : 14, {_}:
21983 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
21984 [35, 34] by left_alternative ?34 ?35
21985 20844: Id : 15, {_}:
21986 associator ?37 ?38 ?39
21988 add (multiply (multiply ?37 ?38) ?39)
21989 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
21990 [39, 38, 37] by associator ?37 ?38 ?39
21991 20844: Id : 16, {_}:
21994 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
21995 [42, 41] by commutator ?41 ?42
21996 20844: Id : 17, {_}:
21997 multiply (additive_inverse ?44) (additive_inverse ?45)
22000 [45, 44] by product_of_inverses ?44 ?45
22001 20844: Id : 18, {_}:
22002 multiply (additive_inverse ?47) ?48
22004 additive_inverse (multiply ?47 ?48)
22005 [48, 47] by inverse_product1 ?47 ?48
22006 20844: Id : 19, {_}:
22007 multiply ?50 (additive_inverse ?51)
22009 additive_inverse (multiply ?50 ?51)
22010 [51, 50] by inverse_product2 ?50 ?51
22011 20844: Id : 20, {_}:
22012 multiply ?53 (add ?54 (additive_inverse ?55))
22014 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
22015 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
22016 20844: Id : 21, {_}:
22017 multiply (add ?57 (additive_inverse ?58)) ?59
22019 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
22020 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
22021 20844: Id : 22, {_}:
22022 multiply (additive_inverse ?61) (add ?62 ?63)
22024 add (additive_inverse (multiply ?61 ?62))
22025 (additive_inverse (multiply ?61 ?63))
22026 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
22027 20844: Id : 23, {_}:
22028 multiply (add ?65 ?66) (additive_inverse ?67)
22030 add (additive_inverse (multiply ?65 ?67))
22031 (additive_inverse (multiply ?66 ?67))
22032 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
22034 20844: Id : 1, {_}:
22035 associator (add u v) x y
22037 add (associator u x y) (associator v x y)
22038 [] by prove_linearised_form3
22042 20844: commutator 1 2 0
22043 20844: additive_inverse 22 1 0
22044 20844: multiply 40 2 0
22045 20844: additive_identity 8 0 0
22046 20844: associator 4 3 3 0,2
22049 20844: add 26 2 2 0,1,2
22050 20844: v 2 0 2 2,1,2
22051 20844: u 2 0 2 1,1,2
22052 % SZS status Timeout for RNG021-7.p
22053 NO CLASH, using fixed ground order
22055 20871: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
22056 20871: Id : 3, {_}:
22057 add ?4 additive_identity =>= ?4
22058 [4] by right_additive_identity ?4
22059 20871: Id : 4, {_}:
22060 multiply additive_identity ?6 =>= additive_identity
22061 [6] by left_multiplicative_zero ?6
22062 20871: Id : 5, {_}:
22063 multiply ?8 additive_identity =>= additive_identity
22064 [8] by right_multiplicative_zero ?8
22065 20871: Id : 6, {_}:
22066 add (additive_inverse ?10) ?10 =>= additive_identity
22067 [10] by left_additive_inverse ?10
22068 20871: Id : 7, {_}:
22069 add ?12 (additive_inverse ?12) =>= additive_identity
22070 [12] by right_additive_inverse ?12
22071 20871: Id : 8, {_}:
22072 additive_inverse (additive_inverse ?14) =>= ?14
22073 [14] by additive_inverse_additive_inverse ?14
22074 20871: Id : 9, {_}:
22075 multiply ?16 (add ?17 ?18)
22077 add (multiply ?16 ?17) (multiply ?16 ?18)
22078 [18, 17, 16] by distribute1 ?16 ?17 ?18
22079 20871: Id : 10, {_}:
22080 multiply (add ?20 ?21) ?22
22082 add (multiply ?20 ?22) (multiply ?21 ?22)
22083 [22, 21, 20] by distribute2 ?20 ?21 ?22
22084 20871: Id : 11, {_}:
22085 add ?24 ?25 =?= add ?25 ?24
22086 [25, 24] by commutativity_for_addition ?24 ?25
22087 20871: Id : 12, {_}:
22088 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
22089 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
22090 20871: Id : 13, {_}:
22091 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
22092 [32, 31] by right_alternative ?31 ?32
22093 20871: Id : 14, {_}:
22094 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
22095 [35, 34] by left_alternative ?34 ?35
22096 20871: Id : 15, {_}:
22097 associator ?37 ?38 ?39
22099 add (multiply (multiply ?37 ?38) ?39)
22100 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
22101 [39, 38, 37] by associator ?37 ?38 ?39
22102 20871: Id : 16, {_}:
22105 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
22106 [42, 41] by commutator ?41 ?42
22108 20871: Id : 1, {_}:
22109 add (associator x y z) (associator x z y) =>= additive_identity
22110 [] by prove_equation
22114 20871: commutator 1 2 0
22115 20871: additive_inverse 6 1 0
22116 20871: multiply 22 2 0
22117 20871: additive_identity 9 0 1 3
22118 20871: add 17 2 1 0,2
22119 20871: associator 3 3 2 0,1,2
22120 20871: z 2 0 2 3,1,2
22121 20871: y 2 0 2 2,1,2
22122 20871: x 2 0 2 1,1,2
22123 NO CLASH, using fixed ground order
22125 20872: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
22126 20872: Id : 3, {_}:
22127 add ?4 additive_identity =>= ?4
22128 [4] by right_additive_identity ?4
22129 20872: Id : 4, {_}:
22130 multiply additive_identity ?6 =>= additive_identity
22131 [6] by left_multiplicative_zero ?6
22132 20872: Id : 5, {_}:
22133 multiply ?8 additive_identity =>= additive_identity
22134 [8] by right_multiplicative_zero ?8
22135 20872: Id : 6, {_}:
22136 add (additive_inverse ?10) ?10 =>= additive_identity
22137 [10] by left_additive_inverse ?10
22138 20872: Id : 7, {_}:
22139 add ?12 (additive_inverse ?12) =>= additive_identity
22140 [12] by right_additive_inverse ?12
22141 20872: Id : 8, {_}:
22142 additive_inverse (additive_inverse ?14) =>= ?14
22143 [14] by additive_inverse_additive_inverse ?14
22144 20872: Id : 9, {_}:
22145 multiply ?16 (add ?17 ?18)
22147 add (multiply ?16 ?17) (multiply ?16 ?18)
22148 [18, 17, 16] by distribute1 ?16 ?17 ?18
22149 20872: Id : 10, {_}:
22150 multiply (add ?20 ?21) ?22
22152 add (multiply ?20 ?22) (multiply ?21 ?22)
22153 [22, 21, 20] by distribute2 ?20 ?21 ?22
22154 20872: Id : 11, {_}:
22155 add ?24 ?25 =?= add ?25 ?24
22156 [25, 24] by commutativity_for_addition ?24 ?25
22157 20872: Id : 12, {_}:
22158 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
22159 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
22160 20872: Id : 13, {_}:
22161 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
22162 [32, 31] by right_alternative ?31 ?32
22163 20872: Id : 14, {_}:
22164 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
22165 [35, 34] by left_alternative ?34 ?35
22166 20872: Id : 15, {_}:
22167 associator ?37 ?38 ?39
22169 add (multiply (multiply ?37 ?38) ?39)
22170 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
22171 [39, 38, 37] by associator ?37 ?38 ?39
22172 20872: Id : 16, {_}:
22175 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
22176 [42, 41] by commutator ?41 ?42
22178 20872: Id : 1, {_}:
22179 add (associator x y z) (associator x z y) =>= additive_identity
22180 [] by prove_equation
22184 20872: commutator 1 2 0
22185 20872: additive_inverse 6 1 0
22186 20872: multiply 22 2 0
22187 20872: additive_identity 9 0 1 3
22188 20872: add 17 2 1 0,2
22189 20872: associator 3 3 2 0,1,2
22190 20872: z 2 0 2 3,1,2
22191 20872: y 2 0 2 2,1,2
22192 20872: x 2 0 2 1,1,2
22193 NO CLASH, using fixed ground order
22195 20873: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
22196 20873: Id : 3, {_}:
22197 add ?4 additive_identity =>= ?4
22198 [4] by right_additive_identity ?4
22199 20873: Id : 4, {_}:
22200 multiply additive_identity ?6 =>= additive_identity
22201 [6] by left_multiplicative_zero ?6
22202 20873: Id : 5, {_}:
22203 multiply ?8 additive_identity =>= additive_identity
22204 [8] by right_multiplicative_zero ?8
22205 20873: Id : 6, {_}:
22206 add (additive_inverse ?10) ?10 =>= additive_identity
22207 [10] by left_additive_inverse ?10
22208 20873: Id : 7, {_}:
22209 add ?12 (additive_inverse ?12) =>= additive_identity
22210 [12] by right_additive_inverse ?12
22211 20873: Id : 8, {_}:
22212 additive_inverse (additive_inverse ?14) =>= ?14
22213 [14] by additive_inverse_additive_inverse ?14
22214 20873: Id : 9, {_}:
22215 multiply ?16 (add ?17 ?18)
22217 add (multiply ?16 ?17) (multiply ?16 ?18)
22218 [18, 17, 16] by distribute1 ?16 ?17 ?18
22219 20873: Id : 10, {_}:
22220 multiply (add ?20 ?21) ?22
22222 add (multiply ?20 ?22) (multiply ?21 ?22)
22223 [22, 21, 20] by distribute2 ?20 ?21 ?22
22224 20873: Id : 11, {_}:
22225 add ?24 ?25 =?= add ?25 ?24
22226 [25, 24] by commutativity_for_addition ?24 ?25
22227 20873: Id : 12, {_}:
22228 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
22229 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
22230 20873: Id : 13, {_}:
22231 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
22232 [32, 31] by right_alternative ?31 ?32
22233 20873: Id : 14, {_}:
22234 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
22235 [35, 34] by left_alternative ?34 ?35
22236 20873: Id : 15, {_}:
22237 associator ?37 ?38 ?39
22239 add (multiply (multiply ?37 ?38) ?39)
22240 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
22241 [39, 38, 37] by associator ?37 ?38 ?39
22242 20873: Id : 16, {_}:
22245 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
22246 [42, 41] by commutator ?41 ?42
22248 20873: Id : 1, {_}:
22249 add (associator x y z) (associator x z y) =>= additive_identity
22250 [] by prove_equation
22254 20873: commutator 1 2 0
22255 20873: additive_inverse 6 1 0
22256 20873: multiply 22 2 0
22257 20873: additive_identity 9 0 1 3
22258 20873: add 17 2 1 0,2
22259 20873: associator 3 3 2 0,1,2
22260 20873: z 2 0 2 3,1,2
22261 20873: y 2 0 2 2,1,2
22262 20873: x 2 0 2 1,1,2
22263 % SZS status Timeout for RNG025-4.p
22264 NO CLASH, using fixed ground order
22266 20890: Id : 2, {_}:
22267 add ?2 ?3 =?= add ?3 ?2
22268 [3, 2] by commutativity_for_addition ?2 ?3
22269 20890: Id : 3, {_}:
22270 add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
22271 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
22272 20890: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
22273 20890: Id : 5, {_}:
22274 add ?11 additive_identity =>= ?11
22275 [11] by right_additive_identity ?11
22276 20890: Id : 6, {_}:
22277 multiply additive_identity ?13 =>= additive_identity
22278 [13] by left_multiplicative_zero ?13
22279 20890: Id : 7, {_}:
22280 multiply ?15 additive_identity =>= additive_identity
22281 [15] by right_multiplicative_zero ?15
22282 20890: Id : 8, {_}:
22283 add (additive_inverse ?17) ?17 =>= additive_identity
22284 [17] by left_additive_inverse ?17
22285 20890: Id : 9, {_}:
22286 add ?19 (additive_inverse ?19) =>= additive_identity
22287 [19] by right_additive_inverse ?19
22288 20890: Id : 10, {_}:
22289 multiply ?21 (add ?22 ?23)
22291 add (multiply ?21 ?22) (multiply ?21 ?23)
22292 [23, 22, 21] by distribute1 ?21 ?22 ?23
22293 20890: Id : 11, {_}:
22294 multiply (add ?25 ?26) ?27
22296 add (multiply ?25 ?27) (multiply ?26 ?27)
22297 [27, 26, 25] by distribute2 ?25 ?26 ?27
22298 20890: Id : 12, {_}:
22299 additive_inverse (additive_inverse ?29) =>= ?29
22300 [29] by additive_inverse_additive_inverse ?29
22301 20890: Id : 13, {_}:
22302 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
22303 [32, 31] by right_alternative ?31 ?32
22304 20890: Id : 14, {_}:
22305 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
22306 [35, 34] by left_alternative ?34 ?35
22307 20890: Id : 15, {_}:
22308 associator ?37 ?38 (add ?39 ?40)
22310 add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
22311 [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
22312 20890: Id : 16, {_}:
22313 associator ?42 (add ?43 ?44) ?45
22315 add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
22316 [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
22317 20890: Id : 17, {_}:
22318 associator (add ?47 ?48) ?49 ?50
22320 add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
22321 [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
22322 NO CLASH, using fixed ground order
22324 20891: Id : 2, {_}:
22325 add ?2 ?3 =?= add ?3 ?2
22326 [3, 2] by commutativity_for_addition ?2 ?3
22327 20891: Id : 3, {_}:
22328 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
22329 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
22330 20891: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
22331 20891: Id : 5, {_}:
22332 add ?11 additive_identity =>= ?11
22333 [11] by right_additive_identity ?11
22334 20891: Id : 6, {_}:
22335 multiply additive_identity ?13 =>= additive_identity
22336 [13] by left_multiplicative_zero ?13
22337 20891: Id : 7, {_}:
22338 multiply ?15 additive_identity =>= additive_identity
22339 [15] by right_multiplicative_zero ?15
22340 20891: Id : 8, {_}:
22341 add (additive_inverse ?17) ?17 =>= additive_identity
22342 [17] by left_additive_inverse ?17
22343 20891: Id : 9, {_}:
22344 add ?19 (additive_inverse ?19) =>= additive_identity
22345 [19] by right_additive_inverse ?19
22346 NO CLASH, using fixed ground order
22348 20892: Id : 2, {_}:
22349 add ?2 ?3 =?= add ?3 ?2
22350 [3, 2] by commutativity_for_addition ?2 ?3
22351 20892: Id : 3, {_}:
22352 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
22353 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
22354 20892: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
22355 20892: Id : 5, {_}:
22356 add ?11 additive_identity =>= ?11
22357 [11] by right_additive_identity ?11
22358 20892: Id : 6, {_}:
22359 multiply additive_identity ?13 =>= additive_identity
22360 [13] by left_multiplicative_zero ?13
22361 20892: Id : 7, {_}:
22362 multiply ?15 additive_identity =>= additive_identity
22363 [15] by right_multiplicative_zero ?15
22364 20892: Id : 8, {_}:
22365 add (additive_inverse ?17) ?17 =>= additive_identity
22366 [17] by left_additive_inverse ?17
22367 20892: Id : 9, {_}:
22368 add ?19 (additive_inverse ?19) =>= additive_identity
22369 [19] by right_additive_inverse ?19
22370 20892: Id : 10, {_}:
22371 multiply ?21 (add ?22 ?23)
22373 add (multiply ?21 ?22) (multiply ?21 ?23)
22374 [23, 22, 21] by distribute1 ?21 ?22 ?23
22375 20891: Id : 10, {_}:
22376 multiply ?21 (add ?22 ?23)
22378 add (multiply ?21 ?22) (multiply ?21 ?23)
22379 [23, 22, 21] by distribute1 ?21 ?22 ?23
22380 20890: Id : 18, {_}:
22383 add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
22384 [53, 52] by commutator ?52 ?53
22386 20892: Id : 11, {_}:
22387 multiply (add ?25 ?26) ?27
22389 add (multiply ?25 ?27) (multiply ?26 ?27)
22390 [27, 26, 25] by distribute2 ?25 ?26 ?27
22391 20890: Id : 1, {_}:
22392 add (associator a b c) (associator a c b) =>= additive_identity
22393 [] by prove_flexible_law
22397 20892: Id : 12, {_}:
22398 additive_inverse (additive_inverse ?29) =>= ?29
22399 [29] by additive_inverse_additive_inverse ?29
22400 20892: Id : 13, {_}:
22401 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
22402 [32, 31] by right_alternative ?31 ?32
22403 20892: Id : 14, {_}:
22404 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
22405 [35, 34] by left_alternative ?34 ?35
22406 20892: Id : 15, {_}:
22407 associator ?37 ?38 (add ?39 ?40)
22409 add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
22410 [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
22411 20892: Id : 16, {_}:
22412 associator ?42 (add ?43 ?44) ?45
22414 add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
22415 [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
22416 20892: Id : 17, {_}:
22417 associator (add ?47 ?48) ?49 ?50
22419 add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
22420 [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
22421 20892: Id : 18, {_}:
22424 add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
22425 [53, 52] by commutator ?52 ?53
22427 20892: Id : 1, {_}:
22428 add (associator a b c) (associator a c b) =>= additive_identity
22429 [] by prove_flexible_law
22433 20892: commutator 1 2 0
22434 20892: additive_inverse 5 1 0
22435 20892: multiply 18 2 0
22436 20892: additive_identity 9 0 1 3
22437 20892: add 22 2 1 0,2
22438 20892: associator 11 3 2 0,1,2
22439 20892: c 2 0 2 3,1,2
22440 20892: b 2 0 2 2,1,2
22441 20892: a 2 0 2 1,1,2
22442 20891: Id : 11, {_}:
22443 multiply (add ?25 ?26) ?27
22445 add (multiply ?25 ?27) (multiply ?26 ?27)
22446 [27, 26, 25] by distribute2 ?25 ?26 ?27
22447 20890: commutator 1 2 0
22448 20890: additive_inverse 5 1 0
22449 20890: multiply 18 2 0
22450 20890: additive_identity 9 0 1 3
22451 20890: add 22 2 1 0,2
22452 20890: associator 11 3 2 0,1,2
22453 20890: c 2 0 2 3,1,2
22454 20890: b 2 0 2 2,1,2
22455 20890: a 2 0 2 1,1,2
22456 20891: Id : 12, {_}:
22457 additive_inverse (additive_inverse ?29) =>= ?29
22458 [29] by additive_inverse_additive_inverse ?29
22459 20891: Id : 13, {_}:
22460 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
22461 [32, 31] by right_alternative ?31 ?32
22462 20891: Id : 14, {_}:
22463 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
22464 [35, 34] by left_alternative ?34 ?35
22465 20891: Id : 15, {_}:
22466 associator ?37 ?38 (add ?39 ?40)
22468 add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
22469 [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
22470 20891: Id : 16, {_}:
22471 associator ?42 (add ?43 ?44) ?45
22473 add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
22474 [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
22475 20891: Id : 17, {_}:
22476 associator (add ?47 ?48) ?49 ?50
22478 add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
22479 [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
22480 20891: Id : 18, {_}:
22483 add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
22484 [53, 52] by commutator ?52 ?53
22486 20891: Id : 1, {_}:
22487 add (associator a b c) (associator a c b) =>= additive_identity
22488 [] by prove_flexible_law
22492 20891: commutator 1 2 0
22493 20891: additive_inverse 5 1 0
22494 20891: multiply 18 2 0
22495 20891: additive_identity 9 0 1 3
22496 20891: add 22 2 1 0,2
22497 20891: associator 11 3 2 0,1,2
22498 20891: c 2 0 2 3,1,2
22499 20891: b 2 0 2 2,1,2
22500 20891: a 2 0 2 1,1,2
22501 % SZS status Timeout for RNG025-8.p
22502 NO CLASH, using fixed ground order
22504 20920: Id : 2, {_}:
22505 multiply (additive_inverse ?2) (additive_inverse ?3)
22508 [3, 2] by product_of_inverses ?2 ?3
22509 20920: Id : 3, {_}:
22510 multiply (additive_inverse ?5) ?6
22512 additive_inverse (multiply ?5 ?6)
22513 [6, 5] by inverse_product1 ?5 ?6
22514 20920: Id : 4, {_}:
22515 multiply ?8 (additive_inverse ?9)
22517 additive_inverse (multiply ?8 ?9)
22518 [9, 8] by inverse_product2 ?8 ?9
22519 20920: Id : 5, {_}:
22520 multiply ?11 (add ?12 (additive_inverse ?13))
22522 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
22523 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
22524 20920: Id : 6, {_}:
22525 multiply (add ?15 (additive_inverse ?16)) ?17
22527 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
22528 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
22529 20920: Id : 7, {_}:
22530 multiply (additive_inverse ?19) (add ?20 ?21)
22532 add (additive_inverse (multiply ?19 ?20))
22533 (additive_inverse (multiply ?19 ?21))
22534 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
22535 20920: Id : 8, {_}:
22536 multiply (add ?23 ?24) (additive_inverse ?25)
22538 add (additive_inverse (multiply ?23 ?25))
22539 (additive_inverse (multiply ?24 ?25))
22540 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
22541 20920: Id : 9, {_}:
22542 add ?27 ?28 =?= add ?28 ?27
22543 [28, 27] by commutativity_for_addition ?27 ?28
22544 20920: Id : 10, {_}:
22545 add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
22546 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
22547 20920: Id : 11, {_}:
22548 add additive_identity ?34 =>= ?34
22549 [34] by left_additive_identity ?34
22550 20920: Id : 12, {_}:
22551 add ?36 additive_identity =>= ?36
22552 [36] by right_additive_identity ?36
22553 20920: Id : 13, {_}:
22554 multiply additive_identity ?38 =>= additive_identity
22555 [38] by left_multiplicative_zero ?38
22556 20920: Id : 14, {_}:
22557 multiply ?40 additive_identity =>= additive_identity
22558 [40] by right_multiplicative_zero ?40
22559 20920: Id : 15, {_}:
22560 add (additive_inverse ?42) ?42 =>= additive_identity
22561 [42] by left_additive_inverse ?42
22562 20920: Id : 16, {_}:
22563 add ?44 (additive_inverse ?44) =>= additive_identity
22564 [44] by right_additive_inverse ?44
22565 20920: Id : 17, {_}:
22566 multiply ?46 (add ?47 ?48)
22568 add (multiply ?46 ?47) (multiply ?46 ?48)
22569 [48, 47, 46] by distribute1 ?46 ?47 ?48
22570 20920: Id : 18, {_}:
22571 multiply (add ?50 ?51) ?52
22573 add (multiply ?50 ?52) (multiply ?51 ?52)
22574 [52, 51, 50] by distribute2 ?50 ?51 ?52
22575 20920: Id : 19, {_}:
22576 additive_inverse (additive_inverse ?54) =>= ?54
22577 [54] by additive_inverse_additive_inverse ?54
22578 20920: Id : 20, {_}:
22579 multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
22580 [57, 56] by right_alternative ?56 ?57
22581 20920: Id : 21, {_}:
22582 multiply (multiply ?59 ?59) ?60 =?= multiply ?59 (multiply ?59 ?60)
22583 [60, 59] by left_alternative ?59 ?60
22584 20920: Id : 22, {_}:
22585 associator ?62 ?63 (add ?64 ?65)
22587 add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
22588 [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
22589 20920: Id : 23, {_}:
22590 associator ?67 (add ?68 ?69) ?70
22592 add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
22593 [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
22594 20920: Id : 24, {_}:
22595 associator (add ?72 ?73) ?74 ?75
22597 add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
22598 [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
22599 20920: Id : 25, {_}:
22602 add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
22603 [78, 77] by commutator ?77 ?78
22605 20920: Id : 1, {_}:
22606 add (associator a b c) (associator a c b) =>= additive_identity
22607 [] by prove_flexible_law
22611 20920: commutator 1 2 0
22612 20920: multiply 36 2 0 add
22613 20920: additive_inverse 21 1 0
22614 20920: additive_identity 9 0 1 3
22615 20920: add 30 2 1 0,2
22616 20920: associator 11 3 2 0,1,2
22617 20920: c 2 0 2 3,1,2
22618 20920: b 2 0 2 2,1,2
22619 20920: a 2 0 2 1,1,2
22620 NO CLASH, using fixed ground order
22622 20921: Id : 2, {_}:
22623 multiply (additive_inverse ?2) (additive_inverse ?3)
22626 [3, 2] by product_of_inverses ?2 ?3
22627 20921: Id : 3, {_}:
22628 multiply (additive_inverse ?5) ?6
22630 additive_inverse (multiply ?5 ?6)
22631 [6, 5] by inverse_product1 ?5 ?6
22632 20921: Id : 4, {_}:
22633 multiply ?8 (additive_inverse ?9)
22635 additive_inverse (multiply ?8 ?9)
22636 [9, 8] by inverse_product2 ?8 ?9
22637 20921: Id : 5, {_}:
22638 multiply ?11 (add ?12 (additive_inverse ?13))
22640 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
22641 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
22642 20921: Id : 6, {_}:
22643 multiply (add ?15 (additive_inverse ?16)) ?17
22645 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
22646 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
22647 20921: Id : 7, {_}:
22648 multiply (additive_inverse ?19) (add ?20 ?21)
22650 add (additive_inverse (multiply ?19 ?20))
22651 (additive_inverse (multiply ?19 ?21))
22652 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
22653 20921: Id : 8, {_}:
22654 multiply (add ?23 ?24) (additive_inverse ?25)
22656 add (additive_inverse (multiply ?23 ?25))
22657 (additive_inverse (multiply ?24 ?25))
22658 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
22659 20921: Id : 9, {_}:
22660 add ?27 ?28 =?= add ?28 ?27
22661 [28, 27] by commutativity_for_addition ?27 ?28
22662 20921: Id : 10, {_}:
22663 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
22664 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
22665 20921: Id : 11, {_}:
22666 add additive_identity ?34 =>= ?34
22667 [34] by left_additive_identity ?34
22668 20921: Id : 12, {_}:
22669 add ?36 additive_identity =>= ?36
22670 [36] by right_additive_identity ?36
22671 20921: Id : 13, {_}:
22672 multiply additive_identity ?38 =>= additive_identity
22673 [38] by left_multiplicative_zero ?38
22674 20921: Id : 14, {_}:
22675 multiply ?40 additive_identity =>= additive_identity
22676 [40] by right_multiplicative_zero ?40
22677 20921: Id : 15, {_}:
22678 add (additive_inverse ?42) ?42 =>= additive_identity
22679 [42] by left_additive_inverse ?42
22680 20921: Id : 16, {_}:
22681 add ?44 (additive_inverse ?44) =>= additive_identity
22682 [44] by right_additive_inverse ?44
22683 20921: Id : 17, {_}:
22684 multiply ?46 (add ?47 ?48)
22686 add (multiply ?46 ?47) (multiply ?46 ?48)
22687 [48, 47, 46] by distribute1 ?46 ?47 ?48
22688 20921: Id : 18, {_}:
22689 multiply (add ?50 ?51) ?52
22691 add (multiply ?50 ?52) (multiply ?51 ?52)
22692 [52, 51, 50] by distribute2 ?50 ?51 ?52
22693 20921: Id : 19, {_}:
22694 additive_inverse (additive_inverse ?54) =>= ?54
22695 [54] by additive_inverse_additive_inverse ?54
22696 20921: Id : 20, {_}:
22697 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
22698 [57, 56] by right_alternative ?56 ?57
22699 20921: Id : 21, {_}:
22700 multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
22701 [60, 59] by left_alternative ?59 ?60
22702 20921: Id : 22, {_}:
22703 associator ?62 ?63 (add ?64 ?65)
22705 add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
22706 [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
22707 20921: Id : 23, {_}:
22708 associator ?67 (add ?68 ?69) ?70
22710 add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
22711 [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
22712 20921: Id : 24, {_}:
22713 associator (add ?72 ?73) ?74 ?75
22715 add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
22716 [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
22717 20921: Id : 25, {_}:
22720 add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
22721 [78, 77] by commutator ?77 ?78
22723 20921: Id : 1, {_}:
22724 add (associator a b c) (associator a c b) =>= additive_identity
22725 [] by prove_flexible_law
22729 20921: commutator 1 2 0
22730 20921: multiply 36 2 0 add
22731 20921: additive_inverse 21 1 0
22732 20921: additive_identity 9 0 1 3
22733 20921: add 30 2 1 0,2
22734 20921: associator 11 3 2 0,1,2
22735 20921: c 2 0 2 3,1,2
22736 20921: b 2 0 2 2,1,2
22737 20921: a 2 0 2 1,1,2
22738 NO CLASH, using fixed ground order
22740 20922: Id : 2, {_}:
22741 multiply (additive_inverse ?2) (additive_inverse ?3)
22744 [3, 2] by product_of_inverses ?2 ?3
22745 20922: Id : 3, {_}:
22746 multiply (additive_inverse ?5) ?6
22748 additive_inverse (multiply ?5 ?6)
22749 [6, 5] by inverse_product1 ?5 ?6
22750 20922: Id : 4, {_}:
22751 multiply ?8 (additive_inverse ?9)
22753 additive_inverse (multiply ?8 ?9)
22754 [9, 8] by inverse_product2 ?8 ?9
22755 20922: Id : 5, {_}:
22756 multiply ?11 (add ?12 (additive_inverse ?13))
22758 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
22759 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
22760 20922: Id : 6, {_}:
22761 multiply (add ?15 (additive_inverse ?16)) ?17
22763 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
22764 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
22765 20922: Id : 7, {_}:
22766 multiply (additive_inverse ?19) (add ?20 ?21)
22768 add (additive_inverse (multiply ?19 ?20))
22769 (additive_inverse (multiply ?19 ?21))
22770 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
22771 20922: Id : 8, {_}:
22772 multiply (add ?23 ?24) (additive_inverse ?25)
22774 add (additive_inverse (multiply ?23 ?25))
22775 (additive_inverse (multiply ?24 ?25))
22776 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
22777 20922: Id : 9, {_}:
22778 add ?27 ?28 =?= add ?28 ?27
22779 [28, 27] by commutativity_for_addition ?27 ?28
22780 20922: Id : 10, {_}:
22781 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
22782 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
22783 20922: Id : 11, {_}:
22784 add additive_identity ?34 =>= ?34
22785 [34] by left_additive_identity ?34
22786 20922: Id : 12, {_}:
22787 add ?36 additive_identity =>= ?36
22788 [36] by right_additive_identity ?36
22789 20922: Id : 13, {_}:
22790 multiply additive_identity ?38 =>= additive_identity
22791 [38] by left_multiplicative_zero ?38
22792 20922: Id : 14, {_}:
22793 multiply ?40 additive_identity =>= additive_identity
22794 [40] by right_multiplicative_zero ?40
22795 20922: Id : 15, {_}:
22796 add (additive_inverse ?42) ?42 =>= additive_identity
22797 [42] by left_additive_inverse ?42
22798 20922: Id : 16, {_}:
22799 add ?44 (additive_inverse ?44) =>= additive_identity
22800 [44] by right_additive_inverse ?44
22801 20922: Id : 17, {_}:
22802 multiply ?46 (add ?47 ?48)
22804 add (multiply ?46 ?47) (multiply ?46 ?48)
22805 [48, 47, 46] by distribute1 ?46 ?47 ?48
22806 20922: Id : 18, {_}:
22807 multiply (add ?50 ?51) ?52
22809 add (multiply ?50 ?52) (multiply ?51 ?52)
22810 [52, 51, 50] by distribute2 ?50 ?51 ?52
22811 20922: Id : 19, {_}:
22812 additive_inverse (additive_inverse ?54) =>= ?54
22813 [54] by additive_inverse_additive_inverse ?54
22814 20922: Id : 20, {_}:
22815 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
22816 [57, 56] by right_alternative ?56 ?57
22817 20922: Id : 21, {_}:
22818 multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
22819 [60, 59] by left_alternative ?59 ?60
22820 20922: Id : 22, {_}:
22821 associator ?62 ?63 (add ?64 ?65)
22823 add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
22824 [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
22825 20922: Id : 23, {_}:
22826 associator ?67 (add ?68 ?69) ?70
22828 add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
22829 [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
22830 20922: Id : 24, {_}:
22831 associator (add ?72 ?73) ?74 ?75
22833 add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
22834 [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
22835 20922: Id : 25, {_}:
22838 add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
22839 [78, 77] by commutator ?77 ?78
22841 20922: Id : 1, {_}:
22842 add (associator a b c) (associator a c b) =>= additive_identity
22843 [] by prove_flexible_law
22847 20922: commutator 1 2 0
22848 20922: multiply 36 2 0 add
22849 20922: additive_inverse 21 1 0
22850 20922: additive_identity 9 0 1 3
22851 20922: add 30 2 1 0,2
22852 20922: associator 11 3 2 0,1,2
22853 20922: c 2 0 2 3,1,2
22854 20922: b 2 0 2 2,1,2
22855 20922: a 2 0 2 1,1,2
22856 % SZS status Timeout for RNG025-9.p
22857 NO CLASH, using fixed ground order
22859 20954: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
22860 20954: Id : 3, {_}:
22861 multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
22862 [7, 6, 5] by multiply_add_property ?5 ?6 ?7
22863 20954: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
22864 20954: Id : 5, {_}:
22867 add (multiply ?11 (inverse ?12))
22868 (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
22869 [13, 12, 11] by pixley_defn ?11 ?12 ?13
22870 20954: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
22871 20954: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
22872 20954: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
22874 20954: Id : 1, {_}:
22875 add a (multiply b c) =<= multiply (add a b) (add a c)
22876 [] by prove_add_multiply_property
22880 20954: pixley 4 3 0
22882 20954: inverse 3 1 0
22883 20954: add 9 2 3 0,2
22884 20954: multiply 9 2 2 0,2,2
22885 20954: c 2 0 2 2,2,2
22886 20954: b 2 0 2 1,2,2
22888 NO CLASH, using fixed ground order
22890 20955: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
22891 20955: Id : 3, {_}:
22892 multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
22893 [7, 6, 5] by multiply_add_property ?5 ?6 ?7
22894 20955: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
22895 20955: Id : 5, {_}:
22898 add (multiply ?11 (inverse ?12))
22899 (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
22900 [13, 12, 11] by pixley_defn ?11 ?12 ?13
22901 20955: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
22902 20955: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
22903 20955: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
22905 20955: Id : 1, {_}:
22906 add a (multiply b c) =<= multiply (add a b) (add a c)
22907 [] by prove_add_multiply_property
22911 20955: pixley 4 3 0
22913 20955: inverse 3 1 0
22914 20955: add 9 2 3 0,2
22915 20955: multiply 9 2 2 0,2,2
22916 20955: c 2 0 2 2,2,2
22917 20955: b 2 0 2 1,2,2
22919 NO CLASH, using fixed ground order
22921 20956: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
22922 20956: Id : 3, {_}:
22923 multiply ?5 (add ?6 ?7) =?= add (multiply ?6 ?5) (multiply ?7 ?5)
22924 [7, 6, 5] by multiply_add_property ?5 ?6 ?7
22925 20956: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
22926 20956: Id : 5, {_}:
22929 add (multiply ?11 (inverse ?12))
22930 (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
22931 [13, 12, 11] by pixley_defn ?11 ?12 ?13
22932 20956: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
22933 20956: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
22934 20956: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
22936 20956: Id : 1, {_}:
22937 add a (multiply b c) =<= multiply (add a b) (add a c)
22938 [] by prove_add_multiply_property
22942 20956: pixley 4 3 0
22944 20956: inverse 3 1 0
22945 20956: add 9 2 3 0,2
22946 20956: multiply 9 2 2 0,2,2
22947 20956: c 2 0 2 2,2,2
22948 20956: b 2 0 2 1,2,2
22952 Found proof, 38.942991s
22953 % SZS status Unsatisfiable for BOO023-1.p
22954 % SZS output start CNFRefutation for BOO023-1.p
22955 Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
22956 Id : 12, {_}: multiply ?33 (add ?34 ?35) =<= add (multiply ?34 ?33) (multiply ?35 ?33) [35, 34, 33] by multiply_add_property ?33 ?34 ?35
22957 Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
22958 Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
22959 Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
22960 Id : 5, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) [13, 12, 11] by pixley_defn ?11 ?12 ?13
22961 Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
22962 Id : 3, {_}: multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) [7, 6, 5] by multiply_add_property ?5 ?6 ?7
22963 Id : 19, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (multiply ?13 (add ?11 (inverse ?12))) [13, 12, 11] by Demod 5 with 3 at 2,3
22964 Id : 485, {_}: multiply (pixley ?939 ?940 ?941) (multiply ?941 (add ?939 (inverse ?940))) =>= multiply ?941 (add ?939 (inverse ?940)) [941, 940, 939] by Super 2 with 19 at 1,2
22965 Id : 505, {_}: multiply ?1017 (multiply ?1018 (add ?1017 (inverse ?1018))) =>= multiply ?1018 (add ?1017 (inverse ?1018)) [1018, 1017] by Super 485 with 7 at 1,2
22966 Id : 21, {_}: pixley ?58 ?59 ?60 =<= add (multiply ?58 (inverse ?59)) (multiply ?60 (add ?58 (inverse ?59))) [60, 59, 58] by Demod 5 with 3 at 2,3
22967 Id : 22, {_}: pixley ?62 ?62 ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [63, 62] by Super 21 with 4 at 2,2,3
22968 Id : 413, {_}: ?825 =<= add (multiply ?826 (inverse ?826)) (multiply ?825 n1) [826, 825] by Demod 22 with 6 at 2
22969 Id : 16, {_}: multiply n1 (inverse ?49) =>= inverse ?49 [49] by Super 2 with 4 at 1,2
22970 Id : 428, {_}: ?870 =<= add (inverse n1) (multiply ?870 n1) [870] by Super 413 with 16 at 1,3
22971 Id : 14, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= add ?41 (multiply ?43 ?41) [43, 42, 41] by Super 12 with 2 at 1,3
22972 Id : 548, {_}: ?1062 =<= add (inverse n1) (multiply ?1062 n1) [1062] by Super 413 with 16 at 1,3
22973 Id : 593, {_}: add ?1120 n1 =?= add (inverse n1) n1 [1120] by Super 548 with 2 at 2,3
22974 Id : 553, {_}: add ?1072 n1 =?= add (inverse n1) n1 [1072] by Super 548 with 2 at 2,3
22975 Id : 607, {_}: add ?1148 n1 =?= add ?1149 n1 [1149, 1148] by Super 593 with 553 at 3
22976 Id : 13, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= add (multiply ?38 ?37) ?37 [39, 38, 37] by Super 12 with 2 at 2,3
22977 Id : 408, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [62, 63] by Demod 22 with 6 at 2
22978 Id : 412, {_}: multiply (multiply ?822 n1) (add ?823 ?822) =<= add (multiply ?823 (multiply ?822 n1)) (multiply ?822 n1) [823, 822] by Super 13 with 408 at 2,2,2
22979 Id : 274, {_}: multiply (multiply ?502 (add ?503 ?504)) (multiply ?504 ?502) =>= multiply ?504 ?502 [504, 503, 502] by Super 2 with 3 at 1,2
22980 Id : 284, {_}: multiply (multiply ?542 n1) (multiply (inverse ?543) ?542) =>= multiply (inverse ?543) ?542 [543, 542] by Super 274 with 4 at 2,1,2
22981 Id : 173, {_}: multiply (inverse ?334) (add ?335 n1) =<= add (multiply ?335 (inverse ?334)) (inverse ?334) [335, 334] by Super 3 with 16 at 2,3
22982 Id : 1514, {_}: multiply ?2669 (multiply ?2670 (add ?2669 (inverse ?2670))) =>= multiply ?2670 (add ?2669 (inverse ?2670)) [2670, 2669] by Super 485 with 7 at 1,2
22983 Id : 672, {_}: multiply (multiply ?1271 n1) (multiply (inverse ?1272) ?1271) =>= multiply (inverse ?1272) ?1271 [1272, 1271] by Super 274 with 4 at 2,1,2
22984 Id : 688, {_}: multiply n1 (multiply (inverse ?1320) (add ?1321 n1)) =>= multiply (inverse ?1320) (add ?1321 n1) [1321, 1320] by Super 672 with 2 at 1,2
22985 Id : 199, {_}: multiply (inverse ?371) (add ?372 n1) =<= add (multiply ?372 (inverse ?371)) (inverse ?371) [372, 371] by Super 3 with 16 at 2,3
22986 Id : 210, {_}: multiply (inverse ?404) (add (add ?405 (inverse ?404)) n1) =>= add (inverse ?404) (inverse ?404) [405, 404] by Super 199 with 2 at 1,3
22987 Id : 966, {_}: add (inverse ?404) (multiply n1 (inverse ?404)) =>= add (inverse ?404) (inverse ?404) [404] by Demod 210 with 14 at 2
22988 Id : 174, {_}: multiply (inverse ?337) (add n1 ?338) =<= add (inverse ?337) (multiply ?338 (inverse ?337)) [338, 337] by Super 3 with 16 at 1,3
22989 Id : 967, {_}: multiply (inverse ?404) (add n1 n1) =?= add (inverse ?404) (inverse ?404) [404] by Demod 966 with 174 at 2
22990 Id : 982, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) (add n1 n1) [1904] by Super 688 with 967 at 2,2
22991 Id : 1530, {_}: multiply (inverse n1) (multiply (inverse n1) (add n1 n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Super 1514 with 982 at 2,2
22992 Id : 1554, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 1530 with 967 at 2,2
22993 Id : 1555, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply (inverse n1) (add n1 n1) [] by Demod 1554 with 982 at 3
22994 Id : 1556, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 1555 with 967 at 3
22995 Id : 1568, {_}: pixley (inverse n1) n1 (inverse n1) =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Super 19 with 1556 at 2,3
22996 Id : 1597, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1568 with 8 at 2
22997 Id : 1814, {_}: multiply (inverse n1) (inverse n1) =<= add (multiply (multiply (inverse n1) (inverse n1)) (inverse n1)) (inverse n1) [] by Super 13 with 1597 at 2,2
22998 Id : 1906, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add (multiply (inverse n1) (inverse n1)) n1) [] by Demod 1814 with 173 at 3
22999 Id : 1990, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3163 n1) [3163] by Super 1906 with 607 at 2,3
23000 Id : 2009, {_}: multiply (inverse n1) (inverse n1) =>= add (inverse n1) (inverse n1) [] by Super 1990 with 967 at 3
23001 Id : 2048, {_}: multiply (inverse n1) (add (inverse n1) n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Super 173 with 2009 at 1,3
23002 Id : 1928, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Super 1906 with 607 at 2,3
23003 Id : 2040, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 1928 with 2009 at 2
23004 Id : 2082, {_}: add (inverse n1) (inverse n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Demod 2048 with 2040 at 2
23005 Id : 2135, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Super 14 with 2082 at 2,2
23006 Id : 2186, {_}: add (inverse n1) (inverse n1) =<= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Demod 2135 with 1556 at 2
23007 Id : 2187, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add n1 (inverse n1)) [] by Demod 2186 with 174 at 3
23008 Id : 2188, {_}: add (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2187 with 4 at 2,3
23009 Id : 2041, {_}: inverse n1 =<= add (add (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1597 with 2009 at 1,3
23010 Id : 2225, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (add (inverse n1) (inverse n1)) [] by Demod 2041 with 2188 at 1,3
23011 Id : 2226, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (multiply (inverse n1) n1) [] by Demod 2225 with 2188 at 2,3
23012 Id : 2235, {_}: inverse n1 =<= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 2226 with 3 at 3
23013 Id : 2236, {_}: inverse n1 =<= multiply (inverse n1) (add n1 n1) [] by Demod 2235 with 982 at 3
23014 Id : 2237, {_}: inverse n1 =<= add (inverse n1) (inverse n1) [] by Demod 2236 with 967 at 3
23015 Id : 2238, {_}: inverse n1 =<= multiply (inverse n1) n1 [] by Demod 2237 with 2188 at 3
23016 Id : 2244, {_}: add (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2188 with 2238 at 3
23017 Id : 2259, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= add (multiply ?3306 (inverse n1)) (inverse n1) [3306] by Super 13 with 2244 at 2,2,2
23018 Id : 2294, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= multiply (inverse n1) (add ?3306 n1) [3306] by Demod 2259 with 173 at 3
23019 Id : 2232, {_}: multiply (inverse n1) n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2040 with 2188 at 2
23020 Id : 2243, {_}: inverse n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2232 with 2238 at 2
23021 Id : 2295, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= inverse n1 [3306] by Demod 2294 with 2243 at 3
23022 Id : 2419, {_}: multiply (multiply (add ?3405 (inverse n1)) n1) (inverse n1) =>= multiply (inverse n1) (add ?3405 (inverse n1)) [3405] by Super 284 with 2295 at 2,2
23023 Id : 3205, {_}: multiply (multiply (add ?4259 (inverse n1)) n1) (inverse n1) =>= inverse n1 [4259] by Demod 2419 with 2295 at 3
23024 Id : 3222, {_}: multiply (multiply n1 n1) (inverse n1) =>= inverse n1 [] by Super 3205 with 4 at 1,1,2
23025 Id : 3294, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= add (inverse n1) (multiply ?4332 (inverse n1)) [4332] by Super 3 with 3222 at 1,3
23026 Id : 3323, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= multiply (inverse n1) (add n1 ?4332) [4332] by Demod 3294 with 174 at 3
23027 Id : 24, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add (add ?69 (inverse ?70)) (inverse ?70))) [71, 70, 69] by Super 21 with 2 at 1,3
23028 Id : 2249, {_}: pixley (add (inverse n1) (inverse n1)) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Super 24 with 2244 at 1,2,2,3
23029 Id : 2310, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Demod 2249 with 2244 at 1,2
23030 Id : 2311, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (inverse n1)) [3289] by Demod 2310 with 2244 at 2,2,3
23031 Id : 2312, {_}: pixley (inverse n1) n1 ?3289 =<= multiply (inverse n1) (add n1 ?3289) [3289] by Demod 2311 with 174 at 3
23032 Id : 3528, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4508) =>= pixley (inverse n1) n1 ?4508 [4508] by Demod 3323 with 2312 at 3
23033 Id : 3542, {_}: multiply (inverse n1) (multiply n1 (add n1 ?4535)) =>= pixley (inverse n1) n1 (multiply ?4535 n1) [4535] by Super 3528 with 3 at 2,2
23034 Id : 2258, {_}: pixley (inverse n1) n1 ?3304 =<= add (multiply (inverse n1) (inverse n1)) (multiply ?3304 (inverse n1)) [3304] by Super 19 with 2244 at 2,2,3
23035 Id : 2766, {_}: pixley (inverse n1) n1 ?3924 =<= multiply (inverse n1) (add (inverse n1) ?3924) [3924] by Demod 2258 with 3 at 3
23036 Id : 2784, {_}: pixley (inverse n1) n1 (multiply ?3959 n1) =>= multiply (inverse n1) ?3959 [3959] by Super 2766 with 428 at 2,3
23037 Id : 4047, {_}: multiply (inverse n1) (multiply n1 (add n1 ?5164)) =>= multiply (inverse n1) ?5164 [5164] by Demod 3542 with 2784 at 3
23038 Id : 4052, {_}: multiply (inverse n1) (multiply n1 n1) =>= multiply (inverse n1) (inverse n1) [] by Super 4047 with 4 at 2,2,2
23039 Id : 2233, {_}: multiply (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2009 with 2188 at 3
23040 Id : 2242, {_}: multiply (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2233 with 2238 at 3
23041 Id : 4088, {_}: multiply (inverse n1) (multiply n1 n1) =>= inverse n1 [] by Demod 4052 with 2242 at 3
23042 Id : 4118, {_}: multiply (multiply n1 n1) (add (inverse n1) n1) =>= add (inverse n1) (multiply n1 n1) [] by Super 412 with 4088 at 1,3
23043 Id : 1137, {_}: multiply (multiply ?2152 n1) (add ?2152 ?2153) =<= add (multiply ?2152 n1) (multiply ?2153 (multiply ?2152 n1)) [2153, 2152] by Super 14 with 408 at 1,2,2
23044 Id : 411, {_}: multiply ?820 (multiply ?820 n1) =>= multiply ?820 n1 [820] by Super 2 with 408 at 1,2
23045 Id : 1151, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= add (multiply ?2193 n1) (multiply ?2193 n1) [2193] by Super 1137 with 411 at 2,3
23046 Id : 1282, {_}: multiply (multiply ?2412 n1) (add ?2412 ?2412) =>= multiply n1 (add ?2412 ?2412) [2412] by Demod 1151 with 3 at 3
23047 Id : 1286, {_}: multiply (multiply n1 n1) (add ?2420 n1) =>= multiply n1 (add n1 n1) [2420] by Super 1282 with 607 at 2,2
23048 Id : 4147, {_}: multiply n1 (add n1 n1) =<= add (inverse n1) (multiply n1 n1) [] by Demod 4118 with 1286 at 2
23049 Id : 4148, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3
23050 Id : 4590, {_}: multiply (add n1 n1) (add n1 ?5598) =>= add n1 (multiply ?5598 (add n1 n1)) [5598] by Super 3 with 4148 at 1,3
23051 Id : 4186, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3
23052 Id : 4194, {_}: multiply n1 (add ?5284 n1) =>= n1 [5284] by Super 4186 with 607 at 2,2
23053 Id : 4313, {_}: n1 =<= add n1 (multiply n1 n1) [] by Super 14 with 4194 at 2
23054 Id : 4601, {_}: multiply (add n1 n1) n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Super 4590 with 4313 at 2,2
23055 Id : 4648, {_}: n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Demod 4601 with 2 at 2
23056 Id : 1187, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= multiply n1 (add ?2193 ?2193) [2193] by Demod 1151 with 3 at 3
23057 Id : 4649, {_}: n1 =<= add n1 (multiply n1 (add n1 n1)) [] by Demod 4648 with 1187 at 2,3
23058 Id : 4650, {_}: n1 =<= add n1 n1 [] by Demod 4649 with 4194 at 2,3
23059 Id : 4692, {_}: add ?5677 n1 =>= n1 [5677] by Super 607 with 4650 at 3
23060 Id : 5124, {_}: multiply ?6342 n1 =<= add ?6342 (multiply n1 ?6342) [6342] by Super 14 with 4692 at 2,2
23061 Id : 4670, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) n1 [1904] by Demod 982 with 4650 at 2,3
23062 Id : 4669, {_}: multiply (inverse ?404) n1 =<= add (inverse ?404) (inverse ?404) [404] by Demod 967 with 4650 at 2,2
23063 Id : 4674, {_}: multiply n1 (multiply (inverse ?1904) n1) =>= multiply (inverse ?1904) n1 [1904] by Demod 4670 with 4669 at 2,2
23064 Id : 5136, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= add (multiply (inverse ?6367) n1) (multiply (inverse ?6367) n1) [6367] by Super 5124 with 4674 at 2,3
23065 Id : 5182, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= multiply n1 (add (inverse ?6367) (inverse ?6367)) [6367] by Demod 5136 with 3 at 3
23066 Id : 5183, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply n1 (multiply (inverse ?6367) n1) [6367] by Demod 5182 with 4669 at 2,3
23067 Id : 5184, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply (inverse ?6367) n1 [6367] by Demod 5183 with 4674 at 3
23068 Id : 5206, {_}: multiply (inverse ?6424) n1 =<= add (inverse n1) (multiply (inverse ?6424) n1) [6424] by Super 428 with 5184 at 2,3
23069 Id : 5244, {_}: multiply (inverse ?6424) n1 =>= inverse ?6424 [6424] by Demod 5206 with 428 at 3
23070 Id : 5308, {_}: inverse ?6512 =<= add (inverse n1) (inverse ?6512) [6512] by Super 428 with 5244 at 2,3
23071 Id : 5370, {_}: pixley (inverse n1) ?6557 ?6558 =<= add (multiply (inverse n1) (inverse ?6557)) (multiply ?6558 (inverse ?6557)) [6558, 6557] by Super 19 with 5308 at 2,2,3
23072 Id : 7459, {_}: pixley (inverse n1) ?8766 ?8767 =<= multiply (inverse ?8766) (add (inverse n1) ?8767) [8767, 8766] by Demod 5370 with 3 at 3
23073 Id : 5371, {_}: inverse (inverse n1) =>= n1 [] by Super 4 with 5308 at 2
23074 Id : 7482, {_}: pixley (inverse n1) (inverse n1) ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Super 7459 with 5371 at 1,3
23075 Id : 7542, {_}: ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Demod 7482 with 6 at 2
23076 Id : 5466, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 (inverse (inverse n1))) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Super 19 with 5371 at 2,2,2,3
23077 Id : 5516, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Demod 5466 with 5371 at 2,1,3
23078 Id : 5517, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 n1) [6673, 6672] by Demod 5516 with 4692 at 2,2,3
23079 Id : 5854, {_}: pixley ?6987 (inverse n1) ?6988 =<= multiply n1 (add ?6987 ?6988) [6988, 6987] by Demod 5517 with 3 at 3
23080 Id : 5871, {_}: pixley (inverse n1) (inverse n1) (multiply ?7040 n1) =>= multiply n1 ?7040 [7040] by Super 5854 with 428 at 2,3
23081 Id : 5916, {_}: multiply ?7040 n1 =?= multiply n1 ?7040 [7040] by Demod 5871 with 6 at 2
23082 Id : 5518, {_}: pixley ?6672 (inverse n1) ?6673 =<= multiply n1 (add ?6672 ?6673) [6673, 6672] by Demod 5517 with 3 at 3
23083 Id : 5837, {_}: multiply ?6926 (pixley ?6926 (inverse n1) (inverse n1)) =>= multiply n1 (add ?6926 (inverse n1)) [6926] by Super 505 with 5518 at 2,2
23084 Id : 5906, {_}: multiply ?6926 ?6926 =?= multiply n1 (add ?6926 (inverse n1)) [6926] by Demod 5837 with 7 at 2,2
23085 Id : 5907, {_}: multiply ?6926 ?6926 =?= pixley ?6926 (inverse n1) (inverse n1) [6926] by Demod 5906 with 5518 at 3
23086 Id : 5908, {_}: multiply ?6926 ?6926 =>= ?6926 [6926] by Demod 5907 with 7 at 3
23087 Id : 7131, {_}: multiply ?8481 (add ?8482 ?8481) =>= add (multiply ?8482 ?8481) ?8481 [8482, 8481] by Super 3 with 5908 at 2,3
23088 Id : 5066, {_}: multiply ?6275 n1 =<= add ?6275 (multiply n1 ?6275) [6275] by Super 14 with 4692 at 2,2
23089 Id : 6609, {_}: multiply ?7988 n1 =<= add ?7988 (multiply ?7988 n1) [7988] by Super 5066 with 5916 at 2,3
23090 Id : 7156, {_}: multiply (multiply ?8553 n1) (multiply ?8553 n1) =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Super 7131 with 6609 at 2,2
23091 Id : 7254, {_}: multiply ?8553 n1 =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Demod 7156 with 5908 at 2
23092 Id : 7255, {_}: multiply ?8553 n1 =<= multiply (multiply ?8553 n1) (add ?8553 ?8553) [8553] by Demod 7254 with 412 at 3
23093 Id : 5833, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= pixley ?2193 (inverse n1) ?2193 [2193] by Demod 1187 with 5518 at 3
23094 Id : 5835, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5833 with 8 at 3
23095 Id : 7256, {_}: multiply ?8553 n1 =>= ?8553 [8553] by Demod 7255 with 5835 at 3
23096 Id : 7273, {_}: ?7040 =<= multiply n1 ?7040 [7040] by Demod 5916 with 7256 at 2
23097 Id : 7543, {_}: ?8832 =<= add (inverse n1) ?8832 [8832] by Demod 7542 with 7273 at 3
23098 Id : 7582, {_}: multiply (inverse n1) (multiply ?8919 (inverse ?8919)) =?= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Super 505 with 7543 at 2,2,2
23099 Id : 5473, {_}: multiply ?6687 (multiply (inverse n1) (add ?6687 n1)) =?= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Super 505 with 5371 at 2,2,2,2
23100 Id : 5499, {_}: multiply ?6687 (multiply (inverse n1) n1) =<= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Demod 5473 with 4692 at 2,2,2
23101 Id : 5500, {_}: multiply ?6687 (multiply (inverse n1) n1) =?= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5499 with 5371 at 2,2,3
23102 Id : 5501, {_}: multiply ?6687 (inverse n1) =<= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5500 with 5244 at 2,2
23103 Id : 5502, {_}: multiply ?6687 (inverse n1) =?= multiply (inverse n1) n1 [6687] by Demod 5501 with 4692 at 2,3
23104 Id : 5503, {_}: multiply ?6687 (inverse n1) =>= inverse n1 [6687] by Demod 5502 with 5244 at 3
23105 Id : 5615, {_}: multiply (inverse n1) (add n1 ?6752) =>= add (inverse n1) (inverse n1) [6752] by Super 174 with 5503 at 2,3
23106 Id : 5636, {_}: pixley (inverse n1) n1 ?6752 =?= add (inverse n1) (inverse n1) [6752] by Demod 5615 with 2312 at 2
23107 Id : 5285, {_}: inverse ?404 =<= add (inverse ?404) (inverse ?404) [404] by Demod 4669 with 5244 at 2
23108 Id : 5637, {_}: pixley (inverse n1) n1 ?6752 =>= inverse n1 [6752] by Demod 5636 with 5285 at 3
23109 Id : 5782, {_}: inverse n1 =<= multiply (inverse n1) ?3959 [3959] by Demod 2784 with 5637 at 2
23110 Id : 7613, {_}: inverse n1 =<= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Demod 7582 with 5782 at 2
23111 Id : 7614, {_}: inverse n1 =<= multiply ?8919 (inverse ?8919) [8919] by Demod 7613 with 7543 at 2,3
23112 Id : 7674, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =?= add (inverse n1) (multiply ?8985 (inverse ?8984)) [8985, 8984] by Super 3 with 7614 at 1,3
23113 Id : 7731, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =>= multiply ?8985 (inverse ?8984) [8985, 8984] by Demod 7674 with 7543 at 3
23114 Id : 289, {_}: multiply (multiply ?563 (multiply (inverse ?564) (add ?565 n1))) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [565, 564, 563] by Super 274 with 173 at 2,1,2
23115 Id : 8394, {_}: multiply (multiply ?563 (multiply (inverse ?564) n1)) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [564, 563] by Demod 289 with 4692 at 2,2,1,2
23116 Id : 8406, {_}: multiply (multiply ?9773 (inverse ?9774)) (multiply (inverse ?9774) ?9773) =>= multiply (inverse ?9774) ?9773 [9774, 9773] by Demod 8394 with 7256 at 2,1,2
23117 Id : 8444, {_}: multiply (inverse n1) (multiply (inverse ?9877) ?9877) =>= multiply (inverse ?9877) ?9877 [9877] by Super 8406 with 7614 at 1,2
23118 Id : 8534, {_}: inverse n1 =<= multiply (inverse ?9877) ?9877 [9877] by Demod 8444 with 5782 at 2
23119 Id : 8551, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= add (multiply ?9926 ?9925) (inverse n1) [9926, 9925] by Super 3 with 8534 at 2,3
23120 Id : 367, {_}: multiply ?731 (add (add ?732 ?731) ?733) =>= add ?731 (multiply ?733 ?731) [733, 732, 731] by Super 12 with 2 at 1,3
23121 Id : 379, {_}: multiply ?780 n1 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Super 367 with 4 at 2,2
23122 Id : 7285, {_}: ?780 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Demod 379 with 7256 at 2
23123 Id : 7585, {_}: ?8927 =<= add ?8927 (multiply (inverse ?8927) ?8927) [8927] by Super 7285 with 7543 at 1,1,2,3
23124 Id : 8670, {_}: ?8927 =<= add ?8927 (inverse n1) [8927] by Demod 7585 with 8534 at 2,3
23125 Id : 9041, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= multiply ?9926 ?9925 [9926, 9925] by Demod 8551 with 8670 at 3
23126 Id : 172, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 (add n1 (inverse ?331))) [332, 331] by Super 19 with 16 at 1,3
23127 Id : 9053, {_}: pixley n1 ?10412 ?10412 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Super 172 with 9041 at 2,3
23128 Id : 9135, {_}: n1 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Demod 9053 with 7 at 2
23129 Id : 9136, {_}: n1 =<= add (inverse ?10412) ?10412 [10412] by Demod 9135 with 7273 at 2,3
23130 Id : 9201, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =<= add (multiply (inverse (inverse ?10589)) (inverse ?10589)) (multiply ?10590 n1) [10590, 10589] by Super 19 with 9136 at 2,2,3
23131 Id : 9238, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =?= add (inverse n1) (multiply ?10590 n1) [10590, 10589] by Demod 9201 with 8534 at 1,3
23132 Id : 9239, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= add (inverse n1) ?10590 [10590, 10589] by Demod 9238 with 7256 at 2,3
23133 Id : 9240, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= ?10590 [10590, 10589] by Demod 9239 with 7543 at 3
23134 Id : 10446, {_}: ?12102 =<= inverse (inverse ?12102) [12102] by Super 7 with 9240 at 2
23135 Id : 10555, {_}: multiply (inverse ?12273) (add ?12274 ?12273) =>= multiply ?12274 (inverse ?12273) [12274, 12273] by Super 9041 with 10446 at 2,2,2
23136 Id : 11456, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 (inverse (inverse ?13532)) =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Super 24 with 10555 at 2,3
23137 Id : 11548, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Demod 11456 with 10446 at 3,2
23138 Id : 8892, {_}: multiply (inverse ?10244) (add ?10244 ?10245) =>= multiply ?10245 (inverse ?10244) [10245, 10244] by Demod 7674 with 7543 at 3
23139 Id : 7580, {_}: multiply ?8914 (add ?8915 ?8914) =?= add (multiply (inverse n1) ?8914) ?8914 [8915, 8914] by Super 13 with 7543 at 2,2
23140 Id : 5958, {_}: multiply ?7147 (add ?7148 ?7147) =>= add (multiply ?7148 ?7147) ?7147 [7148, 7147] by Super 3 with 5908 at 2,3
23141 Id : 7619, {_}: add (multiply ?8915 ?8914) ?8914 =?= add (multiply (inverse n1) ?8914) ?8914 [8914, 8915] by Demod 7580 with 5958 at 2
23142 Id : 7620, {_}: add (multiply ?8915 ?8914) ?8914 =>= add (inverse n1) ?8914 [8914, 8915] by Demod 7619 with 5782 at 1,3
23143 Id : 7775, {_}: add (multiply ?9114 ?9115) ?9115 =>= ?9115 [9115, 9114] by Demod 7620 with 7543 at 3
23144 Id : 7621, {_}: add (multiply ?8915 ?8914) ?8914 =>= ?8914 [8914, 8915] by Demod 7620 with 7543 at 3
23145 Id : 7749, {_}: multiply ?7147 (add ?7148 ?7147) =>= ?7147 [7148, 7147] by Demod 5958 with 7621 at 3
23146 Id : 7792, {_}: add ?9167 (add ?9168 ?9167) =>= add ?9168 ?9167 [9168, 9167] by Super 7775 with 7749 at 1,2
23147 Id : 8900, {_}: multiply (inverse ?10265) (add ?10266 ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10266, 10265] by Super 8892 with 7792 at 2,2
23148 Id : 11444, {_}: multiply ?10266 (inverse ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10265, 10266] by Demod 8900 with 10555 at 2
23149 Id : 11549, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =?= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11548 with 11444 at 2,3
23150 Id : 11550, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11549 with 7 at 2
23151 Id : 11551, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 ?13532) [13532, 13531] by Demod 11550 with 10446 at 2,2,3
23152 Id : 11841, {_}: multiply (inverse (inverse ?13951)) (add ?13952 (inverse ?13951)) =>= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13952, 13951] by Super 7731 with 11551 at 2,2
23153 Id : 11918, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13951, 13952] by Demod 11841 with 10555 at 2
23154 Id : 11919, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11918 with 10446 at 2,3
23155 Id : 11920, {_}: multiply ?13952 ?13951 =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11919 with 10446 at 2,2
23156 Id : 12244, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= add (multiply ?14435 ?14434) (multiply ?14436 ?14434) [14436, 14435, 14434] by Super 3 with 11920 at 2,3
23157 Id : 29011, {_}: multiply ?35505 (add ?35506 (multiply ?35507 ?35505)) =>= multiply ?35505 (add ?35506 ?35507) [35507, 35506, 35505] by Demod 12244 with 3 at 3
23158 Id : 29060, {_}: multiply ?35715 (add ?35716 (inverse n1)) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Super 29011 with 8534 at 2,2,2
23159 Id : 11860, {_}: add ?14021 (inverse ?14022) =<= add (inverse ?14022) (multiply ?14021 ?14022) [14022, 14021] by Demod 11550 with 10446 at 2,2,3
23160 Id : 11890, {_}: add n1 (inverse ?14122) =<= add (inverse ?14122) ?14122 [14122] by Super 11860 with 7273 at 2,3
23161 Id : 11943, {_}: add n1 (inverse ?14122) =>= n1 [14122] by Demod 11890 with 9136 at 3
23162 Id : 11977, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 n1) [332, 331] by Demod 172 with 11943 at 2,2,3
23163 Id : 11984, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) ?332 [332, 331] by Demod 11977 with 7256 at 2,3
23164 Id : 11991, {_}: add ?13531 (inverse ?13532) =<= pixley n1 ?13532 (multiply ?13531 ?13532) [13532, 13531] by Demod 11551 with 11984 at 3
23165 Id : 12023, {_}: add n1 (inverse ?14257) =>= n1 [14257] by Demod 11890 with 9136 at 3
23166 Id : 12028, {_}: add n1 ?14267 =>= n1 [14267] by Super 12023 with 10446 at 2,2
23167 Id : 12137, {_}: multiply ?14331 (add n1 ?14332) =?= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Super 14 with 12028 at 1,2,2
23168 Id : 12188, {_}: multiply ?14331 n1 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12137 with 12028 at 2,2
23169 Id : 12598, {_}: ?14940 =<= add ?14940 (multiply ?14941 ?14940) [14941, 14940] by Demod 12188 with 7256 at 2
23170 Id : 409, {_}: multiply (multiply ?814 n1) (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Super 14 with 408 at 1,2,2
23171 Id : 7278, {_}: multiply ?814 (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 409 with 7256 at 1,2
23172 Id : 7279, {_}: multiply ?814 (add ?814 ?815) =<= add ?814 (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 7278 with 7256 at 1,3
23173 Id : 7280, {_}: multiply ?814 (add ?814 ?815) =>= add ?814 (multiply ?815 ?814) [815, 814] by Demod 7279 with 7256 at 2,2,3
23174 Id : 12189, {_}: ?14331 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12188 with 7256 at 2
23175 Id : 12573, {_}: multiply ?814 (add ?814 ?815) =>= ?814 [815, 814] by Demod 7280 with 12189 at 3
23176 Id : 12624, {_}: add ?15025 ?15026 =<= add (add ?15025 ?15026) ?15025 [15026, 15025] by Super 12598 with 12573 at 2,3
23177 Id : 12720, {_}: multiply ?15175 (add (inverse ?15175) ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Super 9041 with 12624 at 2,2
23178 Id : 12767, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Demod 12720 with 11984 at 2,2
23179 Id : 12768, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15176, 15175] by Demod 12767 with 11984 at 1,3
23180 Id : 8552, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= add (inverse n1) (multiply ?9929 ?9928) [9929, 9928] by Super 3 with 8534 at 1,3
23181 Id : 8614, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8552 with 7543 at 3
23182 Id : 11985, {_}: multiply ?9928 (pixley n1 ?9928 ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8614 with 11984 at 2,2
23183 Id : 12769, {_}: multiply ?15176 ?15175 =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15175, 15176] by Demod 12768 with 11985 at 2
23184 Id : 15132, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= pixley n1 ?18424 (multiply ?18425 ?18424) [18425, 18424] by Super 11991 with 12769 at 3,3
23185 Id : 15170, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15132 with 11991 at 3
23186 Id : 12729, {_}: add ?15203 ?15204 =<= add (add ?15203 ?15204) ?15203 [15204, 15203] by Super 12598 with 12573 at 2,3
23187 Id : 12745, {_}: add (inverse ?15249) ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Super 12729 with 11984 at 1,3
23188 Id : 12826, {_}: pixley n1 ?15249 ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Demod 12745 with 11984 at 2
23189 Id : 23185, {_}: pixley n1 ?18424 ?18425 =<= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15170 with 12826 at 2
23190 Id : 29209, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Demod 29060 with 23185 at 2,2
23191 Id : 29210, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29209 with 23185 at 2,3
23192 Id : 29211, {_}: multiply ?35715 ?35716 =<= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29210 with 6 at 2,2
23193 Id : 29212, {_}: multiply ?35715 ?35716 =?= multiply ?35716 ?35715 [35716, 35715] by Demod 29211 with 11985 at 3
23194 Id : 11904, {_}: add ?14161 (inverse (inverse ?14162)) =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Super 11860 with 10446 at 1,3
23195 Id : 11970, {_}: add ?14161 ?14162 =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Demod 11904 with 10446 at 2,2
23196 Id : 15099, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18302 (multiply ?18303 (inverse ?18302)) [18303, 18302] by Super 11970 with 12769 at 2,3
23197 Id : 15201, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15099 with 11970 at 3
23198 Id : 10547, {_}: pixley n1 (inverse ?12250) ?12251 =<= add (inverse (inverse ?12250)) (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Super 172 with 10446 at 2,2,2,3
23199 Id : 10574, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Demod 10547 with 10446 at 1,3
23200 Id : 17614, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 n1) [12251, 12250] by Demod 10574 with 12028 at 2,2,3
23201 Id : 17615, {_}: pixley n1 (inverse ?12250) ?12251 =>= add ?12250 ?12251 [12251, 12250] by Demod 17614 with 7256 at 2,3
23202 Id : 23377, {_}: add (add ?18302 ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15201 with 17615 at 1,2
23203 Id : 23378, {_}: add ?18302 ?18303 =?= add ?18303 ?18302 [18303, 18302] by Demod 23377 with 12624 at 2
23204 Id : 363, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =<= add (multiply ?716 (add (add ?713 ?714) ?715)) (add ?714 (multiply ?715 ?714)) [716, 715, 714, 713] by Super 3 with 14 at 2,3
23205 Id : 33202, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =>= add (multiply ?716 (add (add ?713 ?714) ?715)) ?714 [716, 715, 714, 713] by Demod 363 with 12189 at 2,3
23206 Id : 33249, {_}: multiply (add (add ?41120 ?41121) ?41122) (add ?41123 ?41121) =>= add ?41121 (multiply ?41123 (add (add ?41120 ?41121) ?41122)) [41123, 41122, 41121, 41120] by Demod 33202 with 23378 at 3
23207 Id : 7276, {_}: multiply ?2193 (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5835 with 7256 at 1,2
23208 Id : 7300, {_}: add (multiply ?2193 ?2193) ?2193 =>= ?2193 [2193] by Demod 7276 with 5958 at 2
23209 Id : 7301, {_}: add ?2193 ?2193 =>= ?2193 [2193] by Demod 7300 with 5908 at 1,2
23210 Id : 33300, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =<= add ?41375 (multiply ?41376 (add (add ?41374 ?41375) (add ?41374 ?41375))) [41376, 41375, 41374] by Super 33249 with 7301 at 1,2
23211 Id : 33433, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =>= add ?41375 (multiply ?41376 (add ?41374 ?41375)) [41376, 41375, 41374] by Demod 33300 with 7301 at 2,2,3
23212 Id : 42671, {_}: multiply ?52830 (add ?52831 ?52832) =<= add (multiply ?52830 ?52831) (multiply ?52832 ?52830) [52832, 52831, 52830] by Super 3 with 29212 at 1,3
23213 Id : 42679, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add (multiply (add ?52859 ?52860) ?52861) ?52860 [52861, 52860, 52859] by Super 42671 with 7749 at 2,3
23214 Id : 42859, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52861, 52860, 52859] by Demod 42679 with 23378 at 3
23215 Id : 58778, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =?= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52859, 52861, 52860] by Demod 42859 with 33433 at 2
23216 Id : 42225, {_}: multiply ?51978 (add ?51979 ?51980) =<= add (multiply ?51979 ?51978) (multiply ?51978 ?51980) [51980, 51979, 51978] by Super 3 with 29212 at 2,3
23217 Id : 56980, {_}: multiply (add ?78761 ?78762) (add ?78762 ?78763) =>= add ?78762 (multiply (add ?78761 ?78762) ?78763) [78763, 78762, 78761] by Super 42225 with 7749 at 1,3
23218 Id : 57032, {_}: multiply (add ?78985 ?78986) (add ?78985 ?78987) =>= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Super 56980 with 23378 at 1,2
23219 Id : 42307, {_}: multiply (add ?52335 ?52336) (add ?52335 ?52337) =>= add ?52335 (multiply (add ?52335 ?52336) ?52337) [52337, 52336, 52335] by Super 42225 with 12573 at 1,3
23220 Id : 69246, {_}: add ?78985 (multiply (add ?78985 ?78986) ?78987) =?= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 57032 with 42307 at 2
23221 Id : 42691, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add (multiply (add ?52915 ?52916) ?52917) ?52915 [52917, 52916, 52915] by Super 42671 with 12573 at 2,3
23222 Id : 42878, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 42691 with 23378 at 3
23223 Id : 33277, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =<= add ?41259 (multiply ?41261 (add (add ?41259 ?41259) ?41260)) [41261, 41260, 41259] by Super 33249 with 7301 at 1,1,2
23224 Id : 33397, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =>= add ?41259 (multiply ?41261 (add ?41259 ?41260)) [41261, 41260, 41259] by Demod 33277 with 7301 at 1,2,2,3
23225 Id : 59822, {_}: add ?52915 (multiply ?52917 (add ?52915 ?52916)) =?= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52916, 52917, 52915] by Demod 42878 with 33397 at 2
23226 Id : 49363, {_}: multiply (add ?63432 ?63433) (add ?63433 ?63434) =>= add ?63433 (multiply ?63432 (add ?63433 ?63434)) [63434, 63433, 63432] by Super 29212 with 33397 at 3
23227 Id : 42295, {_}: multiply (add ?52279 ?52280) (add ?52280 ?52281) =>= add ?52280 (multiply (add ?52279 ?52280) ?52281) [52281, 52280, 52279] by Super 42225 with 7749 at 1,3
23228 Id : 65944, {_}: add ?95703 (multiply (add ?95704 ?95703) ?95705) =?= add ?95703 (multiply ?95704 (add ?95703 ?95705)) [95705, 95704, 95703] by Demod 49363 with 42295 at 2
23229 Id : 12345, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= multiply ?14434 (add ?14435 ?14436) [14436, 14435, 14434] by Demod 12244 with 3 at 3
23230 Id : 66007, {_}: add ?95981 (multiply (add ?95982 ?95981) (multiply ?95983 ?95982)) =>= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95983, 95982, 95981] by Super 65944 with 12345 at 2,3
23231 Id : 12571, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= ?41 [43, 42, 41] by Demod 14 with 12189 at 3
23232 Id : 12574, {_}: multiply (multiply ?14855 ?14856) (add ?14856 ?14857) =>= multiply ?14855 ?14856 [14857, 14856, 14855] by Super 12571 with 12189 at 1,2,2
23233 Id : 32599, {_}: multiply (add ?39770 ?39771) (multiply ?39772 ?39770) =>= multiply ?39772 ?39770 [39772, 39771, 39770] by Super 29212 with 12574 at 3
23234 Id : 66421, {_}: add ?95981 (multiply ?95983 ?95982) =<= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95982, 95983, 95981] by Demod 66007 with 32599 at 2,2
23235 Id : 74546, {_}: add ?52915 (multiply ?52916 ?52917) =<= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 59822 with 66421 at 2
23236 Id : 74547, {_}: add ?78985 (multiply ?78986 ?78987) =<= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 69246 with 74546 at 2
23237 Id : 74549, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =>= add ?52860 (multiply ?52859 ?52861) [52859, 52861, 52860] by Demod 58778 with 74547 at 3
23238 Id : 75087, {_}: add a (multiply c b) =?= add a (multiply c b) [] by Demod 57307 with 74549 at 3
23239 Id : 57307, {_}: add a (multiply c b) =<= add a (multiply b (add c a)) [] by Demod 57306 with 33433 at 3
23240 Id : 57306, {_}: add a (multiply c b) =<= multiply (add c a) (add b a) [] by Demod 57305 with 29212 at 3
23241 Id : 57305, {_}: add a (multiply c b) =<= multiply (add b a) (add c a) [] by Demod 57304 with 23378 at 2,3
23242 Id : 57304, {_}: add a (multiply c b) =<= multiply (add b a) (add a c) [] by Demod 57303 with 23378 at 1,3
23243 Id : 57303, {_}: add a (multiply c b) =<= multiply (add a b) (add a c) [] by Demod 1 with 29212 at 2,2
23244 Id : 1, {_}: add a (multiply b c) =<= multiply (add a b) (add a c) [] by prove_add_multiply_property
23245 % SZS output end CNFRefutation for BOO023-1.p
23246 20955: solved BOO023-1.p in 19.273203 using kbo
23247 20955: status Unsatisfiable for BOO023-1.p
23248 NO CLASH, using fixed ground order
23250 NO CLASH, using fixed ground order
23252 21166: Id : 2, {_}:
23253 multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
23255 multiply ?2 ?3 (multiply ?4 ?5 ?6)
23256 [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
23257 21166: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
23258 21166: Id : 4, {_}:
23259 multiply ?11 ?11 ?12 =>= ?11
23260 [12, 11] by ternary_multiply_2 ?11 ?12
23261 21166: Id : 5, {_}:
23262 multiply (inverse ?14) ?14 ?15 =>= ?15
23263 [15, 14] by left_inverse ?14 ?15
23264 21166: Id : 6, {_}:
23265 multiply ?17 ?18 (inverse ?18) =>= ?17
23266 [18, 17] by right_inverse ?17 ?18
23268 21166: Id : 1, {_}:
23269 multiply (multiply a (inverse a) b)
23270 (inverse (multiply (multiply c d e) f (multiply c d g)))
23271 (multiply d (multiply g f e) c)
23274 [] by prove_single_axiom
23278 21166: g 2 0 2 3,3,1,2,2
23279 21166: f 2 0 2 2,1,2,2
23280 21166: e 2 0 2 3,1,1,2,2
23281 21166: d 3 0 3 2,1,1,2,2
23282 21166: c 3 0 3 1,1,1,2,2
23283 21166: multiply 16 3 7 0,2
23284 21166: b 2 0 2 3,1,2
23285 21166: inverse 4 1 2 0,2,1,2
23286 21166: a 2 0 2 1,1,2
23287 NO CLASH, using fixed ground order
23289 21167: Id : 2, {_}:
23290 multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
23292 multiply ?2 ?3 (multiply ?4 ?5 ?6)
23293 [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
23294 21167: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
23295 21167: Id : 4, {_}:
23296 multiply ?11 ?11 ?12 =>= ?11
23297 [12, 11] by ternary_multiply_2 ?11 ?12
23298 21167: Id : 5, {_}:
23299 multiply (inverse ?14) ?14 ?15 =>= ?15
23300 [15, 14] by left_inverse ?14 ?15
23301 21167: Id : 6, {_}:
23302 multiply ?17 ?18 (inverse ?18) =>= ?17
23303 [18, 17] by right_inverse ?17 ?18
23305 21167: Id : 1, {_}:
23306 multiply (multiply a (inverse a) b)
23307 (inverse (multiply (multiply c d e) f (multiply c d g)))
23308 (multiply d (multiply g f e) c)
23311 [] by prove_single_axiom
23315 21167: g 2 0 2 3,3,1,2,2
23316 21167: f 2 0 2 2,1,2,2
23317 21167: e 2 0 2 3,1,1,2,2
23318 21167: d 3 0 3 2,1,1,2,2
23319 21167: c 3 0 3 1,1,1,2,2
23320 21167: multiply 16 3 7 0,2
23321 21167: b 2 0 2 3,1,2
23322 21167: inverse 4 1 2 0,2,1,2
23323 21167: a 2 0 2 1,1,2
23324 21165: Id : 2, {_}:
23325 multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
23327 multiply ?2 ?3 (multiply ?4 ?5 ?6)
23328 [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
23329 21165: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
23330 21165: Id : 4, {_}:
23331 multiply ?11 ?11 ?12 =>= ?11
23332 [12, 11] by ternary_multiply_2 ?11 ?12
23333 21165: Id : 5, {_}:
23334 multiply (inverse ?14) ?14 ?15 =>= ?15
23335 [15, 14] by left_inverse ?14 ?15
23336 21165: Id : 6, {_}:
23337 multiply ?17 ?18 (inverse ?18) =>= ?17
23338 [18, 17] by right_inverse ?17 ?18
23340 21165: Id : 1, {_}:
23341 multiply (multiply a (inverse a) b)
23342 (inverse (multiply (multiply c d e) f (multiply c d g)))
23343 (multiply d (multiply g f e) c)
23346 [] by prove_single_axiom
23350 21165: g 2 0 2 3,3,1,2,2
23351 21165: f 2 0 2 2,1,2,2
23352 21165: e 2 0 2 3,1,1,2,2
23353 21165: d 3 0 3 2,1,1,2,2
23354 21165: c 3 0 3 1,1,1,2,2
23355 21165: multiply 16 3 7 0,2
23356 21165: b 2 0 2 3,1,2
23357 21165: inverse 4 1 2 0,2,1,2
23358 21165: a 2 0 2 1,1,2
23361 Found proof, 10.936664s
23362 % SZS status Unsatisfiable for BOO034-1.p
23363 % SZS output start CNFRefutation for BOO034-1.p
23364 Id : 5, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
23365 Id : 4, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
23366 Id : 6, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
23367 Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
23368 Id : 2, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
23369 Id : 12, {_}: multiply (multiply ?48 ?49 ?50) ?51 ?49 =?= multiply ?48 ?49 (multiply ?50 ?51 ?49) [51, 50, 49, 48] by Super 2 with 3 at 3,2
23370 Id : 13, {_}: multiply ?53 ?54 (multiply ?55 ?53 ?56) =?= multiply ?55 ?53 (multiply ?53 ?54 ?56) [56, 55, 54, 53] by Super 2 with 3 at 1,2
23371 Id : 920, {_}: multiply (multiply ?2937 ?2938 ?2939) ?2937 ?2938 =?= multiply ?2939 ?2937 (multiply ?2937 ?2938 ?2938) [2939, 2938, 2937] by Super 12 with 13 at 3
23372 Id : 1359, {_}: multiply (multiply ?4051 ?4052 ?4053) ?4051 ?4052 =>= multiply ?4053 ?4051 ?4052 [4053, 4052, 4051] by Demod 920 with 3 at 3,3
23373 Id : 1364, {_}: multiply ?4070 ?4070 ?4071 =?= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Super 1359 with 6 at 1,2
23374 Id : 1413, {_}: ?4070 =<= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Demod 1364 with 4 at 2
23375 Id : 1453, {_}: multiply (multiply ?4288 ?4289 (inverse ?4289)) ?4290 ?4289 =>= multiply ?4288 ?4289 ?4290 [4290, 4289, 4288] by Super 12 with 1413 at 3,3
23376 Id : 1476, {_}: multiply ?4288 ?4290 ?4289 =?= multiply ?4288 ?4289 ?4290 [4289, 4290, 4288] by Demod 1453 with 6 at 1,2
23377 Id : 519, {_}: multiply (multiply ?1786 ?1787 ?1788) ?1789 ?1787 =?= multiply ?1786 ?1787 (multiply ?1788 ?1789 ?1787) [1789, 1788, 1787, 1786] by Super 2 with 3 at 3,2
23378 Id : 659, {_}: multiply (multiply ?2172 ?2173 ?2174) ?2174 ?2173 =>= multiply ?2172 ?2173 ?2174 [2174, 2173, 2172] by Super 519 with 4 at 3,3
23379 Id : 664, {_}: multiply ?2191 (inverse ?2192) ?2192 =?= multiply ?2191 ?2192 (inverse ?2192) [2192, 2191] by Super 659 with 6 at 1,2
23380 Id : 701, {_}: multiply ?2191 (inverse ?2192) ?2192 =>= ?2191 [2192, 2191] by Demod 664 with 6 at 3
23381 Id : 1371, {_}: multiply ?4106 ?4106 (inverse ?4107) =?= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Super 1359 with 701 at 1,2
23382 Id : 1415, {_}: ?4106 =<= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Demod 1371 with 4 at 2
23383 Id : 1522, {_}: multiply ?4441 ?4442 (multiply ?4443 ?4441 (inverse ?4441)) =>= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Super 13 with 1415 at 3,3
23384 Id : 1536, {_}: multiply ?4441 ?4442 ?4443 =?= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Demod 1522 with 6 at 3,2
23385 Id : 727, {_}: inverse (inverse ?2329) =>= ?2329 [2329] by Super 5 with 701 at 2
23386 Id : 761, {_}: multiply ?2420 (inverse ?2420) ?2421 =>= ?2421 [2421, 2420] by Super 5 with 727 at 1,2
23387 Id : 40424, {_}: b === b [] by Demod 40423 with 6 at 2
23388 Id : 40423, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 40422 with 1476 at 3,1,3,2
23389 Id : 40422, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 40421 with 1536 at 3,1,3,2
23390 Id : 40421, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f g e))) =>= b [] by Demod 40420 with 1476 at 3,1,3,2
23391 Id : 40420, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f e g))) =>= b [] by Demod 40419 with 1536 at 3,1,3,2
23392 Id : 40419, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e g f))) =>= b [] by Demod 40418 with 1476 at 3,1,3,2
23393 Id : 40418, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e f g))) =>= b [] by Demod 40417 with 1476 at 1,3,2
23394 Id : 40417, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40416 with 1476 at 2
23395 Id : 40416, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d c (multiply g f e)) =>= b [] by Demod 40415 with 1536 at 2
23396 Id : 40415, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40414 with 1536 at 1,3,2
23397 Id : 40414, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40413 with 761 at 2,2
23398 Id : 40413, {_}: multiply (multiply d c (multiply g f e)) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40412 with 1476 at 1,2
23399 Id : 40412, {_}: multiply (multiply d (multiply g f e) c) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40411 with 1476 at 2
23400 Id : 40411, {_}: multiply (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) (multiply a (inverse a) b) =>= b [] by Demod 40410 with 1536 at 2
23401 Id : 40410, {_}: multiply (multiply a (inverse a) b) (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 11 with 1476 at 2
23402 Id : 11, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 1 with 2 at 1,2,2
23403 Id : 1, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
23404 % SZS output end CNFRefutation for BOO034-1.p
23405 21165: solved BOO034-1.p in 10.220638 using nrkbo
23406 21165: status Unsatisfiable for BOO034-1.p
23407 CLASH, statistics insufficient
23409 21378: Id : 2, {_}:
23410 apply (apply (apply s ?3) ?4) ?5
23412 apply (apply ?3 ?5) (apply ?4 ?5)
23413 [5, 4, 3] by s_definition ?3 ?4 ?5
23414 21378: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
23416 21378: Id : 1, {_}:
23417 apply (apply ?1 (f ?1)) (g ?1)
23419 apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
23420 [1] by prove_u_combinator ?1
23426 21378: g 3 1 3 0,2,2
23427 21378: apply 13 2 5 0,2
23428 21378: f 3 1 3 0,2,1,2
23429 CLASH, statistics insufficient
23431 21379: Id : 2, {_}:
23432 apply (apply (apply s ?3) ?4) ?5
23434 apply (apply ?3 ?5) (apply ?4 ?5)
23435 [5, 4, 3] by s_definition ?3 ?4 ?5
23436 21379: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
23438 21379: Id : 1, {_}:
23439 apply (apply ?1 (f ?1)) (g ?1)
23441 apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
23442 [1] by prove_u_combinator ?1
23448 21379: g 3 1 3 0,2,2
23449 21379: apply 13 2 5 0,2
23450 21379: f 3 1 3 0,2,1,2
23451 CLASH, statistics insufficient
23453 21380: Id : 2, {_}:
23454 apply (apply (apply s ?3) ?4) ?5
23456 apply (apply ?3 ?5) (apply ?4 ?5)
23457 [5, 4, 3] by s_definition ?3 ?4 ?5
23458 21380: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
23460 21380: Id : 1, {_}:
23461 apply (apply ?1 (f ?1)) (g ?1)
23463 apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
23464 [1] by prove_u_combinator ?1
23470 21380: g 3 1 3 0,2,2
23471 21380: apply 13 2 5 0,2
23472 21380: f 3 1 3 0,2,1,2
23473 % SZS status Timeout for COL004-1.p
23474 NO CLASH, using fixed ground order
23476 21607: Id : 2, {_}:
23477 apply (apply (apply s ?2) ?3) ?4
23479 apply (apply ?2 ?4) (apply ?3 ?4)
23480 [4, 3, 2] by s_definition ?2 ?3 ?4
23481 21607: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
23482 21607: Id : 4, {_}:
23488 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
23489 (apply (apply s (apply (apply s (apply k s)) k))
23491 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
23492 [] by strong_fixed_point
23494 21607: Id : 1, {_}:
23495 apply strong_fixed_point fixed_pt
23497 apply fixed_pt (apply strong_fixed_point fixed_pt)
23498 [] by prove_strong_fixed_point
23504 21607: apply 32 2 3 0,2
23505 21607: fixed_pt 3 0 3 2,2
23506 21607: strong_fixed_point 3 0 2 1,2
23507 NO CLASH, using fixed ground order
23509 21608: Id : 2, {_}:
23510 apply (apply (apply s ?2) ?3) ?4
23512 apply (apply ?2 ?4) (apply ?3 ?4)
23513 [4, 3, 2] by s_definition ?2 ?3 ?4
23514 21608: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
23515 21608: Id : 4, {_}:
23521 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
23522 (apply (apply s (apply (apply s (apply k s)) k))
23524 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
23525 [] by strong_fixed_point
23527 21608: Id : 1, {_}:
23528 apply strong_fixed_point fixed_pt
23530 apply fixed_pt (apply strong_fixed_point fixed_pt)
23531 [] by prove_strong_fixed_point
23537 21608: apply 32 2 3 0,2
23538 21608: fixed_pt 3 0 3 2,2
23539 21608: strong_fixed_point 3 0 2 1,2
23540 NO CLASH, using fixed ground order
23542 21609: Id : 2, {_}:
23543 apply (apply (apply s ?2) ?3) ?4
23545 apply (apply ?2 ?4) (apply ?3 ?4)
23546 [4, 3, 2] by s_definition ?2 ?3 ?4
23547 21609: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
23548 21609: Id : 4, {_}:
23554 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
23555 (apply (apply s (apply (apply s (apply k s)) k))
23557 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
23558 [] by strong_fixed_point
23560 21609: Id : 1, {_}:
23561 apply strong_fixed_point fixed_pt
23563 apply fixed_pt (apply strong_fixed_point fixed_pt)
23564 [] by prove_strong_fixed_point
23570 21609: apply 32 2 3 0,2
23571 21609: fixed_pt 3 0 3 2,2
23572 21609: strong_fixed_point 3 0 2 1,2
23573 % SZS status Timeout for COL006-6.p
23574 CLASH, statistics insufficient
23576 21625: Id : 2, {_}:
23577 apply (apply (apply s ?3) ?4) ?5
23579 apply (apply ?3 ?5) (apply ?4 ?5)
23580 [5, 4, 3] by s_definition ?3 ?4 ?5
23581 21625: Id : 3, {_}:
23582 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
23583 [9, 8, 7] by b_definition ?7 ?8 ?9
23584 21625: Id : 4, {_}:
23585 apply (apply t ?11) ?12 =>= apply ?12 ?11
23586 [12, 11] by t_definition ?11 ?12
23588 21625: Id : 1, {_}:
23589 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
23590 [1] by prove_fixed_point ?1
23597 21625: apply 17 2 3 0,2
23598 21625: f 3 1 3 0,2,2
23599 CLASH, statistics insufficient
23601 21626: Id : 2, {_}:
23602 apply (apply (apply s ?3) ?4) ?5
23604 apply (apply ?3 ?5) (apply ?4 ?5)
23605 [5, 4, 3] by s_definition ?3 ?4 ?5
23606 21626: Id : 3, {_}:
23607 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
23608 [9, 8, 7] by b_definition ?7 ?8 ?9
23609 21626: Id : 4, {_}:
23610 apply (apply t ?11) ?12 =>= apply ?12 ?11
23611 [12, 11] by t_definition ?11 ?12
23613 21626: Id : 1, {_}:
23614 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
23615 [1] by prove_fixed_point ?1
23622 21626: apply 17 2 3 0,2
23623 21626: f 3 1 3 0,2,2
23624 CLASH, statistics insufficient
23626 21627: Id : 2, {_}:
23627 apply (apply (apply s ?3) ?4) ?5
23629 apply (apply ?3 ?5) (apply ?4 ?5)
23630 [5, 4, 3] by s_definition ?3 ?4 ?5
23631 21627: Id : 3, {_}:
23632 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
23633 [9, 8, 7] by b_definition ?7 ?8 ?9
23634 21627: Id : 4, {_}:
23635 apply (apply t ?11) ?12 =?= apply ?12 ?11
23636 [12, 11] by t_definition ?11 ?12
23638 21627: Id : 1, {_}:
23639 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
23640 [1] by prove_fixed_point ?1
23647 21627: apply 17 2 3 0,2
23648 21627: f 3 1 3 0,2,2
23649 % SZS status Timeout for COL036-1.p
23650 CLASH, statistics insufficient
23652 21654: Id : 2, {_}:
23653 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
23654 [5, 4, 3] by b_definition ?3 ?4 ?5
23655 CLASH, statistics insufficient
23657 21655: Id : 2, {_}:
23658 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
23659 [5, 4, 3] by b_definition ?3 ?4 ?5
23660 21655: Id : 3, {_}:
23661 apply (apply t ?7) ?8 =>= apply ?8 ?7
23662 [8, 7] by t_definition ?7 ?8
23664 21655: Id : 1, {_}:
23665 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
23667 apply (apply (h ?1) (g ?1)) (f ?1)
23668 [1] by prove_f_combinator ?1
23674 21655: h 2 1 2 0,2,2
23675 21655: g 2 1 2 0,2,1,2
23676 21655: apply 13 2 5 0,2
23677 21655: f 2 1 2 0,2,1,1,2
23678 21654: Id : 3, {_}:
23679 apply (apply t ?7) ?8 =>= apply ?8 ?7
23680 [8, 7] by t_definition ?7 ?8
23682 21654: Id : 1, {_}:
23683 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
23685 apply (apply (h ?1) (g ?1)) (f ?1)
23686 [1] by prove_f_combinator ?1
23692 21654: h 2 1 2 0,2,2
23693 21654: g 2 1 2 0,2,1,2
23694 21654: apply 13 2 5 0,2
23695 21654: f 2 1 2 0,2,1,1,2
23696 CLASH, statistics insufficient
23698 21656: Id : 2, {_}:
23699 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
23700 [5, 4, 3] by b_definition ?3 ?4 ?5
23701 21656: Id : 3, {_}:
23702 apply (apply t ?7) ?8 =?= apply ?8 ?7
23703 [8, 7] by t_definition ?7 ?8
23705 21656: Id : 1, {_}:
23706 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
23708 apply (apply (h ?1) (g ?1)) (f ?1)
23709 [1] by prove_f_combinator ?1
23715 21656: h 2 1 2 0,2,2
23716 21656: g 2 1 2 0,2,1,2
23717 21656: apply 13 2 5 0,2
23718 21656: f 2 1 2 0,2,1,1,2
23722 Found proof, 5.123186s
23723 % SZS status Unsatisfiable for COL063-1.p
23724 % SZS output start CNFRefutation for COL063-1.p
23725 Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
23726 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
23727 Id : 3189, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3184 with 3 at 2
23728 Id : 3184, {_}: apply (apply ?10590 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) [10590] by Super 3164 with 3 at 2,2
23729 Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
23730 Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
23731 Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
23732 Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
23733 Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (f (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
23734 Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) (f (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
23735 Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1
23736 % SZS output end CNFRefutation for COL063-1.p
23737 21654: solved COL063-1.p in 5.12832 using nrkbo
23738 21654: status Unsatisfiable for COL063-1.p
23739 NO CLASH, using fixed ground order
23741 21661: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
23742 21661: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
23743 21661: Id : 4, {_}:
23744 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
23745 [8, 7, 6] by associativity ?6 ?7 ?8
23746 21661: Id : 5, {_}:
23747 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
23748 [11, 10] by symmetry_of_glb ?10 ?11
23749 21661: Id : 6, {_}:
23750 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
23751 [14, 13] by symmetry_of_lub ?13 ?14
23752 21661: Id : 7, {_}:
23753 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
23755 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
23756 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
23757 21661: Id : 8, {_}:
23758 least_upper_bound ?20 (least_upper_bound ?21 ?22)
23760 least_upper_bound (least_upper_bound ?20 ?21) ?22
23761 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
23762 21661: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
23763 21661: Id : 10, {_}:
23764 greatest_lower_bound ?26 ?26 =>= ?26
23765 [26] by idempotence_of_gld ?26
23766 21661: Id : 11, {_}:
23767 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
23768 [29, 28] by lub_absorbtion ?28 ?29
23769 21661: Id : 12, {_}:
23770 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
23771 [32, 31] by glb_absorbtion ?31 ?32
23772 21661: Id : 13, {_}:
23773 multiply ?34 (least_upper_bound ?35 ?36)
23775 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
23776 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
23777 21661: Id : 14, {_}:
23778 multiply ?38 (greatest_lower_bound ?39 ?40)
23780 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
23781 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
23782 21661: Id : 15, {_}:
23783 multiply (least_upper_bound ?42 ?43) ?44
23785 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
23786 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
23787 21661: Id : 16, {_}:
23788 multiply (greatest_lower_bound ?46 ?47) ?48
23790 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
23791 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
23793 21661: Id : 1, {_}:
23796 multiply (least_upper_bound a identity)
23797 (greatest_lower_bound a identity)
23802 21661: inverse 1 1 0
23803 21661: multiply 19 2 1 0,3
23804 21661: greatest_lower_bound 14 2 1 0,2,3
23805 21661: least_upper_bound 14 2 1 0,1,3
23806 21661: identity 4 0 2 2,1,3
23808 NO CLASH, using fixed ground order
23810 21662: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
23811 21662: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
23812 21662: Id : 4, {_}:
23813 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
23814 [8, 7, 6] by associativity ?6 ?7 ?8
23815 21662: Id : 5, {_}:
23816 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
23817 [11, 10] by symmetry_of_glb ?10 ?11
23818 21662: Id : 6, {_}:
23819 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
23820 [14, 13] by symmetry_of_lub ?13 ?14
23821 21662: Id : 7, {_}:
23822 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
23824 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
23825 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
23826 21662: Id : 8, {_}:
23827 least_upper_bound ?20 (least_upper_bound ?21 ?22)
23829 least_upper_bound (least_upper_bound ?20 ?21) ?22
23830 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
23831 21662: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
23832 21662: Id : 10, {_}:
23833 greatest_lower_bound ?26 ?26 =>= ?26
23834 [26] by idempotence_of_gld ?26
23835 21662: Id : 11, {_}:
23836 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
23837 [29, 28] by lub_absorbtion ?28 ?29
23838 21662: Id : 12, {_}:
23839 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
23840 [32, 31] by glb_absorbtion ?31 ?32
23841 21662: Id : 13, {_}:
23842 multiply ?34 (least_upper_bound ?35 ?36)
23844 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
23845 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
23846 21662: Id : 14, {_}:
23847 multiply ?38 (greatest_lower_bound ?39 ?40)
23849 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
23850 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
23851 21662: Id : 15, {_}:
23852 multiply (least_upper_bound ?42 ?43) ?44
23854 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
23855 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
23856 21662: Id : 16, {_}:
23857 multiply (greatest_lower_bound ?46 ?47) ?48
23859 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
23860 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
23862 21662: Id : 1, {_}:
23865 multiply (least_upper_bound a identity)
23866 (greatest_lower_bound a identity)
23871 21662: inverse 1 1 0
23872 21662: multiply 19 2 1 0,3
23873 21662: greatest_lower_bound 14 2 1 0,2,3
23874 21662: least_upper_bound 14 2 1 0,1,3
23875 21662: identity 4 0 2 2,1,3
23877 NO CLASH, using fixed ground order
23879 21663: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
23880 21663: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
23881 21663: Id : 4, {_}:
23882 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
23883 [8, 7, 6] by associativity ?6 ?7 ?8
23884 21663: Id : 5, {_}:
23885 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
23886 [11, 10] by symmetry_of_glb ?10 ?11
23887 21663: Id : 6, {_}:
23888 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
23889 [14, 13] by symmetry_of_lub ?13 ?14
23890 21663: Id : 7, {_}:
23891 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
23893 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
23894 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
23895 21663: Id : 8, {_}:
23896 least_upper_bound ?20 (least_upper_bound ?21 ?22)
23898 least_upper_bound (least_upper_bound ?20 ?21) ?22
23899 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
23900 21663: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
23901 21663: Id : 10, {_}:
23902 greatest_lower_bound ?26 ?26 =>= ?26
23903 [26] by idempotence_of_gld ?26
23904 21663: Id : 11, {_}:
23905 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
23906 [29, 28] by lub_absorbtion ?28 ?29
23907 21663: Id : 12, {_}:
23908 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
23909 [32, 31] by glb_absorbtion ?31 ?32
23910 21663: Id : 13, {_}:
23911 multiply ?34 (least_upper_bound ?35 ?36)
23913 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
23914 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
23915 21663: Id : 14, {_}:
23916 multiply ?38 (greatest_lower_bound ?39 ?40)
23918 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
23919 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
23920 21663: Id : 15, {_}:
23921 multiply (least_upper_bound ?42 ?43) ?44
23923 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
23924 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
23925 21663: Id : 16, {_}:
23926 multiply (greatest_lower_bound ?46 ?47) ?48
23928 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
23929 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
23931 21663: Id : 1, {_}:
23934 multiply (least_upper_bound a identity)
23935 (greatest_lower_bound a identity)
23940 21663: inverse 1 1 0
23941 21663: multiply 19 2 1 0,3
23942 21663: greatest_lower_bound 14 2 1 0,2,3
23943 21663: least_upper_bound 14 2 1 0,1,3
23944 21663: identity 4 0 2 2,1,3
23946 % SZS status Timeout for GRP167-3.p
23947 NO CLASH, using fixed ground order
23949 21683: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
23950 21683: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
23951 21683: Id : 4, {_}:
23952 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
23953 [8, 7, 6] by associativity ?6 ?7 ?8
23954 21683: Id : 5, {_}:
23955 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
23956 [11, 10] by symmetry_of_glb ?10 ?11
23957 21683: Id : 6, {_}:
23958 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
23959 [14, 13] by symmetry_of_lub ?13 ?14
23960 21683: Id : 7, {_}:
23961 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
23963 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
23964 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
23965 21683: Id : 8, {_}:
23966 least_upper_bound ?20 (least_upper_bound ?21 ?22)
23968 least_upper_bound (least_upper_bound ?20 ?21) ?22
23969 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
23970 21683: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
23971 21683: Id : 10, {_}:
23972 greatest_lower_bound ?26 ?26 =>= ?26
23973 [26] by idempotence_of_gld ?26
23974 21683: Id : 11, {_}:
23975 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
23976 [29, 28] by lub_absorbtion ?28 ?29
23977 21683: Id : 12, {_}:
23978 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
23979 [32, 31] by glb_absorbtion ?31 ?32
23980 21683: Id : 13, {_}:
23981 multiply ?34 (least_upper_bound ?35 ?36)
23983 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
23984 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
23985 21683: Id : 14, {_}:
23986 multiply ?38 (greatest_lower_bound ?39 ?40)
23988 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
23989 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
23990 21683: Id : 15, {_}:
23991 multiply (least_upper_bound ?42 ?43) ?44
23993 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
23994 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
23995 21683: Id : 16, {_}:
23996 multiply (greatest_lower_bound ?46 ?47) ?48
23998 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
23999 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24001 21683: Id : 1, {_}:
24002 inverse (least_upper_bound a b)
24004 greatest_lower_bound (inverse a) (inverse b)
24009 21683: multiply 18 2 0
24010 21683: identity 2 0 0
24011 21683: greatest_lower_bound 14 2 1 0,3
24012 21683: inverse 4 1 3 0,2
24013 21683: least_upper_bound 14 2 1 0,1,2
24014 21683: b 2 0 2 2,1,2
24015 21683: a 2 0 2 1,1,2
24016 NO CLASH, using fixed ground order
24018 21684: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24019 21684: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24020 21684: Id : 4, {_}:
24021 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24022 [8, 7, 6] by associativity ?6 ?7 ?8
24023 21684: Id : 5, {_}:
24024 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24025 [11, 10] by symmetry_of_glb ?10 ?11
24026 21684: Id : 6, {_}:
24027 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24028 [14, 13] by symmetry_of_lub ?13 ?14
24029 21684: Id : 7, {_}:
24030 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24032 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24033 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24034 21684: Id : 8, {_}:
24035 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24037 least_upper_bound (least_upper_bound ?20 ?21) ?22
24038 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24039 21684: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24040 21684: Id : 10, {_}:
24041 greatest_lower_bound ?26 ?26 =>= ?26
24042 [26] by idempotence_of_gld ?26
24043 21684: Id : 11, {_}:
24044 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24045 [29, 28] by lub_absorbtion ?28 ?29
24046 21684: Id : 12, {_}:
24047 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24048 [32, 31] by glb_absorbtion ?31 ?32
24049 21684: Id : 13, {_}:
24050 multiply ?34 (least_upper_bound ?35 ?36)
24052 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24053 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24054 NO CLASH, using fixed ground order
24056 21685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24057 21685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24058 21685: Id : 4, {_}:
24059 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24060 [8, 7, 6] by associativity ?6 ?7 ?8
24061 21685: Id : 5, {_}:
24062 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24063 [11, 10] by symmetry_of_glb ?10 ?11
24064 21685: Id : 6, {_}:
24065 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24066 [14, 13] by symmetry_of_lub ?13 ?14
24067 21685: Id : 7, {_}:
24068 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24070 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24071 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24072 21685: Id : 8, {_}:
24073 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24075 least_upper_bound (least_upper_bound ?20 ?21) ?22
24076 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24077 21685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24078 21685: Id : 10, {_}:
24079 greatest_lower_bound ?26 ?26 =>= ?26
24080 [26] by idempotence_of_gld ?26
24081 21685: Id : 11, {_}:
24082 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24083 [29, 28] by lub_absorbtion ?28 ?29
24084 21685: Id : 12, {_}:
24085 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24086 [32, 31] by glb_absorbtion ?31 ?32
24087 21685: Id : 13, {_}:
24088 multiply ?34 (least_upper_bound ?35 ?36)
24090 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24091 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24092 21685: Id : 14, {_}:
24093 multiply ?38 (greatest_lower_bound ?39 ?40)
24095 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24096 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24097 21685: Id : 15, {_}:
24098 multiply (least_upper_bound ?42 ?43) ?44
24100 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24101 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24102 21685: Id : 16, {_}:
24103 multiply (greatest_lower_bound ?46 ?47) ?48
24105 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24106 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24108 21685: Id : 1, {_}:
24109 inverse (least_upper_bound a b)
24111 greatest_lower_bound (inverse a) (inverse b)
24116 21685: multiply 18 2 0
24117 21685: identity 2 0 0
24118 21685: greatest_lower_bound 14 2 1 0,3
24119 21685: inverse 4 1 3 0,2
24120 21685: least_upper_bound 14 2 1 0,1,2
24121 21685: b 2 0 2 2,1,2
24122 21685: a 2 0 2 1,1,2
24123 21684: Id : 14, {_}:
24124 multiply ?38 (greatest_lower_bound ?39 ?40)
24126 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24127 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24128 21684: Id : 15, {_}:
24129 multiply (least_upper_bound ?42 ?43) ?44
24131 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24132 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24133 21684: Id : 16, {_}:
24134 multiply (greatest_lower_bound ?46 ?47) ?48
24136 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24137 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24139 21684: Id : 1, {_}:
24140 inverse (least_upper_bound a b)
24142 greatest_lower_bound (inverse a) (inverse b)
24147 21684: multiply 18 2 0
24148 21684: identity 2 0 0
24149 21684: greatest_lower_bound 14 2 1 0,3
24150 21684: inverse 4 1 3 0,2
24151 21684: least_upper_bound 14 2 1 0,1,2
24152 21684: b 2 0 2 2,1,2
24153 21684: a 2 0 2 1,1,2
24154 % SZS status Timeout for GRP179-1.p
24155 NO CLASH, using fixed ground order
24157 21733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24158 21733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24159 21733: Id : 4, {_}:
24160 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24161 [8, 7, 6] by associativity ?6 ?7 ?8
24162 21733: Id : 5, {_}:
24163 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24164 [11, 10] by symmetry_of_glb ?10 ?11
24165 21733: Id : 6, {_}:
24166 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24167 [14, 13] by symmetry_of_lub ?13 ?14
24168 21733: Id : 7, {_}:
24169 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24171 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24172 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24173 21733: Id : 8, {_}:
24174 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24176 least_upper_bound (least_upper_bound ?20 ?21) ?22
24177 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24178 21733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24179 21733: Id : 10, {_}:
24180 greatest_lower_bound ?26 ?26 =>= ?26
24181 [26] by idempotence_of_gld ?26
24182 21733: Id : 11, {_}:
24183 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24184 [29, 28] by lub_absorbtion ?28 ?29
24185 21733: Id : 12, {_}:
24186 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24187 [32, 31] by glb_absorbtion ?31 ?32
24188 21733: Id : 13, {_}:
24189 multiply ?34 (least_upper_bound ?35 ?36)
24191 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24192 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24193 21733: Id : 14, {_}:
24194 multiply ?38 (greatest_lower_bound ?39 ?40)
24196 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24197 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24198 21733: Id : 15, {_}:
24199 multiply (least_upper_bound ?42 ?43) ?44
24201 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24202 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24203 21733: Id : 16, {_}:
24204 multiply (greatest_lower_bound ?46 ?47) ?48
24206 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24207 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24209 21733: Id : 1, {_}:
24210 least_upper_bound (inverse a) identity
24212 inverse (greatest_lower_bound a identity)
24217 21733: multiply 18 2 0
24218 21733: greatest_lower_bound 14 2 1 0,1,3
24219 21733: least_upper_bound 14 2 1 0,2
24220 21733: identity 4 0 2 2,2
24221 21733: inverse 3 1 2 0,1,2
24222 21733: a 2 0 2 1,1,2
24223 NO CLASH, using fixed ground order
24225 21732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24226 21732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24227 21732: Id : 4, {_}:
24228 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
24229 [8, 7, 6] by associativity ?6 ?7 ?8
24230 21732: Id : 5, {_}:
24231 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24232 [11, 10] by symmetry_of_glb ?10 ?11
24233 21732: Id : 6, {_}:
24234 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24235 [14, 13] by symmetry_of_lub ?13 ?14
24236 21732: Id : 7, {_}:
24237 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24239 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24240 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24241 21732: Id : 8, {_}:
24242 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24244 least_upper_bound (least_upper_bound ?20 ?21) ?22
24245 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24246 21732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24247 21732: Id : 10, {_}:
24248 greatest_lower_bound ?26 ?26 =>= ?26
24249 [26] by idempotence_of_gld ?26
24250 21732: Id : 11, {_}:
24251 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24252 [29, 28] by lub_absorbtion ?28 ?29
24253 21732: Id : 12, {_}:
24254 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24255 [32, 31] by glb_absorbtion ?31 ?32
24256 21732: Id : 13, {_}:
24257 multiply ?34 (least_upper_bound ?35 ?36)
24259 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24260 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24261 21732: Id : 14, {_}:
24262 multiply ?38 (greatest_lower_bound ?39 ?40)
24264 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24265 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24266 21732: Id : 15, {_}:
24267 multiply (least_upper_bound ?42 ?43) ?44
24269 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24270 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24271 21732: Id : 16, {_}:
24272 multiply (greatest_lower_bound ?46 ?47) ?48
24274 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24275 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24277 21732: Id : 1, {_}:
24278 least_upper_bound (inverse a) identity
24280 inverse (greatest_lower_bound a identity)
24285 21732: multiply 18 2 0
24286 21732: greatest_lower_bound 14 2 1 0,1,3
24287 21732: least_upper_bound 14 2 1 0,2
24288 21732: identity 4 0 2 2,2
24289 21732: inverse 3 1 2 0,1,2
24290 21732: a 2 0 2 1,1,2
24291 NO CLASH, using fixed ground order
24293 21734: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24294 21734: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24295 21734: Id : 4, {_}:
24296 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24297 [8, 7, 6] by associativity ?6 ?7 ?8
24298 21734: Id : 5, {_}:
24299 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24300 [11, 10] by symmetry_of_glb ?10 ?11
24301 21734: Id : 6, {_}:
24302 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24303 [14, 13] by symmetry_of_lub ?13 ?14
24304 21734: Id : 7, {_}:
24305 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24307 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24308 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24309 21734: Id : 8, {_}:
24310 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24312 least_upper_bound (least_upper_bound ?20 ?21) ?22
24313 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24314 21734: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24315 21734: Id : 10, {_}:
24316 greatest_lower_bound ?26 ?26 =>= ?26
24317 [26] by idempotence_of_gld ?26
24318 21734: Id : 11, {_}:
24319 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24320 [29, 28] by lub_absorbtion ?28 ?29
24321 21734: Id : 12, {_}:
24322 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24323 [32, 31] by glb_absorbtion ?31 ?32
24324 21734: Id : 13, {_}:
24325 multiply ?34 (least_upper_bound ?35 ?36)
24327 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24328 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24329 21734: Id : 14, {_}:
24330 multiply ?38 (greatest_lower_bound ?39 ?40)
24332 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24333 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24334 21734: Id : 15, {_}:
24335 multiply (least_upper_bound ?42 ?43) ?44
24337 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24338 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24339 21734: Id : 16, {_}:
24340 multiply (greatest_lower_bound ?46 ?47) ?48
24342 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24343 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24345 21734: Id : 1, {_}:
24346 least_upper_bound (inverse a) identity
24348 inverse (greatest_lower_bound a identity)
24353 21734: multiply 18 2 0
24354 21734: greatest_lower_bound 14 2 1 0,1,3
24355 21734: least_upper_bound 14 2 1 0,2
24356 21734: identity 4 0 2 2,2
24357 21734: inverse 3 1 2 0,1,2
24358 21734: a 2 0 2 1,1,2
24359 % SZS status Timeout for GRP179-2.p
24360 NO CLASH, using fixed ground order
24362 21751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24363 21751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24364 21751: Id : 4, {_}:
24365 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
24366 [8, 7, 6] by associativity ?6 ?7 ?8
24367 21751: Id : 5, {_}:
24368 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24369 [11, 10] by symmetry_of_glb ?10 ?11
24370 21751: Id : 6, {_}:
24371 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24372 [14, 13] by symmetry_of_lub ?13 ?14
24373 21751: Id : 7, {_}:
24374 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24376 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24377 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24378 21751: Id : 8, {_}:
24379 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24381 least_upper_bound (least_upper_bound ?20 ?21) ?22
24382 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24383 21751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24384 21751: Id : 10, {_}:
24385 greatest_lower_bound ?26 ?26 =>= ?26
24386 [26] by idempotence_of_gld ?26
24387 21751: Id : 11, {_}:
24388 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24389 [29, 28] by lub_absorbtion ?28 ?29
24390 21751: Id : 12, {_}:
24391 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24392 [32, 31] by glb_absorbtion ?31 ?32
24393 21751: Id : 13, {_}:
24394 multiply ?34 (least_upper_bound ?35 ?36)
24396 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24397 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24398 21751: Id : 14, {_}:
24399 multiply ?38 (greatest_lower_bound ?39 ?40)
24401 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24402 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24403 21751: Id : 15, {_}:
24404 multiply (least_upper_bound ?42 ?43) ?44
24406 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24407 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24408 21751: Id : 16, {_}:
24409 multiply (greatest_lower_bound ?46 ?47) ?48
24411 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24412 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24414 21751: Id : 1, {_}:
24415 multiply a (multiply (inverse (greatest_lower_bound a b)) b)
24417 least_upper_bound a b
24422 21751: identity 2 0 0
24423 21751: least_upper_bound 14 2 1 0,3
24424 21751: multiply 20 2 2 0,2
24425 21751: inverse 2 1 1 0,1,2,2
24426 21751: greatest_lower_bound 14 2 1 0,1,1,2,2
24427 21751: b 3 0 3 2,1,1,2,2
24429 NO CLASH, using fixed ground order
24431 21752: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24432 21752: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24433 21752: Id : 4, {_}:
24434 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24435 [8, 7, 6] by associativity ?6 ?7 ?8
24436 21752: Id : 5, {_}:
24437 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24438 [11, 10] by symmetry_of_glb ?10 ?11
24439 21752: Id : 6, {_}:
24440 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24441 [14, 13] by symmetry_of_lub ?13 ?14
24442 21752: Id : 7, {_}:
24443 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24445 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24446 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24447 21752: Id : 8, {_}:
24448 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24450 least_upper_bound (least_upper_bound ?20 ?21) ?22
24451 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24452 21752: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24453 21752: Id : 10, {_}:
24454 greatest_lower_bound ?26 ?26 =>= ?26
24455 [26] by idempotence_of_gld ?26
24456 21752: Id : 11, {_}:
24457 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24458 [29, 28] by lub_absorbtion ?28 ?29
24459 21752: Id : 12, {_}:
24460 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24461 [32, 31] by glb_absorbtion ?31 ?32
24462 21752: Id : 13, {_}:
24463 multiply ?34 (least_upper_bound ?35 ?36)
24465 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24466 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24467 21752: Id : 14, {_}:
24468 multiply ?38 (greatest_lower_bound ?39 ?40)
24470 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24471 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24472 21752: Id : 15, {_}:
24473 multiply (least_upper_bound ?42 ?43) ?44
24475 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24476 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24477 21752: Id : 16, {_}:
24478 multiply (greatest_lower_bound ?46 ?47) ?48
24480 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24481 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24483 21752: Id : 1, {_}:
24484 multiply a (multiply (inverse (greatest_lower_bound a b)) b)
24486 least_upper_bound a b
24491 21752: identity 2 0 0
24492 21752: least_upper_bound 14 2 1 0,3
24493 21752: multiply 20 2 2 0,2
24494 21752: inverse 2 1 1 0,1,2,2
24495 21752: greatest_lower_bound 14 2 1 0,1,1,2,2
24496 21752: b 3 0 3 2,1,1,2,2
24498 NO CLASH, using fixed ground order
24500 21753: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24501 21753: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24502 21753: Id : 4, {_}:
24503 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24504 [8, 7, 6] by associativity ?6 ?7 ?8
24505 21753: Id : 5, {_}:
24506 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24507 [11, 10] by symmetry_of_glb ?10 ?11
24508 21753: Id : 6, {_}:
24509 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24510 [14, 13] by symmetry_of_lub ?13 ?14
24511 21753: Id : 7, {_}:
24512 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24514 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24515 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24516 21753: Id : 8, {_}:
24517 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24519 least_upper_bound (least_upper_bound ?20 ?21) ?22
24520 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24521 21753: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24522 21753: Id : 10, {_}:
24523 greatest_lower_bound ?26 ?26 =>= ?26
24524 [26] by idempotence_of_gld ?26
24525 21753: Id : 11, {_}:
24526 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24527 [29, 28] by lub_absorbtion ?28 ?29
24528 21753: Id : 12, {_}:
24529 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24530 [32, 31] by glb_absorbtion ?31 ?32
24531 21753: Id : 13, {_}:
24532 multiply ?34 (least_upper_bound ?35 ?36)
24534 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24535 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24536 21753: Id : 14, {_}:
24537 multiply ?38 (greatest_lower_bound ?39 ?40)
24539 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24540 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24541 21753: Id : 15, {_}:
24542 multiply (least_upper_bound ?42 ?43) ?44
24544 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24545 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24546 21753: Id : 16, {_}:
24547 multiply (greatest_lower_bound ?46 ?47) ?48
24549 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24550 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24552 21753: Id : 1, {_}:
24553 multiply a (multiply (inverse (greatest_lower_bound a b)) b)
24555 least_upper_bound a b
24560 21753: identity 2 0 0
24561 21753: least_upper_bound 14 2 1 0,3
24562 21753: multiply 20 2 2 0,2
24563 21753: inverse 2 1 1 0,1,2,2
24564 21753: greatest_lower_bound 14 2 1 0,1,1,2,2
24565 21753: b 3 0 3 2,1,1,2,2
24567 % SZS status Timeout for GRP180-1.p
24568 NO CLASH, using fixed ground order
24570 21783: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24571 21783: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24572 21783: Id : 4, {_}:
24573 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
24574 [8, 7, 6] by associativity ?6 ?7 ?8
24575 21783: Id : 5, {_}:
24576 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24577 [11, 10] by symmetry_of_glb ?10 ?11
24578 21783: Id : 6, {_}:
24579 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24580 [14, 13] by symmetry_of_lub ?13 ?14
24581 21783: Id : 7, {_}:
24582 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24584 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24585 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24586 21783: Id : 8, {_}:
24587 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24589 least_upper_bound (least_upper_bound ?20 ?21) ?22
24590 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24591 21783: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24592 21783: Id : 10, {_}:
24593 greatest_lower_bound ?26 ?26 =>= ?26
24594 [26] by idempotence_of_gld ?26
24595 21783: Id : 11, {_}:
24596 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24597 [29, 28] by lub_absorbtion ?28 ?29
24598 21783: Id : 12, {_}:
24599 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24600 [32, 31] by glb_absorbtion ?31 ?32
24601 21783: Id : 13, {_}:
24602 multiply ?34 (least_upper_bound ?35 ?36)
24604 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24605 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24606 21783: Id : 14, {_}:
24607 multiply ?38 (greatest_lower_bound ?39 ?40)
24609 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24610 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24611 21783: Id : 15, {_}:
24612 multiply (least_upper_bound ?42 ?43) ?44
24614 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24615 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24616 21783: Id : 16, {_}:
24617 multiply (greatest_lower_bound ?46 ?47) ?48
24619 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24620 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24621 21783: Id : 17, {_}: inverse identity =>= identity [] by p20_1
24622 21783: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
24623 21783: Id : 19, {_}:
24624 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
24625 [54, 53] by p20_3 ?53 ?54
24627 21783: Id : 1, {_}:
24628 greatest_lower_bound (least_upper_bound a identity)
24629 (inverse (greatest_lower_bound a identity))
24636 21783: multiply 20 2 0
24637 21783: inverse 8 1 1 0,2,2
24638 21783: greatest_lower_bound 15 2 2 0,2
24639 21783: least_upper_bound 14 2 1 0,1,2
24640 21783: identity 7 0 3 2,1,2
24641 21783: a 2 0 2 1,1,2
24642 NO CLASH, using fixed ground order
24644 21785: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24645 21785: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24646 21785: Id : 4, {_}:
24647 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24648 [8, 7, 6] by associativity ?6 ?7 ?8
24649 21785: Id : 5, {_}:
24650 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24651 [11, 10] by symmetry_of_glb ?10 ?11
24652 21785: Id : 6, {_}:
24653 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24654 [14, 13] by symmetry_of_lub ?13 ?14
24655 21785: Id : 7, {_}:
24656 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24658 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24659 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24660 21785: Id : 8, {_}:
24661 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24663 least_upper_bound (least_upper_bound ?20 ?21) ?22
24664 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24665 21785: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24666 21785: Id : 10, {_}:
24667 greatest_lower_bound ?26 ?26 =>= ?26
24668 [26] by idempotence_of_gld ?26
24669 21785: Id : 11, {_}:
24670 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24671 [29, 28] by lub_absorbtion ?28 ?29
24672 21785: Id : 12, {_}:
24673 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24674 [32, 31] by glb_absorbtion ?31 ?32
24675 21785: Id : 13, {_}:
24676 multiply ?34 (least_upper_bound ?35 ?36)
24678 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24679 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24680 21785: Id : 14, {_}:
24681 multiply ?38 (greatest_lower_bound ?39 ?40)
24683 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24684 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24685 21785: Id : 15, {_}:
24686 multiply (least_upper_bound ?42 ?43) ?44
24688 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24689 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24690 21785: Id : 16, {_}:
24691 multiply (greatest_lower_bound ?46 ?47) ?48
24693 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24694 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24695 21785: Id : 17, {_}: inverse identity =>= identity [] by p20_1
24696 21785: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
24697 21785: Id : 19, {_}:
24698 inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
24699 [54, 53] by p20_3 ?53 ?54
24701 21785: Id : 1, {_}:
24702 greatest_lower_bound (least_upper_bound a identity)
24703 (inverse (greatest_lower_bound a identity))
24710 21785: multiply 20 2 0
24711 21785: inverse 8 1 1 0,2,2
24712 21785: greatest_lower_bound 15 2 2 0,2
24713 21785: least_upper_bound 14 2 1 0,1,2
24714 21785: identity 7 0 3 2,1,2
24715 21785: a 2 0 2 1,1,2
24716 NO CLASH, using fixed ground order
24718 21784: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24719 21784: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24720 21784: Id : 4, {_}:
24721 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24722 [8, 7, 6] by associativity ?6 ?7 ?8
24723 21784: Id : 5, {_}:
24724 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24725 [11, 10] by symmetry_of_glb ?10 ?11
24726 21784: Id : 6, {_}:
24727 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24728 [14, 13] by symmetry_of_lub ?13 ?14
24729 21784: Id : 7, {_}:
24730 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24732 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24733 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24734 21784: Id : 8, {_}:
24735 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24737 least_upper_bound (least_upper_bound ?20 ?21) ?22
24738 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24739 21784: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24740 21784: Id : 10, {_}:
24741 greatest_lower_bound ?26 ?26 =>= ?26
24742 [26] by idempotence_of_gld ?26
24743 21784: Id : 11, {_}:
24744 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24745 [29, 28] by lub_absorbtion ?28 ?29
24746 21784: Id : 12, {_}:
24747 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24748 [32, 31] by glb_absorbtion ?31 ?32
24749 21784: Id : 13, {_}:
24750 multiply ?34 (least_upper_bound ?35 ?36)
24752 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24753 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24754 21784: Id : 14, {_}:
24755 multiply ?38 (greatest_lower_bound ?39 ?40)
24757 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24758 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24759 21784: Id : 15, {_}:
24760 multiply (least_upper_bound ?42 ?43) ?44
24762 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24763 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24764 21784: Id : 16, {_}:
24765 multiply (greatest_lower_bound ?46 ?47) ?48
24767 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24768 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24769 21784: Id : 17, {_}: inverse identity =>= identity [] by p20_1
24770 21784: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
24771 21784: Id : 19, {_}:
24772 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
24773 [54, 53] by p20_3 ?53 ?54
24775 21784: Id : 1, {_}:
24776 greatest_lower_bound (least_upper_bound a identity)
24777 (inverse (greatest_lower_bound a identity))
24784 21784: multiply 20 2 0
24785 21784: inverse 8 1 1 0,2,2
24786 21784: greatest_lower_bound 15 2 2 0,2
24787 21784: least_upper_bound 14 2 1 0,1,2
24788 21784: identity 7 0 3 2,1,2
24789 21784: a 2 0 2 1,1,2
24790 % SZS status Timeout for GRP183-2.p
24791 NO CLASH, using fixed ground order
24793 21802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24794 21802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24795 21802: Id : 4, {_}:
24796 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
24797 [8, 7, 6] by associativity ?6 ?7 ?8
24798 21802: Id : 5, {_}:
24799 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24800 [11, 10] by symmetry_of_glb ?10 ?11
24801 21802: Id : 6, {_}:
24802 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24803 [14, 13] by symmetry_of_lub ?13 ?14
24804 21802: Id : 7, {_}:
24805 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24807 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24808 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24809 21802: Id : 8, {_}:
24810 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24812 least_upper_bound (least_upper_bound ?20 ?21) ?22
24813 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24814 21802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24815 21802: Id : 10, {_}:
24816 greatest_lower_bound ?26 ?26 =>= ?26
24817 [26] by idempotence_of_gld ?26
24818 21802: Id : 11, {_}:
24819 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24820 [29, 28] by lub_absorbtion ?28 ?29
24821 21802: Id : 12, {_}:
24822 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24823 [32, 31] by glb_absorbtion ?31 ?32
24824 21802: Id : 13, {_}:
24825 multiply ?34 (least_upper_bound ?35 ?36)
24827 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24828 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24829 21802: Id : 14, {_}:
24830 multiply ?38 (greatest_lower_bound ?39 ?40)
24832 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24833 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24834 21802: Id : 15, {_}:
24835 multiply (least_upper_bound ?42 ?43) ?44
24837 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24838 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24839 21802: Id : 16, {_}:
24840 multiply (greatest_lower_bound ?46 ?47) ?48
24842 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24843 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24845 21802: Id : 1, {_}:
24846 least_upper_bound (multiply a b) identity
24848 multiply a (inverse (greatest_lower_bound a (inverse b)))
24853 21802: greatest_lower_bound 14 2 1 0,1,2,3
24854 21802: inverse 3 1 2 0,2,3
24855 21802: least_upper_bound 14 2 1 0,2
24856 21802: identity 3 0 1 2,2
24857 21802: multiply 20 2 2 0,1,2
24858 21802: b 2 0 2 2,1,2
24859 21802: a 3 0 3 1,1,2
24860 NO CLASH, using fixed ground order
24862 21803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24863 21803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24864 21803: Id : 4, {_}:
24865 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24866 [8, 7, 6] by associativity ?6 ?7 ?8
24867 21803: Id : 5, {_}:
24868 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24869 [11, 10] by symmetry_of_glb ?10 ?11
24870 21803: Id : 6, {_}:
24871 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24872 [14, 13] by symmetry_of_lub ?13 ?14
24873 21803: Id : 7, {_}:
24874 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24876 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24877 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24878 21803: Id : 8, {_}:
24879 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24881 least_upper_bound (least_upper_bound ?20 ?21) ?22
24882 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24883 21803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24884 21803: Id : 10, {_}:
24885 greatest_lower_bound ?26 ?26 =>= ?26
24886 [26] by idempotence_of_gld ?26
24887 21803: Id : 11, {_}:
24888 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24889 [29, 28] by lub_absorbtion ?28 ?29
24890 21803: Id : 12, {_}:
24891 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24892 [32, 31] by glb_absorbtion ?31 ?32
24893 21803: Id : 13, {_}:
24894 multiply ?34 (least_upper_bound ?35 ?36)
24896 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24897 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24898 21803: Id : 14, {_}:
24899 multiply ?38 (greatest_lower_bound ?39 ?40)
24901 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24902 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24903 21803: Id : 15, {_}:
24904 multiply (least_upper_bound ?42 ?43) ?44
24906 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24907 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24908 21803: Id : 16, {_}:
24909 multiply (greatest_lower_bound ?46 ?47) ?48
24911 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24912 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24914 21803: Id : 1, {_}:
24915 least_upper_bound (multiply a b) identity
24917 multiply a (inverse (greatest_lower_bound a (inverse b)))
24922 21803: greatest_lower_bound 14 2 1 0,1,2,3
24923 21803: inverse 3 1 2 0,2,3
24924 21803: least_upper_bound 14 2 1 0,2
24925 21803: identity 3 0 1 2,2
24926 21803: multiply 20 2 2 0,1,2
24927 21803: b 2 0 2 2,1,2
24928 21803: a 3 0 3 1,1,2
24929 NO CLASH, using fixed ground order
24931 21804: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
24932 21804: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
24933 21804: Id : 4, {_}:
24934 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
24935 [8, 7, 6] by associativity ?6 ?7 ?8
24936 21804: Id : 5, {_}:
24937 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
24938 [11, 10] by symmetry_of_glb ?10 ?11
24939 21804: Id : 6, {_}:
24940 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
24941 [14, 13] by symmetry_of_lub ?13 ?14
24942 21804: Id : 7, {_}:
24943 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
24945 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
24946 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
24947 21804: Id : 8, {_}:
24948 least_upper_bound ?20 (least_upper_bound ?21 ?22)
24950 least_upper_bound (least_upper_bound ?20 ?21) ?22
24951 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
24952 21804: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
24953 21804: Id : 10, {_}:
24954 greatest_lower_bound ?26 ?26 =>= ?26
24955 [26] by idempotence_of_gld ?26
24956 21804: Id : 11, {_}:
24957 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
24958 [29, 28] by lub_absorbtion ?28 ?29
24959 21804: Id : 12, {_}:
24960 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
24961 [32, 31] by glb_absorbtion ?31 ?32
24962 21804: Id : 13, {_}:
24963 multiply ?34 (least_upper_bound ?35 ?36)
24965 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
24966 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
24967 21804: Id : 14, {_}:
24968 multiply ?38 (greatest_lower_bound ?39 ?40)
24970 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
24971 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
24972 21804: Id : 15, {_}:
24973 multiply (least_upper_bound ?42 ?43) ?44
24975 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
24976 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
24977 21804: Id : 16, {_}:
24978 multiply (greatest_lower_bound ?46 ?47) ?48
24980 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
24981 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
24983 21804: Id : 1, {_}:
24984 least_upper_bound (multiply a b) identity
24986 multiply a (inverse (greatest_lower_bound a (inverse b)))
24991 21804: greatest_lower_bound 14 2 1 0,1,2,3
24992 21804: inverse 3 1 2 0,2,3
24993 21804: least_upper_bound 14 2 1 0,2
24994 21804: identity 3 0 1 2,2
24995 21804: multiply 20 2 2 0,1,2
24996 21804: b 2 0 2 2,1,2
24997 21804: a 3 0 3 1,1,2
24998 % SZS status Timeout for GRP186-1.p
24999 NO CLASH, using fixed ground order
25001 21831: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
25002 21831: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
25003 21831: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
25004 21831: Id : 5, {_}:
25005 meet ?9 ?10 =?= meet ?10 ?9
25006 [10, 9] by commutativity_of_meet ?9 ?10
25007 21831: Id : 6, {_}:
25008 join ?12 ?13 =?= join ?13 ?12
25009 [13, 12] by commutativity_of_join ?12 ?13
25010 21831: Id : 7, {_}:
25011 meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
25012 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
25013 21831: Id : 8, {_}:
25014 join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
25015 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
25016 21831: Id : 9, {_}:
25017 complement (complement ?23) =>= ?23
25018 [23] by complement_involution ?23
25019 21831: Id : 10, {_}:
25020 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
25021 [26, 25] by join_complement ?25 ?26
25022 21831: Id : 11, {_}:
25023 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
25024 [29, 28] by meet_complement ?28 ?29
25026 21831: Id : 1, {_}:
25029 (meet (complement a) (meet (join a (complement b)) (join a b)))
25030 (meet (complement a)
25031 (join (meet (complement a) b)
25032 (meet (complement a) (complement b)))))
25041 21831: meet 14 2 5 0,1,2,2
25042 21831: join 17 2 5 0,2
25043 21831: b 4 0 4 1,2,1,2,1,2,2
25044 21831: complement 15 1 6 0,1,1,2,2
25046 NO CLASH, using fixed ground order
25048 21832: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
25049 21832: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
25050 21832: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
25051 21832: Id : 5, {_}:
25052 meet ?9 ?10 =?= meet ?10 ?9
25053 [10, 9] by commutativity_of_meet ?9 ?10
25054 21832: Id : 6, {_}:
25055 join ?12 ?13 =?= join ?13 ?12
25056 [13, 12] by commutativity_of_join ?12 ?13
25057 21832: Id : 7, {_}:
25058 meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
25059 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
25060 21832: Id : 8, {_}:
25061 join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
25062 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
25063 21832: Id : 9, {_}:
25064 complement (complement ?23) =>= ?23
25065 [23] by complement_involution ?23
25066 21832: Id : 10, {_}:
25067 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
25068 [26, 25] by join_complement ?25 ?26
25069 21832: Id : 11, {_}:
25070 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
25071 [29, 28] by meet_complement ?28 ?29
25073 21832: Id : 1, {_}:
25076 (meet (complement a) (meet (join a (complement b)) (join a b)))
25077 (meet (complement a)
25078 (join (meet (complement a) b)
25079 (meet (complement a) (complement b)))))
25088 21832: meet 14 2 5 0,1,2,2
25089 21832: join 17 2 5 0,2
25090 21832: b 4 0 4 1,2,1,2,1,2,2
25091 21832: complement 15 1 6 0,1,1,2,2
25093 NO CLASH, using fixed ground order
25095 21833: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
25096 21833: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
25097 21833: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
25098 21833: Id : 5, {_}:
25099 meet ?9 ?10 =?= meet ?10 ?9
25100 [10, 9] by commutativity_of_meet ?9 ?10
25101 21833: Id : 6, {_}:
25102 join ?12 ?13 =?= join ?13 ?12
25103 [13, 12] by commutativity_of_join ?12 ?13
25104 21833: Id : 7, {_}:
25105 meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
25106 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
25107 21833: Id : 8, {_}:
25108 join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
25109 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
25110 21833: Id : 9, {_}:
25111 complement (complement ?23) =>= ?23
25112 [23] by complement_involution ?23
25113 21833: Id : 10, {_}:
25114 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
25115 [26, 25] by join_complement ?25 ?26
25116 21833: Id : 11, {_}:
25117 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
25118 [29, 28] by meet_complement ?28 ?29
25120 21833: Id : 1, {_}:
25123 (meet (complement a) (meet (join a (complement b)) (join a b)))
25124 (meet (complement a)
25125 (join (meet (complement a) b)
25126 (meet (complement a) (complement b)))))
25135 21833: meet 14 2 5 0,1,2,2
25136 21833: join 17 2 5 0,2
25137 21833: b 4 0 4 1,2,1,2,1,2,2
25138 21833: complement 15 1 6 0,1,1,2,2
25140 % SZS status Timeout for LAT017-1.p
25141 NO CLASH, using fixed ground order
25143 21853: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
25144 21853: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
25145 21853: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
25146 21853: Id : 5, {_}:
25147 join ?9 ?10 =?= join ?10 ?9
25148 [10, 9] by commutativity_of_join ?9 ?10
25149 21853: Id : 6, {_}:
25150 meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
25151 [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
25152 21853: Id : 7, {_}:
25153 join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
25154 [18, 17, 16] by associativity_of_join ?16 ?17 ?18
25155 21853: Id : 8, {_}:
25156 join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
25158 meet ?20 (join ?21 ?22)
25159 [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
25160 21853: Id : 9, {_}:
25161 meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
25163 join ?24 (meet ?25 ?26)
25164 [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
25165 21853: Id : 10, {_}:
25166 join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
25168 meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
25169 [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
25171 21853: Id : 1, {_}:
25172 meet a (join b c) =<= join (meet a b) (meet a c)
25173 [] by prove_distributivity
25177 21853: meet 21 2 3 0,2
25178 21853: join 20 2 2 0,2,2
25179 21853: c 2 0 2 2,2,2
25180 21853: b 2 0 2 1,2,2
25182 NO CLASH, using fixed ground order
25184 21854: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
25185 21854: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
25186 21854: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
25187 21854: Id : 5, {_}:
25188 join ?9 ?10 =?= join ?10 ?9
25189 [10, 9] by commutativity_of_join ?9 ?10
25190 21854: Id : 6, {_}:
25191 meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
25192 [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
25193 21854: Id : 7, {_}:
25194 join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
25195 [18, 17, 16] by associativity_of_join ?16 ?17 ?18
25196 21854: Id : 8, {_}:
25197 join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
25199 meet ?20 (join ?21 ?22)
25200 [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
25201 21854: Id : 9, {_}:
25202 meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
25204 join ?24 (meet ?25 ?26)
25205 [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
25206 21854: Id : 10, {_}:
25207 join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
25209 meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
25210 [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
25212 21854: Id : 1, {_}:
25213 meet a (join b c) =<= join (meet a b) (meet a c)
25214 [] by prove_distributivity
25218 21854: meet 21 2 3 0,2
25219 21854: join 20 2 2 0,2,2
25220 21854: c 2 0 2 2,2,2
25221 21854: b 2 0 2 1,2,2
25223 NO CLASH, using fixed ground order
25225 21855: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
25226 21855: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
25227 21855: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
25228 21855: Id : 5, {_}:
25229 join ?9 ?10 =?= join ?10 ?9
25230 [10, 9] by commutativity_of_join ?9 ?10
25231 21855: Id : 6, {_}:
25232 meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
25233 [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
25234 21855: Id : 7, {_}:
25235 join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
25236 [18, 17, 16] by associativity_of_join ?16 ?17 ?18
25237 21855: Id : 8, {_}:
25238 join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
25240 meet ?20 (join ?21 ?22)
25241 [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
25242 21855: Id : 9, {_}:
25243 meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
25245 join ?24 (meet ?25 ?26)
25246 [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
25247 21855: Id : 10, {_}:
25248 join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
25250 meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
25251 [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
25253 21855: Id : 1, {_}:
25254 meet a (join b c) =<= join (meet a b) (meet a c)
25255 [] by prove_distributivity
25259 21855: meet 21 2 3 0,2
25260 21855: join 20 2 2 0,2,2
25261 21855: c 2 0 2 2,2,2
25262 21855: b 2 0 2 1,2,2
25264 % SZS status Timeout for LAT020-1.p
25265 NO CLASH, using fixed ground order
25267 21955: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
25268 21955: Id : 3, {_}:
25269 add ?4 additive_identity =>= ?4
25270 [4] by right_additive_identity ?4
25271 21955: Id : 4, {_}:
25272 multiply additive_identity ?6 =>= additive_identity
25273 [6] by left_multiplicative_zero ?6
25274 21955: Id : 5, {_}:
25275 multiply ?8 additive_identity =>= additive_identity
25276 [8] by right_multiplicative_zero ?8
25277 21955: Id : 6, {_}:
25278 add (additive_inverse ?10) ?10 =>= additive_identity
25279 [10] by left_additive_inverse ?10
25280 21955: Id : 7, {_}:
25281 add ?12 (additive_inverse ?12) =>= additive_identity
25282 [12] by right_additive_inverse ?12
25283 21955: Id : 8, {_}:
25284 additive_inverse (additive_inverse ?14) =>= ?14
25285 [14] by additive_inverse_additive_inverse ?14
25286 21955: Id : 9, {_}:
25287 multiply ?16 (add ?17 ?18)
25289 add (multiply ?16 ?17) (multiply ?16 ?18)
25290 [18, 17, 16] by distribute1 ?16 ?17 ?18
25291 21955: Id : 10, {_}:
25292 multiply (add ?20 ?21) ?22
25294 add (multiply ?20 ?22) (multiply ?21 ?22)
25295 [22, 21, 20] by distribute2 ?20 ?21 ?22
25296 21955: Id : 11, {_}:
25297 add ?24 ?25 =?= add ?25 ?24
25298 [25, 24] by commutativity_for_addition ?24 ?25
25299 21955: Id : 12, {_}:
25300 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
25301 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
25302 21955: Id : 13, {_}:
25303 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
25304 [32, 31] by right_alternative ?31 ?32
25305 21955: Id : 14, {_}:
25306 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
25307 [35, 34] by left_alternative ?34 ?35
25308 21955: Id : 15, {_}:
25309 associator ?37 ?38 ?39
25311 add (multiply (multiply ?37 ?38) ?39)
25312 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
25313 [39, 38, 37] by associator ?37 ?38 ?39
25314 21955: Id : 16, {_}:
25317 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
25318 [42, 41] by commutator ?41 ?42
25319 21955: Id : 17, {_}:
25320 multiply (additive_inverse ?44) (additive_inverse ?45)
25323 [45, 44] by product_of_inverses ?44 ?45
25324 21955: Id : 18, {_}:
25325 multiply (additive_inverse ?47) ?48
25327 additive_inverse (multiply ?47 ?48)
25328 [48, 47] by inverse_product1 ?47 ?48
25329 21955: Id : 19, {_}:
25330 multiply ?50 (additive_inverse ?51)
25332 additive_inverse (multiply ?50 ?51)
25333 [51, 50] by inverse_product2 ?50 ?51
25334 21955: Id : 20, {_}:
25335 multiply ?53 (add ?54 (additive_inverse ?55))
25337 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
25338 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
25339 21955: Id : 21, {_}:
25340 multiply (add ?57 (additive_inverse ?58)) ?59
25342 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
25343 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
25344 21955: Id : 22, {_}:
25345 multiply (additive_inverse ?61) (add ?62 ?63)
25347 add (additive_inverse (multiply ?61 ?62))
25348 (additive_inverse (multiply ?61 ?63))
25349 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
25350 21955: Id : 23, {_}:
25351 multiply (add ?65 ?66) (additive_inverse ?67)
25353 add (additive_inverse (multiply ?65 ?67))
25354 (additive_inverse (multiply ?66 ?67))
25355 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
25357 21955: Id : 1, {_}:
25358 add (associator x y z) (associator x z y) =>= additive_identity
25359 [] by prove_equation
25363 21955: commutator 1 2 0
25364 21955: additive_inverse 22 1 0
25365 21955: multiply 40 2 0
25366 21955: additive_identity 9 0 1 3
25367 21955: add 25 2 1 0,2
25368 21955: associator 3 3 2 0,1,2
25369 21955: z 2 0 2 3,1,2
25370 21955: y 2 0 2 2,1,2
25371 21955: x 2 0 2 1,1,2
25372 NO CLASH, using fixed ground order
25374 21956: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
25375 21956: Id : 3, {_}:
25376 add ?4 additive_identity =>= ?4
25377 [4] by right_additive_identity ?4
25378 21956: Id : 4, {_}:
25379 multiply additive_identity ?6 =>= additive_identity
25380 [6] by left_multiplicative_zero ?6
25381 21956: Id : 5, {_}:
25382 multiply ?8 additive_identity =>= additive_identity
25383 [8] by right_multiplicative_zero ?8
25384 21956: Id : 6, {_}:
25385 add (additive_inverse ?10) ?10 =>= additive_identity
25386 [10] by left_additive_inverse ?10
25387 21956: Id : 7, {_}:
25388 add ?12 (additive_inverse ?12) =>= additive_identity
25389 [12] by right_additive_inverse ?12
25390 21956: Id : 8, {_}:
25391 additive_inverse (additive_inverse ?14) =>= ?14
25392 [14] by additive_inverse_additive_inverse ?14
25393 21956: Id : 9, {_}:
25394 multiply ?16 (add ?17 ?18)
25396 add (multiply ?16 ?17) (multiply ?16 ?18)
25397 [18, 17, 16] by distribute1 ?16 ?17 ?18
25398 21956: Id : 10, {_}:
25399 multiply (add ?20 ?21) ?22
25401 add (multiply ?20 ?22) (multiply ?21 ?22)
25402 [22, 21, 20] by distribute2 ?20 ?21 ?22
25403 21956: Id : 11, {_}:
25404 add ?24 ?25 =?= add ?25 ?24
25405 [25, 24] by commutativity_for_addition ?24 ?25
25406 21956: Id : 12, {_}:
25407 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
25408 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
25409 21956: Id : 13, {_}:
25410 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
25411 [32, 31] by right_alternative ?31 ?32
25412 21956: Id : 14, {_}:
25413 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
25414 [35, 34] by left_alternative ?34 ?35
25415 21956: Id : 15, {_}:
25416 associator ?37 ?38 ?39
25418 add (multiply (multiply ?37 ?38) ?39)
25419 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
25420 [39, 38, 37] by associator ?37 ?38 ?39
25421 21956: Id : 16, {_}:
25424 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
25425 [42, 41] by commutator ?41 ?42
25426 21956: Id : 17, {_}:
25427 multiply (additive_inverse ?44) (additive_inverse ?45)
25430 [45, 44] by product_of_inverses ?44 ?45
25431 21956: Id : 18, {_}:
25432 multiply (additive_inverse ?47) ?48
25434 additive_inverse (multiply ?47 ?48)
25435 [48, 47] by inverse_product1 ?47 ?48
25436 21956: Id : 19, {_}:
25437 multiply ?50 (additive_inverse ?51)
25439 additive_inverse (multiply ?50 ?51)
25440 [51, 50] by inverse_product2 ?50 ?51
25441 21956: Id : 20, {_}:
25442 multiply ?53 (add ?54 (additive_inverse ?55))
25444 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
25445 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
25446 21956: Id : 21, {_}:
25447 multiply (add ?57 (additive_inverse ?58)) ?59
25449 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
25450 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
25451 21956: Id : 22, {_}:
25452 multiply (additive_inverse ?61) (add ?62 ?63)
25454 add (additive_inverse (multiply ?61 ?62))
25455 (additive_inverse (multiply ?61 ?63))
25456 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
25457 21956: Id : 23, {_}:
25458 multiply (add ?65 ?66) (additive_inverse ?67)
25460 add (additive_inverse (multiply ?65 ?67))
25461 (additive_inverse (multiply ?66 ?67))
25462 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
25464 21956: Id : 1, {_}:
25465 add (associator x y z) (associator x z y) =>= additive_identity
25466 [] by prove_equation
25470 21956: commutator 1 2 0
25471 21956: additive_inverse 22 1 0
25472 21956: multiply 40 2 0
25473 21956: additive_identity 9 0 1 3
25474 21956: add 25 2 1 0,2
25475 21956: associator 3 3 2 0,1,2
25476 21956: z 2 0 2 3,1,2
25477 21956: y 2 0 2 2,1,2
25478 21956: x 2 0 2 1,1,2
25479 NO CLASH, using fixed ground order
25481 21957: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
25482 21957: Id : 3, {_}:
25483 add ?4 additive_identity =>= ?4
25484 [4] by right_additive_identity ?4
25485 21957: Id : 4, {_}:
25486 multiply additive_identity ?6 =>= additive_identity
25487 [6] by left_multiplicative_zero ?6
25488 21957: Id : 5, {_}:
25489 multiply ?8 additive_identity =>= additive_identity
25490 [8] by right_multiplicative_zero ?8
25491 21957: Id : 6, {_}:
25492 add (additive_inverse ?10) ?10 =>= additive_identity
25493 [10] by left_additive_inverse ?10
25494 21957: Id : 7, {_}:
25495 add ?12 (additive_inverse ?12) =>= additive_identity
25496 [12] by right_additive_inverse ?12
25497 21957: Id : 8, {_}:
25498 additive_inverse (additive_inverse ?14) =>= ?14
25499 [14] by additive_inverse_additive_inverse ?14
25500 21957: Id : 9, {_}:
25501 multiply ?16 (add ?17 ?18)
25503 add (multiply ?16 ?17) (multiply ?16 ?18)
25504 [18, 17, 16] by distribute1 ?16 ?17 ?18
25505 21957: Id : 10, {_}:
25506 multiply (add ?20 ?21) ?22
25508 add (multiply ?20 ?22) (multiply ?21 ?22)
25509 [22, 21, 20] by distribute2 ?20 ?21 ?22
25510 21957: Id : 11, {_}:
25511 add ?24 ?25 =?= add ?25 ?24
25512 [25, 24] by commutativity_for_addition ?24 ?25
25513 21957: Id : 12, {_}:
25514 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
25515 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
25516 21957: Id : 13, {_}:
25517 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
25518 [32, 31] by right_alternative ?31 ?32
25519 21957: Id : 14, {_}:
25520 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
25521 [35, 34] by left_alternative ?34 ?35
25522 21957: Id : 15, {_}:
25523 associator ?37 ?38 ?39
25525 add (multiply (multiply ?37 ?38) ?39)
25526 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
25527 [39, 38, 37] by associator ?37 ?38 ?39
25528 21957: Id : 16, {_}:
25531 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
25532 [42, 41] by commutator ?41 ?42
25533 21957: Id : 17, {_}:
25534 multiply (additive_inverse ?44) (additive_inverse ?45)
25537 [45, 44] by product_of_inverses ?44 ?45
25538 21957: Id : 18, {_}:
25539 multiply (additive_inverse ?47) ?48
25541 additive_inverse (multiply ?47 ?48)
25542 [48, 47] by inverse_product1 ?47 ?48
25543 21957: Id : 19, {_}:
25544 multiply ?50 (additive_inverse ?51)
25546 additive_inverse (multiply ?50 ?51)
25547 [51, 50] by inverse_product2 ?50 ?51
25548 21957: Id : 20, {_}:
25549 multiply ?53 (add ?54 (additive_inverse ?55))
25551 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
25552 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
25553 21957: Id : 21, {_}:
25554 multiply (add ?57 (additive_inverse ?58)) ?59
25556 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
25557 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
25558 21957: Id : 22, {_}:
25559 multiply (additive_inverse ?61) (add ?62 ?63)
25561 add (additive_inverse (multiply ?61 ?62))
25562 (additive_inverse (multiply ?61 ?63))
25563 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
25564 21957: Id : 23, {_}:
25565 multiply (add ?65 ?66) (additive_inverse ?67)
25567 add (additive_inverse (multiply ?65 ?67))
25568 (additive_inverse (multiply ?66 ?67))
25569 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
25571 21957: Id : 1, {_}:
25572 add (associator x y z) (associator x z y) =>= additive_identity
25573 [] by prove_equation
25577 21957: commutator 1 2 0
25578 21957: additive_inverse 22 1 0
25579 21957: multiply 40 2 0
25580 21957: additive_identity 9 0 1 3
25581 21957: add 25 2 1 0,2
25582 21957: associator 3 3 2 0,1,2
25583 21957: z 2 0 2 3,1,2
25584 21957: y 2 0 2 2,1,2
25585 21957: x 2 0 2 1,1,2
25586 % SZS status Timeout for RNG025-5.p
25587 NO CLASH, using fixed ground order
25589 21975: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
25590 21975: Id : 3, {_}:
25591 add ?4 additive_identity =>= ?4
25592 [4] by right_additive_identity ?4
25593 21975: Id : 4, {_}:
25594 multiply additive_identity ?6 =>= additive_identity
25595 [6] by left_multiplicative_zero ?6
25596 21975: Id : 5, {_}:
25597 multiply ?8 additive_identity =>= additive_identity
25598 [8] by right_multiplicative_zero ?8
25599 21975: Id : 6, {_}:
25600 add (additive_inverse ?10) ?10 =>= additive_identity
25601 [10] by left_additive_inverse ?10
25602 21975: Id : 7, {_}:
25603 add ?12 (additive_inverse ?12) =>= additive_identity
25604 [12] by right_additive_inverse ?12
25605 21975: Id : 8, {_}:
25606 additive_inverse (additive_inverse ?14) =>= ?14
25607 [14] by additive_inverse_additive_inverse ?14
25608 21975: Id : 9, {_}:
25609 multiply ?16 (add ?17 ?18)
25611 add (multiply ?16 ?17) (multiply ?16 ?18)
25612 [18, 17, 16] by distribute1 ?16 ?17 ?18
25613 21975: Id : 10, {_}:
25614 multiply (add ?20 ?21) ?22
25616 add (multiply ?20 ?22) (multiply ?21 ?22)
25617 [22, 21, 20] by distribute2 ?20 ?21 ?22
25618 21975: Id : 11, {_}:
25619 add ?24 ?25 =?= add ?25 ?24
25620 [25, 24] by commutativity_for_addition ?24 ?25
25621 21975: Id : 12, {_}:
25622 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
25623 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
25624 21975: Id : 13, {_}:
25625 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
25626 [32, 31] by right_alternative ?31 ?32
25627 21975: Id : 14, {_}:
25628 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
25629 [35, 34] by left_alternative ?34 ?35
25630 21975: Id : 15, {_}:
25631 associator ?37 ?38 ?39
25633 add (multiply (multiply ?37 ?38) ?39)
25634 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
25635 [39, 38, 37] by associator ?37 ?38 ?39
25636 21975: Id : 16, {_}:
25639 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
25640 [42, 41] by commutator ?41 ?42
25641 21975: Id : 17, {_}:
25642 multiply (additive_inverse ?44) (additive_inverse ?45)
25645 [45, 44] by product_of_inverses ?44 ?45
25646 21975: Id : 18, {_}:
25647 multiply (additive_inverse ?47) ?48
25649 additive_inverse (multiply ?47 ?48)
25650 [48, 47] by inverse_product1 ?47 ?48
25651 21975: Id : 19, {_}:
25652 multiply ?50 (additive_inverse ?51)
25654 additive_inverse (multiply ?50 ?51)
25655 [51, 50] by inverse_product2 ?50 ?51
25656 21975: Id : 20, {_}:
25657 multiply ?53 (add ?54 (additive_inverse ?55))
25659 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
25660 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
25661 21975: Id : 21, {_}:
25662 multiply (add ?57 (additive_inverse ?58)) ?59
25664 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
25665 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
25666 21975: Id : 22, {_}:
25667 multiply (additive_inverse ?61) (add ?62 ?63)
25669 add (additive_inverse (multiply ?61 ?62))
25670 (additive_inverse (multiply ?61 ?63))
25671 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
25672 21975: Id : 23, {_}:
25673 multiply (add ?65 ?66) (additive_inverse ?67)
25675 add (additive_inverse (multiply ?65 ?67))
25676 (additive_inverse (multiply ?66 ?67))
25677 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
25679 21975: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
25683 21975: commutator 1 2 0
25684 21975: additive_inverse 22 1 0
25685 21975: multiply 40 2 0
25687 21975: additive_identity 9 0 1 3
25688 21975: associator 2 3 1 0,2
25691 NO CLASH, using fixed ground order
25693 21976: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
25694 21976: Id : 3, {_}:
25695 add ?4 additive_identity =>= ?4
25696 [4] by right_additive_identity ?4
25697 21976: Id : 4, {_}:
25698 multiply additive_identity ?6 =>= additive_identity
25699 [6] by left_multiplicative_zero ?6
25700 21976: Id : 5, {_}:
25701 multiply ?8 additive_identity =>= additive_identity
25702 [8] by right_multiplicative_zero ?8
25703 21976: Id : 6, {_}:
25704 add (additive_inverse ?10) ?10 =>= additive_identity
25705 [10] by left_additive_inverse ?10
25706 21976: Id : 7, {_}:
25707 add ?12 (additive_inverse ?12) =>= additive_identity
25708 [12] by right_additive_inverse ?12
25709 21976: Id : 8, {_}:
25710 additive_inverse (additive_inverse ?14) =>= ?14
25711 [14] by additive_inverse_additive_inverse ?14
25712 21976: Id : 9, {_}:
25713 multiply ?16 (add ?17 ?18)
25715 add (multiply ?16 ?17) (multiply ?16 ?18)
25716 [18, 17, 16] by distribute1 ?16 ?17 ?18
25717 21976: Id : 10, {_}:
25718 multiply (add ?20 ?21) ?22
25720 add (multiply ?20 ?22) (multiply ?21 ?22)
25721 [22, 21, 20] by distribute2 ?20 ?21 ?22
25722 21976: Id : 11, {_}:
25723 add ?24 ?25 =?= add ?25 ?24
25724 [25, 24] by commutativity_for_addition ?24 ?25
25725 21976: Id : 12, {_}:
25726 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
25727 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
25728 21976: Id : 13, {_}:
25729 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
25730 [32, 31] by right_alternative ?31 ?32
25731 21976: Id : 14, {_}:
25732 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
25733 [35, 34] by left_alternative ?34 ?35
25734 21976: Id : 15, {_}:
25735 associator ?37 ?38 ?39
25737 add (multiply (multiply ?37 ?38) ?39)
25738 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
25739 [39, 38, 37] by associator ?37 ?38 ?39
25740 21976: Id : 16, {_}:
25743 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
25744 [42, 41] by commutator ?41 ?42
25745 21976: Id : 17, {_}:
25746 multiply (additive_inverse ?44) (additive_inverse ?45)
25749 [45, 44] by product_of_inverses ?44 ?45
25750 21976: Id : 18, {_}:
25751 multiply (additive_inverse ?47) ?48
25753 additive_inverse (multiply ?47 ?48)
25754 [48, 47] by inverse_product1 ?47 ?48
25755 21976: Id : 19, {_}:
25756 multiply ?50 (additive_inverse ?51)
25758 additive_inverse (multiply ?50 ?51)
25759 [51, 50] by inverse_product2 ?50 ?51
25760 21976: Id : 20, {_}:
25761 multiply ?53 (add ?54 (additive_inverse ?55))
25763 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
25764 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
25765 21976: Id : 21, {_}:
25766 multiply (add ?57 (additive_inverse ?58)) ?59
25768 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
25769 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
25770 21976: Id : 22, {_}:
25771 multiply (additive_inverse ?61) (add ?62 ?63)
25773 add (additive_inverse (multiply ?61 ?62))
25774 (additive_inverse (multiply ?61 ?63))
25775 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
25776 21976: Id : 23, {_}:
25777 multiply (add ?65 ?66) (additive_inverse ?67)
25779 add (additive_inverse (multiply ?65 ?67))
25780 (additive_inverse (multiply ?66 ?67))
25781 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
25783 21976: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
25787 21976: commutator 1 2 0
25788 21976: additive_inverse 22 1 0
25789 21976: multiply 40 2 0
25791 21976: additive_identity 9 0 1 3
25792 21976: associator 2 3 1 0,2
25795 NO CLASH, using fixed ground order
25797 21977: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
25798 21977: Id : 3, {_}:
25799 add ?4 additive_identity =>= ?4
25800 [4] by right_additive_identity ?4
25801 21977: Id : 4, {_}:
25802 multiply additive_identity ?6 =>= additive_identity
25803 [6] by left_multiplicative_zero ?6
25804 21977: Id : 5, {_}:
25805 multiply ?8 additive_identity =>= additive_identity
25806 [8] by right_multiplicative_zero ?8
25807 21977: Id : 6, {_}:
25808 add (additive_inverse ?10) ?10 =>= additive_identity
25809 [10] by left_additive_inverse ?10
25810 21977: Id : 7, {_}:
25811 add ?12 (additive_inverse ?12) =>= additive_identity
25812 [12] by right_additive_inverse ?12
25813 21977: Id : 8, {_}:
25814 additive_inverse (additive_inverse ?14) =>= ?14
25815 [14] by additive_inverse_additive_inverse ?14
25816 21977: Id : 9, {_}:
25817 multiply ?16 (add ?17 ?18)
25819 add (multiply ?16 ?17) (multiply ?16 ?18)
25820 [18, 17, 16] by distribute1 ?16 ?17 ?18
25821 21977: Id : 10, {_}:
25822 multiply (add ?20 ?21) ?22
25824 add (multiply ?20 ?22) (multiply ?21 ?22)
25825 [22, 21, 20] by distribute2 ?20 ?21 ?22
25826 21977: Id : 11, {_}:
25827 add ?24 ?25 =?= add ?25 ?24
25828 [25, 24] by commutativity_for_addition ?24 ?25
25829 21977: Id : 12, {_}:
25830 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
25831 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
25832 21977: Id : 13, {_}:
25833 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
25834 [32, 31] by right_alternative ?31 ?32
25835 21977: Id : 14, {_}:
25836 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
25837 [35, 34] by left_alternative ?34 ?35
25838 21977: Id : 15, {_}:
25839 associator ?37 ?38 ?39
25841 add (multiply (multiply ?37 ?38) ?39)
25842 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
25843 [39, 38, 37] by associator ?37 ?38 ?39
25844 21977: Id : 16, {_}:
25847 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
25848 [42, 41] by commutator ?41 ?42
25849 21977: Id : 17, {_}:
25850 multiply (additive_inverse ?44) (additive_inverse ?45)
25853 [45, 44] by product_of_inverses ?44 ?45
25854 21977: Id : 18, {_}:
25855 multiply (additive_inverse ?47) ?48
25857 additive_inverse (multiply ?47 ?48)
25858 [48, 47] by inverse_product1 ?47 ?48
25859 21977: Id : 19, {_}:
25860 multiply ?50 (additive_inverse ?51)
25862 additive_inverse (multiply ?50 ?51)
25863 [51, 50] by inverse_product2 ?50 ?51
25864 21977: Id : 20, {_}:
25865 multiply ?53 (add ?54 (additive_inverse ?55))
25867 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
25868 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
25869 21977: Id : 21, {_}:
25870 multiply (add ?57 (additive_inverse ?58)) ?59
25872 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
25873 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
25874 21977: Id : 22, {_}:
25875 multiply (additive_inverse ?61) (add ?62 ?63)
25877 add (additive_inverse (multiply ?61 ?62))
25878 (additive_inverse (multiply ?61 ?63))
25879 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
25880 21977: Id : 23, {_}:
25881 multiply (add ?65 ?66) (additive_inverse ?67)
25883 add (additive_inverse (multiply ?65 ?67))
25884 (additive_inverse (multiply ?66 ?67))
25885 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
25887 21977: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
25891 21977: commutator 1 2 0
25892 21977: additive_inverse 22 1 0
25893 21977: multiply 40 2 0
25895 21977: additive_identity 9 0 1 3
25896 21977: associator 2 3 1 0,2
25899 % SZS status Timeout for RNG025-7.p
25900 CLASH, statistics insufficient
25902 22004: Id : 2, {_}:
25903 apply (apply (apply s ?3) ?4) ?5
25905 apply (apply ?3 ?5) (apply ?4 ?5)
25906 [5, 4, 3] by s_definition ?3 ?4 ?5
25907 CLASH, statistics insufficient
25909 22005: Id : 2, {_}:
25910 apply (apply (apply s ?3) ?4) ?5
25912 apply (apply ?3 ?5) (apply ?4 ?5)
25913 [5, 4, 3] by s_definition ?3 ?4 ?5
25914 22005: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
25916 22005: Id : 1, {_}:
25917 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
25918 [1] by prove_fixed_point ?1
25924 22005: apply 11 2 3 0,2
25925 22005: f 3 1 3 0,2,2
25926 22004: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
25928 22004: Id : 1, {_}:
25929 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
25930 [1] by prove_fixed_point ?1
25936 22004: apply 11 2 3 0,2
25937 22004: f 3 1 3 0,2,2
25938 CLASH, statistics insufficient
25940 22006: Id : 2, {_}:
25941 apply (apply (apply s ?3) ?4) ?5
25943 apply (apply ?3 ?5) (apply ?4 ?5)
25944 [5, 4, 3] by s_definition ?3 ?4 ?5
25945 22006: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
25947 22006: Id : 1, {_}:
25948 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
25949 [1] by prove_fixed_point ?1
25955 22006: apply 11 2 3 0,2
25956 22006: f 3 1 3 0,2,2
25957 % SZS status Timeout for COL006-1.p
25958 NO CLASH, using fixed ground order
25960 22027: Id : 2, {_}:
25961 apply (apply (apply s ?2) ?3) ?4
25963 apply (apply ?2 ?4) (apply ?3 ?4)
25964 [4, 3, 2] by s_definition ?2 ?3 ?4
25965 22027: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
25966 NO CLASH, using fixed ground order
25968 22028: Id : 2, {_}:
25969 apply (apply (apply s ?2) ?3) ?4
25971 apply (apply ?2 ?4) (apply ?3 ?4)
25972 [4, 3, 2] by s_definition ?2 ?3 ?4
25973 22028: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
25974 22028: Id : 4, {_}:
25980 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
25981 (apply (apply s (apply k (apply (apply s s) (apply s k))))
25982 (apply (apply s (apply k s)) k))
25983 [] by strong_fixed_point
25985 22028: Id : 1, {_}:
25986 apply strong_fixed_point fixed_pt
25988 apply fixed_pt (apply strong_fixed_point fixed_pt)
25989 [] by prove_strong_fixed_point
25995 22028: apply 29 2 3 0,2
25996 22028: fixed_pt 3 0 3 2,2
25997 22028: strong_fixed_point 3 0 2 1,2
25998 22027: Id : 4, {_}:
26004 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
26005 (apply (apply s (apply k (apply (apply s s) (apply s k))))
26006 (apply (apply s (apply k s)) k))
26007 [] by strong_fixed_point
26009 22027: Id : 1, {_}:
26010 apply strong_fixed_point fixed_pt
26012 apply fixed_pt (apply strong_fixed_point fixed_pt)
26013 [] by prove_strong_fixed_point
26019 22027: apply 29 2 3 0,2
26020 22027: fixed_pt 3 0 3 2,2
26021 22027: strong_fixed_point 3 0 2 1,2
26022 NO CLASH, using fixed ground order
26024 22029: Id : 2, {_}:
26025 apply (apply (apply s ?2) ?3) ?4
26027 apply (apply ?2 ?4) (apply ?3 ?4)
26028 [4, 3, 2] by s_definition ?2 ?3 ?4
26029 22029: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
26030 22029: Id : 4, {_}:
26036 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
26037 (apply (apply s (apply k (apply (apply s s) (apply s k))))
26038 (apply (apply s (apply k s)) k))
26039 [] by strong_fixed_point
26041 22029: Id : 1, {_}:
26042 apply strong_fixed_point fixed_pt
26044 apply fixed_pt (apply strong_fixed_point fixed_pt)
26045 [] by prove_strong_fixed_point
26051 22029: apply 29 2 3 0,2
26052 22029: fixed_pt 3 0 3 2,2
26053 22029: strong_fixed_point 3 0 2 1,2
26054 % SZS status Timeout for COL006-5.p
26055 NO CLASH, using fixed ground order
26057 22056: Id : 2, {_}:
26058 apply (apply (apply s ?2) ?3) ?4
26060 apply (apply ?2 ?4) (apply ?3 ?4)
26061 [4, 3, 2] by s_definition ?2 ?3 ?4
26062 22056: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
26063 22056: Id : 4, {_}:
26069 (apply (apply (apply s s) (apply (apply s k) k))
26070 (apply (apply s s) (apply s k)))))
26071 (apply (apply s (apply k s)) k)
26072 [] by strong_fixed_point
26074 22056: Id : 1, {_}:
26075 apply strong_fixed_point fixed_pt
26077 apply fixed_pt (apply strong_fixed_point fixed_pt)
26078 [] by prove_strong_fixed_point
26084 22056: apply 25 2 3 0,2
26085 22056: fixed_pt 3 0 3 2,2
26086 22056: strong_fixed_point 3 0 2 1,2
26087 NO CLASH, using fixed ground order
26089 22057: Id : 2, {_}:
26090 apply (apply (apply s ?2) ?3) ?4
26092 apply (apply ?2 ?4) (apply ?3 ?4)
26093 [4, 3, 2] by s_definition ?2 ?3 ?4
26094 22057: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
26095 22057: Id : 4, {_}:
26101 (apply (apply (apply s s) (apply (apply s k) k))
26102 (apply (apply s s) (apply s k)))))
26103 (apply (apply s (apply k s)) k)
26104 [] by strong_fixed_point
26106 22057: Id : 1, {_}:
26107 apply strong_fixed_point fixed_pt
26109 apply fixed_pt (apply strong_fixed_point fixed_pt)
26110 [] by prove_strong_fixed_point
26116 22057: apply 25 2 3 0,2
26117 22057: fixed_pt 3 0 3 2,2
26118 22057: strong_fixed_point 3 0 2 1,2
26119 NO CLASH, using fixed ground order
26121 22058: Id : 2, {_}:
26122 apply (apply (apply s ?2) ?3) ?4
26124 apply (apply ?2 ?4) (apply ?3 ?4)
26125 [4, 3, 2] by s_definition ?2 ?3 ?4
26126 22058: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
26127 22058: Id : 4, {_}:
26133 (apply (apply (apply s s) (apply (apply s k) k))
26134 (apply (apply s s) (apply s k)))))
26135 (apply (apply s (apply k s)) k)
26136 [] by strong_fixed_point
26138 22058: Id : 1, {_}:
26139 apply strong_fixed_point fixed_pt
26141 apply fixed_pt (apply strong_fixed_point fixed_pt)
26142 [] by prove_strong_fixed_point
26148 22058: apply 25 2 3 0,2
26149 22058: fixed_pt 3 0 3 2,2
26150 22058: strong_fixed_point 3 0 2 1,2
26151 % SZS status Timeout for COL006-7.p
26152 NO CLASH, using fixed ground order
26154 22074: Id : 2, {_}:
26155 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
26156 [4, 3, 2] by b_definition ?2 ?3 ?4
26157 22074: Id : 3, {_}:
26158 apply (apply (apply n ?6) ?7) ?8
26160 apply (apply (apply ?6 ?8) ?7) ?8
26161 [8, 7, 6] by n_definition ?6 ?7 ?8
26162 22074: Id : 4, {_}:
26172 (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
26173 [] by strong_fixed_point
26175 22074: Id : 1, {_}:
26176 apply strong_fixed_point fixed_pt
26178 apply fixed_pt (apply strong_fixed_point fixed_pt)
26179 [] by prove_strong_fixed_point
26185 22074: apply 26 2 3 0,2
26186 22074: fixed_pt 3 0 3 2,2
26187 22074: strong_fixed_point 3 0 2 1,2
26188 NO CLASH, using fixed ground order
26190 22075: Id : 2, {_}:
26191 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
26192 [4, 3, 2] by b_definition ?2 ?3 ?4
26193 22075: Id : 3, {_}:
26194 apply (apply (apply n ?6) ?7) ?8
26196 apply (apply (apply ?6 ?8) ?7) ?8
26197 [8, 7, 6] by n_definition ?6 ?7 ?8
26198 22075: Id : 4, {_}:
26208 (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
26209 [] by strong_fixed_point
26211 22075: Id : 1, {_}:
26212 apply strong_fixed_point fixed_pt
26214 apply fixed_pt (apply strong_fixed_point fixed_pt)
26215 [] by prove_strong_fixed_point
26221 22075: apply 26 2 3 0,2
26222 22075: fixed_pt 3 0 3 2,2
26223 22075: strong_fixed_point 3 0 2 1,2
26224 NO CLASH, using fixed ground order
26226 22076: Id : 2, {_}:
26227 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
26228 [4, 3, 2] by b_definition ?2 ?3 ?4
26229 22076: Id : 3, {_}:
26230 apply (apply (apply n ?6) ?7) ?8
26232 apply (apply (apply ?6 ?8) ?7) ?8
26233 [8, 7, 6] by n_definition ?6 ?7 ?8
26234 22076: Id : 4, {_}:
26244 (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
26245 [] by strong_fixed_point
26247 22076: Id : 1, {_}:
26248 apply strong_fixed_point fixed_pt
26250 apply fixed_pt (apply strong_fixed_point fixed_pt)
26251 [] by prove_strong_fixed_point
26257 22076: apply 26 2 3 0,2
26258 22076: fixed_pt 3 0 3 2,2
26259 22076: strong_fixed_point 3 0 2 1,2
26260 % SZS status Timeout for COL044-6.p
26261 NO CLASH, using fixed ground order
26263 22116: Id : 2, {_}:
26264 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
26265 [4, 3, 2] by b_definition ?2 ?3 ?4
26266 22116: Id : 3, {_}:
26267 apply (apply (apply n ?6) ?7) ?8
26269 apply (apply (apply ?6 ?8) ?7) ?8
26270 [8, 7, 6] by n_definition ?6 ?7 ?8
26271 22116: Id : 4, {_}:
26281 (apply (apply n (apply n (apply b b))) n))) n)) b)) b
26282 [] by strong_fixed_point
26284 22116: Id : 1, {_}:
26285 apply strong_fixed_point fixed_pt
26287 apply fixed_pt (apply strong_fixed_point fixed_pt)
26288 [] by prove_strong_fixed_point
26294 22116: apply 26 2 3 0,2
26295 22116: fixed_pt 3 0 3 2,2
26296 22116: strong_fixed_point 3 0 2 1,2
26297 NO CLASH, using fixed ground order
26299 22117: Id : 2, {_}:
26300 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
26301 [4, 3, 2] by b_definition ?2 ?3 ?4
26302 22117: Id : 3, {_}:
26303 apply (apply (apply n ?6) ?7) ?8
26305 apply (apply (apply ?6 ?8) ?7) ?8
26306 [8, 7, 6] by n_definition ?6 ?7 ?8
26307 22117: Id : 4, {_}:
26317 (apply (apply n (apply n (apply b b))) n))) n)) b)) b
26318 [] by strong_fixed_point
26320 22117: Id : 1, {_}:
26321 apply strong_fixed_point fixed_pt
26323 apply fixed_pt (apply strong_fixed_point fixed_pt)
26324 [] by prove_strong_fixed_point
26330 22117: apply 26 2 3 0,2
26331 22117: fixed_pt 3 0 3 2,2
26332 22117: strong_fixed_point 3 0 2 1,2
26333 NO CLASH, using fixed ground order
26335 22118: Id : 2, {_}:
26336 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
26337 [4, 3, 2] by b_definition ?2 ?3 ?4
26338 22118: Id : 3, {_}:
26339 apply (apply (apply n ?6) ?7) ?8
26341 apply (apply (apply ?6 ?8) ?7) ?8
26342 [8, 7, 6] by n_definition ?6 ?7 ?8
26343 22118: Id : 4, {_}:
26353 (apply (apply n (apply n (apply b b))) n))) n)) b)) b
26354 [] by strong_fixed_point
26356 22118: Id : 1, {_}:
26357 apply strong_fixed_point fixed_pt
26359 apply fixed_pt (apply strong_fixed_point fixed_pt)
26360 [] by prove_strong_fixed_point
26366 22118: apply 26 2 3 0,2
26367 22118: fixed_pt 3 0 3 2,2
26368 22118: strong_fixed_point 3 0 2 1,2
26369 % SZS status Timeout for COL044-7.p
26370 CLASH, statistics insufficient
26372 22135: Id : 2, {_}:
26373 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
26374 [5, 4, 3] by b_definition ?3 ?4 ?5
26375 22135: Id : 3, {_}:
26376 apply (apply t ?7) ?8 =>= apply ?8 ?7
26377 [8, 7] by t_definition ?7 ?8
26379 22135: Id : 1, {_}:
26380 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
26382 apply (apply (h ?1) (f ?1)) (g ?1)
26383 [1] by prove_v_combinator ?1
26389 22135: h 2 1 2 0,2,2
26390 22135: g 2 1 2 0,2,1,2
26391 22135: apply 13 2 5 0,2
26392 22135: f 2 1 2 0,2,1,1,2
26393 CLASH, statistics insufficient
26395 22136: Id : 2, {_}:
26396 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
26397 [5, 4, 3] by b_definition ?3 ?4 ?5
26398 22136: Id : 3, {_}:
26399 apply (apply t ?7) ?8 =>= apply ?8 ?7
26400 [8, 7] by t_definition ?7 ?8
26402 22136: Id : 1, {_}:
26403 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
26405 apply (apply (h ?1) (f ?1)) (g ?1)
26406 [1] by prove_v_combinator ?1
26412 22136: h 2 1 2 0,2,2
26413 22136: g 2 1 2 0,2,1,2
26414 22136: apply 13 2 5 0,2
26415 22136: f 2 1 2 0,2,1,1,2
26416 CLASH, statistics insufficient
26418 22137: Id : 2, {_}:
26419 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
26420 [5, 4, 3] by b_definition ?3 ?4 ?5
26421 22137: Id : 3, {_}:
26422 apply (apply t ?7) ?8 =?= apply ?8 ?7
26423 [8, 7] by t_definition ?7 ?8
26425 22137: Id : 1, {_}:
26426 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
26428 apply (apply (h ?1) (f ?1)) (g ?1)
26429 [1] by prove_v_combinator ?1
26435 22137: h 2 1 2 0,2,2
26436 22137: g 2 1 2 0,2,1,2
26437 22137: apply 13 2 5 0,2
26438 22137: f 2 1 2 0,2,1,1,2
26442 Found proof, 35.273110s
26443 % SZS status Unsatisfiable for COL064-1.p
26444 % SZS output start CNFRefutation for COL064-1.p
26445 Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
26446 Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
26447 Id : 10997, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10996 with 3 at 2
26448 Id : 10996, {_}: apply (apply ?37685 (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) [37685] by Super 3193 with 2 at 2
26449 Id : 3193, {_}: apply (apply (apply ?10612 (apply ?10613 (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) [10613, 10612] by Super 3188 with 2 at 1,1,2
26450 Id : 3188, {_}: apply (apply (apply ?10602 (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) [10602] by Super 3164 with 3 at 2
26451 Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
26452 Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
26453 Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
26454 Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
26455 Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (f (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
26456 Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (f (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
26457 Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1
26458 % SZS output end CNFRefutation for COL064-1.p
26459 22135: solved COL064-1.p in 35.146196 using nrkbo
26460 22135: status Unsatisfiable for COL064-1.p
26461 CLASH, statistics insufficient
26463 22153: Id : 2, {_}:
26464 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
26465 [5, 4, 3] by b_definition ?3 ?4 ?5
26466 22153: Id : 3, {_}:
26467 apply (apply t ?7) ?8 =>= apply ?8 ?7
26468 [8, 7] by t_definition ?7 ?8
26470 22153: Id : 1, {_}:
26471 apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
26473 apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
26474 [1] by prove_g_combinator ?1
26480 22153: i 2 1 2 0,2,2
26481 22153: h 2 1 2 0,2,1,2
26482 22153: g 2 1 2 0,2,1,1,2
26483 22153: apply 15 2 7 0,2
26484 22153: f 2 1 2 0,2,1,1,1,2
26485 CLASH, statistics insufficient
26487 22154: Id : 2, {_}:
26488 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
26489 [5, 4, 3] by b_definition ?3 ?4 ?5
26490 22154: Id : 3, {_}:
26491 apply (apply t ?7) ?8 =>= apply ?8 ?7
26492 [8, 7] by t_definition ?7 ?8
26494 22154: Id : 1, {_}:
26495 apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
26497 apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
26498 [1] by prove_g_combinator ?1
26504 22154: i 2 1 2 0,2,2
26505 22154: h 2 1 2 0,2,1,2
26506 22154: g 2 1 2 0,2,1,1,2
26507 22154: apply 15 2 7 0,2
26508 22154: f 2 1 2 0,2,1,1,1,2
26509 CLASH, statistics insufficient
26511 22155: Id : 2, {_}:
26512 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
26513 [5, 4, 3] by b_definition ?3 ?4 ?5
26514 22155: Id : 3, {_}:
26515 apply (apply t ?7) ?8 =?= apply ?8 ?7
26516 [8, 7] by t_definition ?7 ?8
26518 22155: Id : 1, {_}:
26519 apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
26521 apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
26522 [1] by prove_g_combinator ?1
26528 22155: i 2 1 2 0,2,2
26529 22155: h 2 1 2 0,2,1,2
26530 22155: g 2 1 2 0,2,1,1,2
26531 22155: apply 15 2 7 0,2
26532 22155: f 2 1 2 0,2,1,1,1,2
26533 % SZS status Timeout for COL065-1.p
26534 CLASH, statistics insufficient
26536 22171: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
26537 22171: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
26538 22171: Id : 4, {_}:
26539 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
26540 [8, 7, 6] by associativity ?6 ?7 ?8
26541 22171: Id : 5, {_}:
26542 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
26543 [11, 10] by symmetry_of_glb ?10 ?11
26544 22171: Id : 6, {_}:
26545 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
26546 [14, 13] by symmetry_of_lub ?13 ?14
26547 22171: Id : 7, {_}:
26548 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
26550 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
26551 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
26552 22171: Id : 8, {_}:
26553 least_upper_bound ?20 (least_upper_bound ?21 ?22)
26555 least_upper_bound (least_upper_bound ?20 ?21) ?22
26556 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
26557 22171: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
26558 22171: Id : 10, {_}:
26559 greatest_lower_bound ?26 ?26 =>= ?26
26560 [26] by idempotence_of_gld ?26
26561 22171: Id : 11, {_}:
26562 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
26563 [29, 28] by lub_absorbtion ?28 ?29
26564 22171: Id : 12, {_}:
26565 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
26566 [32, 31] by glb_absorbtion ?31 ?32
26567 22171: Id : 13, {_}:
26568 multiply ?34 (least_upper_bound ?35 ?36)
26570 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
26571 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
26572 22171: Id : 14, {_}:
26573 multiply ?38 (greatest_lower_bound ?39 ?40)
26575 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
26576 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
26577 22171: Id : 15, {_}:
26578 multiply (least_upper_bound ?42 ?43) ?44
26580 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
26581 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
26582 22171: Id : 16, {_}:
26583 multiply (greatest_lower_bound ?46 ?47) ?48
26585 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
26586 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
26587 22171: Id : 17, {_}:
26588 greatest_lower_bound a c =>= greatest_lower_bound b c
26590 22171: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
26592 22171: Id : 1, {_}: a =>= b [] by prove_p12
26597 22171: least_upper_bound 15 2 0
26598 22171: greatest_lower_bound 15 2 0
26599 22171: inverse 1 1 0
26600 22171: multiply 18 2 0
26601 22171: identity 2 0 0
26604 CLASH, statistics insufficient
26606 22172: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
26607 22172: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
26608 22172: Id : 4, {_}:
26609 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
26610 [8, 7, 6] by associativity ?6 ?7 ?8
26611 22172: Id : 5, {_}:
26612 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
26613 [11, 10] by symmetry_of_glb ?10 ?11
26614 22172: Id : 6, {_}:
26615 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
26616 [14, 13] by symmetry_of_lub ?13 ?14
26617 22172: Id : 7, {_}:
26618 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
26620 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
26621 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
26622 22172: Id : 8, {_}:
26623 least_upper_bound ?20 (least_upper_bound ?21 ?22)
26625 least_upper_bound (least_upper_bound ?20 ?21) ?22
26626 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
26627 22172: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
26628 22172: Id : 10, {_}:
26629 greatest_lower_bound ?26 ?26 =>= ?26
26630 [26] by idempotence_of_gld ?26
26631 22172: Id : 11, {_}:
26632 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
26633 [29, 28] by lub_absorbtion ?28 ?29
26634 22172: Id : 12, {_}:
26635 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
26636 [32, 31] by glb_absorbtion ?31 ?32
26637 22172: Id : 13, {_}:
26638 multiply ?34 (least_upper_bound ?35 ?36)
26640 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
26641 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
26642 22172: Id : 14, {_}:
26643 multiply ?38 (greatest_lower_bound ?39 ?40)
26645 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
26646 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
26647 22172: Id : 15, {_}:
26648 multiply (least_upper_bound ?42 ?43) ?44
26650 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
26651 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
26652 22172: Id : 16, {_}:
26653 multiply (greatest_lower_bound ?46 ?47) ?48
26655 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
26656 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
26657 22172: Id : 17, {_}:
26658 greatest_lower_bound a c =>= greatest_lower_bound b c
26660 22172: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
26662 22172: Id : 1, {_}: a =>= b [] by prove_p12
26667 22172: least_upper_bound 15 2 0
26668 22172: greatest_lower_bound 15 2 0
26669 22172: inverse 1 1 0
26670 22172: multiply 18 2 0
26671 22172: identity 2 0 0
26674 CLASH, statistics insufficient
26676 22173: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
26677 22173: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
26678 22173: Id : 4, {_}:
26679 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
26680 [8, 7, 6] by associativity ?6 ?7 ?8
26681 22173: Id : 5, {_}:
26682 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
26683 [11, 10] by symmetry_of_glb ?10 ?11
26684 22173: Id : 6, {_}:
26685 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
26686 [14, 13] by symmetry_of_lub ?13 ?14
26687 22173: Id : 7, {_}:
26688 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
26690 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
26691 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
26692 22173: Id : 8, {_}:
26693 least_upper_bound ?20 (least_upper_bound ?21 ?22)
26695 least_upper_bound (least_upper_bound ?20 ?21) ?22
26696 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
26697 22173: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
26698 22173: Id : 10, {_}:
26699 greatest_lower_bound ?26 ?26 =>= ?26
26700 [26] by idempotence_of_gld ?26
26701 22173: Id : 11, {_}:
26702 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
26703 [29, 28] by lub_absorbtion ?28 ?29
26704 22173: Id : 12, {_}:
26705 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
26706 [32, 31] by glb_absorbtion ?31 ?32
26707 22173: Id : 13, {_}:
26708 multiply ?34 (least_upper_bound ?35 ?36)
26710 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
26711 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
26712 22173: Id : 14, {_}:
26713 multiply ?38 (greatest_lower_bound ?39 ?40)
26715 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
26716 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
26717 22173: Id : 15, {_}:
26718 multiply (least_upper_bound ?42 ?43) ?44
26720 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
26721 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
26722 22173: Id : 16, {_}:
26723 multiply (greatest_lower_bound ?46 ?47) ?48
26725 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
26726 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
26727 22173: Id : 17, {_}:
26728 greatest_lower_bound a c =>= greatest_lower_bound b c
26730 22173: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
26732 22173: Id : 1, {_}: a =>= b [] by prove_p12
26737 22173: least_upper_bound 15 2 0
26738 22173: greatest_lower_bound 15 2 0
26739 22173: inverse 1 1 0
26740 22173: multiply 18 2 0
26741 22173: identity 2 0 0
26744 % SZS status Timeout for GRP181-1.p
26745 CLASH, statistics insufficient
26747 22201: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
26748 22201: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
26749 22201: Id : 4, {_}:
26750 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
26751 [8, 7, 6] by associativity ?6 ?7 ?8
26752 22201: Id : 5, {_}:
26753 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
26754 [11, 10] by symmetry_of_glb ?10 ?11
26755 22201: Id : 6, {_}:
26756 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
26757 [14, 13] by symmetry_of_lub ?13 ?14
26758 22201: Id : 7, {_}:
26759 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
26761 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
26762 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
26763 22201: Id : 8, {_}:
26764 least_upper_bound ?20 (least_upper_bound ?21 ?22)
26766 least_upper_bound (least_upper_bound ?20 ?21) ?22
26767 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
26768 22201: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
26769 22201: Id : 10, {_}:
26770 greatest_lower_bound ?26 ?26 =>= ?26
26771 [26] by idempotence_of_gld ?26
26772 22201: Id : 11, {_}:
26773 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
26774 [29, 28] by lub_absorbtion ?28 ?29
26775 22201: Id : 12, {_}:
26776 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
26777 [32, 31] by glb_absorbtion ?31 ?32
26778 22201: Id : 13, {_}:
26779 multiply ?34 (least_upper_bound ?35 ?36)
26781 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
26782 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
26783 22201: Id : 14, {_}:
26784 multiply ?38 (greatest_lower_bound ?39 ?40)
26786 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
26787 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
26788 22201: Id : 15, {_}:
26789 multiply (least_upper_bound ?42 ?43) ?44
26791 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
26792 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
26793 22201: Id : 16, {_}:
26794 multiply (greatest_lower_bound ?46 ?47) ?48
26796 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
26797 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
26798 22201: Id : 17, {_}: inverse identity =>= identity [] by p12_1
26799 22201: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
26800 22201: Id : 19, {_}:
26801 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
26802 [54, 53] by p12_3 ?53 ?54
26803 22201: Id : 20, {_}:
26804 greatest_lower_bound a c =>= greatest_lower_bound b c
26806 22201: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
26808 22201: Id : 1, {_}: a =>= b [] by prove_p12
26813 22201: least_upper_bound 15 2 0
26814 22201: greatest_lower_bound 15 2 0
26815 22201: inverse 7 1 0
26816 22201: multiply 20 2 0
26817 22201: identity 4 0 0
26820 CLASH, statistics insufficient
26822 22202: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
26823 22202: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
26824 22202: Id : 4, {_}:
26825 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
26826 [8, 7, 6] by associativity ?6 ?7 ?8
26827 22202: Id : 5, {_}:
26828 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
26829 [11, 10] by symmetry_of_glb ?10 ?11
26830 22202: Id : 6, {_}:
26831 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
26832 [14, 13] by symmetry_of_lub ?13 ?14
26833 22202: Id : 7, {_}:
26834 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
26836 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
26837 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
26838 22202: Id : 8, {_}:
26839 least_upper_bound ?20 (least_upper_bound ?21 ?22)
26841 least_upper_bound (least_upper_bound ?20 ?21) ?22
26842 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
26843 22202: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
26844 22202: Id : 10, {_}:
26845 greatest_lower_bound ?26 ?26 =>= ?26
26846 [26] by idempotence_of_gld ?26
26847 22202: Id : 11, {_}:
26848 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
26849 [29, 28] by lub_absorbtion ?28 ?29
26850 22202: Id : 12, {_}:
26851 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
26852 [32, 31] by glb_absorbtion ?31 ?32
26853 22202: Id : 13, {_}:
26854 multiply ?34 (least_upper_bound ?35 ?36)
26856 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
26857 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
26858 22202: Id : 14, {_}:
26859 multiply ?38 (greatest_lower_bound ?39 ?40)
26861 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
26862 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
26863 22202: Id : 15, {_}:
26864 multiply (least_upper_bound ?42 ?43) ?44
26866 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
26867 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
26868 22202: Id : 16, {_}:
26869 multiply (greatest_lower_bound ?46 ?47) ?48
26871 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
26872 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
26873 22202: Id : 17, {_}: inverse identity =>= identity [] by p12_1
26874 22202: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
26875 22202: Id : 19, {_}:
26876 inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
26877 [54, 53] by p12_3 ?53 ?54
26878 22202: Id : 20, {_}:
26879 greatest_lower_bound a c =>= greatest_lower_bound b c
26881 22202: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
26883 22202: Id : 1, {_}: a =>= b [] by prove_p12
26888 22202: least_upper_bound 15 2 0
26889 22202: greatest_lower_bound 15 2 0
26890 22202: inverse 7 1 0
26891 22202: multiply 20 2 0
26892 22202: identity 4 0 0
26895 CLASH, statistics insufficient
26897 22200: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
26898 22200: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
26899 22200: Id : 4, {_}:
26900 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
26901 [8, 7, 6] by associativity ?6 ?7 ?8
26902 22200: Id : 5, {_}:
26903 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
26904 [11, 10] by symmetry_of_glb ?10 ?11
26905 22200: Id : 6, {_}:
26906 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
26907 [14, 13] by symmetry_of_lub ?13 ?14
26908 22200: Id : 7, {_}:
26909 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
26911 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
26912 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
26913 22200: Id : 8, {_}:
26914 least_upper_bound ?20 (least_upper_bound ?21 ?22)
26916 least_upper_bound (least_upper_bound ?20 ?21) ?22
26917 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
26918 22200: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
26919 22200: Id : 10, {_}:
26920 greatest_lower_bound ?26 ?26 =>= ?26
26921 [26] by idempotence_of_gld ?26
26922 22200: Id : 11, {_}:
26923 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
26924 [29, 28] by lub_absorbtion ?28 ?29
26925 22200: Id : 12, {_}:
26926 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
26927 [32, 31] by glb_absorbtion ?31 ?32
26928 22200: Id : 13, {_}:
26929 multiply ?34 (least_upper_bound ?35 ?36)
26931 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
26932 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
26933 22200: Id : 14, {_}:
26934 multiply ?38 (greatest_lower_bound ?39 ?40)
26936 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
26937 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
26938 22200: Id : 15, {_}:
26939 multiply (least_upper_bound ?42 ?43) ?44
26941 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
26942 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
26943 22200: Id : 16, {_}:
26944 multiply (greatest_lower_bound ?46 ?47) ?48
26946 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
26947 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
26948 22200: Id : 17, {_}: inverse identity =>= identity [] by p12_1
26949 22200: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
26950 22200: Id : 19, {_}:
26951 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
26952 [54, 53] by p12_3 ?53 ?54
26953 22200: Id : 20, {_}:
26954 greatest_lower_bound a c =>= greatest_lower_bound b c
26956 22200: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
26958 22200: Id : 1, {_}: a =>= b [] by prove_p12
26963 22200: least_upper_bound 15 2 0
26964 22200: greatest_lower_bound 15 2 0
26965 22200: inverse 7 1 0
26966 22200: multiply 20 2 0
26967 22200: identity 4 0 0
26970 % SZS status Timeout for GRP181-2.p
26971 NO CLASH, using fixed ground order
26973 22218: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
26974 22218: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
26975 22218: Id : 4, {_}:
26976 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
26977 [8, 7, 6] by associativity ?6 ?7 ?8
26978 22218: Id : 5, {_}:
26979 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
26980 [11, 10] by symmetry_of_glb ?10 ?11
26981 22218: Id : 6, {_}:
26982 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
26983 [14, 13] by symmetry_of_lub ?13 ?14
26984 22218: Id : 7, {_}:
26985 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
26987 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
26988 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
26989 22218: Id : 8, {_}:
26990 least_upper_bound ?20 (least_upper_bound ?21 ?22)
26992 least_upper_bound (least_upper_bound ?20 ?21) ?22
26993 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
26994 22218: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
26995 22218: Id : 10, {_}:
26996 greatest_lower_bound ?26 ?26 =>= ?26
26997 [26] by idempotence_of_gld ?26
26998 22218: Id : 11, {_}:
26999 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
27000 [29, 28] by lub_absorbtion ?28 ?29
27001 22218: Id : 12, {_}:
27002 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
27003 [32, 31] by glb_absorbtion ?31 ?32
27004 22218: Id : 13, {_}:
27005 multiply ?34 (least_upper_bound ?35 ?36)
27007 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
27008 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
27009 22218: Id : 14, {_}:
27010 multiply ?38 (greatest_lower_bound ?39 ?40)
27012 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
27013 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
27014 22218: Id : 15, {_}:
27015 multiply (least_upper_bound ?42 ?43) ?44
27017 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
27018 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
27019 22218: Id : 16, {_}:
27020 multiply (greatest_lower_bound ?46 ?47) ?48
27022 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
27023 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
27024 22218: Id : 17, {_}:
27025 greatest_lower_bound (least_upper_bound a (inverse a))
27026 (least_upper_bound b (inverse b))
27031 22218: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
27035 22218: least_upper_bound 15 2 0
27036 22218: greatest_lower_bound 14 2 0
27037 22218: inverse 3 1 0
27038 22218: identity 3 0 0
27039 22218: multiply 20 2 2 0,2
27042 NO CLASH, using fixed ground order
27044 22219: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
27045 22219: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
27046 22219: Id : 4, {_}:
27047 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
27048 [8, 7, 6] by associativity ?6 ?7 ?8
27049 22219: Id : 5, {_}:
27050 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
27051 [11, 10] by symmetry_of_glb ?10 ?11
27052 22219: Id : 6, {_}:
27053 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
27054 [14, 13] by symmetry_of_lub ?13 ?14
27055 22219: Id : 7, {_}:
27056 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
27058 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
27059 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
27060 22219: Id : 8, {_}:
27061 least_upper_bound ?20 (least_upper_bound ?21 ?22)
27063 least_upper_bound (least_upper_bound ?20 ?21) ?22
27064 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
27065 22219: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
27066 22219: Id : 10, {_}:
27067 greatest_lower_bound ?26 ?26 =>= ?26
27068 [26] by idempotence_of_gld ?26
27069 22219: Id : 11, {_}:
27070 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
27071 [29, 28] by lub_absorbtion ?28 ?29
27072 22219: Id : 12, {_}:
27073 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
27074 [32, 31] by glb_absorbtion ?31 ?32
27075 22219: Id : 13, {_}:
27076 multiply ?34 (least_upper_bound ?35 ?36)
27078 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
27079 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
27080 22219: Id : 14, {_}:
27081 multiply ?38 (greatest_lower_bound ?39 ?40)
27083 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
27084 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
27085 22219: Id : 15, {_}:
27086 multiply (least_upper_bound ?42 ?43) ?44
27088 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
27089 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
27090 22219: Id : 16, {_}:
27091 multiply (greatest_lower_bound ?46 ?47) ?48
27093 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
27094 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
27095 22219: Id : 17, {_}:
27096 greatest_lower_bound (least_upper_bound a (inverse a))
27097 (least_upper_bound b (inverse b))
27102 22219: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
27106 22219: least_upper_bound 15 2 0
27107 22219: greatest_lower_bound 14 2 0
27108 22219: inverse 3 1 0
27109 22219: identity 3 0 0
27110 22219: multiply 20 2 2 0,2
27113 NO CLASH, using fixed ground order
27115 22220: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
27116 22220: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
27117 22220: Id : 4, {_}:
27118 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
27119 [8, 7, 6] by associativity ?6 ?7 ?8
27120 22220: Id : 5, {_}:
27121 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
27122 [11, 10] by symmetry_of_glb ?10 ?11
27123 22220: Id : 6, {_}:
27124 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
27125 [14, 13] by symmetry_of_lub ?13 ?14
27126 22220: Id : 7, {_}:
27127 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
27129 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
27130 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
27131 22220: Id : 8, {_}:
27132 least_upper_bound ?20 (least_upper_bound ?21 ?22)
27134 least_upper_bound (least_upper_bound ?20 ?21) ?22
27135 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
27136 22220: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
27137 22220: Id : 10, {_}:
27138 greatest_lower_bound ?26 ?26 =>= ?26
27139 [26] by idempotence_of_gld ?26
27140 22220: Id : 11, {_}:
27141 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
27142 [29, 28] by lub_absorbtion ?28 ?29
27143 22220: Id : 12, {_}:
27144 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
27145 [32, 31] by glb_absorbtion ?31 ?32
27146 22220: Id : 13, {_}:
27147 multiply ?34 (least_upper_bound ?35 ?36)
27149 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
27150 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
27151 22220: Id : 14, {_}:
27152 multiply ?38 (greatest_lower_bound ?39 ?40)
27154 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
27155 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
27156 22220: Id : 15, {_}:
27157 multiply (least_upper_bound ?42 ?43) ?44
27159 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
27160 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
27161 22220: Id : 16, {_}:
27162 multiply (greatest_lower_bound ?46 ?47) ?48
27164 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
27165 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
27166 22220: Id : 17, {_}:
27167 greatest_lower_bound (least_upper_bound a (inverse a))
27168 (least_upper_bound b (inverse b))
27173 22220: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
27177 22220: least_upper_bound 15 2 0
27178 22220: greatest_lower_bound 14 2 0
27179 22220: inverse 3 1 0
27180 22220: identity 3 0 0
27181 22220: multiply 20 2 2 0,2
27184 % SZS status Timeout for GRP187-1.p
27185 NO CLASH, using fixed ground order
27187 22280: Id : 2, {_}:
27192 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27193 (multiply (inverse (multiply ?4 ?5))
27196 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27200 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27202 22280: Id : 1, {_}:
27203 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
27204 [] by prove_these_axioms_1
27208 22280: b1 2 0 2 1,1,3
27209 22280: multiply 12 2 2 0,2
27210 22280: inverse 9 1 2 0,1,2
27211 22280: a1 2 0 2 1,1,2
27212 NO CLASH, using fixed ground order
27214 22281: Id : 2, {_}:
27219 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27220 (multiply (inverse (multiply ?4 ?5))
27223 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27227 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27229 22281: Id : 1, {_}:
27230 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
27231 [] by prove_these_axioms_1
27235 22281: b1 2 0 2 1,1,3
27236 22281: multiply 12 2 2 0,2
27237 22281: inverse 9 1 2 0,1,2
27238 22281: a1 2 0 2 1,1,2
27239 NO CLASH, using fixed ground order
27241 22282: Id : 2, {_}:
27246 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27247 (multiply (inverse (multiply ?4 ?5))
27250 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27254 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27256 22282: Id : 1, {_}:
27257 multiply (inverse a1) a1 =>= multiply (inverse b1) b1
27258 [] by prove_these_axioms_1
27262 22282: b1 2 0 2 1,1,3
27263 22282: multiply 12 2 2 0,2
27264 22282: inverse 9 1 2 0,1,2
27265 22282: a1 2 0 2 1,1,2
27266 % SZS status Timeout for GRP505-1.p
27267 NO CLASH, using fixed ground order
27269 22298: Id : 2, {_}:
27274 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27275 (multiply (inverse (multiply ?4 ?5))
27278 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27282 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27284 22298: Id : 1, {_}:
27285 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
27286 [] by prove_these_axioms_3
27290 22298: inverse 7 1 0
27291 22298: c3 2 0 2 2,2
27292 22298: multiply 14 2 4 0,2
27293 22298: b3 2 0 2 2,1,2
27294 22298: a3 2 0 2 1,1,2
27295 NO CLASH, using fixed ground order
27297 22299: Id : 2, {_}:
27302 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27303 (multiply (inverse (multiply ?4 ?5))
27306 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27310 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27312 22299: Id : 1, {_}:
27313 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
27314 [] by prove_these_axioms_3
27318 22299: inverse 7 1 0
27319 22299: c3 2 0 2 2,2
27320 22299: multiply 14 2 4 0,2
27321 22299: b3 2 0 2 2,1,2
27322 22299: a3 2 0 2 1,1,2
27323 NO CLASH, using fixed ground order
27325 22300: Id : 2, {_}:
27330 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27331 (multiply (inverse (multiply ?4 ?5))
27334 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27338 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27340 22300: Id : 1, {_}:
27341 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
27342 [] by prove_these_axioms_3
27346 22300: inverse 7 1 0
27347 22300: c3 2 0 2 2,2
27348 22300: multiply 14 2 4 0,2
27349 22300: b3 2 0 2 2,1,2
27350 22300: a3 2 0 2 1,1,2
27351 % SZS status Timeout for GRP507-1.p
27352 NO CLASH, using fixed ground order
27354 22343: Id : 2, {_}:
27359 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27360 (multiply (inverse (multiply ?4 ?5))
27363 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27367 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27369 22343: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
27373 22343: inverse 7 1 0
27374 22343: multiply 12 2 2 0,2
27377 NO CLASH, using fixed ground order
27379 22344: Id : 2, {_}:
27384 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27385 (multiply (inverse (multiply ?4 ?5))
27388 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27392 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27394 22344: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
27398 22344: inverse 7 1 0
27399 22344: multiply 12 2 2 0,2
27402 NO CLASH, using fixed ground order
27404 22345: Id : 2, {_}:
27409 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
27410 (multiply (inverse (multiply ?4 ?5))
27413 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
27417 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27419 22345: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
27423 22345: inverse 7 1 0
27424 22345: multiply 12 2 2 0,2
27427 % SZS status Timeout for GRP508-1.p
27428 NO CLASH, using fixed ground order
27430 22381: Id : 2, {_}:
27431 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27433 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
27437 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
27440 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
27441 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
27442 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27445 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
27447 22381: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
27452 22381: meet 19 2 1 0,2
27454 NO CLASH, using fixed ground order
27456 22382: Id : 2, {_}:
27457 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27459 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
27463 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
27466 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
27467 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
27468 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27471 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
27473 22382: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
27478 22382: meet 19 2 1 0,2
27480 NO CLASH, using fixed ground order
27482 22383: Id : 2, {_}:
27483 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27485 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
27489 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
27492 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
27493 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
27494 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27497 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
27499 22383: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
27504 22383: meet 19 2 1 0,2
27506 % SZS status Timeout for LAT080-1.p
27507 NO CLASH, using fixed ground order
27509 22413: Id : 2, {_}:
27510 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27512 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
27516 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
27519 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
27520 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
27521 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27524 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
27526 22413: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
27531 22413: join 21 2 1 0,2
27533 NO CLASH, using fixed ground order
27535 22414: Id : 2, {_}:
27536 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27538 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
27542 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
27545 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
27546 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
27547 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27550 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
27552 22414: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
27557 22414: join 21 2 1 0,2
27559 NO CLASH, using fixed ground order
27561 22415: Id : 2, {_}:
27562 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27564 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
27568 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
27571 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
27572 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
27573 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27576 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
27578 22415: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
27583 22415: join 21 2 1 0,2
27585 % SZS status Timeout for LAT083-1.p
27586 NO CLASH, using fixed ground order
27588 22432: Id : 2, {_}:
27589 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27591 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27593 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27595 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27596 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27597 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27600 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27602 22432: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
27607 22432: meet 19 2 1 0,2
27609 NO CLASH, using fixed ground order
27611 22434: Id : 2, {_}:
27612 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27614 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27616 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27618 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27619 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27620 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27623 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27625 22434: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
27630 22434: meet 19 2 1 0,2
27632 NO CLASH, using fixed ground order
27634 22433: Id : 2, {_}:
27635 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27637 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27639 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27641 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27642 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27643 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27646 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27648 22433: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
27653 22433: meet 19 2 1 0,2
27655 % SZS status Timeout for LAT092-1.p
27656 NO CLASH, using fixed ground order
27658 22466: Id : 2, {_}:
27659 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27661 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27663 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27665 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27666 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27667 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27670 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27672 22466: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
27677 22466: meet 20 2 2 0,2
27680 NO CLASH, using fixed ground order
27682 22467: Id : 2, {_}:
27683 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27685 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27687 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27689 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27690 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27691 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27694 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27696 22467: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
27701 22467: meet 20 2 2 0,2
27704 NO CLASH, using fixed ground order
27706 22468: Id : 2, {_}:
27707 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27709 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27711 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27713 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27714 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27715 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27718 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27720 22468: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
27725 22468: meet 20 2 2 0,2
27728 % SZS status Timeout for LAT093-1.p
27729 NO CLASH, using fixed ground order
27731 22493: Id : 2, {_}:
27732 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27734 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27736 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27738 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27739 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27740 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27743 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27745 22493: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
27750 22493: join 19 2 1 0,2
27752 NO CLASH, using fixed ground order
27754 22494: Id : 2, {_}:
27755 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27757 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27759 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27761 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27762 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27763 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27766 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27768 22494: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
27773 22494: join 19 2 1 0,2
27775 NO CLASH, using fixed ground order
27777 22495: Id : 2, {_}:
27778 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27780 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27782 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27784 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27785 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27786 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27789 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27791 22495: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
27796 22495: join 19 2 1 0,2
27798 % SZS status Timeout for LAT094-1.p
27799 NO CLASH, using fixed ground order
27801 22522: Id : 2, {_}:
27802 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27804 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27806 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27808 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27809 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27810 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27813 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27815 22522: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
27820 22522: join 20 2 2 0,2
27823 NO CLASH, using fixed ground order
27825 22523: Id : 2, {_}:
27826 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27828 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27830 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27832 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27833 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27834 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27837 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27839 22523: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
27844 22523: join 20 2 2 0,2
27847 NO CLASH, using fixed ground order
27849 22524: Id : 2, {_}:
27850 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27852 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27854 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27856 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27857 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27858 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27861 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27863 22524: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
27868 22524: join 20 2 2 0,2
27871 % SZS status Timeout for LAT095-1.p
27872 NO CLASH, using fixed ground order
27874 22540: Id : 2, {_}:
27875 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27877 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27879 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27881 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27882 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27883 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27886 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27888 22540: Id : 1, {_}:
27889 meet (meet (join a b) (join c b)) b =>= b
27890 [] by prove_wal_axioms_5
27894 22540: meet 20 2 2 0,2
27895 22540: c 1 0 1 1,2,1,2
27896 22540: join 20 2 2 0,1,1,2
27897 22540: b 4 0 4 2,1,1,2
27898 22540: a 1 0 1 1,1,1,2
27899 NO CLASH, using fixed ground order
27901 22541: Id : 2, {_}:
27902 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27904 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27906 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27908 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27909 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27910 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27913 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27915 22541: Id : 1, {_}:
27916 meet (meet (join a b) (join c b)) b =>= b
27917 [] by prove_wal_axioms_5
27921 22541: meet 20 2 2 0,2
27922 22541: c 1 0 1 1,2,1,2
27923 22541: join 20 2 2 0,1,1,2
27924 22541: b 4 0 4 2,1,1,2
27925 22541: a 1 0 1 1,1,1,2
27926 NO CLASH, using fixed ground order
27928 22542: Id : 2, {_}:
27929 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27931 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27933 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27935 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27936 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27937 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27940 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27942 22542: Id : 1, {_}:
27943 meet (meet (join a b) (join c b)) b =>= b
27944 [] by prove_wal_axioms_5
27948 22542: meet 20 2 2 0,2
27949 22542: c 1 0 1 1,2,1,2
27950 22542: join 20 2 2 0,1,1,2
27951 22542: b 4 0 4 2,1,1,2
27952 22542: a 1 0 1 1,1,1,2
27953 % SZS status Timeout for LAT096-1.p
27954 NO CLASH, using fixed ground order
27956 22569: Id : 2, {_}:
27957 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27959 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27961 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27963 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27964 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27965 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27968 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27970 22569: Id : 1, {_}:
27971 join (join (meet a b) (meet c b)) b =>= b
27972 [] by prove_wal_axioms_6
27976 22569: join 20 2 2 0,2
27977 22569: c 1 0 1 1,2,1,2
27978 22569: meet 20 2 2 0,1,1,2
27979 22569: b 4 0 4 2,1,1,2
27980 22569: a 1 0 1 1,1,1,2
27981 NO CLASH, using fixed ground order
27983 22570: Id : 2, {_}:
27984 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
27986 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
27988 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
27990 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
27991 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
27992 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
27995 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
27997 22570: Id : 1, {_}:
27998 join (join (meet a b) (meet c b)) b =>= b
27999 [] by prove_wal_axioms_6
28003 22570: join 20 2 2 0,2
28004 22570: c 1 0 1 1,2,1,2
28005 22570: meet 20 2 2 0,1,1,2
28006 22570: b 4 0 4 2,1,1,2
28007 22570: a 1 0 1 1,1,1,2
28008 NO CLASH, using fixed ground order
28010 22571: Id : 2, {_}:
28011 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
28013 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
28015 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
28017 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
28018 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
28019 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
28022 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
28024 22571: Id : 1, {_}:
28025 join (join (meet a b) (meet c b)) b =>= b
28026 [] by prove_wal_axioms_6
28030 22571: join 20 2 2 0,2
28031 22571: c 1 0 1 1,2,1,2
28032 22571: meet 20 2 2 0,1,1,2
28033 22571: b 4 0 4 2,1,1,2
28034 22571: a 1 0 1 1,1,1,2
28035 % SZS status Timeout for LAT097-1.p
28036 NO CLASH, using fixed ground order
28038 22740: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28039 22740: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28040 22740: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28041 22740: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28042 22740: Id : 6, {_}:
28043 meet ?12 ?13 =?= meet ?13 ?12
28044 [13, 12] by commutativity_of_meet ?12 ?13
28045 22740: Id : 7, {_}:
28046 join ?15 ?16 =?= join ?16 ?15
28047 [16, 15] by commutativity_of_join ?15 ?16
28048 22740: Id : 8, {_}:
28049 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
28050 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28051 22740: Id : 9, {_}:
28052 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
28053 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28054 22740: Id : 10, {_}:
28055 meet ?26 (join ?27 (meet ?28 ?29))
28057 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
28058 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
28060 22740: Id : 1, {_}:
28061 meet a (join b (meet a (meet c d)))
28063 meet a (join b (meet c (meet d (join a (meet b d)))))
28068 22740: join 16 2 3 0,2,2
28069 22740: meet 21 2 7 0,2
28070 22740: d 3 0 3 2,2,2,2,2
28071 22740: c 2 0 2 1,2,2,2,2
28072 22740: b 3 0 3 1,2,2
28074 NO CLASH, using fixed ground order
28076 22742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28077 22742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28078 22742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28079 22742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28080 22742: Id : 6, {_}:
28081 meet ?12 ?13 =?= meet ?13 ?12
28082 [13, 12] by commutativity_of_meet ?12 ?13
28083 22742: Id : 7, {_}:
28084 join ?15 ?16 =?= join ?16 ?15
28085 [16, 15] by commutativity_of_join ?15 ?16
28086 22742: Id : 8, {_}:
28087 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28088 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28089 22742: Id : 9, {_}:
28090 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28091 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28092 22742: Id : 10, {_}:
28093 meet ?26 (join ?27 (meet ?28 ?29))
28095 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
28096 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
28098 22742: Id : 1, {_}:
28099 meet a (join b (meet a (meet c d)))
28101 meet a (join b (meet c (meet d (join a (meet b d)))))
28106 22742: join 16 2 3 0,2,2
28107 22742: meet 21 2 7 0,2
28108 22742: d 3 0 3 2,2,2,2,2
28109 22742: c 2 0 2 1,2,2,2,2
28110 22742: b 3 0 3 1,2,2
28112 NO CLASH, using fixed ground order
28114 22741: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28115 22741: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28116 22741: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28117 22741: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28118 22741: Id : 6, {_}:
28119 meet ?12 ?13 =?= meet ?13 ?12
28120 [13, 12] by commutativity_of_meet ?12 ?13
28121 22741: Id : 7, {_}:
28122 join ?15 ?16 =?= join ?16 ?15
28123 [16, 15] by commutativity_of_join ?15 ?16
28124 22741: Id : 8, {_}:
28125 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28126 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28127 22741: Id : 9, {_}:
28128 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28129 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28130 22741: Id : 10, {_}:
28131 meet ?26 (join ?27 (meet ?28 ?29))
28133 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
28134 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
28136 22741: Id : 1, {_}:
28137 meet a (join b (meet a (meet c d)))
28139 meet a (join b (meet c (meet d (join a (meet b d)))))
28144 22741: join 16 2 3 0,2,2
28145 22741: meet 21 2 7 0,2
28146 22741: d 3 0 3 2,2,2,2,2
28147 22741: c 2 0 2 1,2,2,2,2
28148 22741: b 3 0 3 1,2,2
28150 % SZS status Timeout for LAT146-1.p
28151 NO CLASH, using fixed ground order
28153 22773: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28154 22773: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28155 22773: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28156 22773: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28157 22773: Id : 6, {_}:
28158 meet ?12 ?13 =?= meet ?13 ?12
28159 [13, 12] by commutativity_of_meet ?12 ?13
28160 22773: Id : 7, {_}:
28161 join ?15 ?16 =?= join ?16 ?15
28162 [16, 15] by commutativity_of_join ?15 ?16
28163 22773: Id : 8, {_}:
28164 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
28165 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28166 22773: Id : 9, {_}:
28167 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
28168 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28169 22773: Id : 10, {_}:
28170 meet ?26 (join ?27 (meet ?28 ?29))
28172 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
28173 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
28175 22773: Id : 1, {_}:
28176 meet a (join b (meet a c))
28178 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
28183 22773: join 17 2 4 0,2,2
28184 22773: meet 20 2 6 0,2
28185 22773: c 2 0 2 2,2,2,2
28186 22773: b 4 0 4 1,2,2
28188 NO CLASH, using fixed ground order
28190 22774: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28191 22774: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28192 22774: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28193 22774: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28194 22774: Id : 6, {_}:
28195 meet ?12 ?13 =?= meet ?13 ?12
28196 [13, 12] by commutativity_of_meet ?12 ?13
28197 22774: Id : 7, {_}:
28198 join ?15 ?16 =?= join ?16 ?15
28199 [16, 15] by commutativity_of_join ?15 ?16
28200 22774: Id : 8, {_}:
28201 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28202 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28203 22774: Id : 9, {_}:
28204 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28205 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28206 22774: Id : 10, {_}:
28207 meet ?26 (join ?27 (meet ?28 ?29))
28209 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
28210 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
28212 22774: Id : 1, {_}:
28213 meet a (join b (meet a c))
28215 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
28220 22774: join 17 2 4 0,2,2
28221 22774: meet 20 2 6 0,2
28222 22774: c 2 0 2 2,2,2,2
28223 22774: b 4 0 4 1,2,2
28225 NO CLASH, using fixed ground order
28227 22775: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28228 22775: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28229 22775: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28230 22775: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28231 22775: Id : 6, {_}:
28232 meet ?12 ?13 =?= meet ?13 ?12
28233 [13, 12] by commutativity_of_meet ?12 ?13
28234 22775: Id : 7, {_}:
28235 join ?15 ?16 =?= join ?16 ?15
28236 [16, 15] by commutativity_of_join ?15 ?16
28237 22775: Id : 8, {_}:
28238 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28239 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28240 22775: Id : 9, {_}:
28241 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28242 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28243 22775: Id : 10, {_}:
28244 meet ?26 (join ?27 (meet ?28 ?29))
28246 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
28247 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
28249 22775: Id : 1, {_}:
28250 meet a (join b (meet a c))
28252 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
28257 22775: join 17 2 4 0,2,2
28258 22775: meet 20 2 6 0,2
28259 22775: c 2 0 2 2,2,2,2
28260 22775: b 4 0 4 1,2,2
28262 % SZS status Timeout for LAT148-1.p
28263 NO CLASH, using fixed ground order
28265 22791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28266 22791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28267 22791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28268 22791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28269 22791: Id : 6, {_}:
28270 meet ?12 ?13 =?= meet ?13 ?12
28271 [13, 12] by commutativity_of_meet ?12 ?13
28272 22791: Id : 7, {_}:
28273 join ?15 ?16 =?= join ?16 ?15
28274 [16, 15] by commutativity_of_join ?15 ?16
28275 22791: Id : 8, {_}:
28276 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
28277 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28278 22791: Id : 9, {_}:
28279 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
28280 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28281 22791: Id : 10, {_}:
28282 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
28284 meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
28285 [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
28287 22791: Id : 1, {_}:
28288 meet a (join b (meet a c))
28290 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
28295 22791: join 18 2 4 0,2,2
28296 22791: meet 20 2 6 0,2
28297 22791: c 3 0 3 2,2,2,2
28298 22791: b 3 0 3 1,2,2
28300 NO CLASH, using fixed ground order
28302 22792: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28303 22792: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28304 22792: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28305 22792: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28306 22792: Id : 6, {_}:
28307 meet ?12 ?13 =?= meet ?13 ?12
28308 [13, 12] by commutativity_of_meet ?12 ?13
28309 22792: Id : 7, {_}:
28310 join ?15 ?16 =?= join ?16 ?15
28311 [16, 15] by commutativity_of_join ?15 ?16
28312 22792: Id : 8, {_}:
28313 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28314 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28315 22792: Id : 9, {_}:
28316 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28317 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28318 22792: Id : 10, {_}:
28319 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
28321 meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
28322 [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
28324 22792: Id : 1, {_}:
28325 meet a (join b (meet a c))
28327 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
28332 22792: join 18 2 4 0,2,2
28333 22792: meet 20 2 6 0,2
28334 22792: c 3 0 3 2,2,2,2
28335 22792: b 3 0 3 1,2,2
28337 NO CLASH, using fixed ground order
28339 22793: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28340 22793: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28341 22793: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28342 22793: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28343 22793: Id : 6, {_}:
28344 meet ?12 ?13 =?= meet ?13 ?12
28345 [13, 12] by commutativity_of_meet ?12 ?13
28346 22793: Id : 7, {_}:
28347 join ?15 ?16 =?= join ?16 ?15
28348 [16, 15] by commutativity_of_join ?15 ?16
28349 22793: Id : 8, {_}:
28350 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28351 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28352 22793: Id : 9, {_}:
28353 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28354 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28355 22793: Id : 10, {_}:
28356 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
28358 meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
28359 [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
28361 22793: Id : 1, {_}:
28362 meet a (join b (meet a c))
28364 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
28369 22793: join 18 2 4 0,2,2
28370 22793: meet 20 2 6 0,2
28371 22793: c 3 0 3 2,2,2,2
28372 22793: b 3 0 3 1,2,2
28374 % SZS status Timeout for LAT156-1.p
28375 NO CLASH, using fixed ground order
28376 NO CLASH, using fixed ground order
28378 22830: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28379 22830: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28380 22830: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28381 22830: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28382 22830: Id : 6, {_}:
28383 meet ?12 ?13 =?= meet ?13 ?12
28384 [13, 12] by commutativity_of_meet ?12 ?13
28385 22830: Id : 7, {_}:
28386 join ?15 ?16 =?= join ?16 ?15
28387 [16, 15] by commutativity_of_join ?15 ?16
28388 22830: Id : 8, {_}:
28389 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28390 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28391 22830: Id : 9, {_}:
28392 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28393 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28394 22830: Id : 10, {_}:
28395 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
28397 meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
28398 [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
28400 22830: Id : 1, {_}:
28401 meet a (join b (meet c (join a d)))
28403 meet a (join b (join (meet a c) (meet c d)))
28408 22830: meet 19 2 5 0,2
28409 22830: join 18 2 4 0,2,2
28410 22830: d 2 0 2 2,2,2,2,2
28411 22830: c 3 0 3 1,2,2,2
28412 22830: b 2 0 2 1,2,2
28414 NO CLASH, using fixed ground order
28416 22831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28417 22831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28418 22831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28419 22831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28420 22831: Id : 6, {_}:
28421 meet ?12 ?13 =?= meet ?13 ?12
28422 [13, 12] by commutativity_of_meet ?12 ?13
28423 22831: Id : 7, {_}:
28424 join ?15 ?16 =?= join ?16 ?15
28425 [16, 15] by commutativity_of_join ?15 ?16
28426 22831: Id : 8, {_}:
28427 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
28428 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28429 22831: Id : 9, {_}:
28430 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
28431 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28432 22831: Id : 10, {_}:
28433 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
28435 meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
28436 [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
28438 22831: Id : 1, {_}:
28439 meet a (join b (meet c (join a d)))
28441 meet a (join b (join (meet a c) (meet c d)))
28446 22831: meet 19 2 5 0,2
28447 22831: join 18 2 4 0,2,2
28448 22831: d 2 0 2 2,2,2,2,2
28449 22831: c 3 0 3 1,2,2,2
28450 22831: b 2 0 2 1,2,2
28453 22829: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
28454 22829: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
28455 22829: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
28456 22829: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
28457 22829: Id : 6, {_}:
28458 meet ?12 ?13 =?= meet ?13 ?12
28459 [13, 12] by commutativity_of_meet ?12 ?13
28460 22829: Id : 7, {_}:
28461 join ?15 ?16 =?= join ?16 ?15
28462 [16, 15] by commutativity_of_join ?15 ?16
28463 22829: Id : 8, {_}:
28464 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
28465 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
28466 22829: Id : 9, {_}:
28467 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
28468 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
28469 22829: Id : 10, {_}:
28470 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
28472 meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
28473 [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
28475 22829: Id : 1, {_}:
28476 meet a (join b (meet c (join a d)))
28478 meet a (join b (join (meet a c) (meet c d)))
28483 22829: meet 19 2 5 0,2
28484 22829: join 18 2 4 0,2,2
28485 22829: d 2 0 2 2,2,2,2,2
28486 22829: c 3 0 3 1,2,2,2
28487 22829: b 2 0 2 1,2,2
28489 % SZS status Timeout for LAT160-1.p
28490 NO CLASH, using fixed ground order
28492 22849: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
28493 22849: Id : 3, {_}:
28494 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
28497 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
28498 22849: Id : 4, {_}:
28499 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
28500 [9, 8] by wajsberg_3 ?8 ?9
28501 22849: Id : 5, {_}:
28502 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
28503 [12, 11] by wajsberg_4 ?11 ?12
28504 22849: Id : 6, {_}:
28505 or ?14 ?15 =<= implies (not ?14) ?15
28506 [15, 14] by or_definition ?14 ?15
28507 22849: Id : 7, {_}:
28508 or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
28509 [19, 18, 17] by or_associativity ?17 ?18 ?19
28510 22849: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
28511 22849: Id : 9, {_}:
28512 and ?24 ?25 =<= not (or (not ?24) (not ?25))
28513 [25, 24] by and_definition ?24 ?25
28514 22849: Id : 10, {_}:
28515 and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
28516 [29, 28, 27] by and_associativity ?27 ?28 ?29
28517 22849: Id : 11, {_}:
28518 and ?31 ?32 =?= and ?32 ?31
28519 [32, 31] by and_commutativity ?31 ?32
28520 22849: Id : 12, {_}:
28521 xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
28522 [35, 34] by xor_definition ?34 ?35
28523 22849: Id : 13, {_}:
28524 xor ?37 ?38 =?= xor ?38 ?37
28525 [38, 37] by xor_commutativity ?37 ?38
28526 22849: Id : 14, {_}:
28527 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
28528 [41, 40] by and_star_definition ?40 ?41
28529 22849: Id : 15, {_}:
28530 and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
28531 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
28532 22849: Id : 16, {_}:
28533 and_star ?47 ?48 =?= and_star ?48 ?47
28534 [48, 47] by and_star_commutativity ?47 ?48
28535 22849: Id : 17, {_}: not truth =>= falsehood [] by false_definition
28537 22849: Id : 1, {_}:
28538 and_star (xor (and_star (xor truth x) y) truth) y
28540 and_star (xor (and_star (xor truth y) x) truth) x
28541 [] by prove_alternative_wajsberg_axiom
28545 22849: falsehood 1 0 0
28549 22849: implies 14 2 0
28550 22849: and_star 11 2 4 0,2
28551 22849: y 3 0 3 2,1,1,2
28552 22849: xor 7 2 4 0,1,2
28553 22849: x 3 0 3 2,1,1,1,2
28554 22849: truth 8 0 4 1,1,1,1,2
28555 NO CLASH, using fixed ground order
28557 22850: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
28558 22850: Id : 3, {_}:
28559 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
28562 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
28563 22850: Id : 4, {_}:
28564 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
28565 [9, 8] by wajsberg_3 ?8 ?9
28566 22850: Id : 5, {_}:
28567 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
28568 [12, 11] by wajsberg_4 ?11 ?12
28569 22850: Id : 6, {_}:
28570 or ?14 ?15 =<= implies (not ?14) ?15
28571 [15, 14] by or_definition ?14 ?15
28572 22850: Id : 7, {_}:
28573 or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
28574 [19, 18, 17] by or_associativity ?17 ?18 ?19
28575 22850: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
28576 22850: Id : 9, {_}:
28577 and ?24 ?25 =<= not (or (not ?24) (not ?25))
28578 [25, 24] by and_definition ?24 ?25
28579 22850: Id : 10, {_}:
28580 and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
28581 [29, 28, 27] by and_associativity ?27 ?28 ?29
28582 22850: Id : 11, {_}:
28583 and ?31 ?32 =?= and ?32 ?31
28584 [32, 31] by and_commutativity ?31 ?32
28585 22850: Id : 12, {_}:
28586 xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
28587 [35, 34] by xor_definition ?34 ?35
28588 22850: Id : 13, {_}:
28589 xor ?37 ?38 =?= xor ?38 ?37
28590 [38, 37] by xor_commutativity ?37 ?38
28591 22850: Id : 14, {_}:
28592 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
28593 [41, 40] by and_star_definition ?40 ?41
28594 22850: Id : 15, {_}:
28595 and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
28596 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
28597 22850: Id : 16, {_}:
28598 and_star ?47 ?48 =?= and_star ?48 ?47
28599 [48, 47] by and_star_commutativity ?47 ?48
28600 22850: Id : 17, {_}: not truth =>= falsehood [] by false_definition
28602 22850: Id : 1, {_}:
28603 and_star (xor (and_star (xor truth x) y) truth) y
28605 and_star (xor (and_star (xor truth y) x) truth) x
28606 [] by prove_alternative_wajsberg_axiom
28610 22850: falsehood 1 0 0
28614 22850: implies 14 2 0
28615 22850: and_star 11 2 4 0,2
28616 22850: y 3 0 3 2,1,1,2
28617 22850: xor 7 2 4 0,1,2
28618 22850: x 3 0 3 2,1,1,1,2
28619 22850: truth 8 0 4 1,1,1,1,2
28620 NO CLASH, using fixed ground order
28622 22851: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
28623 22851: Id : 3, {_}:
28624 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
28627 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
28628 22851: Id : 4, {_}:
28629 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
28630 [9, 8] by wajsberg_3 ?8 ?9
28631 22851: Id : 5, {_}:
28632 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
28633 [12, 11] by wajsberg_4 ?11 ?12
28634 22851: Id : 6, {_}:
28635 or ?14 ?15 =<= implies (not ?14) ?15
28636 [15, 14] by or_definition ?14 ?15
28637 22851: Id : 7, {_}:
28638 or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
28639 [19, 18, 17] by or_associativity ?17 ?18 ?19
28640 22851: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
28641 22851: Id : 9, {_}:
28642 and ?24 ?25 =<= not (or (not ?24) (not ?25))
28643 [25, 24] by and_definition ?24 ?25
28644 22851: Id : 10, {_}:
28645 and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
28646 [29, 28, 27] by and_associativity ?27 ?28 ?29
28647 22851: Id : 11, {_}:
28648 and ?31 ?32 =?= and ?32 ?31
28649 [32, 31] by and_commutativity ?31 ?32
28650 22851: Id : 12, {_}:
28651 xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35)
28652 [35, 34] by xor_definition ?34 ?35
28653 22851: Id : 13, {_}:
28654 xor ?37 ?38 =?= xor ?38 ?37
28655 [38, 37] by xor_commutativity ?37 ?38
28656 22851: Id : 14, {_}:
28657 and_star ?40 ?41 =>= not (or (not ?40) (not ?41))
28658 [41, 40] by and_star_definition ?40 ?41
28659 22851: Id : 15, {_}:
28660 and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
28661 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
28662 22851: Id : 16, {_}:
28663 and_star ?47 ?48 =?= and_star ?48 ?47
28664 [48, 47] by and_star_commutativity ?47 ?48
28665 22851: Id : 17, {_}: not truth =>= falsehood [] by false_definition
28667 22851: Id : 1, {_}:
28668 and_star (xor (and_star (xor truth x) y) truth) y
28670 and_star (xor (and_star (xor truth y) x) truth) x
28671 [] by prove_alternative_wajsberg_axiom
28675 22851: falsehood 1 0 0
28679 22851: implies 14 2 0
28680 22851: and_star 11 2 4 0,2
28681 22851: y 3 0 3 2,1,1,2
28682 22851: xor 7 2 4 0,1,2
28683 22851: x 3 0 3 2,1,1,1,2
28684 22851: truth 8 0 4 1,1,1,1,2
28685 % SZS status Timeout for LCL160-1.p
28686 NO CLASH, using fixed ground order
28688 22879: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
28689 22879: Id : 3, {_}:
28690 add ?4 (additive_inverse ?4) =>= additive_identity
28691 [4] by right_additive_inverse ?4
28692 22879: Id : 4, {_}:
28693 multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
28694 [8, 7, 6] by distribute1 ?6 ?7 ?8
28695 22879: Id : 5, {_}:
28696 multiply (add ?10 ?11) ?12
28698 add (multiply ?10 ?12) (multiply ?11 ?12)
28699 [12, 11, 10] by distribute2 ?10 ?11 ?12
28700 22879: Id : 6, {_}:
28701 add (add ?14 ?15) ?16 =?= add ?14 (add ?15 ?16)
28702 [16, 15, 14] by associative_addition ?14 ?15 ?16
28703 22879: Id : 7, {_}:
28704 add ?18 ?19 =?= add ?19 ?18
28705 [19, 18] by commutative_addition ?18 ?19
28706 22879: Id : 8, {_}:
28707 multiply (multiply ?21 ?22) ?23 =?= multiply ?21 (multiply ?22 ?23)
28708 [23, 22, 21] by associative_multiplication ?21 ?22 ?23
28709 22879: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
28711 22879: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
28715 22879: additive_inverse 1 1 0
28717 22879: additive_identity 2 0 0
28718 22879: multiply 14 2 2 0,2
28721 NO CLASH, using fixed ground order
28723 22880: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
28724 22880: Id : 3, {_}:
28725 add ?4 (additive_inverse ?4) =>= additive_identity
28726 [4] by right_additive_inverse ?4
28727 22880: Id : 4, {_}:
28728 multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
28729 [8, 7, 6] by distribute1 ?6 ?7 ?8
28730 22880: Id : 5, {_}:
28731 multiply (add ?10 ?11) ?12
28733 add (multiply ?10 ?12) (multiply ?11 ?12)
28734 [12, 11, 10] by distribute2 ?10 ?11 ?12
28735 22880: Id : 6, {_}:
28736 add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
28737 [16, 15, 14] by associative_addition ?14 ?15 ?16
28738 22880: Id : 7, {_}:
28739 add ?18 ?19 =?= add ?19 ?18
28740 [19, 18] by commutative_addition ?18 ?19
28741 22880: Id : 8, {_}:
28742 multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
28743 [23, 22, 21] by associative_multiplication ?21 ?22 ?23
28744 22880: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
28746 22880: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
28750 22880: additive_inverse 1 1 0
28752 22880: additive_identity 2 0 0
28753 22880: multiply 14 2 2 0,2
28756 NO CLASH, using fixed ground order
28758 22881: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
28759 22881: Id : 3, {_}:
28760 add ?4 (additive_inverse ?4) =>= additive_identity
28761 [4] by right_additive_inverse ?4
28762 22881: Id : 4, {_}:
28763 multiply ?6 (add ?7 ?8) =>= add (multiply ?6 ?7) (multiply ?6 ?8)
28764 [8, 7, 6] by distribute1 ?6 ?7 ?8
28765 22881: Id : 5, {_}:
28766 multiply (add ?10 ?11) ?12
28768 add (multiply ?10 ?12) (multiply ?11 ?12)
28769 [12, 11, 10] by distribute2 ?10 ?11 ?12
28770 22881: Id : 6, {_}:
28771 add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
28772 [16, 15, 14] by associative_addition ?14 ?15 ?16
28773 22881: Id : 7, {_}:
28774 add ?18 ?19 =?= add ?19 ?18
28775 [19, 18] by commutative_addition ?18 ?19
28776 22881: Id : 8, {_}:
28777 multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
28778 [23, 22, 21] by associative_multiplication ?21 ?22 ?23
28779 22881: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
28781 22881: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
28785 22881: additive_inverse 1 1 0
28787 22881: additive_identity 2 0 0
28788 22881: multiply 14 2 2 0,2
28791 % SZS status Timeout for RNG009-5.p
28792 NO CLASH, using fixed ground order
28793 NO CLASH, using fixed ground order
28795 22919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
28796 22919: Id : 3, {_}:
28797 add ?4 additive_identity =>= ?4
28798 [4] by right_additive_identity ?4
28799 22919: Id : 4, {_}:
28800 add (additive_inverse ?6) ?6 =>= additive_identity
28801 [6] by left_additive_inverse ?6
28802 22919: Id : 5, {_}:
28803 add ?8 (additive_inverse ?8) =>= additive_identity
28804 [8] by right_additive_inverse ?8
28805 22919: Id : 6, {_}:
28806 add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
28807 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
28808 22919: Id : 7, {_}:
28809 add ?14 ?15 =?= add ?15 ?14
28810 [15, 14] by commutativity_for_addition ?14 ?15
28811 22919: Id : 8, {_}:
28812 multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
28813 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
28814 22919: Id : 9, {_}:
28815 multiply ?21 (add ?22 ?23)
28817 add (multiply ?21 ?22) (multiply ?21 ?23)
28818 [23, 22, 21] by distribute1 ?21 ?22 ?23
28819 22919: Id : 10, {_}:
28820 multiply (add ?25 ?26) ?27
28822 add (multiply ?25 ?27) (multiply ?26 ?27)
28823 [27, 26, 25] by distribute2 ?25 ?26 ?27
28824 22919: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
28825 22919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
28827 22919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
28831 22919: additive_inverse 2 1 0
28833 22919: additive_identity 4 0 0
28835 22919: multiply 14 2 1 0,2
28839 22918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
28840 22918: Id : 3, {_}:
28841 add ?4 additive_identity =>= ?4
28842 [4] by right_additive_identity ?4
28843 22918: Id : 4, {_}:
28844 add (additive_inverse ?6) ?6 =>= additive_identity
28845 [6] by left_additive_inverse ?6
28846 22918: Id : 5, {_}:
28847 add ?8 (additive_inverse ?8) =>= additive_identity
28848 [8] by right_additive_inverse ?8
28849 22918: Id : 6, {_}:
28850 add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
28851 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
28852 22918: Id : 7, {_}:
28853 add ?14 ?15 =?= add ?15 ?14
28854 [15, 14] by commutativity_for_addition ?14 ?15
28855 22918: Id : 8, {_}:
28856 multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
28857 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
28858 22918: Id : 9, {_}:
28859 multiply ?21 (add ?22 ?23)
28861 add (multiply ?21 ?22) (multiply ?21 ?23)
28862 [23, 22, 21] by distribute1 ?21 ?22 ?23
28863 22918: Id : 10, {_}:
28864 multiply (add ?25 ?26) ?27
28866 add (multiply ?25 ?27) (multiply ?26 ?27)
28867 [27, 26, 25] by distribute2 ?25 ?26 ?27
28868 22918: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
28869 22918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
28871 22918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
28875 22918: additive_inverse 2 1 0
28877 22918: additive_identity 4 0 0
28879 22918: multiply 14 2 1 0,2
28882 NO CLASH, using fixed ground order
28884 22920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
28885 22920: Id : 3, {_}:
28886 add ?4 additive_identity =>= ?4
28887 [4] by right_additive_identity ?4
28888 22920: Id : 4, {_}:
28889 add (additive_inverse ?6) ?6 =>= additive_identity
28890 [6] by left_additive_inverse ?6
28891 22920: Id : 5, {_}:
28892 add ?8 (additive_inverse ?8) =>= additive_identity
28893 [8] by right_additive_inverse ?8
28894 22920: Id : 6, {_}:
28895 add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
28896 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
28897 22920: Id : 7, {_}:
28898 add ?14 ?15 =?= add ?15 ?14
28899 [15, 14] by commutativity_for_addition ?14 ?15
28900 22920: Id : 8, {_}:
28901 multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
28902 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
28903 22920: Id : 9, {_}:
28904 multiply ?21 (add ?22 ?23)
28906 add (multiply ?21 ?22) (multiply ?21 ?23)
28907 [23, 22, 21] by distribute1 ?21 ?22 ?23
28908 22920: Id : 10, {_}:
28909 multiply (add ?25 ?26) ?27
28911 add (multiply ?25 ?27) (multiply ?26 ?27)
28912 [27, 26, 25] by distribute2 ?25 ?26 ?27
28913 22920: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
28914 22920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
28916 22920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
28920 22920: additive_inverse 2 1 0
28922 22920: additive_identity 4 0 0
28924 22920: multiply 14 2 1 0,2
28927 % SZS status Timeout for RNG009-7.p
28928 NO CLASH, using fixed ground order
28930 22947: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
28931 22947: Id : 3, {_}:
28932 add ?4 additive_identity =>= ?4
28933 [4] by right_additive_identity ?4
28934 22947: Id : 4, {_}:
28935 multiply additive_identity ?6 =>= additive_identity
28936 [6] by left_multiplicative_zero ?6
28937 22947: Id : 5, {_}:
28938 multiply ?8 additive_identity =>= additive_identity
28939 [8] by right_multiplicative_zero ?8
28940 22947: Id : 6, {_}:
28941 add (additive_inverse ?10) ?10 =>= additive_identity
28942 [10] by left_additive_inverse ?10
28943 22947: Id : 7, {_}:
28944 add ?12 (additive_inverse ?12) =>= additive_identity
28945 [12] by right_additive_inverse ?12
28946 22947: Id : 8, {_}:
28947 additive_inverse (additive_inverse ?14) =>= ?14
28948 [14] by additive_inverse_additive_inverse ?14
28949 22947: Id : 9, {_}:
28950 multiply ?16 (add ?17 ?18)
28952 add (multiply ?16 ?17) (multiply ?16 ?18)
28953 [18, 17, 16] by distribute1 ?16 ?17 ?18
28954 22947: Id : 10, {_}:
28955 multiply (add ?20 ?21) ?22
28957 add (multiply ?20 ?22) (multiply ?21 ?22)
28958 [22, 21, 20] by distribute2 ?20 ?21 ?22
28959 22947: Id : 11, {_}:
28960 add ?24 ?25 =?= add ?25 ?24
28961 [25, 24] by commutativity_for_addition ?24 ?25
28962 22947: Id : 12, {_}:
28963 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
28964 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
28965 22947: Id : 13, {_}:
28966 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
28967 [32, 31] by right_alternative ?31 ?32
28968 22947: Id : 14, {_}:
28969 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
28970 [35, 34] by left_alternative ?34 ?35
28971 22947: Id : 15, {_}:
28972 associator ?37 ?38 ?39
28974 add (multiply (multiply ?37 ?38) ?39)
28975 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
28976 [39, 38, 37] by associator ?37 ?38 ?39
28977 22947: Id : 16, {_}:
28980 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
28981 [42, 41] by commutator ?41 ?42
28983 22947: Id : 1, {_}:
28985 (add (associator (multiply a b) c d)
28986 (associator a b (multiply c d)))
28989 (add (associator a (multiply b c) d)
28990 (multiply a (associator b c d)))
28991 (multiply (associator a b c) d)))
28994 [] by prove_teichmuller_identity
28998 22947: commutator 1 2 0
28999 22947: additive_identity 9 0 1 3
29000 22947: additive_inverse 7 1 1 0,2,2
29001 22947: add 20 2 4 0,2
29002 22947: associator 6 3 5 0,1,1,2
29003 22947: d 5 0 5 3,1,1,2
29004 22947: c 5 0 5 2,1,1,2
29005 22947: multiply 27 2 5 0,1,1,1,2
29006 22947: b 5 0 5 2,1,1,1,2
29007 22947: a 5 0 5 1,1,1,1,2
29008 NO CLASH, using fixed ground order
29010 22948: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
29011 22948: Id : 3, {_}:
29012 add ?4 additive_identity =>= ?4
29013 [4] by right_additive_identity ?4
29014 22948: Id : 4, {_}:
29015 multiply additive_identity ?6 =>= additive_identity
29016 [6] by left_multiplicative_zero ?6
29017 22948: Id : 5, {_}:
29018 multiply ?8 additive_identity =>= additive_identity
29019 [8] by right_multiplicative_zero ?8
29020 22948: Id : 6, {_}:
29021 add (additive_inverse ?10) ?10 =>= additive_identity
29022 [10] by left_additive_inverse ?10
29023 22948: Id : 7, {_}:
29024 add ?12 (additive_inverse ?12) =>= additive_identity
29025 [12] by right_additive_inverse ?12
29026 22948: Id : 8, {_}:
29027 additive_inverse (additive_inverse ?14) =>= ?14
29028 [14] by additive_inverse_additive_inverse ?14
29029 22948: Id : 9, {_}:
29030 multiply ?16 (add ?17 ?18)
29032 add (multiply ?16 ?17) (multiply ?16 ?18)
29033 [18, 17, 16] by distribute1 ?16 ?17 ?18
29034 22948: Id : 10, {_}:
29035 multiply (add ?20 ?21) ?22
29037 add (multiply ?20 ?22) (multiply ?21 ?22)
29038 [22, 21, 20] by distribute2 ?20 ?21 ?22
29039 22948: Id : 11, {_}:
29040 add ?24 ?25 =?= add ?25 ?24
29041 [25, 24] by commutativity_for_addition ?24 ?25
29042 22948: Id : 12, {_}:
29043 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
29044 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
29045 22948: Id : 13, {_}:
29046 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
29047 [32, 31] by right_alternative ?31 ?32
29048 22948: Id : 14, {_}:
29049 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
29050 [35, 34] by left_alternative ?34 ?35
29051 22948: Id : 15, {_}:
29052 associator ?37 ?38 ?39
29054 add (multiply (multiply ?37 ?38) ?39)
29055 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
29056 [39, 38, 37] by associator ?37 ?38 ?39
29057 22948: Id : 16, {_}:
29060 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
29061 [42, 41] by commutator ?41 ?42
29063 22948: Id : 1, {_}:
29065 (add (associator (multiply a b) c d)
29066 (associator a b (multiply c d)))
29069 (add (associator a (multiply b c) d)
29070 (multiply a (associator b c d)))
29071 (multiply (associator a b c) d)))
29074 [] by prove_teichmuller_identity
29078 22948: commutator 1 2 0
29079 22948: additive_identity 9 0 1 3
29080 22948: additive_inverse 7 1 1 0,2,2
29081 22948: add 20 2 4 0,2
29082 22948: associator 6 3 5 0,1,1,2
29083 22948: d 5 0 5 3,1,1,2
29084 22948: c 5 0 5 2,1,1,2
29085 22948: multiply 27 2 5 0,1,1,1,2
29086 22948: b 5 0 5 2,1,1,1,2
29087 22948: a 5 0 5 1,1,1,1,2
29088 NO CLASH, using fixed ground order
29090 22949: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
29091 22949: Id : 3, {_}:
29092 add ?4 additive_identity =>= ?4
29093 [4] by right_additive_identity ?4
29094 22949: Id : 4, {_}:
29095 multiply additive_identity ?6 =>= additive_identity
29096 [6] by left_multiplicative_zero ?6
29097 22949: Id : 5, {_}:
29098 multiply ?8 additive_identity =>= additive_identity
29099 [8] by right_multiplicative_zero ?8
29100 22949: Id : 6, {_}:
29101 add (additive_inverse ?10) ?10 =>= additive_identity
29102 [10] by left_additive_inverse ?10
29103 22949: Id : 7, {_}:
29104 add ?12 (additive_inverse ?12) =>= additive_identity
29105 [12] by right_additive_inverse ?12
29106 22949: Id : 8, {_}:
29107 additive_inverse (additive_inverse ?14) =>= ?14
29108 [14] by additive_inverse_additive_inverse ?14
29109 22949: Id : 9, {_}:
29110 multiply ?16 (add ?17 ?18)
29112 add (multiply ?16 ?17) (multiply ?16 ?18)
29113 [18, 17, 16] by distribute1 ?16 ?17 ?18
29114 22949: Id : 10, {_}:
29115 multiply (add ?20 ?21) ?22
29117 add (multiply ?20 ?22) (multiply ?21 ?22)
29118 [22, 21, 20] by distribute2 ?20 ?21 ?22
29119 22949: Id : 11, {_}:
29120 add ?24 ?25 =?= add ?25 ?24
29121 [25, 24] by commutativity_for_addition ?24 ?25
29122 22949: Id : 12, {_}:
29123 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
29124 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
29125 22949: Id : 13, {_}:
29126 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
29127 [32, 31] by right_alternative ?31 ?32
29128 22949: Id : 14, {_}:
29129 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
29130 [35, 34] by left_alternative ?34 ?35
29131 22949: Id : 15, {_}:
29132 associator ?37 ?38 ?39
29134 add (multiply (multiply ?37 ?38) ?39)
29135 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
29136 [39, 38, 37] by associator ?37 ?38 ?39
29137 22949: Id : 16, {_}:
29140 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
29141 [42, 41] by commutator ?41 ?42
29143 22949: Id : 1, {_}:
29145 (add (associator (multiply a b) c d)
29146 (associator a b (multiply c d)))
29149 (add (associator a (multiply b c) d)
29150 (multiply a (associator b c d)))
29151 (multiply (associator a b c) d)))
29154 [] by prove_teichmuller_identity
29158 22949: commutator 1 2 0
29159 22949: additive_identity 9 0 1 3
29160 22949: additive_inverse 7 1 1 0,2,2
29161 22949: add 20 2 4 0,2
29162 22949: associator 6 3 5 0,1,1,2
29163 22949: d 5 0 5 3,1,1,2
29164 22949: c 5 0 5 2,1,1,2
29165 22949: multiply 27 2 5 0,1,1,1,2
29166 22949: b 5 0 5 2,1,1,1,2
29167 22949: a 5 0 5 1,1,1,1,2
29168 % SZS status Timeout for RNG026-6.p
29169 NO CLASH, using fixed ground order
29171 NO CLASH, using fixed ground order
29173 22967: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
29174 22967: Id : 3, {_}:
29175 add ?4 additive_identity =>= ?4
29176 [4] by right_additive_identity ?4
29177 22967: Id : 4, {_}:
29178 multiply additive_identity ?6 =>= additive_identity
29179 [6] by left_multiplicative_zero ?6
29180 NO CLASH, using fixed ground order
29181 22966: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
29182 22966: Id : 3, {_}:
29183 add ?4 additive_identity =>= ?4
29184 [4] by right_additive_identity ?4
29185 22966: Id : 4, {_}:
29186 multiply additive_identity ?6 =>= additive_identity
29187 [6] by left_multiplicative_zero ?6
29188 22966: Id : 5, {_}:
29189 multiply ?8 additive_identity =>= additive_identity
29190 [8] by right_multiplicative_zero ?8
29191 22966: Id : 6, {_}:
29192 add (additive_inverse ?10) ?10 =>= additive_identity
29193 [10] by left_additive_inverse ?10
29194 22966: Id : 7, {_}:
29195 add ?12 (additive_inverse ?12) =>= additive_identity
29196 [12] by right_additive_inverse ?12
29197 22966: Id : 8, {_}:
29198 additive_inverse (additive_inverse ?14) =>= ?14
29199 [14] by additive_inverse_additive_inverse ?14
29201 22966: Id : 9, {_}:
29202 multiply ?16 (add ?17 ?18)
29204 add (multiply ?16 ?17) (multiply ?16 ?18)
29205 [18, 17, 16] by distribute1 ?16 ?17 ?18
29206 22966: Id : 10, {_}:
29207 multiply (add ?20 ?21) ?22
29209 add (multiply ?20 ?22) (multiply ?21 ?22)
29210 [22, 21, 20] by distribute2 ?20 ?21 ?22
29211 22966: Id : 11, {_}:
29212 add ?24 ?25 =?= add ?25 ?24
29213 [25, 24] by commutativity_for_addition ?24 ?25
29214 22965: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
29215 22965: Id : 3, {_}:
29216 add ?4 additive_identity =>= ?4
29217 [4] by right_additive_identity ?4
29218 22965: Id : 4, {_}:
29219 multiply additive_identity ?6 =>= additive_identity
29220 [6] by left_multiplicative_zero ?6
29221 22965: Id : 5, {_}:
29222 multiply ?8 additive_identity =>= additive_identity
29223 [8] by right_multiplicative_zero ?8
29224 22965: Id : 6, {_}:
29225 add (additive_inverse ?10) ?10 =>= additive_identity
29226 [10] by left_additive_inverse ?10
29227 22965: Id : 7, {_}:
29228 add ?12 (additive_inverse ?12) =>= additive_identity
29229 [12] by right_additive_inverse ?12
29230 22965: Id : 8, {_}:
29231 additive_inverse (additive_inverse ?14) =>= ?14
29232 [14] by additive_inverse_additive_inverse ?14
29233 22965: Id : 9, {_}:
29234 multiply ?16 (add ?17 ?18)
29236 add (multiply ?16 ?17) (multiply ?16 ?18)
29237 [18, 17, 16] by distribute1 ?16 ?17 ?18
29238 22965: Id : 10, {_}:
29239 multiply (add ?20 ?21) ?22
29241 add (multiply ?20 ?22) (multiply ?21 ?22)
29242 [22, 21, 20] by distribute2 ?20 ?21 ?22
29243 22965: Id : 11, {_}:
29244 add ?24 ?25 =?= add ?25 ?24
29245 [25, 24] by commutativity_for_addition ?24 ?25
29246 22965: Id : 12, {_}:
29247 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
29248 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
29249 22965: Id : 13, {_}:
29250 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
29251 [32, 31] by right_alternative ?31 ?32
29252 22965: Id : 14, {_}:
29253 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
29254 [35, 34] by left_alternative ?34 ?35
29255 22965: Id : 15, {_}:
29256 associator ?37 ?38 ?39
29258 add (multiply (multiply ?37 ?38) ?39)
29259 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
29260 [39, 38, 37] by associator ?37 ?38 ?39
29261 22965: Id : 16, {_}:
29264 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
29265 [42, 41] by commutator ?41 ?42
29266 22965: Id : 17, {_}:
29267 multiply (additive_inverse ?44) (additive_inverse ?45)
29270 [45, 44] by product_of_inverses ?44 ?45
29271 22965: Id : 18, {_}:
29272 multiply (additive_inverse ?47) ?48
29274 additive_inverse (multiply ?47 ?48)
29275 [48, 47] by inverse_product1 ?47 ?48
29276 22965: Id : 19, {_}:
29277 multiply ?50 (additive_inverse ?51)
29279 additive_inverse (multiply ?50 ?51)
29280 [51, 50] by inverse_product2 ?50 ?51
29281 22965: Id : 20, {_}:
29282 multiply ?53 (add ?54 (additive_inverse ?55))
29284 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
29285 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
29286 22965: Id : 21, {_}:
29287 multiply (add ?57 (additive_inverse ?58)) ?59
29289 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
29290 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
29291 22965: Id : 22, {_}:
29292 multiply (additive_inverse ?61) (add ?62 ?63)
29294 add (additive_inverse (multiply ?61 ?62))
29295 (additive_inverse (multiply ?61 ?63))
29296 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
29297 22965: Id : 23, {_}:
29298 multiply (add ?65 ?66) (additive_inverse ?67)
29300 add (additive_inverse (multiply ?65 ?67))
29301 (additive_inverse (multiply ?66 ?67))
29302 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
29304 22965: Id : 1, {_}:
29306 (add (associator (multiply a b) c d)
29307 (associator a b (multiply c d)))
29310 (add (associator a (multiply b c) d)
29311 (multiply a (associator b c d)))
29312 (multiply (associator a b c) d)))
29315 [] by prove_teichmuller_identity
29319 22965: commutator 1 2 0
29320 22965: additive_identity 9 0 1 3
29321 22965: additive_inverse 23 1 1 0,2,2
29322 22965: add 28 2 4 0,2
29323 22965: associator 6 3 5 0,1,1,2
29324 22965: d 5 0 5 3,1,1,2
29325 22965: c 5 0 5 2,1,1,2
29326 22965: multiply 45 2 5 0,1,1,1,2
29327 22965: b 5 0 5 2,1,1,1,2
29328 22965: a 5 0 5 1,1,1,1,2
29329 22967: Id : 5, {_}:
29330 multiply ?8 additive_identity =>= additive_identity
29331 [8] by right_multiplicative_zero ?8
29332 22966: Id : 12, {_}:
29333 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
29334 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
29335 22966: Id : 13, {_}:
29336 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
29337 [32, 31] by right_alternative ?31 ?32
29338 22966: Id : 14, {_}:
29339 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
29340 [35, 34] by left_alternative ?34 ?35
29341 22966: Id : 15, {_}:
29342 associator ?37 ?38 ?39
29344 add (multiply (multiply ?37 ?38) ?39)
29345 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
29346 [39, 38, 37] by associator ?37 ?38 ?39
29347 22966: Id : 16, {_}:
29350 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
29351 [42, 41] by commutator ?41 ?42
29352 22966: Id : 17, {_}:
29353 multiply (additive_inverse ?44) (additive_inverse ?45)
29356 [45, 44] by product_of_inverses ?44 ?45
29357 22966: Id : 18, {_}:
29358 multiply (additive_inverse ?47) ?48
29360 additive_inverse (multiply ?47 ?48)
29361 [48, 47] by inverse_product1 ?47 ?48
29362 22966: Id : 19, {_}:
29363 multiply ?50 (additive_inverse ?51)
29365 additive_inverse (multiply ?50 ?51)
29366 [51, 50] by inverse_product2 ?50 ?51
29367 22966: Id : 20, {_}:
29368 multiply ?53 (add ?54 (additive_inverse ?55))
29370 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
29371 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
29372 22966: Id : 21, {_}:
29373 multiply (add ?57 (additive_inverse ?58)) ?59
29375 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
29376 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
29377 22966: Id : 22, {_}:
29378 multiply (additive_inverse ?61) (add ?62 ?63)
29380 add (additive_inverse (multiply ?61 ?62))
29381 (additive_inverse (multiply ?61 ?63))
29382 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
29383 22966: Id : 23, {_}:
29384 multiply (add ?65 ?66) (additive_inverse ?67)
29386 add (additive_inverse (multiply ?65 ?67))
29387 (additive_inverse (multiply ?66 ?67))
29388 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
29390 22966: Id : 1, {_}:
29392 (add (associator (multiply a b) c d)
29393 (associator a b (multiply c d)))
29396 (add (associator a (multiply b c) d)
29397 (multiply a (associator b c d)))
29398 (multiply (associator a b c) d)))
29401 [] by prove_teichmuller_identity
29405 22966: commutator 1 2 0
29406 22966: additive_identity 9 0 1 3
29407 22966: additive_inverse 23 1 1 0,2,2
29408 22966: add 28 2 4 0,2
29409 22966: associator 6 3 5 0,1,1,2
29410 22966: d 5 0 5 3,1,1,2
29411 22966: c 5 0 5 2,1,1,2
29412 22966: multiply 45 2 5 0,1,1,1,2
29413 22966: b 5 0 5 2,1,1,1,2
29414 22966: a 5 0 5 1,1,1,1,2
29415 22967: Id : 6, {_}:
29416 add (additive_inverse ?10) ?10 =>= additive_identity
29417 [10] by left_additive_inverse ?10
29418 22967: Id : 7, {_}:
29419 add ?12 (additive_inverse ?12) =>= additive_identity
29420 [12] by right_additive_inverse ?12
29421 22967: Id : 8, {_}:
29422 additive_inverse (additive_inverse ?14) =>= ?14
29423 [14] by additive_inverse_additive_inverse ?14
29424 22967: Id : 9, {_}:
29425 multiply ?16 (add ?17 ?18)
29427 add (multiply ?16 ?17) (multiply ?16 ?18)
29428 [18, 17, 16] by distribute1 ?16 ?17 ?18
29429 22967: Id : 10, {_}:
29430 multiply (add ?20 ?21) ?22
29432 add (multiply ?20 ?22) (multiply ?21 ?22)
29433 [22, 21, 20] by distribute2 ?20 ?21 ?22
29434 22967: Id : 11, {_}:
29435 add ?24 ?25 =?= add ?25 ?24
29436 [25, 24] by commutativity_for_addition ?24 ?25
29437 22967: Id : 12, {_}:
29438 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
29439 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
29440 22967: Id : 13, {_}:
29441 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
29442 [32, 31] by right_alternative ?31 ?32
29443 22967: Id : 14, {_}:
29444 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
29445 [35, 34] by left_alternative ?34 ?35
29446 22967: Id : 15, {_}:
29447 associator ?37 ?38 ?39
29449 add (multiply (multiply ?37 ?38) ?39)
29450 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
29451 [39, 38, 37] by associator ?37 ?38 ?39
29452 22967: Id : 16, {_}:
29455 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
29456 [42, 41] by commutator ?41 ?42
29457 22967: Id : 17, {_}:
29458 multiply (additive_inverse ?44) (additive_inverse ?45)
29461 [45, 44] by product_of_inverses ?44 ?45
29462 22967: Id : 18, {_}:
29463 multiply (additive_inverse ?47) ?48
29465 additive_inverse (multiply ?47 ?48)
29466 [48, 47] by inverse_product1 ?47 ?48
29467 22967: Id : 19, {_}:
29468 multiply ?50 (additive_inverse ?51)
29470 additive_inverse (multiply ?50 ?51)
29471 [51, 50] by inverse_product2 ?50 ?51
29472 22967: Id : 20, {_}:
29473 multiply ?53 (add ?54 (additive_inverse ?55))
29475 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
29476 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
29477 22967: Id : 21, {_}:
29478 multiply (add ?57 (additive_inverse ?58)) ?59
29480 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
29481 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
29482 22967: Id : 22, {_}:
29483 multiply (additive_inverse ?61) (add ?62 ?63)
29485 add (additive_inverse (multiply ?61 ?62))
29486 (additive_inverse (multiply ?61 ?63))
29487 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
29488 22967: Id : 23, {_}:
29489 multiply (add ?65 ?66) (additive_inverse ?67)
29491 add (additive_inverse (multiply ?65 ?67))
29492 (additive_inverse (multiply ?66 ?67))
29493 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
29495 22967: Id : 1, {_}:
29497 (add (associator (multiply a b) c d)
29498 (associator a b (multiply c d)))
29501 (add (associator a (multiply b c) d)
29502 (multiply a (associator b c d)))
29503 (multiply (associator a b c) d)))
29506 [] by prove_teichmuller_identity
29510 22967: commutator 1 2 0
29511 22967: additive_identity 9 0 1 3
29512 22967: additive_inverse 23 1 1 0,2,2
29513 22967: add 28 2 4 0,2
29514 22967: associator 6 3 5 0,1,1,2
29515 22967: d 5 0 5 3,1,1,2
29516 22967: c 5 0 5 2,1,1,2
29517 22967: multiply 45 2 5 0,1,1,1,2
29518 22967: b 5 0 5 2,1,1,1,2
29519 22967: a 5 0 5 1,1,1,1,2
29520 % SZS status Timeout for RNG026-7.p
29521 NO CLASH, using fixed ground order
29523 22994: Id : 2, {_}:
29524 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
29525 [4, 3, 2] by sh_1 ?2 ?3 ?4
29527 22994: Id : 1, {_}:
29528 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
29529 [] by prove_meredith_2_basis_2
29533 22994: nand 12 2 6 0,2
29534 22994: c 2 0 2 2,2,2,2
29535 22994: b 3 0 3 1,2,2
29537 NO CLASH, using fixed ground order
29539 22995: Id : 2, {_}:
29540 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
29541 [4, 3, 2] by sh_1 ?2 ?3 ?4
29543 22995: Id : 1, {_}:
29544 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
29545 [] by prove_meredith_2_basis_2
29549 22995: nand 12 2 6 0,2
29550 22995: c 2 0 2 2,2,2,2
29551 22995: b 3 0 3 1,2,2
29553 NO CLASH, using fixed ground order
29555 22996: Id : 2, {_}:
29556 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
29557 [4, 3, 2] by sh_1 ?2 ?3 ?4
29559 22996: Id : 1, {_}:
29560 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
29561 [] by prove_meredith_2_basis_2
29565 22996: nand 12 2 6 0,2
29566 22996: c 2 0 2 2,2,2,2
29567 22996: b 3 0 3 1,2,2
29569 % SZS status Timeout for BOO076-1.p
29570 CLASH, statistics insufficient
29572 23012: Id : 2, {_}:
29573 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
29574 [5, 4, 3] by b_definition ?3 ?4 ?5
29575 23012: Id : 3, {_}:
29576 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
29577 [8, 7] by w_definition ?7 ?8
29579 23012: Id : 1, {_}:
29580 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
29581 [1] by prove_strong_fixed_point ?1
29587 23012: apply 12 2 3 0,2
29588 23012: f 3 1 3 0,2,2
29589 CLASH, statistics insufficient
29591 23013: Id : 2, {_}:
29592 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
29593 [5, 4, 3] by b_definition ?3 ?4 ?5
29594 23013: Id : 3, {_}:
29595 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
29596 [8, 7] by w_definition ?7 ?8
29598 23013: Id : 1, {_}:
29599 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
29600 [1] by prove_strong_fixed_point ?1
29606 23013: apply 12 2 3 0,2
29607 23013: f 3 1 3 0,2,2
29608 CLASH, statistics insufficient
29610 23014: Id : 2, {_}:
29611 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
29612 [5, 4, 3] by b_definition ?3 ?4 ?5
29613 23014: Id : 3, {_}:
29614 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
29615 [8, 7] by w_definition ?7 ?8
29617 23014: Id : 1, {_}:
29618 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
29619 [1] by prove_strong_fixed_point ?1
29625 23014: apply 12 2 3 0,2
29626 23014: f 3 1 3 0,2,2
29627 % SZS status Timeout for COL003-1.p
29628 CLASH, statistics insufficient
29630 23460: Id : 2, {_}:
29631 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
29632 [5, 4, 3] by b_definition ?3 ?4 ?5
29633 23460: Id : 3, {_}:
29634 apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
29635 [8, 7] by w1_definition ?7 ?8
29637 23460: Id : 1, {_}:
29638 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
29639 [1] by prove_fixed_point ?1
29645 23460: apply 12 2 3 0,2
29646 23460: f 3 1 3 0,2,2
29647 CLASH, statistics insufficient
29649 23462: Id : 2, {_}:
29650 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
29651 [5, 4, 3] by b_definition ?3 ?4 ?5
29652 23462: Id : 3, {_}:
29653 apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
29654 [8, 7] by w1_definition ?7 ?8
29656 23462: Id : 1, {_}:
29657 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
29658 [1] by prove_fixed_point ?1
29664 23462: apply 12 2 3 0,2
29665 23462: f 3 1 3 0,2,2
29666 CLASH, statistics insufficient
29668 23461: Id : 2, {_}:
29669 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
29670 [5, 4, 3] by b_definition ?3 ?4 ?5
29671 23461: Id : 3, {_}:
29672 apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
29673 [8, 7] by w1_definition ?7 ?8
29675 23461: Id : 1, {_}:
29676 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
29677 [1] by prove_fixed_point ?1
29683 23461: apply 12 2 3 0,2
29684 23461: f 3 1 3 0,2,2
29685 % SZS status Timeout for COL042-1.p
29686 NO CLASH, using fixed ground order
29688 23502: Id : 2, {_}:
29689 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29690 [4, 3, 2] by b_definition ?2 ?3 ?4
29691 23502: Id : 3, {_}:
29692 apply (apply (apply h ?6) ?7) ?8
29694 apply (apply (apply ?6 ?7) ?8) ?7
29695 [8, 7, 6] by h_definition ?6 ?7 ?8
29696 23502: Id : 4, {_}:
29705 (apply (apply b (apply (apply b h) (apply b b)))
29706 (apply h (apply (apply b h) (apply b b))))) h)) b)) b
29707 [] by strong_fixed_point
29709 23502: Id : 1, {_}:
29710 apply strong_fixed_point fixed_pt
29712 apply fixed_pt (apply strong_fixed_point fixed_pt)
29713 [] by prove_strong_fixed_point
29719 23502: apply 29 2 3 0,2
29720 23502: fixed_pt 3 0 3 2,2
29721 23502: strong_fixed_point 3 0 2 1,2
29722 NO CLASH, using fixed ground order
29724 23503: Id : 2, {_}:
29725 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29726 [4, 3, 2] by b_definition ?2 ?3 ?4
29727 23503: Id : 3, {_}:
29728 apply (apply (apply h ?6) ?7) ?8
29730 apply (apply (apply ?6 ?7) ?8) ?7
29731 [8, 7, 6] by h_definition ?6 ?7 ?8
29732 23503: Id : 4, {_}:
29741 (apply (apply b (apply (apply b h) (apply b b)))
29742 (apply h (apply (apply b h) (apply b b))))) h)) b)) b
29743 [] by strong_fixed_point
29745 23503: Id : 1, {_}:
29746 apply strong_fixed_point fixed_pt
29748 apply fixed_pt (apply strong_fixed_point fixed_pt)
29749 [] by prove_strong_fixed_point
29755 23503: apply 29 2 3 0,2
29756 23503: fixed_pt 3 0 3 2,2
29757 23503: strong_fixed_point 3 0 2 1,2
29758 NO CLASH, using fixed ground order
29760 23504: Id : 2, {_}:
29761 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29762 [4, 3, 2] by b_definition ?2 ?3 ?4
29763 23504: Id : 3, {_}:
29764 apply (apply (apply h ?6) ?7) ?8
29766 apply (apply (apply ?6 ?7) ?8) ?7
29767 [8, 7, 6] by h_definition ?6 ?7 ?8
29768 23504: Id : 4, {_}:
29777 (apply (apply b (apply (apply b h) (apply b b)))
29778 (apply h (apply (apply b h) (apply b b))))) h)) b)) b
29779 [] by strong_fixed_point
29781 23504: Id : 1, {_}:
29782 apply strong_fixed_point fixed_pt
29784 apply fixed_pt (apply strong_fixed_point fixed_pt)
29785 [] by prove_strong_fixed_point
29791 23504: apply 29 2 3 0,2
29792 23504: fixed_pt 3 0 3 2,2
29793 23504: strong_fixed_point 3 0 2 1,2
29794 % SZS status Timeout for COL043-3.p
29795 NO CLASH, using fixed ground order
29797 23537: Id : 2, {_}:
29798 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29799 [4, 3, 2] by b_definition ?2 ?3 ?4
29800 23537: Id : 3, {_}:
29801 apply (apply (apply n ?6) ?7) ?8
29803 apply (apply (apply ?6 ?8) ?7) ?8
29804 [8, 7, 6] by n_definition ?6 ?7 ?8
29805 23537: Id : 4, {_}:
29815 (apply (apply b (apply b b))
29816 (apply n (apply (apply b b) n))))) n)) b)) b
29817 [] by strong_fixed_point
29819 23537: Id : 1, {_}:
29820 apply strong_fixed_point fixed_pt
29822 apply fixed_pt (apply strong_fixed_point fixed_pt)
29823 [] by prove_strong_fixed_point
29829 23537: apply 27 2 3 0,2
29830 23537: fixed_pt 3 0 3 2,2
29831 23537: strong_fixed_point 3 0 2 1,2
29832 NO CLASH, using fixed ground order
29834 23538: Id : 2, {_}:
29835 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29836 [4, 3, 2] by b_definition ?2 ?3 ?4
29837 23538: Id : 3, {_}:
29838 apply (apply (apply n ?6) ?7) ?8
29840 apply (apply (apply ?6 ?8) ?7) ?8
29841 [8, 7, 6] by n_definition ?6 ?7 ?8
29842 23538: Id : 4, {_}:
29852 (apply (apply b (apply b b))
29853 (apply n (apply (apply b b) n))))) n)) b)) b
29854 [] by strong_fixed_point
29856 23538: Id : 1, {_}:
29857 apply strong_fixed_point fixed_pt
29859 apply fixed_pt (apply strong_fixed_point fixed_pt)
29860 [] by prove_strong_fixed_point
29866 23538: apply 27 2 3 0,2
29867 23538: fixed_pt 3 0 3 2,2
29868 23538: strong_fixed_point 3 0 2 1,2
29869 NO CLASH, using fixed ground order
29871 23539: Id : 2, {_}:
29872 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29873 [4, 3, 2] by b_definition ?2 ?3 ?4
29874 23539: Id : 3, {_}:
29875 apply (apply (apply n ?6) ?7) ?8
29877 apply (apply (apply ?6 ?8) ?7) ?8
29878 [8, 7, 6] by n_definition ?6 ?7 ?8
29879 23539: Id : 4, {_}:
29889 (apply (apply b (apply b b))
29890 (apply n (apply (apply b b) n))))) n)) b)) b
29891 [] by strong_fixed_point
29893 23539: Id : 1, {_}:
29894 apply strong_fixed_point fixed_pt
29896 apply fixed_pt (apply strong_fixed_point fixed_pt)
29897 [] by prove_strong_fixed_point
29903 23539: apply 27 2 3 0,2
29904 23539: fixed_pt 3 0 3 2,2
29905 23539: strong_fixed_point 3 0 2 1,2
29906 % SZS status Timeout for COL044-8.p
29907 NO CLASH, using fixed ground order
29908 NO CLASH, using fixed ground order
29910 23557: Id : 2, {_}:
29911 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29912 [4, 3, 2] by b_definition ?2 ?3 ?4
29913 23557: Id : 3, {_}:
29914 apply (apply (apply n ?6) ?7) ?8
29916 apply (apply (apply ?6 ?8) ?7) ?8
29917 [8, 7, 6] by n_definition ?6 ?7 ?8
29918 23557: Id : 4, {_}:
29928 (apply (apply b (apply b b))
29929 (apply n (apply n (apply b b)))))) n)) b)) b
29930 [] by strong_fixed_point
29932 23557: Id : 1, {_}:
29933 apply strong_fixed_point fixed_pt
29935 apply fixed_pt (apply strong_fixed_point fixed_pt)
29936 [] by prove_strong_fixed_point
29942 23557: apply 27 2 3 0,2
29943 23557: fixed_pt 3 0 3 2,2
29944 23557: strong_fixed_point 3 0 2 1,2
29945 NO CLASH, using fixed ground order
29947 23558: Id : 2, {_}:
29948 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29949 [4, 3, 2] by b_definition ?2 ?3 ?4
29950 23558: Id : 3, {_}:
29951 apply (apply (apply n ?6) ?7) ?8
29953 apply (apply (apply ?6 ?8) ?7) ?8
29954 [8, 7, 6] by n_definition ?6 ?7 ?8
29955 23558: Id : 4, {_}:
29965 (apply (apply b (apply b b))
29966 (apply n (apply n (apply b b)))))) n)) b)) b
29967 [] by strong_fixed_point
29969 23558: Id : 1, {_}:
29970 apply strong_fixed_point fixed_pt
29972 apply fixed_pt (apply strong_fixed_point fixed_pt)
29973 [] by prove_strong_fixed_point
29979 23558: apply 27 2 3 0,2
29980 23558: fixed_pt 3 0 3 2,2
29981 23558: strong_fixed_point 3 0 2 1,2
29983 23556: Id : 2, {_}:
29984 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
29985 [4, 3, 2] by b_definition ?2 ?3 ?4
29986 23556: Id : 3, {_}:
29987 apply (apply (apply n ?6) ?7) ?8
29989 apply (apply (apply ?6 ?8) ?7) ?8
29990 [8, 7, 6] by n_definition ?6 ?7 ?8
29991 23556: Id : 4, {_}:
30001 (apply (apply b (apply b b))
30002 (apply n (apply n (apply b b)))))) n)) b)) b
30003 [] by strong_fixed_point
30005 23556: Id : 1, {_}:
30006 apply strong_fixed_point fixed_pt
30008 apply fixed_pt (apply strong_fixed_point fixed_pt)
30009 [] by prove_strong_fixed_point
30015 23556: apply 27 2 3 0,2
30016 23556: fixed_pt 3 0 3 2,2
30017 23556: strong_fixed_point 3 0 2 1,2
30018 % SZS status Timeout for COL044-9.p
30019 NO CLASH, using fixed ground order
30021 23710: Id : 2, {_}:
30026 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
30027 (multiply (inverse (multiply ?4 ?5))
30030 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
30034 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
30036 23710: Id : 1, {_}:
30037 multiply (multiply (inverse b2) b2) a2 =>= a2
30038 [] by prove_these_axioms_2
30042 23710: a2 2 0 2 2,2
30043 23710: multiply 12 2 2 0,2
30044 23710: inverse 8 1 1 0,1,1,2
30045 23710: b2 2 0 2 1,1,1,2
30046 NO CLASH, using fixed ground order
30048 23711: Id : 2, {_}:
30053 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
30054 (multiply (inverse (multiply ?4 ?5))
30057 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
30061 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
30063 23711: Id : 1, {_}:
30064 multiply (multiply (inverse b2) b2) a2 =>= a2
30065 [] by prove_these_axioms_2
30069 23711: a2 2 0 2 2,2
30070 23711: multiply 12 2 2 0,2
30071 23711: inverse 8 1 1 0,1,1,2
30072 23711: b2 2 0 2 1,1,1,2
30073 NO CLASH, using fixed ground order
30075 23712: Id : 2, {_}:
30080 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
30081 (multiply (inverse (multiply ?4 ?5))
30084 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
30088 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
30090 23712: Id : 1, {_}:
30091 multiply (multiply (inverse b2) b2) a2 =>= a2
30092 [] by prove_these_axioms_2
30096 23712: a2 2 0 2 2,2
30097 23712: multiply 12 2 2 0,2
30098 23712: inverse 8 1 1 0,1,1,2
30099 23712: b2 2 0 2 1,1,1,2
30100 % SZS status Timeout for GRP506-1.p
30101 NO CLASH, using fixed ground order
30103 23731: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30104 23731: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30105 23731: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30106 23731: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30107 23731: Id : 6, {_}:
30108 meet ?12 ?13 =?= meet ?13 ?12
30109 [13, 12] by commutativity_of_meet ?12 ?13
30110 23731: Id : 7, {_}:
30111 join ?15 ?16 =?= join ?16 ?15
30112 [16, 15] by commutativity_of_join ?15 ?16
30113 23731: Id : 8, {_}:
30114 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
30115 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30116 23731: Id : 9, {_}:
30117 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
30118 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30119 23731: Id : 10, {_}:
30120 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
30121 [27, 26] by compatibility1 ?26 ?27
30122 23731: Id : 11, {_}:
30123 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
30124 [30, 29] by compatibility2 ?29 ?30
30125 23731: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
30126 23731: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
30127 23731: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
30128 23731: Id : 15, {_}:
30129 join (meet (complement ?38) (join ?38 ?39))
30130 (join (complement ?39) (meet ?38 ?39))
30133 [39, 38] by megill ?38 ?39
30135 23731: Id : 1, {_}:
30136 meet a (join b (meet a (join (complement a) (meet a b))))
30138 meet a (join (complement a) (meet a b))
30145 23731: join 18 2 3 0,2,2
30146 23731: meet 19 2 5 0,2
30147 23731: complement 14 1 2 0,1,2,2,2,2
30148 23731: b 3 0 3 1,2,2
30150 NO CLASH, using fixed ground order
30152 23732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30153 23732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30154 23732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30155 23732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30156 23732: Id : 6, {_}:
30157 meet ?12 ?13 =?= meet ?13 ?12
30158 [13, 12] by commutativity_of_meet ?12 ?13
30159 23732: Id : 7, {_}:
30160 join ?15 ?16 =?= join ?16 ?15
30161 [16, 15] by commutativity_of_join ?15 ?16
30162 23732: Id : 8, {_}:
30163 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30164 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30165 23732: Id : 9, {_}:
30166 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30167 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30168 23732: Id : 10, {_}:
30169 complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
30170 [27, 26] by compatibility1 ?26 ?27
30171 23732: Id : 11, {_}:
30172 complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
30173 [30, 29] by compatibility2 ?29 ?30
30174 23732: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
30175 23732: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
30176 23732: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
30177 23732: Id : 15, {_}:
30178 join (meet (complement ?38) (join ?38 ?39))
30179 (join (complement ?39) (meet ?38 ?39))
30182 [39, 38] by megill ?38 ?39
30184 23732: Id : 1, {_}:
30185 meet a (join b (meet a (join (complement a) (meet a b))))
30187 meet a (join (complement a) (meet a b))
30194 23732: join 18 2 3 0,2,2
30195 23732: meet 19 2 5 0,2
30196 23732: complement 14 1 2 0,1,2,2,2,2
30197 23732: b 3 0 3 1,2,2
30199 NO CLASH, using fixed ground order
30201 23733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30202 23733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30203 23733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30204 23733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30205 23733: Id : 6, {_}:
30206 meet ?12 ?13 =?= meet ?13 ?12
30207 [13, 12] by commutativity_of_meet ?12 ?13
30208 23733: Id : 7, {_}:
30209 join ?15 ?16 =?= join ?16 ?15
30210 [16, 15] by commutativity_of_join ?15 ?16
30211 23733: Id : 8, {_}:
30212 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30213 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30214 23733: Id : 9, {_}:
30215 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30216 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30217 23733: Id : 10, {_}:
30218 complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
30219 [27, 26] by compatibility1 ?26 ?27
30220 23733: Id : 11, {_}:
30221 complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
30222 [30, 29] by compatibility2 ?29 ?30
30223 23733: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
30224 23733: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
30225 23733: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
30226 23733: Id : 15, {_}:
30227 join (meet (complement ?38) (join ?38 ?39))
30228 (join (complement ?39) (meet ?38 ?39))
30231 [39, 38] by megill ?38 ?39
30233 23733: Id : 1, {_}:
30234 meet a (join b (meet a (join (complement a) (meet a b))))
30236 meet a (join (complement a) (meet a b))
30243 23733: join 18 2 3 0,2,2
30244 23733: meet 19 2 5 0,2
30245 23733: complement 14 1 2 0,1,2,2,2,2
30246 23733: b 3 0 3 1,2,2
30248 % SZS status Timeout for LAT053-1.p
30249 NO CLASH, using fixed ground order
30251 NO CLASH, using fixed ground order
30253 23764: Id : 2, {_}:
30254 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30256 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30260 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30263 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30264 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30265 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30268 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30270 23764: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
30275 23764: meet 20 2 2 0,2
30278 23765: Id : 2, {_}:
30279 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30281 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30285 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30288 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30289 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30290 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30293 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30295 23765: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
30300 23765: meet 20 2 2 0,2
30303 NO CLASH, using fixed ground order
30305 23766: Id : 2, {_}:
30306 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30308 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30312 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30315 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30316 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30317 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30320 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30322 23766: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
30327 23766: meet 20 2 2 0,2
30330 % SZS status Timeout for LAT081-1.p
30331 NO CLASH, using fixed ground order
30333 23787: Id : 2, {_}:
30334 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30336 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30340 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30343 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30344 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30345 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30348 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30350 23787: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
30355 23787: join 22 2 2 0,2
30358 NO CLASH, using fixed ground order
30360 23788: Id : 2, {_}:
30361 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30363 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30367 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30370 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30371 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30372 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30375 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30377 23788: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
30382 23788: join 22 2 2 0,2
30385 NO CLASH, using fixed ground order
30387 23789: Id : 2, {_}:
30388 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30390 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30394 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30397 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30398 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30399 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30402 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30404 23789: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
30409 23789: join 22 2 2 0,2
30412 % SZS status Timeout for LAT084-1.p
30413 NO CLASH, using fixed ground order
30415 23816: Id : 2, {_}:
30416 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30418 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30422 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30425 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30426 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30427 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30430 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30432 23816: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
30436 23816: meet 19 2 1 0,2
30437 23816: join 21 2 1 0,2,2
30438 23816: b 1 0 1 2,2,2
30440 NO CLASH, using fixed ground order
30442 23817: Id : 2, {_}:
30443 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30445 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30449 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30452 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30453 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30454 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30457 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30459 23817: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
30463 23817: meet 19 2 1 0,2
30464 23817: join 21 2 1 0,2,2
30465 23817: b 1 0 1 2,2,2
30467 NO CLASH, using fixed ground order
30469 23818: Id : 2, {_}:
30470 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30472 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30476 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30479 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30480 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30481 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30484 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30486 23818: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
30490 23818: meet 19 2 1 0,2
30491 23818: join 21 2 1 0,2,2
30492 23818: b 1 0 1 2,2,2
30494 % SZS status Timeout for LAT086-1.p
30495 NO CLASH, using fixed ground order
30497 23840: Id : 2, {_}:
30498 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30500 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30504 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30507 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30508 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30509 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30512 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30514 23840: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
30518 23840: join 21 2 1 0,2
30519 23840: meet 19 2 1 0,2,2
30520 23840: b 1 0 1 2,2,2
30522 NO CLASH, using fixed ground order
30524 23842: Id : 2, {_}:
30525 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30527 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30531 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30534 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30535 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30536 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30539 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30541 23842: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
30545 23842: join 21 2 1 0,2
30546 23842: meet 19 2 1 0,2,2
30547 23842: b 1 0 1 2,2,2
30549 NO CLASH, using fixed ground order
30551 23841: Id : 2, {_}:
30552 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
30554 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
30558 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
30561 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
30562 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
30563 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
30566 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
30568 23841: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
30572 23841: join 21 2 1 0,2
30573 23841: meet 19 2 1 0,2,2
30574 23841: b 1 0 1 2,2,2
30576 % SZS status Timeout for LAT087-1.p
30577 NO CLASH, using fixed ground order
30579 23873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30580 23873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30581 23873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30582 23873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30583 23873: Id : 6, {_}:
30584 meet ?12 ?13 =?= meet ?13 ?12
30585 [13, 12] by commutativity_of_meet ?12 ?13
30586 23873: Id : 7, {_}:
30587 join ?15 ?16 =?= join ?16 ?15
30588 [16, 15] by commutativity_of_join ?15 ?16
30589 23873: Id : 8, {_}:
30590 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
30591 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30592 23873: Id : 9, {_}:
30593 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
30594 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30595 23873: Id : 10, {_}:
30596 meet ?26 (join ?27 (meet ?26 ?28))
30600 (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
30601 [28, 27, 26] by equation_H3 ?26 ?27 ?28
30603 23873: Id : 1, {_}:
30604 meet a (join b (meet a c))
30606 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
30611 23873: join 17 2 4 0,2,2
30612 23873: meet 21 2 6 0,2
30613 23873: c 4 0 4 2,2,2,2
30614 23873: b 4 0 4 1,2,2
30616 NO CLASH, using fixed ground order
30618 23874: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30619 23874: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30620 23874: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30621 23874: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30622 23874: Id : 6, {_}:
30623 meet ?12 ?13 =?= meet ?13 ?12
30624 [13, 12] by commutativity_of_meet ?12 ?13
30625 23874: Id : 7, {_}:
30626 join ?15 ?16 =?= join ?16 ?15
30627 [16, 15] by commutativity_of_join ?15 ?16
30628 23874: Id : 8, {_}:
30629 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30630 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30631 23874: Id : 9, {_}:
30632 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30633 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30634 23874: Id : 10, {_}:
30635 meet ?26 (join ?27 (meet ?26 ?28))
30639 (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
30640 [28, 27, 26] by equation_H3 ?26 ?27 ?28
30642 23874: Id : 1, {_}:
30643 meet a (join b (meet a c))
30645 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
30650 23874: join 17 2 4 0,2,2
30651 23874: meet 21 2 6 0,2
30652 23874: c 4 0 4 2,2,2,2
30653 23874: b 4 0 4 1,2,2
30655 NO CLASH, using fixed ground order
30657 23875: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30658 23875: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30659 23875: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30660 23875: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30661 23875: Id : 6, {_}:
30662 meet ?12 ?13 =?= meet ?13 ?12
30663 [13, 12] by commutativity_of_meet ?12 ?13
30664 23875: Id : 7, {_}:
30665 join ?15 ?16 =?= join ?16 ?15
30666 [16, 15] by commutativity_of_join ?15 ?16
30667 23875: Id : 8, {_}:
30668 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30669 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30670 23875: Id : 9, {_}:
30671 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30672 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30673 23875: Id : 10, {_}:
30674 meet ?26 (join ?27 (meet ?26 ?28))
30678 (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
30679 [28, 27, 26] by equation_H3 ?26 ?27 ?28
30681 23875: Id : 1, {_}:
30682 meet a (join b (meet a c))
30684 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
30689 23875: join 17 2 4 0,2,2
30690 23875: meet 21 2 6 0,2
30691 23875: c 4 0 4 2,2,2,2
30692 23875: b 4 0 4 1,2,2
30694 % SZS status Timeout for LAT099-1.p
30695 NO CLASH, using fixed ground order
30697 24259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30698 24259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30699 24259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30700 24259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30701 24259: Id : 6, {_}:
30702 meet ?12 ?13 =?= meet ?13 ?12
30703 [13, 12] by commutativity_of_meet ?12 ?13
30704 24259: Id : 7, {_}:
30705 join ?15 ?16 =?= join ?16 ?15
30706 [16, 15] by commutativity_of_join ?15 ?16
30707 24259: Id : 8, {_}:
30708 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
30709 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30710 24259: Id : 9, {_}:
30711 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
30712 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30713 24259: Id : 10, {_}:
30714 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
30716 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
30717 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
30719 24259: Id : 1, {_}:
30720 meet a (join b (meet c (join a d)))
30722 meet a (join b (meet c (join b (join d (meet a c)))))
30727 24259: meet 19 2 5 0,2
30728 24259: join 19 2 5 0,2,2
30729 24259: d 2 0 2 2,2,2,2,2
30730 24259: c 3 0 3 1,2,2,2
30731 24259: b 3 0 3 1,2,2
30733 NO CLASH, using fixed ground order
30735 24260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30736 24260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30737 24260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30738 24260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30739 24260: Id : 6, {_}:
30740 meet ?12 ?13 =?= meet ?13 ?12
30741 [13, 12] by commutativity_of_meet ?12 ?13
30742 24260: Id : 7, {_}:
30743 join ?15 ?16 =?= join ?16 ?15
30744 [16, 15] by commutativity_of_join ?15 ?16
30745 24260: Id : 8, {_}:
30746 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30747 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30748 24260: Id : 9, {_}:
30749 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30750 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30751 24260: Id : 10, {_}:
30752 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
30754 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
30755 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
30757 24260: Id : 1, {_}:
30758 meet a (join b (meet c (join a d)))
30760 meet a (join b (meet c (join b (join d (meet a c)))))
30765 24260: meet 19 2 5 0,2
30766 24260: join 19 2 5 0,2,2
30767 24260: d 2 0 2 2,2,2,2,2
30768 24260: c 3 0 3 1,2,2,2
30769 24260: b 3 0 3 1,2,2
30771 NO CLASH, using fixed ground order
30773 24261: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30774 24261: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30775 24261: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30776 24261: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30777 24261: Id : 6, {_}:
30778 meet ?12 ?13 =?= meet ?13 ?12
30779 [13, 12] by commutativity_of_meet ?12 ?13
30780 24261: Id : 7, {_}:
30781 join ?15 ?16 =?= join ?16 ?15
30782 [16, 15] by commutativity_of_join ?15 ?16
30783 24261: Id : 8, {_}:
30784 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30785 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30786 24261: Id : 9, {_}:
30787 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30788 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30789 24261: Id : 10, {_}:
30790 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
30792 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
30793 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
30795 24261: Id : 1, {_}:
30796 meet a (join b (meet c (join a d)))
30798 meet a (join b (meet c (join b (join d (meet a c)))))
30803 24261: meet 19 2 5 0,2
30804 24261: join 19 2 5 0,2,2
30805 24261: d 2 0 2 2,2,2,2,2
30806 24261: c 3 0 3 1,2,2,2
30807 24261: b 3 0 3 1,2,2
30809 % SZS status Timeout for LAT110-1.p
30810 NO CLASH, using fixed ground order
30812 24393: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30813 24393: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30814 24393: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30815 24393: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30816 24393: Id : 6, {_}:
30817 meet ?12 ?13 =?= meet ?13 ?12
30818 [13, 12] by commutativity_of_meet ?12 ?13
30819 24393: Id : 7, {_}:
30820 join ?15 ?16 =?= join ?16 ?15
30821 [16, 15] by commutativity_of_join ?15 ?16
30822 24393: Id : 8, {_}:
30823 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
30824 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30825 24393: Id : 9, {_}:
30826 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
30827 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30828 24393: Id : 10, {_}:
30829 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
30831 meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
30832 [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
30834 24393: Id : 1, {_}:
30837 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
30842 24393: meet 20 2 5 0,2
30843 24393: join 17 2 4 0,2,2
30844 24393: c 3 0 3 2,2,2
30845 24393: b 3 0 3 1,2,2
30847 NO CLASH, using fixed ground order
30849 24394: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30850 24394: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30851 24394: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30852 24394: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30853 24394: Id : 6, {_}:
30854 meet ?12 ?13 =?= meet ?13 ?12
30855 [13, 12] by commutativity_of_meet ?12 ?13
30856 24394: Id : 7, {_}:
30857 join ?15 ?16 =?= join ?16 ?15
30858 [16, 15] by commutativity_of_join ?15 ?16
30859 24394: Id : 8, {_}:
30860 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30861 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30862 24394: Id : 9, {_}:
30863 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30864 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30865 24394: Id : 10, {_}:
30866 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
30868 meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
30869 [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
30871 24394: Id : 1, {_}:
30874 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
30879 24394: meet 20 2 5 0,2
30880 24394: join 17 2 4 0,2,2
30881 24394: c 3 0 3 2,2,2
30882 24394: b 3 0 3 1,2,2
30884 NO CLASH, using fixed ground order
30886 24395: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30887 24395: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30888 24395: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30889 24395: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30890 24395: Id : 6, {_}:
30891 meet ?12 ?13 =?= meet ?13 ?12
30892 [13, 12] by commutativity_of_meet ?12 ?13
30893 24395: Id : 7, {_}:
30894 join ?15 ?16 =?= join ?16 ?15
30895 [16, 15] by commutativity_of_join ?15 ?16
30896 24395: Id : 8, {_}:
30897 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30898 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30899 24395: Id : 9, {_}:
30900 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30901 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30902 24395: Id : 10, {_}:
30903 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
30905 meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
30906 [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
30908 24395: Id : 1, {_}:
30911 join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
30916 24395: meet 20 2 5 0,2
30917 24395: join 17 2 4 0,2,2
30918 24395: c 3 0 3 2,2,2
30919 24395: b 3 0 3 1,2,2
30921 % SZS status Timeout for LAT118-1.p
30922 NO CLASH, using fixed ground order
30924 24412: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30925 24412: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30926 24412: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30927 24412: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30928 24412: Id : 6, {_}:
30929 meet ?12 ?13 =?= meet ?13 ?12
30930 [13, 12] by commutativity_of_meet ?12 ?13
30931 24412: Id : 7, {_}:
30932 join ?15 ?16 =?= join ?16 ?15
30933 [16, 15] by commutativity_of_join ?15 ?16
30934 24412: Id : 8, {_}:
30935 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
30936 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30937 24412: Id : 9, {_}:
30938 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
30939 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30940 24412: Id : 10, {_}:
30941 join (meet ?26 ?27) (meet ?26 ?28)
30944 (join (meet ?27 (join ?28 (meet ?26 ?27)))
30945 (meet ?28 (join ?26 ?27)))
30946 [28, 27, 26] by equation_H22 ?26 ?27 ?28
30948 24412: Id : 1, {_}:
30949 meet a (join b (meet a c))
30951 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
30956 24412: join 17 2 4 0,2,2
30957 24412: meet 21 2 6 0,2
30958 24412: c 3 0 3 2,2,2,2
30959 24412: b 3 0 3 1,2,2
30961 NO CLASH, using fixed ground order
30963 24413: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
30964 24413: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
30965 24413: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
30966 24413: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
30967 24413: Id : 6, {_}:
30968 meet ?12 ?13 =?= meet ?13 ?12
30969 [13, 12] by commutativity_of_meet ?12 ?13
30970 24413: Id : 7, {_}:
30971 join ?15 ?16 =?= join ?16 ?15
30972 [16, 15] by commutativity_of_join ?15 ?16
30973 24413: Id : 8, {_}:
30974 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
30975 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
30976 24413: Id : 9, {_}:
30977 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
30978 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
30979 24413: Id : 10, {_}:
30980 join (meet ?26 ?27) (meet ?26 ?28)
30983 (join (meet ?27 (join ?28 (meet ?26 ?27)))
30984 (meet ?28 (join ?26 ?27)))
30985 [28, 27, 26] by equation_H22 ?26 ?27 ?28
30987 24413: Id : 1, {_}:
30988 meet a (join b (meet a c))
30990 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
30995 24413: join 17 2 4 0,2,2
30996 24413: meet 21 2 6 0,2
30997 24413: c 3 0 3 2,2,2,2
30998 24413: b 3 0 3 1,2,2
31000 NO CLASH, using fixed ground order
31002 24414: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31003 24414: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31004 24414: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31005 24414: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31006 24414: Id : 6, {_}:
31007 meet ?12 ?13 =?= meet ?13 ?12
31008 [13, 12] by commutativity_of_meet ?12 ?13
31009 24414: Id : 7, {_}:
31010 join ?15 ?16 =?= join ?16 ?15
31011 [16, 15] by commutativity_of_join ?15 ?16
31012 24414: Id : 8, {_}:
31013 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31014 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31015 24414: Id : 9, {_}:
31016 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31017 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31018 24414: Id : 10, {_}:
31019 join (meet ?26 ?27) (meet ?26 ?28)
31022 (join (meet ?27 (join ?28 (meet ?26 ?27)))
31023 (meet ?28 (join ?26 ?27)))
31024 [28, 27, 26] by equation_H22 ?26 ?27 ?28
31026 24414: Id : 1, {_}:
31027 meet a (join b (meet a c))
31029 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
31034 24414: join 17 2 4 0,2,2
31035 24414: meet 21 2 6 0,2
31036 24414: c 3 0 3 2,2,2,2
31037 24414: b 3 0 3 1,2,2
31039 % SZS status Timeout for LAT142-1.p
31040 NO CLASH, using fixed ground order
31042 24444: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31043 24444: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31044 24444: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31045 24444: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31046 24444: Id : 6, {_}:
31047 meet ?12 ?13 =?= meet ?13 ?12
31048 [13, 12] by commutativity_of_meet ?12 ?13
31049 24444: Id : 7, {_}:
31050 join ?15 ?16 =?= join ?16 ?15
31051 [16, 15] by commutativity_of_join ?15 ?16
31052 24444: Id : 8, {_}:
31053 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
31054 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31055 24444: Id : 9, {_}:
31056 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
31057 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31058 24444: Id : 10, {_}:
31059 meet ?26 (join ?27 (meet ?28 ?29))
31061 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
31062 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
31064 24444: Id : 1, {_}:
31065 meet a (meet b (join c (meet a d)))
31067 meet a (meet b (join c (meet d (join a (meet b c)))))
31072 24444: join 16 2 3 0,2,2,2
31073 24444: meet 21 2 7 0,2
31074 24444: d 2 0 2 2,2,2,2,2
31075 24444: c 3 0 3 1,2,2,2
31076 24444: b 3 0 3 1,2,2
31078 NO CLASH, using fixed ground order
31080 24445: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31081 24445: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31082 24445: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31083 24445: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31084 24445: Id : 6, {_}:
31085 meet ?12 ?13 =?= meet ?13 ?12
31086 [13, 12] by commutativity_of_meet ?12 ?13
31087 24445: Id : 7, {_}:
31088 join ?15 ?16 =?= join ?16 ?15
31089 [16, 15] by commutativity_of_join ?15 ?16
31090 24445: Id : 8, {_}:
31091 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31092 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31093 24445: Id : 9, {_}:
31094 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31095 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31096 24445: Id : 10, {_}:
31097 meet ?26 (join ?27 (meet ?28 ?29))
31099 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
31100 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
31102 24445: Id : 1, {_}:
31103 meet a (meet b (join c (meet a d)))
31105 meet a (meet b (join c (meet d (join a (meet b c)))))
31110 24445: join 16 2 3 0,2,2,2
31111 24445: meet 21 2 7 0,2
31112 24445: d 2 0 2 2,2,2,2,2
31113 24445: c 3 0 3 1,2,2,2
31114 24445: b 3 0 3 1,2,2
31116 NO CLASH, using fixed ground order
31118 24446: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31119 24446: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31120 24446: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31121 24446: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31122 24446: Id : 6, {_}:
31123 meet ?12 ?13 =?= meet ?13 ?12
31124 [13, 12] by commutativity_of_meet ?12 ?13
31125 24446: Id : 7, {_}:
31126 join ?15 ?16 =?= join ?16 ?15
31127 [16, 15] by commutativity_of_join ?15 ?16
31128 24446: Id : 8, {_}:
31129 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31130 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31131 24446: Id : 9, {_}:
31132 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31133 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31134 24446: Id : 10, {_}:
31135 meet ?26 (join ?27 (meet ?28 ?29))
31137 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
31138 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
31140 24446: Id : 1, {_}:
31141 meet a (meet b (join c (meet a d)))
31143 meet a (meet b (join c (meet d (join a (meet b c)))))
31148 24446: join 16 2 3 0,2,2,2
31149 24446: meet 21 2 7 0,2
31150 24446: d 2 0 2 2,2,2,2,2
31151 24446: c 3 0 3 1,2,2,2
31152 24446: b 3 0 3 1,2,2
31154 % SZS status Timeout for LAT147-1.p
31155 NO CLASH, using fixed ground order
31157 24463: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31158 24463: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31159 24463: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31160 24463: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31161 24463: Id : 6, {_}:
31162 meet ?12 ?13 =?= meet ?13 ?12
31163 [13, 12] by commutativity_of_meet ?12 ?13
31164 24463: Id : 7, {_}:
31165 join ?15 ?16 =?= join ?16 ?15
31166 [16, 15] by commutativity_of_join ?15 ?16
31167 24463: Id : 8, {_}:
31168 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31169 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31170 24463: Id : 9, {_}:
31171 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31172 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31173 24463: Id : 10, {_}:
31174 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
31176 meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
31177 [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
31179 24463: Id : 1, {_}:
31180 meet a (join b (meet a c))
31182 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
31187 24463: join 18 2 4 0,2,2
31188 24463: meet 20 2 6 0,2
31189 24463: c 3 0 3 2,2,2,2
31190 24463: b 3 0 3 1,2,2
31192 NO CLASH, using fixed ground order
31194 24464: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31195 24464: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31196 24464: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31197 24464: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31198 24464: Id : 6, {_}:
31199 meet ?12 ?13 =?= meet ?13 ?12
31200 [13, 12] by commutativity_of_meet ?12 ?13
31201 24464: Id : 7, {_}:
31202 join ?15 ?16 =?= join ?16 ?15
31203 [16, 15] by commutativity_of_join ?15 ?16
31204 24464: Id : 8, {_}:
31205 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31206 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31207 24464: Id : 9, {_}:
31208 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31209 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31210 24464: Id : 10, {_}:
31211 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
31213 meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
31214 [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
31216 24464: Id : 1, {_}:
31217 meet a (join b (meet a c))
31219 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
31224 24464: join 18 2 4 0,2,2
31225 24464: meet 20 2 6 0,2
31226 24464: c 3 0 3 2,2,2,2
31227 24464: b 3 0 3 1,2,2
31229 NO CLASH, using fixed ground order
31231 24462: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31232 24462: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31233 24462: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31234 24462: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31235 24462: Id : 6, {_}:
31236 meet ?12 ?13 =?= meet ?13 ?12
31237 [13, 12] by commutativity_of_meet ?12 ?13
31238 24462: Id : 7, {_}:
31239 join ?15 ?16 =?= join ?16 ?15
31240 [16, 15] by commutativity_of_join ?15 ?16
31241 24462: Id : 8, {_}:
31242 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
31243 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31244 24462: Id : 9, {_}:
31245 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
31246 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31247 24462: Id : 10, {_}:
31248 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
31250 meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
31251 [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
31253 24462: Id : 1, {_}:
31254 meet a (join b (meet a c))
31256 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
31261 24462: join 18 2 4 0,2,2
31262 24462: meet 20 2 6 0,2
31263 24462: c 3 0 3 2,2,2,2
31264 24462: b 3 0 3 1,2,2
31266 % SZS status Timeout for LAT154-1.p
31267 NO CLASH, using fixed ground order
31269 24500: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31270 24500: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31271 24500: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31272 24500: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31273 24500: Id : 6, {_}:
31274 meet ?12 ?13 =?= meet ?13 ?12
31275 [13, 12] by commutativity_of_meet ?12 ?13
31276 24500: Id : 7, {_}:
31277 join ?15 ?16 =?= join ?16 ?15
31278 [16, 15] by commutativity_of_join ?15 ?16
31279 24500: Id : 8, {_}:
31280 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
31281 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31282 24500: Id : 9, {_}:
31283 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
31284 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31285 24500: Id : 10, {_}:
31286 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
31288 meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
31289 [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
31291 24500: Id : 1, {_}:
31292 meet a (join b (meet a c))
31294 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
31299 24500: join 18 2 4 0,2,2
31300 24500: meet 20 2 6 0,2
31301 24500: c 4 0 4 2,2,2,2
31302 24500: b 4 0 4 1,2,2
31304 NO CLASH, using fixed ground order
31306 24501: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31307 24501: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31308 24501: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31309 24501: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31310 24501: Id : 6, {_}:
31311 meet ?12 ?13 =?= meet ?13 ?12
31312 [13, 12] by commutativity_of_meet ?12 ?13
31313 24501: Id : 7, {_}:
31314 join ?15 ?16 =?= join ?16 ?15
31315 [16, 15] by commutativity_of_join ?15 ?16
31316 24501: Id : 8, {_}:
31317 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31318 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31319 24501: Id : 9, {_}:
31320 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31321 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31322 24501: Id : 10, {_}:
31323 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
31325 meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
31326 [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
31328 24501: Id : 1, {_}:
31329 meet a (join b (meet a c))
31331 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
31336 24501: join 18 2 4 0,2,2
31337 24501: meet 20 2 6 0,2
31338 24501: c 4 0 4 2,2,2,2
31339 24501: b 4 0 4 1,2,2
31341 NO CLASH, using fixed ground order
31343 24502: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31344 24502: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31345 24502: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31346 24502: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31347 24502: Id : 6, {_}:
31348 meet ?12 ?13 =?= meet ?13 ?12
31349 [13, 12] by commutativity_of_meet ?12 ?13
31350 24502: Id : 7, {_}:
31351 join ?15 ?16 =?= join ?16 ?15
31352 [16, 15] by commutativity_of_join ?15 ?16
31353 24502: Id : 8, {_}:
31354 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31355 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31356 24502: Id : 9, {_}:
31357 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31358 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31359 24502: Id : 10, {_}:
31360 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
31362 meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
31363 [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
31365 24502: Id : 1, {_}:
31366 meet a (join b (meet a c))
31368 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
31373 24502: join 18 2 4 0,2,2
31374 24502: meet 20 2 6 0,2
31375 24502: c 4 0 4 2,2,2,2
31376 24502: b 4 0 4 1,2,2
31378 % SZS status Timeout for LAT155-1.p
31379 NO CLASH, using fixed ground order
31381 24518: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31382 24518: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31383 24518: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31384 24518: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31385 24518: Id : 6, {_}:
31386 meet ?12 ?13 =?= meet ?13 ?12
31387 [13, 12] by commutativity_of_meet ?12 ?13
31388 24518: Id : 7, {_}:
31389 join ?15 ?16 =?= join ?16 ?15
31390 [16, 15] by commutativity_of_join ?15 ?16
31391 24518: Id : 8, {_}:
31392 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
31393 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31394 24518: Id : 9, {_}:
31395 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
31396 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31397 24518: Id : 10, {_}:
31398 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
31400 join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
31401 [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
31403 24518: Id : 1, {_}:
31406 meet a (join b (meet (join a b) (join c (meet a b))))
31411 24518: meet 18 2 4 0,2
31412 24518: join 18 2 4 0,2,2
31413 24518: c 2 0 2 2,2,2
31414 24518: b 4 0 4 1,2,2
31416 NO CLASH, using fixed ground order
31418 24519: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31419 24519: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31420 24519: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31421 24519: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31422 24519: Id : 6, {_}:
31423 meet ?12 ?13 =?= meet ?13 ?12
31424 [13, 12] by commutativity_of_meet ?12 ?13
31425 24519: Id : 7, {_}:
31426 join ?15 ?16 =?= join ?16 ?15
31427 [16, 15] by commutativity_of_join ?15 ?16
31428 24519: Id : 8, {_}:
31429 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31430 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31431 24519: Id : 9, {_}:
31432 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31433 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31434 24519: Id : 10, {_}:
31435 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
31437 join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
31438 [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
31440 24519: Id : 1, {_}:
31443 meet a (join b (meet (join a b) (join c (meet a b))))
31448 24519: meet 18 2 4 0,2
31449 24519: join 18 2 4 0,2,2
31450 24519: c 2 0 2 2,2,2
31451 24519: b 4 0 4 1,2,2
31453 NO CLASH, using fixed ground order
31455 24520: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
31456 24520: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
31457 24520: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
31458 24520: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
31459 24520: Id : 6, {_}:
31460 meet ?12 ?13 =?= meet ?13 ?12
31461 [13, 12] by commutativity_of_meet ?12 ?13
31462 24520: Id : 7, {_}:
31463 join ?15 ?16 =?= join ?16 ?15
31464 [16, 15] by commutativity_of_join ?15 ?16
31465 24520: Id : 8, {_}:
31466 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
31467 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
31468 24520: Id : 9, {_}:
31469 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
31470 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
31471 24520: Id : 10, {_}:
31472 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
31474 join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
31475 [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
31477 24520: Id : 1, {_}:
31480 meet a (join b (meet (join a b) (join c (meet a b))))
31485 24520: meet 18 2 4 0,2
31486 24520: join 18 2 4 0,2,2
31487 24520: c 2 0 2 2,2,2
31488 24520: b 4 0 4 1,2,2
31490 % SZS status Timeout for LAT170-1.p
31491 NO CLASH, using fixed ground order
31493 24547: Id : 2, {_}:
31494 add ?2 ?3 =?= add ?3 ?2
31495 [3, 2] by commutativity_for_addition ?2 ?3
31496 24547: Id : 3, {_}:
31497 add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
31498 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
31499 24547: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
31500 24547: Id : 5, {_}:
31501 add ?11 additive_identity =>= ?11
31502 [11] by right_additive_identity ?11
31503 24547: Id : 6, {_}:
31504 multiply additive_identity ?13 =>= additive_identity
31505 [13] by left_multiplicative_zero ?13
31506 24547: Id : 7, {_}:
31507 multiply ?15 additive_identity =>= additive_identity
31508 [15] by right_multiplicative_zero ?15
31509 24547: Id : 8, {_}:
31510 add (additive_inverse ?17) ?17 =>= additive_identity
31511 [17] by left_additive_inverse ?17
31512 24547: Id : 9, {_}:
31513 add ?19 (additive_inverse ?19) =>= additive_identity
31514 [19] by right_additive_inverse ?19
31515 24547: Id : 10, {_}:
31516 multiply ?21 (add ?22 ?23)
31518 add (multiply ?21 ?22) (multiply ?21 ?23)
31519 [23, 22, 21] by distribute1 ?21 ?22 ?23
31520 24547: Id : 11, {_}:
31521 multiply (add ?25 ?26) ?27
31523 add (multiply ?25 ?27) (multiply ?26 ?27)
31524 [27, 26, 25] by distribute2 ?25 ?26 ?27
31525 24547: Id : 12, {_}:
31526 additive_inverse (additive_inverse ?29) =>= ?29
31527 [29] by additive_inverse_additive_inverse ?29
31528 24547: Id : 13, {_}:
31529 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
31530 [32, 31] by right_alternative ?31 ?32
31531 24547: Id : 14, {_}:
31532 associator ?34 ?35 ?36
31534 add (multiply (multiply ?34 ?35) ?36)
31535 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
31536 [36, 35, 34] by associator ?34 ?35 ?36
31537 24547: Id : 15, {_}:
31540 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
31541 [39, 38] by commutator ?38 ?39
31543 24547: Id : 1, {_}:
31545 (multiply (multiply (associator x x y) (associator x x y)) x)
31546 (multiply (associator x x y) (associator x x y))
31549 [] by prove_conjecture_2
31553 24547: commutator 1 2 0
31554 24547: additive_inverse 6 1 0
31556 24547: additive_identity 9 0 1 3
31557 24547: multiply 22 2 4 0,2
31558 24547: associator 5 3 4 0,1,1,1,2
31559 24547: y 4 0 4 3,1,1,1,2
31560 24547: x 9 0 9 1,1,1,1,2
31561 NO CLASH, using fixed ground order
31563 24548: Id : 2, {_}:
31564 add ?2 ?3 =?= add ?3 ?2
31565 [3, 2] by commutativity_for_addition ?2 ?3
31566 24548: Id : 3, {_}:
31567 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
31568 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
31569 24548: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
31570 24548: Id : 5, {_}:
31571 add ?11 additive_identity =>= ?11
31572 [11] by right_additive_identity ?11
31573 24548: Id : 6, {_}:
31574 multiply additive_identity ?13 =>= additive_identity
31575 [13] by left_multiplicative_zero ?13
31576 24548: Id : 7, {_}:
31577 multiply ?15 additive_identity =>= additive_identity
31578 [15] by right_multiplicative_zero ?15
31579 24548: Id : 8, {_}:
31580 add (additive_inverse ?17) ?17 =>= additive_identity
31581 [17] by left_additive_inverse ?17
31582 24548: Id : 9, {_}:
31583 add ?19 (additive_inverse ?19) =>= additive_identity
31584 [19] by right_additive_inverse ?19
31585 24548: Id : 10, {_}:
31586 multiply ?21 (add ?22 ?23)
31588 add (multiply ?21 ?22) (multiply ?21 ?23)
31589 [23, 22, 21] by distribute1 ?21 ?22 ?23
31590 24548: Id : 11, {_}:
31591 multiply (add ?25 ?26) ?27
31593 add (multiply ?25 ?27) (multiply ?26 ?27)
31594 [27, 26, 25] by distribute2 ?25 ?26 ?27
31595 24548: Id : 12, {_}:
31596 additive_inverse (additive_inverse ?29) =>= ?29
31597 [29] by additive_inverse_additive_inverse ?29
31598 24548: Id : 13, {_}:
31599 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
31600 [32, 31] by right_alternative ?31 ?32
31601 24548: Id : 14, {_}:
31602 associator ?34 ?35 ?36
31604 add (multiply (multiply ?34 ?35) ?36)
31605 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
31606 [36, 35, 34] by associator ?34 ?35 ?36
31607 24548: Id : 15, {_}:
31610 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
31611 [39, 38] by commutator ?38 ?39
31613 24548: Id : 1, {_}:
31615 (multiply (multiply (associator x x y) (associator x x y)) x)
31616 (multiply (associator x x y) (associator x x y))
31619 [] by prove_conjecture_2
31623 24548: commutator 1 2 0
31624 24548: additive_inverse 6 1 0
31626 24548: additive_identity 9 0 1 3
31627 24548: multiply 22 2 4 0,2
31628 24548: associator 5 3 4 0,1,1,1,2
31629 24548: y 4 0 4 3,1,1,1,2
31630 24548: x 9 0 9 1,1,1,1,2
31631 NO CLASH, using fixed ground order
31633 24549: Id : 2, {_}:
31634 add ?2 ?3 =?= add ?3 ?2
31635 [3, 2] by commutativity_for_addition ?2 ?3
31636 24549: Id : 3, {_}:
31637 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
31638 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
31639 24549: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
31640 24549: Id : 5, {_}:
31641 add ?11 additive_identity =>= ?11
31642 [11] by right_additive_identity ?11
31643 24549: Id : 6, {_}:
31644 multiply additive_identity ?13 =>= additive_identity
31645 [13] by left_multiplicative_zero ?13
31646 24549: Id : 7, {_}:
31647 multiply ?15 additive_identity =>= additive_identity
31648 [15] by right_multiplicative_zero ?15
31649 24549: Id : 8, {_}:
31650 add (additive_inverse ?17) ?17 =>= additive_identity
31651 [17] by left_additive_inverse ?17
31652 24549: Id : 9, {_}:
31653 add ?19 (additive_inverse ?19) =>= additive_identity
31654 [19] by right_additive_inverse ?19
31655 24549: Id : 10, {_}:
31656 multiply ?21 (add ?22 ?23)
31658 add (multiply ?21 ?22) (multiply ?21 ?23)
31659 [23, 22, 21] by distribute1 ?21 ?22 ?23
31660 24549: Id : 11, {_}:
31661 multiply (add ?25 ?26) ?27
31663 add (multiply ?25 ?27) (multiply ?26 ?27)
31664 [27, 26, 25] by distribute2 ?25 ?26 ?27
31665 24549: Id : 12, {_}:
31666 additive_inverse (additive_inverse ?29) =>= ?29
31667 [29] by additive_inverse_additive_inverse ?29
31668 24549: Id : 13, {_}:
31669 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
31670 [32, 31] by right_alternative ?31 ?32
31671 24549: Id : 14, {_}:
31672 associator ?34 ?35 ?36
31674 add (multiply (multiply ?34 ?35) ?36)
31675 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
31676 [36, 35, 34] by associator ?34 ?35 ?36
31677 24549: Id : 15, {_}:
31680 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
31681 [39, 38] by commutator ?38 ?39
31683 24549: Id : 1, {_}:
31685 (multiply (multiply (associator x x y) (associator x x y)) x)
31686 (multiply (associator x x y) (associator x x y))
31689 [] by prove_conjecture_2
31693 24549: commutator 1 2 0
31694 24549: additive_inverse 6 1 0
31696 24549: additive_identity 9 0 1 3
31697 24549: multiply 22 2 4 0,2
31698 24549: associator 5 3 4 0,1,1,1,2
31699 24549: y 4 0 4 3,1,1,1,2
31700 24549: x 9 0 9 1,1,1,1,2
31701 % SZS status Timeout for RNG031-6.p
31702 NO CLASH, using fixed ground order
31704 24576: Id : 2, {_}:
31705 multiply (additive_inverse ?2) (additive_inverse ?3)
31708 [3, 2] by product_of_inverses ?2 ?3
31709 24576: Id : 3, {_}:
31710 multiply (additive_inverse ?5) ?6
31712 additive_inverse (multiply ?5 ?6)
31713 [6, 5] by inverse_product1 ?5 ?6
31714 24576: Id : 4, {_}:
31715 multiply ?8 (additive_inverse ?9)
31717 additive_inverse (multiply ?8 ?9)
31718 [9, 8] by inverse_product2 ?8 ?9
31719 24576: Id : 5, {_}:
31720 multiply ?11 (add ?12 (additive_inverse ?13))
31722 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
31723 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
31724 24576: Id : 6, {_}:
31725 multiply (add ?15 (additive_inverse ?16)) ?17
31727 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
31728 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
31729 24576: Id : 7, {_}:
31730 multiply (additive_inverse ?19) (add ?20 ?21)
31732 add (additive_inverse (multiply ?19 ?20))
31733 (additive_inverse (multiply ?19 ?21))
31734 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
31735 24576: Id : 8, {_}:
31736 multiply (add ?23 ?24) (additive_inverse ?25)
31738 add (additive_inverse (multiply ?23 ?25))
31739 (additive_inverse (multiply ?24 ?25))
31740 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
31741 24576: Id : 9, {_}:
31742 add ?27 ?28 =?= add ?28 ?27
31743 [28, 27] by commutativity_for_addition ?27 ?28
31744 24576: Id : 10, {_}:
31745 add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
31746 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
31747 24576: Id : 11, {_}:
31748 add additive_identity ?34 =>= ?34
31749 [34] by left_additive_identity ?34
31750 24576: Id : 12, {_}:
31751 add ?36 additive_identity =>= ?36
31752 [36] by right_additive_identity ?36
31753 24576: Id : 13, {_}:
31754 multiply additive_identity ?38 =>= additive_identity
31755 [38] by left_multiplicative_zero ?38
31756 24576: Id : 14, {_}:
31757 multiply ?40 additive_identity =>= additive_identity
31758 [40] by right_multiplicative_zero ?40
31759 24576: Id : 15, {_}:
31760 add (additive_inverse ?42) ?42 =>= additive_identity
31761 [42] by left_additive_inverse ?42
31762 24576: Id : 16, {_}:
31763 add ?44 (additive_inverse ?44) =>= additive_identity
31764 [44] by right_additive_inverse ?44
31765 24576: Id : 17, {_}:
31766 multiply ?46 (add ?47 ?48)
31768 add (multiply ?46 ?47) (multiply ?46 ?48)
31769 [48, 47, 46] by distribute1 ?46 ?47 ?48
31770 24576: Id : 18, {_}:
31771 multiply (add ?50 ?51) ?52
31773 add (multiply ?50 ?52) (multiply ?51 ?52)
31774 [52, 51, 50] by distribute2 ?50 ?51 ?52
31775 24576: Id : 19, {_}:
31776 additive_inverse (additive_inverse ?54) =>= ?54
31777 [54] by additive_inverse_additive_inverse ?54
31778 24576: Id : 20, {_}:
31779 multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
31780 [57, 56] by right_alternative ?56 ?57
31781 24576: Id : 21, {_}:
31782 associator ?59 ?60 ?61
31784 add (multiply (multiply ?59 ?60) ?61)
31785 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
31786 [61, 60, 59] by associator ?59 ?60 ?61
31787 24576: Id : 22, {_}:
31790 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
31791 [64, 63] by commutator ?63 ?64
31793 24576: Id : 1, {_}:
31795 (multiply (multiply (associator x x y) (associator x x y)) x)
31796 (multiply (associator x x y) (associator x x y))
31799 [] by prove_conjecture_2
31803 24576: commutator 1 2 0
31805 24576: additive_inverse 22 1 0
31806 24576: additive_identity 9 0 1 3
31807 24576: multiply 40 2 4 0,2add
31808 24576: associator 5 3 4 0,1,1,1,2
31809 24576: y 4 0 4 3,1,1,1,2
31810 24576: x 9 0 9 1,1,1,1,2
31811 NO CLASH, using fixed ground order
31813 24577: Id : 2, {_}:
31814 multiply (additive_inverse ?2) (additive_inverse ?3)
31817 [3, 2] by product_of_inverses ?2 ?3
31818 NO CLASH, using fixed ground order
31820 24578: Id : 2, {_}:
31821 multiply (additive_inverse ?2) (additive_inverse ?3)
31824 [3, 2] by product_of_inverses ?2 ?3
31825 24578: Id : 3, {_}:
31826 multiply (additive_inverse ?5) ?6
31828 additive_inverse (multiply ?5 ?6)
31829 [6, 5] by inverse_product1 ?5 ?6
31830 24578: Id : 4, {_}:
31831 multiply ?8 (additive_inverse ?9)
31833 additive_inverse (multiply ?8 ?9)
31834 [9, 8] by inverse_product2 ?8 ?9
31835 24578: Id : 5, {_}:
31836 multiply ?11 (add ?12 (additive_inverse ?13))
31838 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
31839 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
31840 24578: Id : 6, {_}:
31841 multiply (add ?15 (additive_inverse ?16)) ?17
31843 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
31844 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
31845 24578: Id : 7, {_}:
31846 multiply (additive_inverse ?19) (add ?20 ?21)
31848 add (additive_inverse (multiply ?19 ?20))
31849 (additive_inverse (multiply ?19 ?21))
31850 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
31851 24578: Id : 8, {_}:
31852 multiply (add ?23 ?24) (additive_inverse ?25)
31854 add (additive_inverse (multiply ?23 ?25))
31855 (additive_inverse (multiply ?24 ?25))
31856 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
31857 24578: Id : 9, {_}:
31858 add ?27 ?28 =?= add ?28 ?27
31859 [28, 27] by commutativity_for_addition ?27 ?28
31860 24578: Id : 10, {_}:
31861 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
31862 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
31863 24578: Id : 11, {_}:
31864 add additive_identity ?34 =>= ?34
31865 [34] by left_additive_identity ?34
31866 24578: Id : 12, {_}:
31867 add ?36 additive_identity =>= ?36
31868 [36] by right_additive_identity ?36
31869 24578: Id : 13, {_}:
31870 multiply additive_identity ?38 =>= additive_identity
31871 [38] by left_multiplicative_zero ?38
31872 24578: Id : 14, {_}:
31873 multiply ?40 additive_identity =>= additive_identity
31874 [40] by right_multiplicative_zero ?40
31875 24578: Id : 15, {_}:
31876 add (additive_inverse ?42) ?42 =>= additive_identity
31877 [42] by left_additive_inverse ?42
31878 24578: Id : 16, {_}:
31879 add ?44 (additive_inverse ?44) =>= additive_identity
31880 [44] by right_additive_inverse ?44
31881 24578: Id : 17, {_}:
31882 multiply ?46 (add ?47 ?48)
31884 add (multiply ?46 ?47) (multiply ?46 ?48)
31885 [48, 47, 46] by distribute1 ?46 ?47 ?48
31886 24578: Id : 18, {_}:
31887 multiply (add ?50 ?51) ?52
31889 add (multiply ?50 ?52) (multiply ?51 ?52)
31890 [52, 51, 50] by distribute2 ?50 ?51 ?52
31891 24578: Id : 19, {_}:
31892 additive_inverse (additive_inverse ?54) =>= ?54
31893 [54] by additive_inverse_additive_inverse ?54
31894 24578: Id : 20, {_}:
31895 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
31896 [57, 56] by right_alternative ?56 ?57
31897 24578: Id : 21, {_}:
31898 associator ?59 ?60 ?61
31900 add (multiply (multiply ?59 ?60) ?61)
31901 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
31902 [61, 60, 59] by associator ?59 ?60 ?61
31903 24578: Id : 22, {_}:
31906 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
31907 [64, 63] by commutator ?63 ?64
31909 24578: Id : 1, {_}:
31911 (multiply (multiply (associator x x y) (associator x x y)) x)
31912 (multiply (associator x x y) (associator x x y))
31915 [] by prove_conjecture_2
31919 24578: commutator 1 2 0
31921 24578: additive_inverse 22 1 0
31922 24578: additive_identity 9 0 1 3
31923 24578: multiply 40 2 4 0,2add
31924 24578: associator 5 3 4 0,1,1,1,2
31925 24578: y 4 0 4 3,1,1,1,2
31926 24578: x 9 0 9 1,1,1,1,2
31927 24577: Id : 3, {_}:
31928 multiply (additive_inverse ?5) ?6
31930 additive_inverse (multiply ?5 ?6)
31931 [6, 5] by inverse_product1 ?5 ?6
31932 24577: Id : 4, {_}:
31933 multiply ?8 (additive_inverse ?9)
31935 additive_inverse (multiply ?8 ?9)
31936 [9, 8] by inverse_product2 ?8 ?9
31937 24577: Id : 5, {_}:
31938 multiply ?11 (add ?12 (additive_inverse ?13))
31940 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
31941 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
31942 24577: Id : 6, {_}:
31943 multiply (add ?15 (additive_inverse ?16)) ?17
31945 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
31946 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
31947 24577: Id : 7, {_}:
31948 multiply (additive_inverse ?19) (add ?20 ?21)
31950 add (additive_inverse (multiply ?19 ?20))
31951 (additive_inverse (multiply ?19 ?21))
31952 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
31953 24577: Id : 8, {_}:
31954 multiply (add ?23 ?24) (additive_inverse ?25)
31956 add (additive_inverse (multiply ?23 ?25))
31957 (additive_inverse (multiply ?24 ?25))
31958 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
31959 24577: Id : 9, {_}:
31960 add ?27 ?28 =?= add ?28 ?27
31961 [28, 27] by commutativity_for_addition ?27 ?28
31962 24577: Id : 10, {_}:
31963 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
31964 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
31965 24577: Id : 11, {_}:
31966 add additive_identity ?34 =>= ?34
31967 [34] by left_additive_identity ?34
31968 24577: Id : 12, {_}:
31969 add ?36 additive_identity =>= ?36
31970 [36] by right_additive_identity ?36
31971 24577: Id : 13, {_}:
31972 multiply additive_identity ?38 =>= additive_identity
31973 [38] by left_multiplicative_zero ?38
31974 24577: Id : 14, {_}:
31975 multiply ?40 additive_identity =>= additive_identity
31976 [40] by right_multiplicative_zero ?40
31977 24577: Id : 15, {_}:
31978 add (additive_inverse ?42) ?42 =>= additive_identity
31979 [42] by left_additive_inverse ?42
31980 24577: Id : 16, {_}:
31981 add ?44 (additive_inverse ?44) =>= additive_identity
31982 [44] by right_additive_inverse ?44
31983 24577: Id : 17, {_}:
31984 multiply ?46 (add ?47 ?48)
31986 add (multiply ?46 ?47) (multiply ?46 ?48)
31987 [48, 47, 46] by distribute1 ?46 ?47 ?48
31988 24577: Id : 18, {_}:
31989 multiply (add ?50 ?51) ?52
31991 add (multiply ?50 ?52) (multiply ?51 ?52)
31992 [52, 51, 50] by distribute2 ?50 ?51 ?52
31993 24577: Id : 19, {_}:
31994 additive_inverse (additive_inverse ?54) =>= ?54
31995 [54] by additive_inverse_additive_inverse ?54
31996 24577: Id : 20, {_}:
31997 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
31998 [57, 56] by right_alternative ?56 ?57
31999 24577: Id : 21, {_}:
32000 associator ?59 ?60 ?61
32002 add (multiply (multiply ?59 ?60) ?61)
32003 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
32004 [61, 60, 59] by associator ?59 ?60 ?61
32005 24577: Id : 22, {_}:
32008 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
32009 [64, 63] by commutator ?63 ?64
32011 24577: Id : 1, {_}:
32013 (multiply (multiply (associator x x y) (associator x x y)) x)
32014 (multiply (associator x x y) (associator x x y))
32017 [] by prove_conjecture_2
32021 24577: commutator 1 2 0
32023 24577: additive_inverse 22 1 0
32024 24577: additive_identity 9 0 1 3
32025 24577: multiply 40 2 4 0,2add
32026 24577: associator 5 3 4 0,1,1,1,2
32027 24577: y 4 0 4 3,1,1,1,2
32028 24577: x 9 0 9 1,1,1,1,2
32029 % SZS status Timeout for RNG031-7.p
32030 NO CLASH, using fixed ground order
32032 24609: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
32033 24609: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
32035 24609: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
32040 24609: g2 2 1 1 0,3
32041 24609: g1 2 1 1 0,2
32042 NO CLASH, using fixed ground order
32044 24610: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
32045 24610: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
32047 24610: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
32052 24610: g2 2 1 1 0,3
32053 24610: g1 2 1 1 0,2
32054 NO CLASH, using fixed ground order
32056 24611: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
32057 24611: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
32059 24611: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
32064 24611: g2 2 1 1 0,3
32065 24611: g1 2 1 1 0,2
32066 24609: status GaveUp for SYN305-1.p
32067 24610: status GaveUp for SYN305-1.p
32068 24611: status GaveUp for SYN305-1.p
32069 % SZS status Timeout for SYN305-1.p
32070 CLASH, statistics insufficient
32072 24616: Id : 2, {_}:
32073 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
32074 [5, 4, 3] by b_definition ?3 ?4 ?5
32075 24616: Id : 3, {_}:
32076 apply (apply (apply h ?7) ?8) ?9
32078 apply (apply (apply ?7 ?8) ?9) ?8
32079 [9, 8, 7] by h_definition ?7 ?8 ?9
32081 24616: Id : 1, {_}:
32082 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
32083 [1] by prove_fixed_point ?1
32089 24616: apply 14 2 3 0,2
32090 24616: f 3 1 3 0,2,2
32091 CLASH, statistics insufficient
32093 24617: Id : 2, {_}:
32094 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
32095 [5, 4, 3] by b_definition ?3 ?4 ?5
32096 24617: Id : 3, {_}:
32097 apply (apply (apply h ?7) ?8) ?9
32099 apply (apply (apply ?7 ?8) ?9) ?8
32100 [9, 8, 7] by h_definition ?7 ?8 ?9
32102 24617: Id : 1, {_}:
32103 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
32104 [1] by prove_fixed_point ?1
32110 24617: apply 14 2 3 0,2
32111 24617: f 3 1 3 0,2,2
32112 CLASH, statistics insufficient
32114 24618: Id : 2, {_}:
32115 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
32116 [5, 4, 3] by b_definition ?3 ?4 ?5
32117 24618: Id : 3, {_}:
32118 apply (apply (apply h ?7) ?8) ?9
32120 apply (apply (apply ?7 ?8) ?9) ?8
32121 [9, 8, 7] by h_definition ?7 ?8 ?9
32123 24618: Id : 1, {_}:
32124 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
32125 [1] by prove_fixed_point ?1
32131 24618: apply 14 2 3 0,2
32132 24618: f 3 1 3 0,2,2
32133 % SZS status Timeout for COL043-1.p
32134 CLASH, statistics insufficient
32136 CLASH, statistics insufficient
32138 24655: Id : 2, {_}:
32139 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
32140 [5, 4, 3] by b_definition ?3 ?4 ?5
32141 24655: Id : 3, {_}:
32142 apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
32143 [9, 8, 7] by q_definition ?7 ?8 ?9
32144 24655: Id : 4, {_}:
32145 apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
32146 [12, 11] by w_definition ?11 ?12
32148 24655: Id : 1, {_}:
32149 apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
32151 apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
32152 [1] by prove_p_combinator ?1
32159 24655: h 2 1 2 0,2,2
32160 24655: g 4 1 4 0,2,1,1,2
32161 24655: apply 22 2 8 0,2
32162 24655: f 3 1 3 0,2,1,1,1,2
32163 CLASH, statistics insufficient
32165 24656: Id : 2, {_}:
32166 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
32167 [5, 4, 3] by b_definition ?3 ?4 ?5
32168 24656: Id : 3, {_}:
32169 apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
32170 [9, 8, 7] by q_definition ?7 ?8 ?9
32171 24656: Id : 4, {_}:
32172 apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
32173 [12, 11] by w_definition ?11 ?12
32175 24656: Id : 1, {_}:
32176 apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
32178 apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
32179 [1] by prove_p_combinator ?1
32186 24656: h 2 1 2 0,2,2
32187 24656: g 4 1 4 0,2,1,1,2
32188 24656: apply 22 2 8 0,2
32189 24656: f 3 1 3 0,2,1,1,1,2
32190 24654: Id : 2, {_}:
32191 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
32192 [5, 4, 3] by b_definition ?3 ?4 ?5
32193 24654: Id : 3, {_}:
32194 apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
32195 [9, 8, 7] by q_definition ?7 ?8 ?9
32196 24654: Id : 4, {_}:
32197 apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
32198 [12, 11] by w_definition ?11 ?12
32200 24654: Id : 1, {_}:
32201 apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
32203 apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
32204 [1] by prove_p_combinator ?1
32211 24654: h 2 1 2 0,2,2
32212 24654: g 4 1 4 0,2,1,1,2
32213 24654: apply 22 2 8 0,2
32214 24654: f 3 1 3 0,2,1,1,1,2
32215 % SZS status Timeout for COL066-1.p
32216 NO CLASH, using fixed ground order
32218 24759: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
32219 24759: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
32220 24759: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
32221 24759: Id : 5, {_}:
32222 meet ?9 ?10 =?= meet ?10 ?9
32223 [10, 9] by commutativity_of_meet ?9 ?10
32224 24759: Id : 6, {_}:
32225 join ?12 ?13 =?= join ?13 ?12
32226 [13, 12] by commutativity_of_join ?12 ?13
32227 24759: Id : 7, {_}:
32228 meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
32229 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
32230 24759: Id : 8, {_}:
32231 join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
32232 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
32233 24759: Id : 9, {_}:
32234 complement (complement ?23) =>= ?23
32235 [23] by complement_involution ?23
32236 24759: Id : 10, {_}:
32237 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
32238 [26, 25] by join_complement ?25 ?26
32239 24759: Id : 11, {_}:
32240 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
32241 [29, 28] by meet_complement ?28 ?29
32243 24759: Id : 1, {_}:
32247 (join (meet (complement a) b)
32248 (meet (complement a) (complement b)))
32249 (meet a (join (complement a) b)))) (join (complement a) b)
32258 24759: join 17 2 5 0,2
32259 24759: meet 12 2 3 0,1,1,1,1,2
32260 24759: b 4 0 4 2,1,1,1,1,2
32261 24759: complement 15 1 6 0,1,2
32262 24759: a 5 0 5 1,1,1,1,1,1,2
32263 NO CLASH, using fixed ground order
32265 24760: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
32266 24760: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
32267 24760: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
32268 24760: Id : 5, {_}:
32269 meet ?9 ?10 =?= meet ?10 ?9
32270 [10, 9] by commutativity_of_meet ?9 ?10
32271 24760: Id : 6, {_}:
32272 join ?12 ?13 =?= join ?13 ?12
32273 [13, 12] by commutativity_of_join ?12 ?13
32274 24760: Id : 7, {_}:
32275 meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
32276 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
32277 24760: Id : 8, {_}:
32278 join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
32279 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
32280 24760: Id : 9, {_}:
32281 complement (complement ?23) =>= ?23
32282 [23] by complement_involution ?23
32283 24760: Id : 10, {_}:
32284 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
32285 [26, 25] by join_complement ?25 ?26
32286 24760: Id : 11, {_}:
32287 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
32288 [29, 28] by meet_complement ?28 ?29
32290 24760: Id : 1, {_}:
32294 (join (meet (complement a) b)
32295 (meet (complement a) (complement b)))
32296 (meet a (join (complement a) b)))) (join (complement a) b)
32305 24760: join 17 2 5 0,2
32306 24760: meet 12 2 3 0,1,1,1,1,2
32307 24760: b 4 0 4 2,1,1,1,1,2
32308 24760: complement 15 1 6 0,1,2
32309 24760: a 5 0 5 1,1,1,1,1,1,2
32310 NO CLASH, using fixed ground order
32312 24761: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
32313 24761: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
32314 24761: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
32315 24761: Id : 5, {_}:
32316 meet ?9 ?10 =?= meet ?10 ?9
32317 [10, 9] by commutativity_of_meet ?9 ?10
32318 24761: Id : 6, {_}:
32319 join ?12 ?13 =?= join ?13 ?12
32320 [13, 12] by commutativity_of_join ?12 ?13
32321 24761: Id : 7, {_}:
32322 meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
32323 [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
32324 24761: Id : 8, {_}:
32325 join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
32326 [21, 20, 19] by associativity_of_join ?19 ?20 ?21
32327 24761: Id : 9, {_}:
32328 complement (complement ?23) =>= ?23
32329 [23] by complement_involution ?23
32330 24761: Id : 10, {_}:
32331 join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
32332 [26, 25] by join_complement ?25 ?26
32333 24761: Id : 11, {_}:
32334 meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
32335 [29, 28] by meet_complement ?28 ?29
32337 24761: Id : 1, {_}:
32341 (join (meet (complement a) b)
32342 (meet (complement a) (complement b)))
32343 (meet a (join (complement a) b)))) (join (complement a) b)
32352 24761: join 17 2 5 0,2
32353 24761: meet 12 2 3 0,1,1,1,1,2
32354 24761: b 4 0 4 2,1,1,1,1,2
32355 24761: complement 15 1 6 0,1,2
32356 24761: a 5 0 5 1,1,1,1,1,1,2
32357 % SZS status Timeout for LAT018-1.p
32358 NO CLASH, using fixed ground order
32360 24778: Id : 2, {_}:
32361 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
32363 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
32367 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
32370 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
32371 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
32372 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
32375 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
32377 24778: Id : 1, {_}:
32378 meet (meet a b) c =>= meet a (meet b c)
32379 [] by prove_normal_axioms_3
32385 24778: meet 22 2 4 0,2
32386 24778: b 2 0 2 2,1,2
32387 24778: a 2 0 2 1,1,2
32388 NO CLASH, using fixed ground order
32390 24779: Id : 2, {_}:
32391 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
32393 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
32397 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
32400 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
32401 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
32402 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
32405 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
32407 24779: Id : 1, {_}:
32408 meet (meet a b) c =>= meet a (meet b c)
32409 [] by prove_normal_axioms_3
32415 24779: meet 22 2 4 0,2
32416 24779: b 2 0 2 2,1,2
32417 24779: a 2 0 2 1,1,2
32418 NO CLASH, using fixed ground order
32420 24780: Id : 2, {_}:
32421 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
32423 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
32427 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
32430 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
32431 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
32432 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
32435 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
32437 24780: Id : 1, {_}:
32438 meet (meet a b) c =>= meet a (meet b c)
32439 [] by prove_normal_axioms_3
32445 24780: meet 22 2 4 0,2
32446 24780: b 2 0 2 2,1,2
32447 24780: a 2 0 2 1,1,2
32448 % SZS status Timeout for LAT082-1.p
32449 NO CLASH, using fixed ground order
32451 24809: Id : 2, {_}:
32452 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
32454 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
32458 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
32461 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
32462 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
32463 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
32466 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
32468 24809: Id : 1, {_}:
32469 join (join a b) c =>= join a (join b c)
32470 [] by prove_normal_axioms_6
32476 24809: join 24 2 4 0,2
32477 24809: b 2 0 2 2,1,2
32478 24809: a 2 0 2 1,1,2
32479 NO CLASH, using fixed ground order
32481 24810: Id : 2, {_}:
32482 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
32484 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
32488 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
32491 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
32492 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
32493 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
32496 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
32498 24810: Id : 1, {_}:
32499 join (join a b) c =>= join a (join b c)
32500 [] by prove_normal_axioms_6
32506 24810: join 24 2 4 0,2
32507 24810: b 2 0 2 2,1,2
32508 24810: a 2 0 2 1,1,2
32509 NO CLASH, using fixed ground order
32511 24808: Id : 2, {_}:
32512 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
32514 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
32518 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
32521 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
32522 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
32523 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
32526 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
32528 24808: Id : 1, {_}:
32529 join (join a b) c =>= join a (join b c)
32530 [] by prove_normal_axioms_6
32536 24808: join 24 2 4 0,2
32537 24808: b 2 0 2 2,1,2
32538 24808: a 2 0 2 1,1,2
32539 % SZS status Timeout for LAT085-1.p
32540 NO CLASH, using fixed ground order
32542 24831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32543 24831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32544 24831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32545 24831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32546 24831: Id : 6, {_}:
32547 meet ?12 ?13 =?= meet ?13 ?12
32548 [13, 12] by commutativity_of_meet ?12 ?13
32549 24831: Id : 7, {_}:
32550 join ?15 ?16 =?= join ?16 ?15
32551 [16, 15] by commutativity_of_join ?15 ?16
32552 24831: Id : 8, {_}:
32553 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
32554 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32555 24831: Id : 9, {_}:
32556 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
32557 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32558 24831: Id : 10, {_}:
32559 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
32561 meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
32562 [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
32564 24831: Id : 1, {_}:
32565 meet a (join b (meet a c))
32567 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
32572 24831: join 16 2 4 0,2,2
32573 24831: meet 22 2 6 0,2
32574 24831: c 4 0 4 2,2,2,2
32575 24831: b 4 0 4 1,2,2
32577 NO CLASH, using fixed ground order
32579 24832: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32580 24832: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32581 24832: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32582 24832: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32583 24832: Id : 6, {_}:
32584 meet ?12 ?13 =?= meet ?13 ?12
32585 [13, 12] by commutativity_of_meet ?12 ?13
32586 24832: Id : 7, {_}:
32587 join ?15 ?16 =?= join ?16 ?15
32588 [16, 15] by commutativity_of_join ?15 ?16
32589 24832: Id : 8, {_}:
32590 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32591 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32592 24832: Id : 9, {_}:
32593 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32594 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32595 24832: Id : 10, {_}:
32596 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
32598 meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
32599 [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
32601 24832: Id : 1, {_}:
32602 meet a (join b (meet a c))
32604 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
32609 24832: join 16 2 4 0,2,2
32610 24832: meet 22 2 6 0,2
32611 24832: c 4 0 4 2,2,2,2
32612 24832: b 4 0 4 1,2,2
32614 NO CLASH, using fixed ground order
32616 24833: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32617 24833: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32618 24833: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32619 24833: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32620 24833: Id : 6, {_}:
32621 meet ?12 ?13 =?= meet ?13 ?12
32622 [13, 12] by commutativity_of_meet ?12 ?13
32623 24833: Id : 7, {_}:
32624 join ?15 ?16 =?= join ?16 ?15
32625 [16, 15] by commutativity_of_join ?15 ?16
32626 24833: Id : 8, {_}:
32627 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32628 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32629 24833: Id : 9, {_}:
32630 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32631 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32632 24833: Id : 10, {_}:
32633 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
32635 meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
32636 [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
32638 24833: Id : 1, {_}:
32639 meet a (join b (meet a c))
32641 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
32646 24833: join 16 2 4 0,2,2
32647 24833: meet 22 2 6 0,2
32648 24833: c 4 0 4 2,2,2,2
32649 24833: b 4 0 4 1,2,2
32651 % SZS status Timeout for LAT144-1.p
32652 NO CLASH, using fixed ground order
32654 24860: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32655 24860: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32656 24860: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32657 24860: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32658 24860: Id : 6, {_}:
32659 meet ?12 ?13 =?= meet ?13 ?12
32660 [13, 12] by commutativity_of_meet ?12 ?13
32661 24860: Id : 7, {_}:
32662 join ?15 ?16 =?= join ?16 ?15
32663 [16, 15] by commutativity_of_join ?15 ?16
32664 24860: Id : 8, {_}:
32665 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
32666 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32667 24860: Id : 9, {_}:
32668 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
32669 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32670 24860: Id : 10, {_}:
32671 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32673 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
32674 [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
32676 24860: Id : 1, {_}:
32677 meet a (join b (meet c (join a d)))
32679 meet a (join b (meet c (join d (meet c (join a b)))))
32684 24860: meet 19 2 5 0,2
32685 24860: join 18 2 5 0,2,2
32686 24860: d 2 0 2 2,2,2,2,2
32687 24860: c 3 0 3 1,2,2,2
32688 24860: b 3 0 3 1,2,2
32690 NO CLASH, using fixed ground order
32692 24861: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32693 24861: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32694 24861: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32695 24861: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32696 24861: Id : 6, {_}:
32697 meet ?12 ?13 =?= meet ?13 ?12
32698 [13, 12] by commutativity_of_meet ?12 ?13
32699 24861: Id : 7, {_}:
32700 join ?15 ?16 =?= join ?16 ?15
32701 [16, 15] by commutativity_of_join ?15 ?16
32702 24861: Id : 8, {_}:
32703 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32704 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32705 24861: Id : 9, {_}:
32706 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32707 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32708 24861: Id : 10, {_}:
32709 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32711 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
32712 [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
32714 24861: Id : 1, {_}:
32715 meet a (join b (meet c (join a d)))
32717 meet a (join b (meet c (join d (meet c (join a b)))))
32722 24861: meet 19 2 5 0,2
32723 24861: join 18 2 5 0,2,2
32724 24861: d 2 0 2 2,2,2,2,2
32725 24861: c 3 0 3 1,2,2,2
32726 24861: b 3 0 3 1,2,2
32728 NO CLASH, using fixed ground order
32730 24862: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32731 24862: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32732 24862: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32733 24862: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32734 24862: Id : 6, {_}:
32735 meet ?12 ?13 =?= meet ?13 ?12
32736 [13, 12] by commutativity_of_meet ?12 ?13
32737 24862: Id : 7, {_}:
32738 join ?15 ?16 =?= join ?16 ?15
32739 [16, 15] by commutativity_of_join ?15 ?16
32740 24862: Id : 8, {_}:
32741 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32742 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32743 24862: Id : 9, {_}:
32744 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32745 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32746 24862: Id : 10, {_}:
32747 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32749 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
32750 [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
32752 24862: Id : 1, {_}:
32753 meet a (join b (meet c (join a d)))
32755 meet a (join b (meet c (join d (meet c (join a b)))))
32760 24862: meet 19 2 5 0,2
32761 24862: join 18 2 5 0,2,2
32762 24862: d 2 0 2 2,2,2,2,2
32763 24862: c 3 0 3 1,2,2,2
32764 24862: b 3 0 3 1,2,2
32766 % SZS status Timeout for LAT150-1.p
32767 NO CLASH, using fixed ground order
32768 NO CLASH, using fixed ground order
32770 24889: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32771 24889: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32772 24889: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32773 24889: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32774 24889: Id : 6, {_}:
32775 meet ?12 ?13 =?= meet ?13 ?12
32776 [13, 12] by commutativity_of_meet ?12 ?13
32777 24889: Id : 7, {_}:
32778 join ?15 ?16 =?= join ?16 ?15
32779 [16, 15] by commutativity_of_join ?15 ?16
32780 24889: Id : 8, {_}:
32781 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32782 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32783 24889: Id : 9, {_}:
32784 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32785 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32786 24889: Id : 10, {_}:
32787 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32789 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
32790 [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
32792 24889: Id : 1, {_}:
32793 meet a (join b (meet c (join a d)))
32795 meet a (join b (meet c (join b (join d (meet a c)))))
32800 24889: meet 19 2 5 0,2
32801 24889: join 18 2 5 0,2,2
32802 24889: d 2 0 2 2,2,2,2,2
32803 24889: c 3 0 3 1,2,2,2
32804 24889: b 3 0 3 1,2,2
32807 24888: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32808 24888: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32809 24888: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32810 24888: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32811 24888: Id : 6, {_}:
32812 meet ?12 ?13 =?= meet ?13 ?12
32813 [13, 12] by commutativity_of_meet ?12 ?13
32814 24888: Id : 7, {_}:
32815 join ?15 ?16 =?= join ?16 ?15
32816 [16, 15] by commutativity_of_join ?15 ?16
32817 24888: Id : 8, {_}:
32818 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
32819 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32820 24888: Id : 9, {_}:
32821 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
32822 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32823 24888: Id : 10, {_}:
32824 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32826 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
32827 [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
32829 24888: Id : 1, {_}:
32830 meet a (join b (meet c (join a d)))
32832 meet a (join b (meet c (join b (join d (meet a c)))))
32837 24888: meet 19 2 5 0,2
32838 24888: join 18 2 5 0,2,2
32839 24888: d 2 0 2 2,2,2,2,2
32840 24888: c 3 0 3 1,2,2,2
32841 24888: b 3 0 3 1,2,2
32843 NO CLASH, using fixed ground order
32845 24890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32846 24890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32847 24890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32848 24890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32849 24890: Id : 6, {_}:
32850 meet ?12 ?13 =?= meet ?13 ?12
32851 [13, 12] by commutativity_of_meet ?12 ?13
32852 24890: Id : 7, {_}:
32853 join ?15 ?16 =?= join ?16 ?15
32854 [16, 15] by commutativity_of_join ?15 ?16
32855 24890: Id : 8, {_}:
32856 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32857 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32858 24890: Id : 9, {_}:
32859 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32860 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32861 24890: Id : 10, {_}:
32862 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32864 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
32865 [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
32867 24890: Id : 1, {_}:
32868 meet a (join b (meet c (join a d)))
32870 meet a (join b (meet c (join b (join d (meet a c)))))
32875 24890: meet 19 2 5 0,2
32876 24890: join 18 2 5 0,2,2
32877 24890: d 2 0 2 2,2,2,2,2
32878 24890: c 3 0 3 1,2,2,2
32879 24890: b 3 0 3 1,2,2
32881 % SZS status Timeout for LAT151-1.p
32882 NO CLASH, using fixed ground order
32884 24921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32885 24921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32886 24921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32887 24921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32888 24921: Id : 6, {_}:
32889 meet ?12 ?13 =?= meet ?13 ?12
32890 [13, 12] by commutativity_of_meet ?12 ?13
32891 24921: Id : 7, {_}:
32892 join ?15 ?16 =?= join ?16 ?15
32893 [16, 15] by commutativity_of_join ?15 ?16
32894 24921: Id : 8, {_}:
32895 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
32896 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32897 24921: Id : 9, {_}:
32898 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
32899 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32900 24921: Id : 10, {_}:
32901 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32903 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
32904 [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
32906 24921: Id : 1, {_}:
32907 meet a (join b (meet a c))
32909 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
32914 24921: join 18 2 4 0,2,2
32915 24921: meet 20 2 6 0,2
32916 24921: c 3 0 3 2,2,2,2
32917 24921: b 3 0 3 1,2,2
32919 NO CLASH, using fixed ground order
32921 24922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32922 24922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32923 24922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32924 24922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32925 24922: Id : 6, {_}:
32926 meet ?12 ?13 =?= meet ?13 ?12
32927 [13, 12] by commutativity_of_meet ?12 ?13
32928 24922: Id : 7, {_}:
32929 join ?15 ?16 =?= join ?16 ?15
32930 [16, 15] by commutativity_of_join ?15 ?16
32931 24922: Id : 8, {_}:
32932 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32933 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32934 24922: Id : 9, {_}:
32935 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32936 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32937 24922: Id : 10, {_}:
32938 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32940 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
32941 [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
32943 24922: Id : 1, {_}:
32944 meet a (join b (meet a c))
32946 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
32951 24922: join 18 2 4 0,2,2
32952 24922: meet 20 2 6 0,2
32953 24922: c 3 0 3 2,2,2,2
32954 24922: b 3 0 3 1,2,2
32956 NO CLASH, using fixed ground order
32958 24923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32959 24923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32960 24923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32961 24923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
32962 24923: Id : 6, {_}:
32963 meet ?12 ?13 =?= meet ?13 ?12
32964 [13, 12] by commutativity_of_meet ?12 ?13
32965 24923: Id : 7, {_}:
32966 join ?15 ?16 =?= join ?16 ?15
32967 [16, 15] by commutativity_of_join ?15 ?16
32968 24923: Id : 8, {_}:
32969 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
32970 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
32971 24923: Id : 9, {_}:
32972 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
32973 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
32974 24923: Id : 10, {_}:
32975 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
32977 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
32978 [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
32980 24923: Id : 1, {_}:
32981 meet a (join b (meet a c))
32983 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
32988 24923: join 18 2 4 0,2,2
32989 24923: meet 20 2 6 0,2
32990 24923: c 3 0 3 2,2,2,2
32991 24923: b 3 0 3 1,2,2
32993 % SZS status Timeout for LAT152-1.p
32994 NO CLASH, using fixed ground order
32996 24939: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
32997 24939: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
32998 24939: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
32999 24939: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33000 24939: Id : 6, {_}:
33001 meet ?12 ?13 =?= meet ?13 ?12
33002 [13, 12] by commutativity_of_meet ?12 ?13
33003 24939: Id : 7, {_}:
33004 join ?15 ?16 =?= join ?16 ?15
33005 [16, 15] by commutativity_of_join ?15 ?16
33006 24939: Id : 8, {_}:
33007 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
33008 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33009 24939: Id : 9, {_}:
33010 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
33011 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33012 24939: Id : 10, {_}:
33013 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
33015 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
33016 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
33018 24939: Id : 1, {_}:
33019 meet a (join b (meet a c))
33021 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
33026 24939: join 18 2 4 0,2,2
33027 24939: meet 20 2 6 0,2
33028 24939: c 2 0 2 2,2,2,2
33029 24939: b 4 0 4 1,2,2
33031 NO CLASH, using fixed ground order
33033 24940: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33034 24940: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33035 24940: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33036 24940: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33037 24940: Id : 6, {_}:
33038 meet ?12 ?13 =?= meet ?13 ?12
33039 [13, 12] by commutativity_of_meet ?12 ?13
33040 24940: Id : 7, {_}:
33041 join ?15 ?16 =?= join ?16 ?15
33042 [16, 15] by commutativity_of_join ?15 ?16
33043 24940: Id : 8, {_}:
33044 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33045 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33046 24940: Id : 9, {_}:
33047 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33048 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33049 24940: Id : 10, {_}:
33050 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
33052 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
33053 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
33055 24940: Id : 1, {_}:
33056 meet a (join b (meet a c))
33058 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
33063 24940: join 18 2 4 0,2,2
33064 24940: meet 20 2 6 0,2
33065 24940: c 2 0 2 2,2,2,2
33066 24940: b 4 0 4 1,2,2
33068 NO CLASH, using fixed ground order
33070 24941: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33071 24941: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33072 24941: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33073 24941: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33074 24941: Id : 6, {_}:
33075 meet ?12 ?13 =?= meet ?13 ?12
33076 [13, 12] by commutativity_of_meet ?12 ?13
33077 24941: Id : 7, {_}:
33078 join ?15 ?16 =?= join ?16 ?15
33079 [16, 15] by commutativity_of_join ?15 ?16
33080 24941: Id : 8, {_}:
33081 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33082 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33083 24941: Id : 9, {_}:
33084 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33085 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33086 24941: Id : 10, {_}:
33087 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
33089 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
33090 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
33092 24941: Id : 1, {_}:
33093 meet a (join b (meet a c))
33095 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
33100 24941: join 18 2 4 0,2,2
33101 24941: meet 20 2 6 0,2
33102 24941: c 2 0 2 2,2,2,2
33103 24941: b 4 0 4 1,2,2
33105 % SZS status Timeout for LAT159-1.p
33106 NO CLASH, using fixed ground order
33108 24972: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33109 24972: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33110 24972: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33111 NO CLASH, using fixed ground order
33112 24972: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33113 24972: Id : 6, {_}:
33114 meet ?12 ?13 =?= meet ?13 ?12
33115 [13, 12] by commutativity_of_meet ?12 ?13
33116 24972: Id : 7, {_}:
33117 join ?15 ?16 =?= join ?16 ?15
33118 [16, 15] by commutativity_of_join ?15 ?16
33119 24972: Id : 8, {_}:
33120 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
33121 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33122 24972: Id : 9, {_}:
33123 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
33124 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33125 24972: Id : 10, {_}:
33126 meet ?26 (join ?27 ?28)
33128 meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
33129 [28, 27, 26] by equation_H68 ?26 ?27 ?28
33131 24972: Id : 1, {_}:
33132 meet a (meet b (join c d))
33134 meet a (meet b (join c (meet a (join d (meet b c)))))
33139 24972: meet 19 2 6 0,2
33140 24972: join 15 2 3 0,2,2,2
33141 24972: d 2 0 2 2,2,2,2
33142 24972: c 3 0 3 1,2,2,2
33143 24972: b 3 0 3 1,2,2
33146 24973: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33147 24973: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33148 24973: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33149 24973: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33150 24973: Id : 6, {_}:
33151 meet ?12 ?13 =?= meet ?13 ?12
33152 [13, 12] by commutativity_of_meet ?12 ?13
33153 24973: Id : 7, {_}:
33154 join ?15 ?16 =?= join ?16 ?15
33155 [16, 15] by commutativity_of_join ?15 ?16
33156 24973: Id : 8, {_}:
33157 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33158 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33159 24973: Id : 9, {_}:
33160 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33161 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33162 24973: Id : 10, {_}:
33163 meet ?26 (join ?27 ?28)
33165 meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
33166 [28, 27, 26] by equation_H68 ?26 ?27 ?28
33168 24973: Id : 1, {_}:
33169 meet a (meet b (join c d))
33171 meet a (meet b (join c (meet a (join d (meet b c)))))
33176 24973: meet 19 2 6 0,2
33177 24973: join 15 2 3 0,2,2,2
33178 24973: d 2 0 2 2,2,2,2
33179 24973: c 3 0 3 1,2,2,2
33180 24973: b 3 0 3 1,2,2
33182 NO CLASH, using fixed ground order
33184 24974: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33185 24974: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33186 24974: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33187 24974: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33188 24974: Id : 6, {_}:
33189 meet ?12 ?13 =?= meet ?13 ?12
33190 [13, 12] by commutativity_of_meet ?12 ?13
33191 24974: Id : 7, {_}:
33192 join ?15 ?16 =?= join ?16 ?15
33193 [16, 15] by commutativity_of_join ?15 ?16
33194 24974: Id : 8, {_}:
33195 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33196 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33197 24974: Id : 9, {_}:
33198 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33199 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33200 24974: Id : 10, {_}:
33201 meet ?26 (join ?27 ?28)
33203 meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
33204 [28, 27, 26] by equation_H68 ?26 ?27 ?28
33206 24974: Id : 1, {_}:
33207 meet a (meet b (join c d))
33209 meet a (meet b (join c (meet a (join d (meet b c)))))
33214 24974: meet 19 2 6 0,2
33215 24974: join 15 2 3 0,2,2,2
33216 24974: d 2 0 2 2,2,2,2
33217 24974: c 3 0 3 1,2,2,2
33218 24974: b 3 0 3 1,2,2
33220 % SZS status Timeout for LAT162-1.p
33221 NO CLASH, using fixed ground order
33223 24990: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33224 24990: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33225 24990: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33226 24990: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33227 24990: Id : 6, {_}:
33228 meet ?12 ?13 =?= meet ?13 ?12
33229 [13, 12] by commutativity_of_meet ?12 ?13
33230 24990: Id : 7, {_}:
33231 join ?15 ?16 =?= join ?16 ?15
33232 [16, 15] by commutativity_of_join ?15 ?16
33233 24990: Id : 8, {_}:
33234 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
33235 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33236 24990: Id : 9, {_}:
33237 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
33238 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33239 24990: Id : 10, {_}:
33240 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
33242 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
33243 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
33245 24990: Id : 1, {_}:
33246 meet a (join b (meet a c))
33248 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
33253 24990: join 17 2 4 0,2,2
33254 24990: meet 20 2 6 0,2
33255 24990: c 3 0 3 2,2,2,2
33256 24990: b 3 0 3 1,2,2
33258 NO CLASH, using fixed ground order
33260 24991: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33261 24991: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33262 24991: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33263 24991: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33264 24991: Id : 6, {_}:
33265 meet ?12 ?13 =?= meet ?13 ?12
33266 [13, 12] by commutativity_of_meet ?12 ?13
33267 24991: Id : 7, {_}:
33268 join ?15 ?16 =?= join ?16 ?15
33269 [16, 15] by commutativity_of_join ?15 ?16
33270 24991: Id : 8, {_}:
33271 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33272 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33273 24991: Id : 9, {_}:
33274 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33275 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33276 24991: Id : 10, {_}:
33277 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
33279 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
33280 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
33282 24991: Id : 1, {_}:
33283 meet a (join b (meet a c))
33285 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
33290 24991: join 17 2 4 0,2,2
33291 24991: meet 20 2 6 0,2
33292 24991: c 3 0 3 2,2,2,2
33293 24991: b 3 0 3 1,2,2
33295 NO CLASH, using fixed ground order
33297 24992: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33298 24992: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33299 24992: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33300 24992: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33301 24992: Id : 6, {_}:
33302 meet ?12 ?13 =?= meet ?13 ?12
33303 [13, 12] by commutativity_of_meet ?12 ?13
33304 24992: Id : 7, {_}:
33305 join ?15 ?16 =?= join ?16 ?15
33306 [16, 15] by commutativity_of_join ?15 ?16
33307 24992: Id : 8, {_}:
33308 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33309 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33310 24992: Id : 9, {_}:
33311 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33312 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33313 24992: Id : 10, {_}:
33314 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
33316 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
33317 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
33319 24992: Id : 1, {_}:
33320 meet a (join b (meet a c))
33322 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
33327 24992: join 17 2 4 0,2,2
33328 24992: meet 20 2 6 0,2
33329 24992: c 3 0 3 2,2,2,2
33330 24992: b 3 0 3 1,2,2
33332 % SZS status Timeout for LAT164-1.p
33333 NO CLASH, using fixed ground order
33335 NO CLASH, using fixed ground order
33337 25020: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33338 25020: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33339 25020: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33340 25020: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33341 25020: Id : 6, {_}:
33342 meet ?12 ?13 =?= meet ?13 ?12
33343 [13, 12] by commutativity_of_meet ?12 ?13
33344 25020: Id : 7, {_}:
33345 join ?15 ?16 =?= join ?16 ?15
33346 [16, 15] by commutativity_of_join ?15 ?16
33347 25020: Id : 8, {_}:
33348 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33349 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33350 25020: Id : 9, {_}:
33351 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33352 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33353 25020: Id : 10, {_}:
33354 meet (join ?26 ?27) (join ?26 ?28)
33357 (meet (join ?27 (meet ?26 (join ?27 ?28)))
33358 (join ?28 (meet ?26 ?27)))
33359 [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
33361 25020: Id : 1, {_}:
33364 meet a (join b (meet (join a b) (join c (meet a b))))
33369 25020: meet 17 2 4 0,2
33370 25020: join 19 2 4 0,2,2
33371 25020: c 2 0 2 2,2,2
33372 25020: b 4 0 4 1,2,2
33374 25019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33375 25019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33376 25019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33377 25019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33378 25019: Id : 6, {_}:
33379 meet ?12 ?13 =?= meet ?13 ?12
33380 [13, 12] by commutativity_of_meet ?12 ?13
33381 25019: Id : 7, {_}:
33382 join ?15 ?16 =?= join ?16 ?15
33383 [16, 15] by commutativity_of_join ?15 ?16
33384 25019: Id : 8, {_}:
33385 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
33386 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33387 NO CLASH, using fixed ground order
33388 25019: Id : 9, {_}:
33389 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
33390 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33391 25019: Id : 10, {_}:
33392 meet (join ?26 ?27) (join ?26 ?28)
33395 (meet (join ?27 (meet ?26 (join ?27 ?28)))
33396 (join ?28 (meet ?26 ?27)))
33397 [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
33399 25019: Id : 1, {_}:
33402 meet a (join b (meet (join a b) (join c (meet a b))))
33407 25019: meet 17 2 4 0,2
33408 25019: join 19 2 4 0,2,2
33409 25019: c 2 0 2 2,2,2
33410 25019: b 4 0 4 1,2,2
33413 25021: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33414 25021: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33415 25021: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33416 25021: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33417 25021: Id : 6, {_}:
33418 meet ?12 ?13 =?= meet ?13 ?12
33419 [13, 12] by commutativity_of_meet ?12 ?13
33420 25021: Id : 7, {_}:
33421 join ?15 ?16 =?= join ?16 ?15
33422 [16, 15] by commutativity_of_join ?15 ?16
33423 25021: Id : 8, {_}:
33424 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33425 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33426 25021: Id : 9, {_}:
33427 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33428 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33429 25021: Id : 10, {_}:
33430 meet (join ?26 ?27) (join ?26 ?28)
33433 (meet (join ?27 (meet ?26 (join ?27 ?28)))
33434 (join ?28 (meet ?26 ?27)))
33435 [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
33437 25021: Id : 1, {_}:
33440 meet a (join b (meet (join a b) (join c (meet a b))))
33445 25021: meet 17 2 4 0,2
33446 25021: join 19 2 4 0,2,2
33447 25021: c 2 0 2 2,2,2
33448 25021: b 4 0 4 1,2,2
33450 % SZS status Timeout for LAT169-1.p
33451 NO CLASH, using fixed ground order
33453 25071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33454 25071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33455 25071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33456 25071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33457 25071: Id : 6, {_}:
33458 meet ?12 ?13 =?= meet ?13 ?12
33459 [13, 12] by commutativity_of_meet ?12 ?13
33460 25071: Id : 7, {_}:
33461 join ?15 ?16 =?= join ?16 ?15
33462 [16, 15] by commutativity_of_join ?15 ?16
33463 25071: Id : 8, {_}:
33464 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
33465 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33466 25071: Id : 9, {_}:
33467 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
33468 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33469 25071: Id : 10, {_}:
33470 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
33472 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
33473 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
33475 25071: Id : 1, {_}:
33476 meet a (join b (meet a c))
33478 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
33483 25071: join 18 2 4 0,2,2
33484 25071: meet 19 2 6 0,2
33485 25071: c 3 0 3 2,2,2,2
33486 25071: b 3 0 3 1,2,2
33488 NO CLASH, using fixed ground order
33490 25072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33491 25072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33492 25072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33493 25072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33494 25072: Id : 6, {_}:
33495 meet ?12 ?13 =?= meet ?13 ?12
33496 [13, 12] by commutativity_of_meet ?12 ?13
33497 25072: Id : 7, {_}:
33498 join ?15 ?16 =?= join ?16 ?15
33499 [16, 15] by commutativity_of_join ?15 ?16
33500 25072: Id : 8, {_}:
33501 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33502 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33503 25072: Id : 9, {_}:
33504 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33505 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33506 25072: Id : 10, {_}:
33507 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
33509 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
33510 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
33512 25072: Id : 1, {_}:
33513 meet a (join b (meet a c))
33515 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
33520 25072: join 18 2 4 0,2,2
33521 25072: meet 19 2 6 0,2
33522 25072: c 3 0 3 2,2,2,2
33523 25072: b 3 0 3 1,2,2
33525 NO CLASH, using fixed ground order
33527 25073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
33528 25073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
33529 25073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
33530 25073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
33531 25073: Id : 6, {_}:
33532 meet ?12 ?13 =?= meet ?13 ?12
33533 [13, 12] by commutativity_of_meet ?12 ?13
33534 25073: Id : 7, {_}:
33535 join ?15 ?16 =?= join ?16 ?15
33536 [16, 15] by commutativity_of_join ?15 ?16
33537 25073: Id : 8, {_}:
33538 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
33539 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
33540 25073: Id : 9, {_}:
33541 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
33542 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
33543 25073: Id : 10, {_}:
33544 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
33546 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
33547 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
33549 25073: Id : 1, {_}:
33550 meet a (join b (meet a c))
33552 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
33557 25073: join 18 2 4 0,2,2
33558 25073: meet 19 2 6 0,2
33559 25073: c 3 0 3 2,2,2,2
33560 25073: b 3 0 3 1,2,2
33562 % SZS status Timeout for LAT174-1.p
33563 NO CLASH, using fixed ground order
33565 25101: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
33566 25101: Id : 3, {_}:
33567 add ?4 additive_identity =>= ?4
33568 [4] by right_additive_identity ?4
33569 25101: Id : 4, {_}:
33570 multiply additive_identity ?6 =>= additive_identity
33571 [6] by left_multiplicative_zero ?6
33572 25101: Id : 5, {_}:
33573 multiply ?8 additive_identity =>= additive_identity
33574 [8] by right_multiplicative_zero ?8
33575 25101: Id : 6, {_}:
33576 add (additive_inverse ?10) ?10 =>= additive_identity
33577 [10] by left_additive_inverse ?10
33578 25101: Id : 7, {_}:
33579 add ?12 (additive_inverse ?12) =>= additive_identity
33580 [12] by right_additive_inverse ?12
33581 25101: Id : 8, {_}:
33582 additive_inverse (additive_inverse ?14) =>= ?14
33583 [14] by additive_inverse_additive_inverse ?14
33584 25101: Id : 9, {_}:
33585 multiply ?16 (add ?17 ?18)
33587 add (multiply ?16 ?17) (multiply ?16 ?18)
33588 [18, 17, 16] by distribute1 ?16 ?17 ?18
33589 25101: Id : 10, {_}:
33590 multiply (add ?20 ?21) ?22
33592 add (multiply ?20 ?22) (multiply ?21 ?22)
33593 [22, 21, 20] by distribute2 ?20 ?21 ?22
33594 25101: Id : 11, {_}:
33595 add ?24 ?25 =?= add ?25 ?24
33596 [25, 24] by commutativity_for_addition ?24 ?25
33597 25101: Id : 12, {_}:
33598 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
33599 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
33600 25101: Id : 13, {_}:
33601 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
33602 [32, 31] by right_alternative ?31 ?32
33603 25101: Id : 14, {_}:
33604 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
33605 [35, 34] by left_alternative ?34 ?35
33606 25101: Id : 15, {_}:
33607 associator ?37 ?38 ?39
33609 add (multiply (multiply ?37 ?38) ?39)
33610 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
33611 [39, 38, 37] by associator ?37 ?38 ?39
33612 25101: Id : 16, {_}:
33615 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
33616 [42, 41] by commutator ?41 ?42
33618 25101: Id : 1, {_}:
33619 multiply cz (multiply cx (multiply cy cx))
33621 multiply (multiply (multiply cz cx) cy) cx
33622 [] by prove_right_moufang
33626 25101: commutator 1 2 0
33627 25101: associator 1 3 0
33628 25101: additive_inverse 6 1 0
33630 25101: additive_identity 8 0 0
33631 25101: multiply 28 2 6 0,2
33632 25101: cy 2 0 2 1,2,2,2
33633 25101: cx 4 0 4 1,2,2
33634 25101: cz 2 0 2 1,2
33635 NO CLASH, using fixed ground order
33637 25102: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
33638 25102: Id : 3, {_}:
33639 add ?4 additive_identity =>= ?4
33640 [4] by right_additive_identity ?4
33641 25102: Id : 4, {_}:
33642 multiply additive_identity ?6 =>= additive_identity
33643 [6] by left_multiplicative_zero ?6
33644 25102: Id : 5, {_}:
33645 multiply ?8 additive_identity =>= additive_identity
33646 [8] by right_multiplicative_zero ?8
33647 25102: Id : 6, {_}:
33648 add (additive_inverse ?10) ?10 =>= additive_identity
33649 [10] by left_additive_inverse ?10
33650 25102: Id : 7, {_}:
33651 add ?12 (additive_inverse ?12) =>= additive_identity
33652 [12] by right_additive_inverse ?12
33653 25102: Id : 8, {_}:
33654 additive_inverse (additive_inverse ?14) =>= ?14
33655 [14] by additive_inverse_additive_inverse ?14
33656 25102: Id : 9, {_}:
33657 multiply ?16 (add ?17 ?18)
33659 add (multiply ?16 ?17) (multiply ?16 ?18)
33660 [18, 17, 16] by distribute1 ?16 ?17 ?18
33661 25102: Id : 10, {_}:
33662 multiply (add ?20 ?21) ?22
33664 add (multiply ?20 ?22) (multiply ?21 ?22)
33665 [22, 21, 20] by distribute2 ?20 ?21 ?22
33666 25102: Id : 11, {_}:
33667 add ?24 ?25 =?= add ?25 ?24
33668 [25, 24] by commutativity_for_addition ?24 ?25
33669 NO CLASH, using fixed ground order
33671 25103: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
33672 25103: Id : 3, {_}:
33673 add ?4 additive_identity =>= ?4
33674 [4] by right_additive_identity ?4
33675 25103: Id : 4, {_}:
33676 multiply additive_identity ?6 =>= additive_identity
33677 [6] by left_multiplicative_zero ?6
33678 25103: Id : 5, {_}:
33679 multiply ?8 additive_identity =>= additive_identity
33680 [8] by right_multiplicative_zero ?8
33681 25103: Id : 6, {_}:
33682 add (additive_inverse ?10) ?10 =>= additive_identity
33683 [10] by left_additive_inverse ?10
33684 25103: Id : 7, {_}:
33685 add ?12 (additive_inverse ?12) =>= additive_identity
33686 [12] by right_additive_inverse ?12
33687 25103: Id : 8, {_}:
33688 additive_inverse (additive_inverse ?14) =>= ?14
33689 [14] by additive_inverse_additive_inverse ?14
33690 25103: Id : 9, {_}:
33691 multiply ?16 (add ?17 ?18)
33693 add (multiply ?16 ?17) (multiply ?16 ?18)
33694 [18, 17, 16] by distribute1 ?16 ?17 ?18
33695 25103: Id : 10, {_}:
33696 multiply (add ?20 ?21) ?22
33698 add (multiply ?20 ?22) (multiply ?21 ?22)
33699 [22, 21, 20] by distribute2 ?20 ?21 ?22
33700 25102: Id : 12, {_}:
33701 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
33702 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
33703 25102: Id : 13, {_}:
33704 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
33705 [32, 31] by right_alternative ?31 ?32
33706 25102: Id : 14, {_}:
33707 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
33708 [35, 34] by left_alternative ?34 ?35
33709 25102: Id : 15, {_}:
33710 associator ?37 ?38 ?39
33712 add (multiply (multiply ?37 ?38) ?39)
33713 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
33714 [39, 38, 37] by associator ?37 ?38 ?39
33715 25102: Id : 16, {_}:
33718 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
33719 [42, 41] by commutator ?41 ?42
33721 25102: Id : 1, {_}:
33722 multiply cz (multiply cx (multiply cy cx))
33724 multiply (multiply (multiply cz cx) cy) cx
33725 [] by prove_right_moufang
33729 25102: commutator 1 2 0
33730 25102: associator 1 3 0
33731 25102: additive_inverse 6 1 0
33733 25102: additive_identity 8 0 0
33734 25102: multiply 28 2 6 0,2
33735 25102: cy 2 0 2 1,2,2,2
33736 25102: cx 4 0 4 1,2,2
33737 25102: cz 2 0 2 1,2
33738 25103: Id : 11, {_}:
33739 add ?24 ?25 =?= add ?25 ?24
33740 [25, 24] by commutativity_for_addition ?24 ?25
33741 25103: Id : 12, {_}:
33742 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
33743 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
33744 25103: Id : 13, {_}:
33745 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
33746 [32, 31] by right_alternative ?31 ?32
33747 25103: Id : 14, {_}:
33748 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
33749 [35, 34] by left_alternative ?34 ?35
33750 25103: Id : 15, {_}:
33751 associator ?37 ?38 ?39
33753 add (multiply (multiply ?37 ?38) ?39)
33754 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
33755 [39, 38, 37] by associator ?37 ?38 ?39
33756 25103: Id : 16, {_}:
33759 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
33760 [42, 41] by commutator ?41 ?42
33762 25103: Id : 1, {_}:
33763 multiply cz (multiply cx (multiply cy cx))
33765 multiply (multiply (multiply cz cx) cy) cx
33766 [] by prove_right_moufang
33770 25103: commutator 1 2 0
33771 25103: associator 1 3 0
33772 25103: additive_inverse 6 1 0
33774 25103: additive_identity 8 0 0
33775 25103: multiply 28 2 6 0,2
33776 25103: cy 2 0 2 1,2,2,2
33777 25103: cx 4 0 4 1,2,2
33778 25103: cz 2 0 2 1,2
33779 % SZS status Timeout for RNG027-5.p
33780 NO CLASH, using fixed ground order
33782 25119: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
33783 25119: Id : 3, {_}:
33784 add ?4 additive_identity =>= ?4
33785 [4] by right_additive_identity ?4
33786 25119: Id : 4, {_}:
33787 multiply additive_identity ?6 =>= additive_identity
33788 [6] by left_multiplicative_zero ?6
33789 25119: Id : 5, {_}:
33790 multiply ?8 additive_identity =>= additive_identity
33791 [8] by right_multiplicative_zero ?8
33792 25119: Id : 6, {_}:
33793 add (additive_inverse ?10) ?10 =>= additive_identity
33794 [10] by left_additive_inverse ?10
33795 25119: Id : 7, {_}:
33796 add ?12 (additive_inverse ?12) =>= additive_identity
33797 [12] by right_additive_inverse ?12
33798 25119: Id : 8, {_}:
33799 additive_inverse (additive_inverse ?14) =>= ?14
33800 [14] by additive_inverse_additive_inverse ?14
33801 25119: Id : 9, {_}:
33802 multiply ?16 (add ?17 ?18)
33804 add (multiply ?16 ?17) (multiply ?16 ?18)
33805 [18, 17, 16] by distribute1 ?16 ?17 ?18
33806 25119: Id : 10, {_}:
33807 multiply (add ?20 ?21) ?22
33809 add (multiply ?20 ?22) (multiply ?21 ?22)
33810 [22, 21, 20] by distribute2 ?20 ?21 ?22
33811 25119: Id : 11, {_}:
33812 add ?24 ?25 =?= add ?25 ?24
33813 [25, 24] by commutativity_for_addition ?24 ?25
33814 25119: Id : 12, {_}:
33815 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
33816 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
33817 25119: Id : 13, {_}:
33818 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
33819 [32, 31] by right_alternative ?31 ?32
33820 25119: Id : 14, {_}:
33821 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
33822 [35, 34] by left_alternative ?34 ?35
33823 25119: Id : 15, {_}:
33824 associator ?37 ?38 ?39
33826 add (multiply (multiply ?37 ?38) ?39)
33827 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
33828 [39, 38, 37] by associator ?37 ?38 ?39
33829 25119: Id : 16, {_}:
33832 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
33833 [42, 41] by commutator ?41 ?42
33834 25119: Id : 17, {_}:
33835 multiply (additive_inverse ?44) (additive_inverse ?45)
33838 [45, 44] by product_of_inverses ?44 ?45
33839 25119: Id : 18, {_}:
33840 multiply (additive_inverse ?47) ?48
33842 additive_inverse (multiply ?47 ?48)
33843 [48, 47] by inverse_product1 ?47 ?48
33844 25119: Id : 19, {_}:
33845 multiply ?50 (additive_inverse ?51)
33847 additive_inverse (multiply ?50 ?51)
33848 [51, 50] by inverse_product2 ?50 ?51
33849 25119: Id : 20, {_}:
33850 multiply ?53 (add ?54 (additive_inverse ?55))
33852 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
33853 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
33854 25119: Id : 21, {_}:
33855 multiply (add ?57 (additive_inverse ?58)) ?59
33857 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
33858 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
33859 25119: Id : 22, {_}:
33860 multiply (additive_inverse ?61) (add ?62 ?63)
33862 add (additive_inverse (multiply ?61 ?62))
33863 (additive_inverse (multiply ?61 ?63))
33864 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
33865 25119: Id : 23, {_}:
33866 multiply (add ?65 ?66) (additive_inverse ?67)
33868 add (additive_inverse (multiply ?65 ?67))
33869 (additive_inverse (multiply ?66 ?67))
33870 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
33872 25119: Id : 1, {_}:
33873 multiply cz (multiply cx (multiply cy cx))
33875 multiply (multiply (multiply cz cx) cy) cx
33876 [] by prove_right_moufang
33880 25119: commutator 1 2 0
33881 25119: associator 1 3 0
33882 25119: additive_inverse 22 1 0
33884 25119: additive_identity 8 0 0
33885 25119: multiply 46 2 6 0,2
33886 25119: cy 2 0 2 1,2,2,2
33887 25119: cx 4 0 4 1,2,2
33888 25119: cz 2 0 2 1,2
33889 NO CLASH, using fixed ground order
33891 25120: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
33892 25120: Id : 3, {_}:
33893 add ?4 additive_identity =>= ?4
33894 [4] by right_additive_identity ?4
33895 25120: Id : 4, {_}:
33896 multiply additive_identity ?6 =>= additive_identity
33897 [6] by left_multiplicative_zero ?6
33898 25120: Id : 5, {_}:
33899 multiply ?8 additive_identity =>= additive_identity
33900 [8] by right_multiplicative_zero ?8
33901 25120: Id : 6, {_}:
33902 add (additive_inverse ?10) ?10 =>= additive_identity
33903 [10] by left_additive_inverse ?10
33904 25120: Id : 7, {_}:
33905 add ?12 (additive_inverse ?12) =>= additive_identity
33906 [12] by right_additive_inverse ?12
33907 25120: Id : 8, {_}:
33908 additive_inverse (additive_inverse ?14) =>= ?14
33909 [14] by additive_inverse_additive_inverse ?14
33910 25120: Id : 9, {_}:
33911 multiply ?16 (add ?17 ?18)
33913 add (multiply ?16 ?17) (multiply ?16 ?18)
33914 [18, 17, 16] by distribute1 ?16 ?17 ?18
33915 25120: Id : 10, {_}:
33916 multiply (add ?20 ?21) ?22
33918 add (multiply ?20 ?22) (multiply ?21 ?22)
33919 [22, 21, 20] by distribute2 ?20 ?21 ?22
33920 25120: Id : 11, {_}:
33921 add ?24 ?25 =?= add ?25 ?24
33922 [25, 24] by commutativity_for_addition ?24 ?25
33923 25120: Id : 12, {_}:
33924 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
33925 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
33926 25120: Id : 13, {_}:
33927 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
33928 [32, 31] by right_alternative ?31 ?32
33929 25120: Id : 14, {_}:
33930 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
33931 [35, 34] by left_alternative ?34 ?35
33932 25120: Id : 15, {_}:
33933 associator ?37 ?38 ?39
33935 add (multiply (multiply ?37 ?38) ?39)
33936 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
33937 [39, 38, 37] by associator ?37 ?38 ?39
33938 25120: Id : 16, {_}:
33941 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
33942 [42, 41] by commutator ?41 ?42
33943 25120: Id : 17, {_}:
33944 multiply (additive_inverse ?44) (additive_inverse ?45)
33947 [45, 44] by product_of_inverses ?44 ?45
33948 25120: Id : 18, {_}:
33949 multiply (additive_inverse ?47) ?48
33951 additive_inverse (multiply ?47 ?48)
33952 [48, 47] by inverse_product1 ?47 ?48
33953 25120: Id : 19, {_}:
33954 multiply ?50 (additive_inverse ?51)
33956 additive_inverse (multiply ?50 ?51)
33957 [51, 50] by inverse_product2 ?50 ?51
33958 25120: Id : 20, {_}:
33959 multiply ?53 (add ?54 (additive_inverse ?55))
33961 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
33962 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
33963 25120: Id : 21, {_}:
33964 multiply (add ?57 (additive_inverse ?58)) ?59
33966 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
33967 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
33968 25120: Id : 22, {_}:
33969 multiply (additive_inverse ?61) (add ?62 ?63)
33971 add (additive_inverse (multiply ?61 ?62))
33972 (additive_inverse (multiply ?61 ?63))
33973 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
33974 25120: Id : 23, {_}:
33975 multiply (add ?65 ?66) (additive_inverse ?67)
33977 add (additive_inverse (multiply ?65 ?67))
33978 (additive_inverse (multiply ?66 ?67))
33979 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
33981 25120: Id : 1, {_}:
33982 multiply cz (multiply cx (multiply cy cx))
33984 multiply (multiply (multiply cz cx) cy) cx
33985 [] by prove_right_moufang
33989 25120: commutator 1 2 0
33990 25120: associator 1 3 0
33991 25120: additive_inverse 22 1 0
33993 25120: additive_identity 8 0 0
33994 25120: multiply 46 2 6 0,2
33995 25120: cy 2 0 2 1,2,2,2
33996 25120: cx 4 0 4 1,2,2
33997 25120: cz 2 0 2 1,2
33998 NO CLASH, using fixed ground order
34000 25121: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34001 25121: Id : 3, {_}:
34002 add ?4 additive_identity =>= ?4
34003 [4] by right_additive_identity ?4
34004 25121: Id : 4, {_}:
34005 multiply additive_identity ?6 =>= additive_identity
34006 [6] by left_multiplicative_zero ?6
34007 25121: Id : 5, {_}:
34008 multiply ?8 additive_identity =>= additive_identity
34009 [8] by right_multiplicative_zero ?8
34010 25121: Id : 6, {_}:
34011 add (additive_inverse ?10) ?10 =>= additive_identity
34012 [10] by left_additive_inverse ?10
34013 25121: Id : 7, {_}:
34014 add ?12 (additive_inverse ?12) =>= additive_identity
34015 [12] by right_additive_inverse ?12
34016 25121: Id : 8, {_}:
34017 additive_inverse (additive_inverse ?14) =>= ?14
34018 [14] by additive_inverse_additive_inverse ?14
34019 25121: Id : 9, {_}:
34020 multiply ?16 (add ?17 ?18)
34022 add (multiply ?16 ?17) (multiply ?16 ?18)
34023 [18, 17, 16] by distribute1 ?16 ?17 ?18
34024 25121: Id : 10, {_}:
34025 multiply (add ?20 ?21) ?22
34027 add (multiply ?20 ?22) (multiply ?21 ?22)
34028 [22, 21, 20] by distribute2 ?20 ?21 ?22
34029 25121: Id : 11, {_}:
34030 add ?24 ?25 =?= add ?25 ?24
34031 [25, 24] by commutativity_for_addition ?24 ?25
34032 25121: Id : 12, {_}:
34033 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
34034 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34035 25121: Id : 13, {_}:
34036 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
34037 [32, 31] by right_alternative ?31 ?32
34038 25121: Id : 14, {_}:
34039 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
34040 [35, 34] by left_alternative ?34 ?35
34041 25121: Id : 15, {_}:
34042 associator ?37 ?38 ?39
34044 add (multiply (multiply ?37 ?38) ?39)
34045 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34046 [39, 38, 37] by associator ?37 ?38 ?39
34047 25121: Id : 16, {_}:
34050 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34051 [42, 41] by commutator ?41 ?42
34052 25121: Id : 17, {_}:
34053 multiply (additive_inverse ?44) (additive_inverse ?45)
34056 [45, 44] by product_of_inverses ?44 ?45
34057 25121: Id : 18, {_}:
34058 multiply (additive_inverse ?47) ?48
34060 additive_inverse (multiply ?47 ?48)
34061 [48, 47] by inverse_product1 ?47 ?48
34062 25121: Id : 19, {_}:
34063 multiply ?50 (additive_inverse ?51)
34065 additive_inverse (multiply ?50 ?51)
34066 [51, 50] by inverse_product2 ?50 ?51
34067 25121: Id : 20, {_}:
34068 multiply ?53 (add ?54 (additive_inverse ?55))
34070 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
34071 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
34072 25121: Id : 21, {_}:
34073 multiply (add ?57 (additive_inverse ?58)) ?59
34075 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
34076 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
34077 25121: Id : 22, {_}:
34078 multiply (additive_inverse ?61) (add ?62 ?63)
34080 add (additive_inverse (multiply ?61 ?62))
34081 (additive_inverse (multiply ?61 ?63))
34082 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
34083 25121: Id : 23, {_}:
34084 multiply (add ?65 ?66) (additive_inverse ?67)
34086 add (additive_inverse (multiply ?65 ?67))
34087 (additive_inverse (multiply ?66 ?67))
34088 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
34090 25121: Id : 1, {_}:
34091 multiply cz (multiply cx (multiply cy cx))
34093 multiply (multiply (multiply cz cx) cy) cx
34094 [] by prove_right_moufang
34098 25121: commutator 1 2 0
34099 25121: associator 1 3 0
34100 25121: additive_inverse 22 1 0
34102 25121: additive_identity 8 0 0
34103 25121: multiply 46 2 6 0,2
34104 25121: cy 2 0 2 1,2,2,2
34105 25121: cx 4 0 4 1,2,2
34106 25121: cz 2 0 2 1,2
34107 % SZS status Timeout for RNG027-7.p
34108 NO CLASH, using fixed ground order
34110 25148: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34111 25148: Id : 3, {_}:
34112 add ?4 additive_identity =>= ?4
34113 [4] by right_additive_identity ?4
34114 25148: Id : 4, {_}:
34115 multiply additive_identity ?6 =>= additive_identity
34116 [6] by left_multiplicative_zero ?6
34117 25148: Id : 5, {_}:
34118 multiply ?8 additive_identity =>= additive_identity
34119 [8] by right_multiplicative_zero ?8
34120 25148: Id : 6, {_}:
34121 add (additive_inverse ?10) ?10 =>= additive_identity
34122 [10] by left_additive_inverse ?10
34123 25148: Id : 7, {_}:
34124 add ?12 (additive_inverse ?12) =>= additive_identity
34125 [12] by right_additive_inverse ?12
34126 25148: Id : 8, {_}:
34127 additive_inverse (additive_inverse ?14) =>= ?14
34128 [14] by additive_inverse_additive_inverse ?14
34129 25148: Id : 9, {_}:
34130 multiply ?16 (add ?17 ?18)
34132 add (multiply ?16 ?17) (multiply ?16 ?18)
34133 [18, 17, 16] by distribute1 ?16 ?17 ?18
34134 25148: Id : 10, {_}:
34135 multiply (add ?20 ?21) ?22
34137 add (multiply ?20 ?22) (multiply ?21 ?22)
34138 [22, 21, 20] by distribute2 ?20 ?21 ?22
34139 25148: Id : 11, {_}:
34140 add ?24 ?25 =?= add ?25 ?24
34141 [25, 24] by commutativity_for_addition ?24 ?25
34142 25148: Id : 12, {_}:
34143 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
34144 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34145 25148: Id : 13, {_}:
34146 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
34147 [32, 31] by right_alternative ?31 ?32
34148 25148: Id : 14, {_}:
34149 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
34150 [35, 34] by left_alternative ?34 ?35
34151 25148: Id : 15, {_}:
34152 associator ?37 ?38 ?39
34154 add (multiply (multiply ?37 ?38) ?39)
34155 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34156 [39, 38, 37] by associator ?37 ?38 ?39
34157 25148: Id : 16, {_}:
34160 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34161 [42, 41] by commutator ?41 ?42
34163 25148: Id : 1, {_}:
34164 associator x (multiply x y) z =<= multiply (associator x y z) x
34165 [] by prove_right_moufang
34169 25148: commutator 1 2 0
34170 25148: additive_inverse 6 1 0
34172 25148: additive_identity 8 0 0
34173 25148: associator 3 3 2 0,2
34175 25148: multiply 24 2 2 0,2,2
34176 25148: y 2 0 2 2,2,2
34178 NO CLASH, using fixed ground order
34180 25149: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34181 25149: Id : 3, {_}:
34182 add ?4 additive_identity =>= ?4
34183 [4] by right_additive_identity ?4
34184 25149: Id : 4, {_}:
34185 multiply additive_identity ?6 =>= additive_identity
34186 [6] by left_multiplicative_zero ?6
34187 25149: Id : 5, {_}:
34188 multiply ?8 additive_identity =>= additive_identity
34189 [8] by right_multiplicative_zero ?8
34190 25149: Id : 6, {_}:
34191 add (additive_inverse ?10) ?10 =>= additive_identity
34192 [10] by left_additive_inverse ?10
34193 25149: Id : 7, {_}:
34194 add ?12 (additive_inverse ?12) =>= additive_identity
34195 [12] by right_additive_inverse ?12
34196 25149: Id : 8, {_}:
34197 additive_inverse (additive_inverse ?14) =>= ?14
34198 [14] by additive_inverse_additive_inverse ?14
34199 25149: Id : 9, {_}:
34200 multiply ?16 (add ?17 ?18)
34202 add (multiply ?16 ?17) (multiply ?16 ?18)
34203 [18, 17, 16] by distribute1 ?16 ?17 ?18
34204 25149: Id : 10, {_}:
34205 multiply (add ?20 ?21) ?22
34207 add (multiply ?20 ?22) (multiply ?21 ?22)
34208 [22, 21, 20] by distribute2 ?20 ?21 ?22
34209 25149: Id : 11, {_}:
34210 add ?24 ?25 =?= add ?25 ?24
34211 [25, 24] by commutativity_for_addition ?24 ?25
34212 25149: Id : 12, {_}:
34213 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
34214 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34215 25149: Id : 13, {_}:
34216 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
34217 [32, 31] by right_alternative ?31 ?32
34218 25149: Id : 14, {_}:
34219 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
34220 [35, 34] by left_alternative ?34 ?35
34221 25149: Id : 15, {_}:
34222 associator ?37 ?38 ?39
34224 add (multiply (multiply ?37 ?38) ?39)
34225 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34226 [39, 38, 37] by associator ?37 ?38 ?39
34227 25149: Id : 16, {_}:
34230 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34231 [42, 41] by commutator ?41 ?42
34233 25149: Id : 1, {_}:
34234 associator x (multiply x y) z =<= multiply (associator x y z) x
34235 [] by prove_right_moufang
34239 25149: commutator 1 2 0
34240 25149: additive_inverse 6 1 0
34242 25149: additive_identity 8 0 0
34243 25149: associator 3 3 2 0,2
34245 25149: multiply 24 2 2 0,2,2
34246 25149: y 2 0 2 2,2,2
34248 NO CLASH, using fixed ground order
34250 25150: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34251 25150: Id : 3, {_}:
34252 add ?4 additive_identity =>= ?4
34253 [4] by right_additive_identity ?4
34254 25150: Id : 4, {_}:
34255 multiply additive_identity ?6 =>= additive_identity
34256 [6] by left_multiplicative_zero ?6
34257 25150: Id : 5, {_}:
34258 multiply ?8 additive_identity =>= additive_identity
34259 [8] by right_multiplicative_zero ?8
34260 25150: Id : 6, {_}:
34261 add (additive_inverse ?10) ?10 =>= additive_identity
34262 [10] by left_additive_inverse ?10
34263 25150: Id : 7, {_}:
34264 add ?12 (additive_inverse ?12) =>= additive_identity
34265 [12] by right_additive_inverse ?12
34266 25150: Id : 8, {_}:
34267 additive_inverse (additive_inverse ?14) =>= ?14
34268 [14] by additive_inverse_additive_inverse ?14
34269 25150: Id : 9, {_}:
34270 multiply ?16 (add ?17 ?18)
34272 add (multiply ?16 ?17) (multiply ?16 ?18)
34273 [18, 17, 16] by distribute1 ?16 ?17 ?18
34274 25150: Id : 10, {_}:
34275 multiply (add ?20 ?21) ?22
34277 add (multiply ?20 ?22) (multiply ?21 ?22)
34278 [22, 21, 20] by distribute2 ?20 ?21 ?22
34279 25150: Id : 11, {_}:
34280 add ?24 ?25 =?= add ?25 ?24
34281 [25, 24] by commutativity_for_addition ?24 ?25
34282 25150: Id : 12, {_}:
34283 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
34284 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34285 25150: Id : 13, {_}:
34286 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
34287 [32, 31] by right_alternative ?31 ?32
34288 25150: Id : 14, {_}:
34289 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
34290 [35, 34] by left_alternative ?34 ?35
34291 25150: Id : 15, {_}:
34292 associator ?37 ?38 ?39
34294 add (multiply (multiply ?37 ?38) ?39)
34295 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34296 [39, 38, 37] by associator ?37 ?38 ?39
34297 25150: Id : 16, {_}:
34300 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34301 [42, 41] by commutator ?41 ?42
34303 25150: Id : 1, {_}:
34304 associator x (multiply x y) z =<= multiply (associator x y z) x
34305 [] by prove_right_moufang
34309 25150: commutator 1 2 0
34310 25150: additive_inverse 6 1 0
34312 25150: additive_identity 8 0 0
34313 25150: associator 3 3 2 0,2
34315 25150: multiply 24 2 2 0,2,2
34316 25150: y 2 0 2 2,2,2
34318 % SZS status Timeout for RNG027-8.p
34319 NO CLASH, using fixed ground order
34321 25166: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34322 25166: Id : 3, {_}:
34323 add ?4 additive_identity =>= ?4
34324 [4] by right_additive_identity ?4
34325 25166: Id : 4, {_}:
34326 multiply additive_identity ?6 =>= additive_identity
34327 [6] by left_multiplicative_zero ?6
34328 25166: Id : 5, {_}:
34329 multiply ?8 additive_identity =>= additive_identity
34330 [8] by right_multiplicative_zero ?8
34331 25166: Id : 6, {_}:
34332 add (additive_inverse ?10) ?10 =>= additive_identity
34333 [10] by left_additive_inverse ?10
34334 25166: Id : 7, {_}:
34335 add ?12 (additive_inverse ?12) =>= additive_identity
34336 [12] by right_additive_inverse ?12
34337 25166: Id : 8, {_}:
34338 additive_inverse (additive_inverse ?14) =>= ?14
34339 [14] by additive_inverse_additive_inverse ?14
34340 25166: Id : 9, {_}:
34341 multiply ?16 (add ?17 ?18)
34343 add (multiply ?16 ?17) (multiply ?16 ?18)
34344 [18, 17, 16] by distribute1 ?16 ?17 ?18
34345 25166: Id : 10, {_}:
34346 multiply (add ?20 ?21) ?22
34348 add (multiply ?20 ?22) (multiply ?21 ?22)
34349 [22, 21, 20] by distribute2 ?20 ?21 ?22
34350 25166: Id : 11, {_}:
34351 add ?24 ?25 =?= add ?25 ?24
34352 [25, 24] by commutativity_for_addition ?24 ?25
34353 25166: Id : 12, {_}:
34354 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
34355 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34356 25166: Id : 13, {_}:
34357 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
34358 [32, 31] by right_alternative ?31 ?32
34359 25166: Id : 14, {_}:
34360 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
34361 [35, 34] by left_alternative ?34 ?35
34362 25166: Id : 15, {_}:
34363 associator ?37 ?38 ?39
34365 add (multiply (multiply ?37 ?38) ?39)
34366 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34367 [39, 38, 37] by associator ?37 ?38 ?39
34368 25166: Id : 16, {_}:
34371 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34372 [42, 41] by commutator ?41 ?42
34373 25166: Id : 17, {_}:
34374 multiply (additive_inverse ?44) (additive_inverse ?45)
34377 [45, 44] by product_of_inverses ?44 ?45
34378 25166: Id : 18, {_}:
34379 multiply (additive_inverse ?47) ?48
34381 additive_inverse (multiply ?47 ?48)
34382 [48, 47] by inverse_product1 ?47 ?48
34383 25166: Id : 19, {_}:
34384 multiply ?50 (additive_inverse ?51)
34386 additive_inverse (multiply ?50 ?51)
34387 [51, 50] by inverse_product2 ?50 ?51
34388 25166: Id : 20, {_}:
34389 multiply ?53 (add ?54 (additive_inverse ?55))
34391 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
34392 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
34393 25166: Id : 21, {_}:
34394 multiply (add ?57 (additive_inverse ?58)) ?59
34396 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
34397 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
34398 25166: Id : 22, {_}:
34399 multiply (additive_inverse ?61) (add ?62 ?63)
34401 add (additive_inverse (multiply ?61 ?62))
34402 (additive_inverse (multiply ?61 ?63))
34403 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
34404 25166: Id : 23, {_}:
34405 multiply (add ?65 ?66) (additive_inverse ?67)
34407 add (additive_inverse (multiply ?65 ?67))
34408 (additive_inverse (multiply ?66 ?67))
34409 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
34411 25166: Id : 1, {_}:
34412 associator x (multiply x y) z =<= multiply (associator x y z) x
34413 [] by prove_right_moufang
34417 25166: commutator 1 2 0
34418 25166: additive_inverse 22 1 0
34420 25166: additive_identity 8 0 0
34421 25166: associator 3 3 2 0,2
34423 25166: multiply 42 2 2 0,2,2
34424 25166: y 2 0 2 2,2,2
34426 NO CLASH, using fixed ground order
34428 25168: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34429 25168: Id : 3, {_}:
34430 add ?4 additive_identity =>= ?4
34431 [4] by right_additive_identity ?4
34432 25168: Id : 4, {_}:
34433 multiply additive_identity ?6 =>= additive_identity
34434 [6] by left_multiplicative_zero ?6
34435 25168: Id : 5, {_}:
34436 multiply ?8 additive_identity =>= additive_identity
34437 [8] by right_multiplicative_zero ?8
34438 25168: Id : 6, {_}:
34439 add (additive_inverse ?10) ?10 =>= additive_identity
34440 [10] by left_additive_inverse ?10
34441 25168: Id : 7, {_}:
34442 add ?12 (additive_inverse ?12) =>= additive_identity
34443 [12] by right_additive_inverse ?12
34444 25168: Id : 8, {_}:
34445 additive_inverse (additive_inverse ?14) =>= ?14
34446 [14] by additive_inverse_additive_inverse ?14
34447 25168: Id : 9, {_}:
34448 multiply ?16 (add ?17 ?18)
34450 add (multiply ?16 ?17) (multiply ?16 ?18)
34451 [18, 17, 16] by distribute1 ?16 ?17 ?18
34452 25168: Id : 10, {_}:
34453 multiply (add ?20 ?21) ?22
34455 add (multiply ?20 ?22) (multiply ?21 ?22)
34456 [22, 21, 20] by distribute2 ?20 ?21 ?22
34457 25168: Id : 11, {_}:
34458 add ?24 ?25 =?= add ?25 ?24
34459 [25, 24] by commutativity_for_addition ?24 ?25
34460 25168: Id : 12, {_}:
34461 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
34462 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34463 25168: Id : 13, {_}:
34464 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
34465 [32, 31] by right_alternative ?31 ?32
34466 25168: Id : 14, {_}:
34467 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
34468 [35, 34] by left_alternative ?34 ?35
34469 25168: Id : 15, {_}:
34470 associator ?37 ?38 ?39
34472 add (multiply (multiply ?37 ?38) ?39)
34473 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34474 [39, 38, 37] by associator ?37 ?38 ?39
34475 25168: Id : 16, {_}:
34478 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34479 [42, 41] by commutator ?41 ?42
34480 25168: Id : 17, {_}:
34481 multiply (additive_inverse ?44) (additive_inverse ?45)
34484 [45, 44] by product_of_inverses ?44 ?45
34485 25168: Id : 18, {_}:
34486 multiply (additive_inverse ?47) ?48
34488 additive_inverse (multiply ?47 ?48)
34489 [48, 47] by inverse_product1 ?47 ?48
34490 25168: Id : 19, {_}:
34491 multiply ?50 (additive_inverse ?51)
34493 additive_inverse (multiply ?50 ?51)
34494 [51, 50] by inverse_product2 ?50 ?51
34495 25168: Id : 20, {_}:
34496 multiply ?53 (add ?54 (additive_inverse ?55))
34498 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
34499 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
34500 25168: Id : 21, {_}:
34501 multiply (add ?57 (additive_inverse ?58)) ?59
34503 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
34504 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
34505 25168: Id : 22, {_}:
34506 multiply (additive_inverse ?61) (add ?62 ?63)
34508 add (additive_inverse (multiply ?61 ?62))
34509 (additive_inverse (multiply ?61 ?63))
34510 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
34511 25168: Id : 23, {_}:
34512 multiply (add ?65 ?66) (additive_inverse ?67)
34514 add (additive_inverse (multiply ?65 ?67))
34515 (additive_inverse (multiply ?66 ?67))
34516 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
34518 25168: Id : 1, {_}:
34519 associator x (multiply x y) z =<= multiply (associator x y z) x
34520 [] by prove_right_moufang
34524 25168: commutator 1 2 0
34525 25168: additive_inverse 22 1 0
34527 25168: additive_identity 8 0 0
34528 25168: associator 3 3 2 0,2
34530 25168: multiply 42 2 2 0,2,2
34531 25168: y 2 0 2 2,2,2
34533 NO CLASH, using fixed ground order
34535 25167: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34536 25167: Id : 3, {_}:
34537 add ?4 additive_identity =>= ?4
34538 [4] by right_additive_identity ?4
34539 25167: Id : 4, {_}:
34540 multiply additive_identity ?6 =>= additive_identity
34541 [6] by left_multiplicative_zero ?6
34542 25167: Id : 5, {_}:
34543 multiply ?8 additive_identity =>= additive_identity
34544 [8] by right_multiplicative_zero ?8
34545 25167: Id : 6, {_}:
34546 add (additive_inverse ?10) ?10 =>= additive_identity
34547 [10] by left_additive_inverse ?10
34548 25167: Id : 7, {_}:
34549 add ?12 (additive_inverse ?12) =>= additive_identity
34550 [12] by right_additive_inverse ?12
34551 25167: Id : 8, {_}:
34552 additive_inverse (additive_inverse ?14) =>= ?14
34553 [14] by additive_inverse_additive_inverse ?14
34554 25167: Id : 9, {_}:
34555 multiply ?16 (add ?17 ?18)
34557 add (multiply ?16 ?17) (multiply ?16 ?18)
34558 [18, 17, 16] by distribute1 ?16 ?17 ?18
34559 25167: Id : 10, {_}:
34560 multiply (add ?20 ?21) ?22
34562 add (multiply ?20 ?22) (multiply ?21 ?22)
34563 [22, 21, 20] by distribute2 ?20 ?21 ?22
34564 25167: Id : 11, {_}:
34565 add ?24 ?25 =?= add ?25 ?24
34566 [25, 24] by commutativity_for_addition ?24 ?25
34567 25167: Id : 12, {_}:
34568 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
34569 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34570 25167: Id : 13, {_}:
34571 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
34572 [32, 31] by right_alternative ?31 ?32
34573 25167: Id : 14, {_}:
34574 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
34575 [35, 34] by left_alternative ?34 ?35
34576 25167: Id : 15, {_}:
34577 associator ?37 ?38 ?39
34579 add (multiply (multiply ?37 ?38) ?39)
34580 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34581 [39, 38, 37] by associator ?37 ?38 ?39
34582 25167: Id : 16, {_}:
34585 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34586 [42, 41] by commutator ?41 ?42
34587 25167: Id : 17, {_}:
34588 multiply (additive_inverse ?44) (additive_inverse ?45)
34591 [45, 44] by product_of_inverses ?44 ?45
34592 25167: Id : 18, {_}:
34593 multiply (additive_inverse ?47) ?48
34595 additive_inverse (multiply ?47 ?48)
34596 [48, 47] by inverse_product1 ?47 ?48
34597 25167: Id : 19, {_}:
34598 multiply ?50 (additive_inverse ?51)
34600 additive_inverse (multiply ?50 ?51)
34601 [51, 50] by inverse_product2 ?50 ?51
34602 25167: Id : 20, {_}:
34603 multiply ?53 (add ?54 (additive_inverse ?55))
34605 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
34606 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
34607 25167: Id : 21, {_}:
34608 multiply (add ?57 (additive_inverse ?58)) ?59
34610 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
34611 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
34612 25167: Id : 22, {_}:
34613 multiply (additive_inverse ?61) (add ?62 ?63)
34615 add (additive_inverse (multiply ?61 ?62))
34616 (additive_inverse (multiply ?61 ?63))
34617 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
34618 25167: Id : 23, {_}:
34619 multiply (add ?65 ?66) (additive_inverse ?67)
34621 add (additive_inverse (multiply ?65 ?67))
34622 (additive_inverse (multiply ?66 ?67))
34623 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
34625 25167: Id : 1, {_}:
34626 associator x (multiply x y) z =<= multiply (associator x y z) x
34627 [] by prove_right_moufang
34631 25167: commutator 1 2 0
34632 25167: additive_inverse 22 1 0
34634 25167: additive_identity 8 0 0
34635 25167: associator 3 3 2 0,2
34637 25167: multiply 42 2 2 0,2,2
34638 25167: y 2 0 2 2,2,2
34640 % SZS status Timeout for RNG027-9.p
34641 NO CLASH, using fixed ground order
34643 25195: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34644 25195: Id : 3, {_}:
34645 add ?4 additive_identity =>= ?4
34646 [4] by right_additive_identity ?4
34647 25195: Id : 4, {_}:
34648 multiply additive_identity ?6 =>= additive_identity
34649 [6] by left_multiplicative_zero ?6
34650 25195: Id : 5, {_}:
34651 multiply ?8 additive_identity =>= additive_identity
34652 [8] by right_multiplicative_zero ?8
34653 25195: Id : 6, {_}:
34654 add (additive_inverse ?10) ?10 =>= additive_identity
34655 [10] by left_additive_inverse ?10
34656 25195: Id : 7, {_}:
34657 add ?12 (additive_inverse ?12) =>= additive_identity
34658 [12] by right_additive_inverse ?12
34659 25195: Id : 8, {_}:
34660 additive_inverse (additive_inverse ?14) =>= ?14
34661 [14] by additive_inverse_additive_inverse ?14
34662 25195: Id : 9, {_}:
34663 multiply ?16 (add ?17 ?18)
34665 add (multiply ?16 ?17) (multiply ?16 ?18)
34666 [18, 17, 16] by distribute1 ?16 ?17 ?18
34667 25195: Id : 10, {_}:
34668 multiply (add ?20 ?21) ?22
34670 add (multiply ?20 ?22) (multiply ?21 ?22)
34671 [22, 21, 20] by distribute2 ?20 ?21 ?22
34672 25195: Id : 11, {_}:
34673 add ?24 ?25 =?= add ?25 ?24
34674 [25, 24] by commutativity_for_addition ?24 ?25
34675 25195: Id : 12, {_}:
34676 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
34677 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34678 25195: Id : 13, {_}:
34679 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
34680 [32, 31] by right_alternative ?31 ?32
34681 25195: Id : 14, {_}:
34682 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
34683 [35, 34] by left_alternative ?34 ?35
34684 25195: Id : 15, {_}:
34685 associator ?37 ?38 ?39
34687 add (multiply (multiply ?37 ?38) ?39)
34688 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34689 [39, 38, 37] by associator ?37 ?38 ?39
34690 25195: Id : 16, {_}:
34693 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34694 [42, 41] by commutator ?41 ?42
34696 25195: Id : 1, {_}:
34697 multiply (multiply cx (multiply cy cx)) cz
34699 multiply cx (multiply cy (multiply cx cz))
34700 [] by prove_left_moufang
34704 25195: commutator 1 2 0
34705 25195: associator 1 3 0
34706 25195: additive_inverse 6 1 0
34708 25195: additive_identity 8 0 0
34709 25195: cz 2 0 2 2,2
34710 25195: multiply 28 2 6 0,2
34711 25195: cy 2 0 2 1,2,1,2
34712 25195: cx 4 0 4 1,1,2
34713 NO CLASH, using fixed ground order
34715 25196: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34716 25196: Id : 3, {_}:
34717 add ?4 additive_identity =>= ?4
34718 [4] by right_additive_identity ?4
34719 25196: Id : 4, {_}:
34720 multiply additive_identity ?6 =>= additive_identity
34721 [6] by left_multiplicative_zero ?6
34722 25196: Id : 5, {_}:
34723 multiply ?8 additive_identity =>= additive_identity
34724 [8] by right_multiplicative_zero ?8
34725 25196: Id : 6, {_}:
34726 add (additive_inverse ?10) ?10 =>= additive_identity
34727 [10] by left_additive_inverse ?10
34728 25196: Id : 7, {_}:
34729 add ?12 (additive_inverse ?12) =>= additive_identity
34730 [12] by right_additive_inverse ?12
34731 25196: Id : 8, {_}:
34732 additive_inverse (additive_inverse ?14) =>= ?14
34733 [14] by additive_inverse_additive_inverse ?14
34734 25196: Id : 9, {_}:
34735 multiply ?16 (add ?17 ?18)
34737 add (multiply ?16 ?17) (multiply ?16 ?18)
34738 [18, 17, 16] by distribute1 ?16 ?17 ?18
34739 25196: Id : 10, {_}:
34740 multiply (add ?20 ?21) ?22
34742 add (multiply ?20 ?22) (multiply ?21 ?22)
34743 [22, 21, 20] by distribute2 ?20 ?21 ?22
34744 25196: Id : 11, {_}:
34745 add ?24 ?25 =?= add ?25 ?24
34746 [25, 24] by commutativity_for_addition ?24 ?25
34747 25196: Id : 12, {_}:
34748 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
34749 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34750 25196: Id : 13, {_}:
34751 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
34752 [32, 31] by right_alternative ?31 ?32
34753 25196: Id : 14, {_}:
34754 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
34755 [35, 34] by left_alternative ?34 ?35
34756 25196: Id : 15, {_}:
34757 associator ?37 ?38 ?39
34759 add (multiply (multiply ?37 ?38) ?39)
34760 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34761 [39, 38, 37] by associator ?37 ?38 ?39
34762 25196: Id : 16, {_}:
34765 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34766 [42, 41] by commutator ?41 ?42
34768 25196: Id : 1, {_}:
34769 multiply (multiply cx (multiply cy cx)) cz
34771 multiply cx (multiply cy (multiply cx cz))
34772 [] by prove_left_moufang
34776 25196: commutator 1 2 0
34777 25196: associator 1 3 0
34778 25196: additive_inverse 6 1 0
34780 25196: additive_identity 8 0 0
34781 25196: cz 2 0 2 2,2
34782 25196: multiply 28 2 6 0,2
34783 25196: cy 2 0 2 1,2,1,2
34784 25196: cx 4 0 4 1,1,2
34785 NO CLASH, using fixed ground order
34787 25197: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34788 25197: Id : 3, {_}:
34789 add ?4 additive_identity =>= ?4
34790 [4] by right_additive_identity ?4
34791 25197: Id : 4, {_}:
34792 multiply additive_identity ?6 =>= additive_identity
34793 [6] by left_multiplicative_zero ?6
34794 25197: Id : 5, {_}:
34795 multiply ?8 additive_identity =>= additive_identity
34796 [8] by right_multiplicative_zero ?8
34797 25197: Id : 6, {_}:
34798 add (additive_inverse ?10) ?10 =>= additive_identity
34799 [10] by left_additive_inverse ?10
34800 25197: Id : 7, {_}:
34801 add ?12 (additive_inverse ?12) =>= additive_identity
34802 [12] by right_additive_inverse ?12
34803 25197: Id : 8, {_}:
34804 additive_inverse (additive_inverse ?14) =>= ?14
34805 [14] by additive_inverse_additive_inverse ?14
34806 25197: Id : 9, {_}:
34807 multiply ?16 (add ?17 ?18)
34809 add (multiply ?16 ?17) (multiply ?16 ?18)
34810 [18, 17, 16] by distribute1 ?16 ?17 ?18
34811 25197: Id : 10, {_}:
34812 multiply (add ?20 ?21) ?22
34814 add (multiply ?20 ?22) (multiply ?21 ?22)
34815 [22, 21, 20] by distribute2 ?20 ?21 ?22
34816 25197: Id : 11, {_}:
34817 add ?24 ?25 =?= add ?25 ?24
34818 [25, 24] by commutativity_for_addition ?24 ?25
34819 25197: Id : 12, {_}:
34820 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
34821 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34822 25197: Id : 13, {_}:
34823 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
34824 [32, 31] by right_alternative ?31 ?32
34825 25197: Id : 14, {_}:
34826 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
34827 [35, 34] by left_alternative ?34 ?35
34828 25197: Id : 15, {_}:
34829 associator ?37 ?38 ?39
34831 add (multiply (multiply ?37 ?38) ?39)
34832 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34833 [39, 38, 37] by associator ?37 ?38 ?39
34834 25197: Id : 16, {_}:
34837 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34838 [42, 41] by commutator ?41 ?42
34840 25197: Id : 1, {_}:
34841 multiply (multiply cx (multiply cy cx)) cz
34843 multiply cx (multiply cy (multiply cx cz))
34844 [] by prove_left_moufang
34848 25197: commutator 1 2 0
34849 25197: associator 1 3 0
34850 25197: additive_inverse 6 1 0
34852 25197: additive_identity 8 0 0
34853 25197: cz 2 0 2 2,2
34854 25197: multiply 28 2 6 0,2
34855 25197: cy 2 0 2 1,2,1,2
34856 25197: cx 4 0 4 1,1,2
34857 % SZS status Timeout for RNG028-5.p
34858 NO CLASH, using fixed ground order
34860 25213: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34861 25213: Id : 3, {_}:
34862 add ?4 additive_identity =>= ?4
34863 [4] by right_additive_identity ?4
34864 25213: Id : 4, {_}:
34865 multiply additive_identity ?6 =>= additive_identity
34866 [6] by left_multiplicative_zero ?6
34867 25213: Id : 5, {_}:
34868 multiply ?8 additive_identity =>= additive_identity
34869 [8] by right_multiplicative_zero ?8
34870 25213: Id : 6, {_}:
34871 add (additive_inverse ?10) ?10 =>= additive_identity
34872 [10] by left_additive_inverse ?10
34873 25213: Id : 7, {_}:
34874 add ?12 (additive_inverse ?12) =>= additive_identity
34875 [12] by right_additive_inverse ?12
34876 25213: Id : 8, {_}:
34877 additive_inverse (additive_inverse ?14) =>= ?14
34878 [14] by additive_inverse_additive_inverse ?14
34879 25213: Id : 9, {_}:
34880 multiply ?16 (add ?17 ?18)
34882 add (multiply ?16 ?17) (multiply ?16 ?18)
34883 [18, 17, 16] by distribute1 ?16 ?17 ?18
34884 25213: Id : 10, {_}:
34885 multiply (add ?20 ?21) ?22
34887 add (multiply ?20 ?22) (multiply ?21 ?22)
34888 [22, 21, 20] by distribute2 ?20 ?21 ?22
34889 25213: Id : 11, {_}:
34890 add ?24 ?25 =?= add ?25 ?24
34891 [25, 24] by commutativity_for_addition ?24 ?25
34892 25213: Id : 12, {_}:
34893 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
34894 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
34895 25213: Id : 13, {_}:
34896 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
34897 [32, 31] by right_alternative ?31 ?32
34898 25213: Id : 14, {_}:
34899 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
34900 [35, 34] by left_alternative ?34 ?35
34901 25213: Id : 15, {_}:
34902 associator ?37 ?38 ?39
34904 add (multiply (multiply ?37 ?38) ?39)
34905 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
34906 [39, 38, 37] by associator ?37 ?38 ?39
34907 25213: Id : 16, {_}:
34910 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
34911 [42, 41] by commutator ?41 ?42
34912 25213: Id : 17, {_}:
34913 multiply (additive_inverse ?44) (additive_inverse ?45)
34916 [45, 44] by product_of_inverses ?44 ?45
34917 25213: Id : 18, {_}:
34918 multiply (additive_inverse ?47) ?48
34920 additive_inverse (multiply ?47 ?48)
34921 [48, 47] by inverse_product1 ?47 ?48
34922 25213: Id : 19, {_}:
34923 multiply ?50 (additive_inverse ?51)
34925 additive_inverse (multiply ?50 ?51)
34926 [51, 50] by inverse_product2 ?50 ?51
34927 25213: Id : 20, {_}:
34928 multiply ?53 (add ?54 (additive_inverse ?55))
34930 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
34931 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
34932 25213: Id : 21, {_}:
34933 multiply (add ?57 (additive_inverse ?58)) ?59
34935 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
34936 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
34937 25213: Id : 22, {_}:
34938 multiply (additive_inverse ?61) (add ?62 ?63)
34940 add (additive_inverse (multiply ?61 ?62))
34941 (additive_inverse (multiply ?61 ?63))
34942 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
34943 25213: Id : 23, {_}:
34944 multiply (add ?65 ?66) (additive_inverse ?67)
34946 add (additive_inverse (multiply ?65 ?67))
34947 (additive_inverse (multiply ?66 ?67))
34948 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
34950 25213: Id : 1, {_}:
34951 multiply (multiply cx (multiply cy cx)) cz
34953 multiply cx (multiply cy (multiply cx cz))
34954 [] by prove_left_moufang
34958 25213: commutator 1 2 0
34959 25213: associator 1 3 0
34960 25213: additive_inverse 22 1 0
34962 25213: additive_identity 8 0 0
34963 25213: cz 2 0 2 2,2
34964 25213: multiply 46 2 6 0,2
34965 25213: cy 2 0 2 1,2,1,2
34966 25213: cx 4 0 4 1,1,2
34967 NO CLASH, using fixed ground order
34969 25214: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
34970 25214: Id : 3, {_}:
34971 add ?4 additive_identity =>= ?4
34972 [4] by right_additive_identity ?4
34973 25214: Id : 4, {_}:
34974 multiply additive_identity ?6 =>= additive_identity
34975 [6] by left_multiplicative_zero ?6
34976 25214: Id : 5, {_}:
34977 multiply ?8 additive_identity =>= additive_identity
34978 [8] by right_multiplicative_zero ?8
34979 25214: Id : 6, {_}:
34980 add (additive_inverse ?10) ?10 =>= additive_identity
34981 [10] by left_additive_inverse ?10
34982 25214: Id : 7, {_}:
34983 add ?12 (additive_inverse ?12) =>= additive_identity
34984 [12] by right_additive_inverse ?12
34985 25214: Id : 8, {_}:
34986 additive_inverse (additive_inverse ?14) =>= ?14
34987 [14] by additive_inverse_additive_inverse ?14
34988 25214: Id : 9, {_}:
34989 multiply ?16 (add ?17 ?18)
34991 add (multiply ?16 ?17) (multiply ?16 ?18)
34992 [18, 17, 16] by distribute1 ?16 ?17 ?18
34993 25214: Id : 10, {_}:
34994 multiply (add ?20 ?21) ?22
34996 add (multiply ?20 ?22) (multiply ?21 ?22)
34997 [22, 21, 20] by distribute2 ?20 ?21 ?22
34998 25214: Id : 11, {_}:
34999 add ?24 ?25 =?= add ?25 ?24
35000 [25, 24] by commutativity_for_addition ?24 ?25
35001 25214: Id : 12, {_}:
35002 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35003 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35004 25214: Id : 13, {_}:
35005 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35006 [32, 31] by right_alternative ?31 ?32
35007 25214: Id : 14, {_}:
35008 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35009 [35, 34] by left_alternative ?34 ?35
35010 25214: Id : 15, {_}:
35011 associator ?37 ?38 ?39
35013 add (multiply (multiply ?37 ?38) ?39)
35014 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35015 [39, 38, 37] by associator ?37 ?38 ?39
35016 25214: Id : 16, {_}:
35019 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35020 [42, 41] by commutator ?41 ?42
35021 25214: Id : 17, {_}:
35022 multiply (additive_inverse ?44) (additive_inverse ?45)
35025 [45, 44] by product_of_inverses ?44 ?45
35026 25214: Id : 18, {_}:
35027 multiply (additive_inverse ?47) ?48
35029 additive_inverse (multiply ?47 ?48)
35030 [48, 47] by inverse_product1 ?47 ?48
35031 25214: Id : 19, {_}:
35032 multiply ?50 (additive_inverse ?51)
35034 additive_inverse (multiply ?50 ?51)
35035 [51, 50] by inverse_product2 ?50 ?51
35036 25214: Id : 20, {_}:
35037 multiply ?53 (add ?54 (additive_inverse ?55))
35039 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
35040 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
35041 25214: Id : 21, {_}:
35042 multiply (add ?57 (additive_inverse ?58)) ?59
35044 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
35045 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
35046 25214: Id : 22, {_}:
35047 multiply (additive_inverse ?61) (add ?62 ?63)
35049 add (additive_inverse (multiply ?61 ?62))
35050 (additive_inverse (multiply ?61 ?63))
35051 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
35052 25214: Id : 23, {_}:
35053 multiply (add ?65 ?66) (additive_inverse ?67)
35055 add (additive_inverse (multiply ?65 ?67))
35056 (additive_inverse (multiply ?66 ?67))
35057 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
35059 25214: Id : 1, {_}:
35060 multiply (multiply cx (multiply cy cx)) cz
35062 multiply cx (multiply cy (multiply cx cz))
35063 [] by prove_left_moufang
35067 25214: commutator 1 2 0
35068 25214: associator 1 3 0
35069 25214: additive_inverse 22 1 0
35071 25214: additive_identity 8 0 0
35072 25214: cz 2 0 2 2,2
35073 25214: multiply 46 2 6 0,2
35074 25214: cy 2 0 2 1,2,1,2
35075 25214: cx 4 0 4 1,1,2
35076 NO CLASH, using fixed ground order
35078 25215: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35079 25215: Id : 3, {_}:
35080 add ?4 additive_identity =>= ?4
35081 [4] by right_additive_identity ?4
35082 25215: Id : 4, {_}:
35083 multiply additive_identity ?6 =>= additive_identity
35084 [6] by left_multiplicative_zero ?6
35085 25215: Id : 5, {_}:
35086 multiply ?8 additive_identity =>= additive_identity
35087 [8] by right_multiplicative_zero ?8
35088 25215: Id : 6, {_}:
35089 add (additive_inverse ?10) ?10 =>= additive_identity
35090 [10] by left_additive_inverse ?10
35091 25215: Id : 7, {_}:
35092 add ?12 (additive_inverse ?12) =>= additive_identity
35093 [12] by right_additive_inverse ?12
35094 25215: Id : 8, {_}:
35095 additive_inverse (additive_inverse ?14) =>= ?14
35096 [14] by additive_inverse_additive_inverse ?14
35097 25215: Id : 9, {_}:
35098 multiply ?16 (add ?17 ?18)
35100 add (multiply ?16 ?17) (multiply ?16 ?18)
35101 [18, 17, 16] by distribute1 ?16 ?17 ?18
35102 25215: Id : 10, {_}:
35103 multiply (add ?20 ?21) ?22
35105 add (multiply ?20 ?22) (multiply ?21 ?22)
35106 [22, 21, 20] by distribute2 ?20 ?21 ?22
35107 25215: Id : 11, {_}:
35108 add ?24 ?25 =?= add ?25 ?24
35109 [25, 24] by commutativity_for_addition ?24 ?25
35110 25215: Id : 12, {_}:
35111 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35112 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35113 25215: Id : 13, {_}:
35114 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35115 [32, 31] by right_alternative ?31 ?32
35116 25215: Id : 14, {_}:
35117 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35118 [35, 34] by left_alternative ?34 ?35
35119 25215: Id : 15, {_}:
35120 associator ?37 ?38 ?39
35122 add (multiply (multiply ?37 ?38) ?39)
35123 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35124 [39, 38, 37] by associator ?37 ?38 ?39
35125 25215: Id : 16, {_}:
35128 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35129 [42, 41] by commutator ?41 ?42
35130 25215: Id : 17, {_}:
35131 multiply (additive_inverse ?44) (additive_inverse ?45)
35134 [45, 44] by product_of_inverses ?44 ?45
35135 25215: Id : 18, {_}:
35136 multiply (additive_inverse ?47) ?48
35138 additive_inverse (multiply ?47 ?48)
35139 [48, 47] by inverse_product1 ?47 ?48
35140 25215: Id : 19, {_}:
35141 multiply ?50 (additive_inverse ?51)
35143 additive_inverse (multiply ?50 ?51)
35144 [51, 50] by inverse_product2 ?50 ?51
35145 25215: Id : 20, {_}:
35146 multiply ?53 (add ?54 (additive_inverse ?55))
35148 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
35149 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
35150 25215: Id : 21, {_}:
35151 multiply (add ?57 (additive_inverse ?58)) ?59
35153 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
35154 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
35155 25215: Id : 22, {_}:
35156 multiply (additive_inverse ?61) (add ?62 ?63)
35158 add (additive_inverse (multiply ?61 ?62))
35159 (additive_inverse (multiply ?61 ?63))
35160 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
35161 25215: Id : 23, {_}:
35162 multiply (add ?65 ?66) (additive_inverse ?67)
35164 add (additive_inverse (multiply ?65 ?67))
35165 (additive_inverse (multiply ?66 ?67))
35166 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
35168 25215: Id : 1, {_}:
35169 multiply (multiply cx (multiply cy cx)) cz
35171 multiply cx (multiply cy (multiply cx cz))
35172 [] by prove_left_moufang
35176 25215: commutator 1 2 0
35177 25215: associator 1 3 0
35178 25215: additive_inverse 22 1 0
35180 25215: additive_identity 8 0 0
35181 25215: cz 2 0 2 2,2
35182 25215: multiply 46 2 6 0,2
35183 25215: cy 2 0 2 1,2,1,2
35184 25215: cx 4 0 4 1,1,2
35185 % SZS status Timeout for RNG028-7.p
35186 NO CLASH, using fixed ground order
35188 25251: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35189 25251: Id : 3, {_}:
35190 add ?4 additive_identity =>= ?4
35191 [4] by right_additive_identity ?4
35192 25251: Id : 4, {_}:
35193 multiply additive_identity ?6 =>= additive_identity
35194 [6] by left_multiplicative_zero ?6
35195 25251: Id : 5, {_}:
35196 multiply ?8 additive_identity =>= additive_identity
35197 [8] by right_multiplicative_zero ?8
35198 25251: Id : 6, {_}:
35199 add (additive_inverse ?10) ?10 =>= additive_identity
35200 [10] by left_additive_inverse ?10
35201 25251: Id : 7, {_}:
35202 add ?12 (additive_inverse ?12) =>= additive_identity
35203 [12] by right_additive_inverse ?12
35204 25251: Id : 8, {_}:
35205 additive_inverse (additive_inverse ?14) =>= ?14
35206 [14] by additive_inverse_additive_inverse ?14
35207 25251: Id : 9, {_}:
35208 multiply ?16 (add ?17 ?18)
35210 add (multiply ?16 ?17) (multiply ?16 ?18)
35211 [18, 17, 16] by distribute1 ?16 ?17 ?18
35212 25251: Id : 10, {_}:
35213 multiply (add ?20 ?21) ?22
35215 add (multiply ?20 ?22) (multiply ?21 ?22)
35216 [22, 21, 20] by distribute2 ?20 ?21 ?22
35217 25251: Id : 11, {_}:
35218 add ?24 ?25 =?= add ?25 ?24
35219 [25, 24] by commutativity_for_addition ?24 ?25
35220 25251: Id : 12, {_}:
35221 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
35222 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35223 25251: Id : 13, {_}:
35224 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
35225 [32, 31] by right_alternative ?31 ?32
35226 25251: Id : 14, {_}:
35227 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
35228 [35, 34] by left_alternative ?34 ?35
35229 25251: Id : 15, {_}:
35230 associator ?37 ?38 ?39
35232 add (multiply (multiply ?37 ?38) ?39)
35233 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35234 [39, 38, 37] by associator ?37 ?38 ?39
35235 25251: Id : 16, {_}:
35238 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35239 [42, 41] by commutator ?41 ?42
35241 25251: Id : 1, {_}:
35242 associator x (multiply y x) z =<= multiply x (associator x y z)
35243 [] by prove_left_moufang
35247 25251: commutator 1 2 0
35248 25251: additive_inverse 6 1 0
35250 25251: additive_identity 8 0 0
35251 25251: associator 3 3 2 0,2
35253 25251: multiply 24 2 2 0,2,2
35254 25251: y 2 0 2 1,2,2
35256 NO CLASH, using fixed ground order
35258 25252: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35259 25252: Id : 3, {_}:
35260 add ?4 additive_identity =>= ?4
35261 [4] by right_additive_identity ?4
35262 25252: Id : 4, {_}:
35263 multiply additive_identity ?6 =>= additive_identity
35264 [6] by left_multiplicative_zero ?6
35265 25252: Id : 5, {_}:
35266 multiply ?8 additive_identity =>= additive_identity
35267 [8] by right_multiplicative_zero ?8
35268 25252: Id : 6, {_}:
35269 add (additive_inverse ?10) ?10 =>= additive_identity
35270 [10] by left_additive_inverse ?10
35271 25252: Id : 7, {_}:
35272 add ?12 (additive_inverse ?12) =>= additive_identity
35273 [12] by right_additive_inverse ?12
35274 25252: Id : 8, {_}:
35275 additive_inverse (additive_inverse ?14) =>= ?14
35276 [14] by additive_inverse_additive_inverse ?14
35277 25252: Id : 9, {_}:
35278 multiply ?16 (add ?17 ?18)
35280 add (multiply ?16 ?17) (multiply ?16 ?18)
35281 [18, 17, 16] by distribute1 ?16 ?17 ?18
35282 25252: Id : 10, {_}:
35283 multiply (add ?20 ?21) ?22
35285 add (multiply ?20 ?22) (multiply ?21 ?22)
35286 [22, 21, 20] by distribute2 ?20 ?21 ?22
35287 25252: Id : 11, {_}:
35288 add ?24 ?25 =?= add ?25 ?24
35289 [25, 24] by commutativity_for_addition ?24 ?25
35290 25252: Id : 12, {_}:
35291 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35292 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35293 25252: Id : 13, {_}:
35294 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35295 [32, 31] by right_alternative ?31 ?32
35296 25252: Id : 14, {_}:
35297 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35298 [35, 34] by left_alternative ?34 ?35
35299 25252: Id : 15, {_}:
35300 associator ?37 ?38 ?39
35302 add (multiply (multiply ?37 ?38) ?39)
35303 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35304 [39, 38, 37] by associator ?37 ?38 ?39
35305 25252: Id : 16, {_}:
35308 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35309 [42, 41] by commutator ?41 ?42
35311 25252: Id : 1, {_}:
35312 associator x (multiply y x) z =<= multiply x (associator x y z)
35313 [] by prove_left_moufang
35317 25252: commutator 1 2 0
35318 25252: additive_inverse 6 1 0
35320 25252: additive_identity 8 0 0
35321 25252: associator 3 3 2 0,2
35323 25252: multiply 24 2 2 0,2,2
35324 25252: y 2 0 2 1,2,2
35326 NO CLASH, using fixed ground order
35328 25253: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35329 25253: Id : 3, {_}:
35330 add ?4 additive_identity =>= ?4
35331 [4] by right_additive_identity ?4
35332 25253: Id : 4, {_}:
35333 multiply additive_identity ?6 =>= additive_identity
35334 [6] by left_multiplicative_zero ?6
35335 25253: Id : 5, {_}:
35336 multiply ?8 additive_identity =>= additive_identity
35337 [8] by right_multiplicative_zero ?8
35338 25253: Id : 6, {_}:
35339 add (additive_inverse ?10) ?10 =>= additive_identity
35340 [10] by left_additive_inverse ?10
35341 25253: Id : 7, {_}:
35342 add ?12 (additive_inverse ?12) =>= additive_identity
35343 [12] by right_additive_inverse ?12
35344 25253: Id : 8, {_}:
35345 additive_inverse (additive_inverse ?14) =>= ?14
35346 [14] by additive_inverse_additive_inverse ?14
35347 25253: Id : 9, {_}:
35348 multiply ?16 (add ?17 ?18)
35350 add (multiply ?16 ?17) (multiply ?16 ?18)
35351 [18, 17, 16] by distribute1 ?16 ?17 ?18
35352 25253: Id : 10, {_}:
35353 multiply (add ?20 ?21) ?22
35355 add (multiply ?20 ?22) (multiply ?21 ?22)
35356 [22, 21, 20] by distribute2 ?20 ?21 ?22
35357 25253: Id : 11, {_}:
35358 add ?24 ?25 =?= add ?25 ?24
35359 [25, 24] by commutativity_for_addition ?24 ?25
35360 25253: Id : 12, {_}:
35361 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35362 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35363 25253: Id : 13, {_}:
35364 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35365 [32, 31] by right_alternative ?31 ?32
35366 25253: Id : 14, {_}:
35367 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35368 [35, 34] by left_alternative ?34 ?35
35369 25253: Id : 15, {_}:
35370 associator ?37 ?38 ?39
35372 add (multiply (multiply ?37 ?38) ?39)
35373 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35374 [39, 38, 37] by associator ?37 ?38 ?39
35375 25253: Id : 16, {_}:
35378 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35379 [42, 41] by commutator ?41 ?42
35381 25253: Id : 1, {_}:
35382 associator x (multiply y x) z =<= multiply x (associator x y z)
35383 [] by prove_left_moufang
35387 25253: commutator 1 2 0
35388 25253: additive_inverse 6 1 0
35390 25253: additive_identity 8 0 0
35391 25253: associator 3 3 2 0,2
35393 25253: multiply 24 2 2 0,2,2
35394 25253: y 2 0 2 1,2,2
35396 % SZS status Timeout for RNG028-8.p
35397 NO CLASH, using fixed ground order
35399 25289: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35400 25289: Id : 3, {_}:
35401 add ?4 additive_identity =>= ?4
35402 [4] by right_additive_identity ?4
35403 25289: Id : 4, {_}:
35404 multiply additive_identity ?6 =>= additive_identity
35405 [6] by left_multiplicative_zero ?6
35406 25289: Id : 5, {_}:
35407 multiply ?8 additive_identity =>= additive_identity
35408 [8] by right_multiplicative_zero ?8
35409 25289: Id : 6, {_}:
35410 add (additive_inverse ?10) ?10 =>= additive_identity
35411 [10] by left_additive_inverse ?10
35412 25289: Id : 7, {_}:
35413 add ?12 (additive_inverse ?12) =>= additive_identity
35414 [12] by right_additive_inverse ?12
35415 25289: Id : 8, {_}:
35416 additive_inverse (additive_inverse ?14) =>= ?14
35417 [14] by additive_inverse_additive_inverse ?14
35418 25289: Id : 9, {_}:
35419 multiply ?16 (add ?17 ?18)
35421 add (multiply ?16 ?17) (multiply ?16 ?18)
35422 [18, 17, 16] by distribute1 ?16 ?17 ?18
35423 25289: Id : 10, {_}:
35424 multiply (add ?20 ?21) ?22
35426 add (multiply ?20 ?22) (multiply ?21 ?22)
35427 [22, 21, 20] by distribute2 ?20 ?21 ?22
35428 25289: Id : 11, {_}:
35429 add ?24 ?25 =?= add ?25 ?24
35430 [25, 24] by commutativity_for_addition ?24 ?25
35431 25289: Id : 12, {_}:
35432 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
35433 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35434 25289: Id : 13, {_}:
35435 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
35436 [32, 31] by right_alternative ?31 ?32
35437 25289: Id : 14, {_}:
35438 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
35439 [35, 34] by left_alternative ?34 ?35
35440 25289: Id : 15, {_}:
35441 associator ?37 ?38 ?39
35443 add (multiply (multiply ?37 ?38) ?39)
35444 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35445 [39, 38, 37] by associator ?37 ?38 ?39
35446 25289: Id : 16, {_}:
35449 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35450 [42, 41] by commutator ?41 ?42
35451 25289: Id : 17, {_}:
35452 multiply (additive_inverse ?44) (additive_inverse ?45)
35455 [45, 44] by product_of_inverses ?44 ?45
35456 25289: Id : 18, {_}:
35457 multiply (additive_inverse ?47) ?48
35459 additive_inverse (multiply ?47 ?48)
35460 [48, 47] by inverse_product1 ?47 ?48
35461 25289: Id : 19, {_}:
35462 multiply ?50 (additive_inverse ?51)
35464 additive_inverse (multiply ?50 ?51)
35465 [51, 50] by inverse_product2 ?50 ?51
35466 25289: Id : 20, {_}:
35467 multiply ?53 (add ?54 (additive_inverse ?55))
35469 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
35470 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
35471 25289: Id : 21, {_}:
35472 multiply (add ?57 (additive_inverse ?58)) ?59
35474 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
35475 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
35476 25289: Id : 22, {_}:
35477 multiply (additive_inverse ?61) (add ?62 ?63)
35479 add (additive_inverse (multiply ?61 ?62))
35480 (additive_inverse (multiply ?61 ?63))
35481 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
35482 25289: Id : 23, {_}:
35483 multiply (add ?65 ?66) (additive_inverse ?67)
35485 add (additive_inverse (multiply ?65 ?67))
35486 (additive_inverse (multiply ?66 ?67))
35487 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
35489 25289: Id : 1, {_}:
35490 associator x (multiply y x) z =<= multiply x (associator x y z)
35491 [] by prove_left_moufang
35495 25289: commutator 1 2 0
35496 25289: additive_inverse 22 1 0
35498 25289: additive_identity 8 0 0
35499 25289: associator 3 3 2 0,2
35501 25289: multiply 42 2 2 0,2,2
35502 25289: y 2 0 2 1,2,2
35504 NO CLASH, using fixed ground order
35506 25290: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35507 25290: Id : 3, {_}:
35508 add ?4 additive_identity =>= ?4
35509 [4] by right_additive_identity ?4
35510 25290: Id : 4, {_}:
35511 multiply additive_identity ?6 =>= additive_identity
35512 [6] by left_multiplicative_zero ?6
35513 25290: Id : 5, {_}:
35514 multiply ?8 additive_identity =>= additive_identity
35515 [8] by right_multiplicative_zero ?8
35516 25290: Id : 6, {_}:
35517 add (additive_inverse ?10) ?10 =>= additive_identity
35518 [10] by left_additive_inverse ?10
35519 25290: Id : 7, {_}:
35520 add ?12 (additive_inverse ?12) =>= additive_identity
35521 [12] by right_additive_inverse ?12
35522 25290: Id : 8, {_}:
35523 additive_inverse (additive_inverse ?14) =>= ?14
35524 [14] by additive_inverse_additive_inverse ?14
35525 25290: Id : 9, {_}:
35526 multiply ?16 (add ?17 ?18)
35528 add (multiply ?16 ?17) (multiply ?16 ?18)
35529 [18, 17, 16] by distribute1 ?16 ?17 ?18
35530 25290: Id : 10, {_}:
35531 multiply (add ?20 ?21) ?22
35533 add (multiply ?20 ?22) (multiply ?21 ?22)
35534 [22, 21, 20] by distribute2 ?20 ?21 ?22
35535 25290: Id : 11, {_}:
35536 add ?24 ?25 =?= add ?25 ?24
35537 [25, 24] by commutativity_for_addition ?24 ?25
35538 25290: Id : 12, {_}:
35539 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35540 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35541 25290: Id : 13, {_}:
35542 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35543 [32, 31] by right_alternative ?31 ?32
35544 25290: Id : 14, {_}:
35545 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35546 [35, 34] by left_alternative ?34 ?35
35547 25290: Id : 15, {_}:
35548 associator ?37 ?38 ?39
35550 add (multiply (multiply ?37 ?38) ?39)
35551 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35552 [39, 38, 37] by associator ?37 ?38 ?39
35553 25290: Id : 16, {_}:
35556 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35557 [42, 41] by commutator ?41 ?42
35558 25290: Id : 17, {_}:
35559 multiply (additive_inverse ?44) (additive_inverse ?45)
35562 [45, 44] by product_of_inverses ?44 ?45
35563 25290: Id : 18, {_}:
35564 multiply (additive_inverse ?47) ?48
35566 additive_inverse (multiply ?47 ?48)
35567 [48, 47] by inverse_product1 ?47 ?48
35568 25290: Id : 19, {_}:
35569 multiply ?50 (additive_inverse ?51)
35571 additive_inverse (multiply ?50 ?51)
35572 [51, 50] by inverse_product2 ?50 ?51
35573 25290: Id : 20, {_}:
35574 multiply ?53 (add ?54 (additive_inverse ?55))
35576 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
35577 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
35578 25290: Id : 21, {_}:
35579 multiply (add ?57 (additive_inverse ?58)) ?59
35581 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
35582 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
35583 25290: Id : 22, {_}:
35584 multiply (additive_inverse ?61) (add ?62 ?63)
35586 add (additive_inverse (multiply ?61 ?62))
35587 (additive_inverse (multiply ?61 ?63))
35588 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
35589 25290: Id : 23, {_}:
35590 multiply (add ?65 ?66) (additive_inverse ?67)
35592 add (additive_inverse (multiply ?65 ?67))
35593 (additive_inverse (multiply ?66 ?67))
35594 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
35596 25290: Id : 1, {_}:
35597 associator x (multiply y x) z =<= multiply x (associator x y z)
35598 [] by prove_left_moufang
35602 25290: commutator 1 2 0
35603 25290: additive_inverse 22 1 0
35605 25290: additive_identity 8 0 0
35606 25290: associator 3 3 2 0,2
35608 25290: multiply 42 2 2 0,2,2
35609 25290: y 2 0 2 1,2,2
35611 NO CLASH, using fixed ground order
35613 25291: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35614 25291: Id : 3, {_}:
35615 add ?4 additive_identity =>= ?4
35616 [4] by right_additive_identity ?4
35617 25291: Id : 4, {_}:
35618 multiply additive_identity ?6 =>= additive_identity
35619 [6] by left_multiplicative_zero ?6
35620 25291: Id : 5, {_}:
35621 multiply ?8 additive_identity =>= additive_identity
35622 [8] by right_multiplicative_zero ?8
35623 25291: Id : 6, {_}:
35624 add (additive_inverse ?10) ?10 =>= additive_identity
35625 [10] by left_additive_inverse ?10
35626 25291: Id : 7, {_}:
35627 add ?12 (additive_inverse ?12) =>= additive_identity
35628 [12] by right_additive_inverse ?12
35629 25291: Id : 8, {_}:
35630 additive_inverse (additive_inverse ?14) =>= ?14
35631 [14] by additive_inverse_additive_inverse ?14
35632 25291: Id : 9, {_}:
35633 multiply ?16 (add ?17 ?18)
35635 add (multiply ?16 ?17) (multiply ?16 ?18)
35636 [18, 17, 16] by distribute1 ?16 ?17 ?18
35637 25291: Id : 10, {_}:
35638 multiply (add ?20 ?21) ?22
35640 add (multiply ?20 ?22) (multiply ?21 ?22)
35641 [22, 21, 20] by distribute2 ?20 ?21 ?22
35642 25291: Id : 11, {_}:
35643 add ?24 ?25 =?= add ?25 ?24
35644 [25, 24] by commutativity_for_addition ?24 ?25
35645 25291: Id : 12, {_}:
35646 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35647 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35648 25291: Id : 13, {_}:
35649 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35650 [32, 31] by right_alternative ?31 ?32
35651 25291: Id : 14, {_}:
35652 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35653 [35, 34] by left_alternative ?34 ?35
35654 25291: Id : 15, {_}:
35655 associator ?37 ?38 ?39
35657 add (multiply (multiply ?37 ?38) ?39)
35658 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35659 [39, 38, 37] by associator ?37 ?38 ?39
35660 25291: Id : 16, {_}:
35663 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35664 [42, 41] by commutator ?41 ?42
35665 25291: Id : 17, {_}:
35666 multiply (additive_inverse ?44) (additive_inverse ?45)
35669 [45, 44] by product_of_inverses ?44 ?45
35670 25291: Id : 18, {_}:
35671 multiply (additive_inverse ?47) ?48
35673 additive_inverse (multiply ?47 ?48)
35674 [48, 47] by inverse_product1 ?47 ?48
35675 25291: Id : 19, {_}:
35676 multiply ?50 (additive_inverse ?51)
35678 additive_inverse (multiply ?50 ?51)
35679 [51, 50] by inverse_product2 ?50 ?51
35680 25291: Id : 20, {_}:
35681 multiply ?53 (add ?54 (additive_inverse ?55))
35683 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
35684 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
35685 25291: Id : 21, {_}:
35686 multiply (add ?57 (additive_inverse ?58)) ?59
35688 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
35689 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
35690 25291: Id : 22, {_}:
35691 multiply (additive_inverse ?61) (add ?62 ?63)
35693 add (additive_inverse (multiply ?61 ?62))
35694 (additive_inverse (multiply ?61 ?63))
35695 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
35696 25291: Id : 23, {_}:
35697 multiply (add ?65 ?66) (additive_inverse ?67)
35699 add (additive_inverse (multiply ?65 ?67))
35700 (additive_inverse (multiply ?66 ?67))
35701 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
35703 25291: Id : 1, {_}:
35704 associator x (multiply y x) z =<= multiply x (associator x y z)
35705 [] by prove_left_moufang
35709 25291: commutator 1 2 0
35710 25291: additive_inverse 22 1 0
35712 25291: additive_identity 8 0 0
35713 25291: associator 3 3 2 0,2
35715 25291: multiply 42 2 2 0,2,2
35716 25291: y 2 0 2 1,2,2
35718 % SZS status Timeout for RNG028-9.p
35719 NO CLASH, using fixed ground order
35721 25318: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35722 25318: Id : 3, {_}:
35723 add ?4 additive_identity =>= ?4
35724 [4] by right_additive_identity ?4
35725 25318: Id : 4, {_}:
35726 multiply additive_identity ?6 =>= additive_identity
35727 [6] by left_multiplicative_zero ?6
35728 25318: Id : 5, {_}:
35729 multiply ?8 additive_identity =>= additive_identity
35730 [8] by right_multiplicative_zero ?8
35731 25318: Id : 6, {_}:
35732 add (additive_inverse ?10) ?10 =>= additive_identity
35733 [10] by left_additive_inverse ?10
35734 25318: Id : 7, {_}:
35735 add ?12 (additive_inverse ?12) =>= additive_identity
35736 [12] by right_additive_inverse ?12
35737 25318: Id : 8, {_}:
35738 additive_inverse (additive_inverse ?14) =>= ?14
35739 [14] by additive_inverse_additive_inverse ?14
35740 25318: Id : 9, {_}:
35741 multiply ?16 (add ?17 ?18)
35743 add (multiply ?16 ?17) (multiply ?16 ?18)
35744 [18, 17, 16] by distribute1 ?16 ?17 ?18
35745 25318: Id : 10, {_}:
35746 multiply (add ?20 ?21) ?22
35748 add (multiply ?20 ?22) (multiply ?21 ?22)
35749 [22, 21, 20] by distribute2 ?20 ?21 ?22
35750 25318: Id : 11, {_}:
35751 add ?24 ?25 =?= add ?25 ?24
35752 [25, 24] by commutativity_for_addition ?24 ?25
35753 25318: Id : 12, {_}:
35754 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
35755 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35756 25318: Id : 13, {_}:
35757 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
35758 [32, 31] by right_alternative ?31 ?32
35759 25318: Id : 14, {_}:
35760 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
35761 [35, 34] by left_alternative ?34 ?35
35762 25318: Id : 15, {_}:
35763 associator ?37 ?38 ?39
35765 add (multiply (multiply ?37 ?38) ?39)
35766 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35767 [39, 38, 37] by associator ?37 ?38 ?39
35768 25318: Id : 16, {_}:
35771 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35772 [42, 41] by commutator ?41 ?42
35774 25318: Id : 1, {_}:
35775 multiply (multiply cx cy) (multiply cz cx)
35777 multiply cx (multiply (multiply cy cz) cx)
35778 [] by prove_middle_law
35782 25318: commutator 1 2 0
35783 25318: associator 1 3 0
35784 25318: additive_inverse 6 1 0
35786 25318: additive_identity 8 0 0
35787 25318: cz 2 0 2 1,2,2
35788 25318: multiply 28 2 6 0,2
35789 25318: cy 2 0 2 2,1,2
35790 25318: cx 4 0 4 1,1,2
35791 NO CLASH, using fixed ground order
35793 25320: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35794 25320: Id : 3, {_}:
35795 add ?4 additive_identity =>= ?4
35796 [4] by right_additive_identity ?4
35797 25320: Id : 4, {_}:
35798 multiply additive_identity ?6 =>= additive_identity
35799 [6] by left_multiplicative_zero ?6
35800 25320: Id : 5, {_}:
35801 multiply ?8 additive_identity =>= additive_identity
35802 [8] by right_multiplicative_zero ?8
35803 25320: Id : 6, {_}:
35804 add (additive_inverse ?10) ?10 =>= additive_identity
35805 [10] by left_additive_inverse ?10
35806 25320: Id : 7, {_}:
35807 add ?12 (additive_inverse ?12) =>= additive_identity
35808 [12] by right_additive_inverse ?12
35809 25320: Id : 8, {_}:
35810 additive_inverse (additive_inverse ?14) =>= ?14
35811 [14] by additive_inverse_additive_inverse ?14
35812 25320: Id : 9, {_}:
35813 multiply ?16 (add ?17 ?18)
35815 add (multiply ?16 ?17) (multiply ?16 ?18)
35816 [18, 17, 16] by distribute1 ?16 ?17 ?18
35817 25320: Id : 10, {_}:
35818 multiply (add ?20 ?21) ?22
35820 add (multiply ?20 ?22) (multiply ?21 ?22)
35821 [22, 21, 20] by distribute2 ?20 ?21 ?22
35822 25320: Id : 11, {_}:
35823 add ?24 ?25 =?= add ?25 ?24
35824 [25, 24] by commutativity_for_addition ?24 ?25
35825 25320: Id : 12, {_}:
35826 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35827 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35828 25320: Id : 13, {_}:
35829 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35830 [32, 31] by right_alternative ?31 ?32
35831 25320: Id : 14, {_}:
35832 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35833 [35, 34] by left_alternative ?34 ?35
35834 25320: Id : 15, {_}:
35835 associator ?37 ?38 ?39
35837 add (multiply (multiply ?37 ?38) ?39)
35838 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35839 [39, 38, 37] by associator ?37 ?38 ?39
35840 25320: Id : 16, {_}:
35843 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35844 [42, 41] by commutator ?41 ?42
35846 25320: Id : 1, {_}:
35847 multiply (multiply cx cy) (multiply cz cx)
35849 multiply cx (multiply (multiply cy cz) cx)
35850 [] by prove_middle_law
35854 25320: commutator 1 2 0
35855 25320: associator 1 3 0
35856 25320: additive_inverse 6 1 0
35858 25320: additive_identity 8 0 0
35859 25320: cz 2 0 2 1,2,2
35860 25320: multiply 28 2 6 0,2
35861 25320: cy 2 0 2 2,1,2
35862 25320: cx 4 0 4 1,1,2
35863 NO CLASH, using fixed ground order
35865 25319: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35866 25319: Id : 3, {_}:
35867 add ?4 additive_identity =>= ?4
35868 [4] by right_additive_identity ?4
35869 25319: Id : 4, {_}:
35870 multiply additive_identity ?6 =>= additive_identity
35871 [6] by left_multiplicative_zero ?6
35872 25319: Id : 5, {_}:
35873 multiply ?8 additive_identity =>= additive_identity
35874 [8] by right_multiplicative_zero ?8
35875 25319: Id : 6, {_}:
35876 add (additive_inverse ?10) ?10 =>= additive_identity
35877 [10] by left_additive_inverse ?10
35878 25319: Id : 7, {_}:
35879 add ?12 (additive_inverse ?12) =>= additive_identity
35880 [12] by right_additive_inverse ?12
35881 25319: Id : 8, {_}:
35882 additive_inverse (additive_inverse ?14) =>= ?14
35883 [14] by additive_inverse_additive_inverse ?14
35884 25319: Id : 9, {_}:
35885 multiply ?16 (add ?17 ?18)
35887 add (multiply ?16 ?17) (multiply ?16 ?18)
35888 [18, 17, 16] by distribute1 ?16 ?17 ?18
35889 25319: Id : 10, {_}:
35890 multiply (add ?20 ?21) ?22
35892 add (multiply ?20 ?22) (multiply ?21 ?22)
35893 [22, 21, 20] by distribute2 ?20 ?21 ?22
35894 25319: Id : 11, {_}:
35895 add ?24 ?25 =?= add ?25 ?24
35896 [25, 24] by commutativity_for_addition ?24 ?25
35897 25319: Id : 12, {_}:
35898 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
35899 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35900 25319: Id : 13, {_}:
35901 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
35902 [32, 31] by right_alternative ?31 ?32
35903 25319: Id : 14, {_}:
35904 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
35905 [35, 34] by left_alternative ?34 ?35
35906 25319: Id : 15, {_}:
35907 associator ?37 ?38 ?39
35909 add (multiply (multiply ?37 ?38) ?39)
35910 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35911 [39, 38, 37] by associator ?37 ?38 ?39
35912 25319: Id : 16, {_}:
35915 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35916 [42, 41] by commutator ?41 ?42
35918 25319: Id : 1, {_}:
35919 multiply (multiply cx cy) (multiply cz cx)
35921 multiply cx (multiply (multiply cy cz) cx)
35922 [] by prove_middle_law
35926 25319: commutator 1 2 0
35927 25319: associator 1 3 0
35928 25319: additive_inverse 6 1 0
35930 25319: additive_identity 8 0 0
35931 25319: cz 2 0 2 1,2,2
35932 25319: multiply 28 2 6 0,2
35933 25319: cy 2 0 2 2,1,2
35934 25319: cx 4 0 4 1,1,2
35935 % SZS status Timeout for RNG029-5.p
35936 NO CLASH, using fixed ground order
35938 25337: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
35939 25337: Id : 3, {_}:
35940 add ?4 additive_identity =>= ?4
35941 [4] by right_additive_identity ?4
35942 25337: Id : 4, {_}:
35943 multiply additive_identity ?6 =>= additive_identity
35944 [6] by left_multiplicative_zero ?6
35945 25337: Id : 5, {_}:
35946 multiply ?8 additive_identity =>= additive_identity
35947 [8] by right_multiplicative_zero ?8
35948 25337: Id : 6, {_}:
35949 add (additive_inverse ?10) ?10 =>= additive_identity
35950 [10] by left_additive_inverse ?10
35951 25337: Id : 7, {_}:
35952 add ?12 (additive_inverse ?12) =>= additive_identity
35953 [12] by right_additive_inverse ?12
35954 25337: Id : 8, {_}:
35955 additive_inverse (additive_inverse ?14) =>= ?14
35956 [14] by additive_inverse_additive_inverse ?14
35957 25337: Id : 9, {_}:
35958 multiply ?16 (add ?17 ?18)
35960 add (multiply ?16 ?17) (multiply ?16 ?18)
35961 [18, 17, 16] by distribute1 ?16 ?17 ?18
35962 25337: Id : 10, {_}:
35963 multiply (add ?20 ?21) ?22
35965 add (multiply ?20 ?22) (multiply ?21 ?22)
35966 [22, 21, 20] by distribute2 ?20 ?21 ?22
35967 25337: Id : 11, {_}:
35968 add ?24 ?25 =?= add ?25 ?24
35969 [25, 24] by commutativity_for_addition ?24 ?25
35970 25337: Id : 12, {_}:
35971 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
35972 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
35973 25337: Id : 13, {_}:
35974 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
35975 [32, 31] by right_alternative ?31 ?32
35976 25337: Id : 14, {_}:
35977 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
35978 [35, 34] by left_alternative ?34 ?35
35979 25337: Id : 15, {_}:
35980 associator ?37 ?38 ?39
35982 add (multiply (multiply ?37 ?38) ?39)
35983 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
35984 [39, 38, 37] by associator ?37 ?38 ?39
35985 25337: Id : 16, {_}:
35988 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
35989 [42, 41] by commutator ?41 ?42
35991 25337: Id : 1, {_}:
35992 multiply (multiply x y) (multiply z x)
35994 multiply (multiply x (multiply y z)) x
35995 [] by prove_middle_moufang
35999 25337: commutator 1 2 0
36000 25337: associator 1 3 0
36001 25337: additive_inverse 6 1 0
36003 25337: additive_identity 8 0 0
36004 25337: z 2 0 2 1,2,2
36005 25337: multiply 28 2 6 0,2
36006 25337: y 2 0 2 2,1,2
36007 25337: x 4 0 4 1,1,2
36008 NO CLASH, using fixed ground order
36010 25338: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
36011 25338: Id : 3, {_}:
36012 add ?4 additive_identity =>= ?4
36013 [4] by right_additive_identity ?4
36014 25338: Id : 4, {_}:
36015 multiply additive_identity ?6 =>= additive_identity
36016 [6] by left_multiplicative_zero ?6
36017 25338: Id : 5, {_}:
36018 multiply ?8 additive_identity =>= additive_identity
36019 [8] by right_multiplicative_zero ?8
36020 25338: Id : 6, {_}:
36021 add (additive_inverse ?10) ?10 =>= additive_identity
36022 [10] by left_additive_inverse ?10
36023 25338: Id : 7, {_}:
36024 add ?12 (additive_inverse ?12) =>= additive_identity
36025 [12] by right_additive_inverse ?12
36026 25338: Id : 8, {_}:
36027 additive_inverse (additive_inverse ?14) =>= ?14
36028 [14] by additive_inverse_additive_inverse ?14
36029 25338: Id : 9, {_}:
36030 multiply ?16 (add ?17 ?18)
36032 add (multiply ?16 ?17) (multiply ?16 ?18)
36033 [18, 17, 16] by distribute1 ?16 ?17 ?18
36034 25338: Id : 10, {_}:
36035 multiply (add ?20 ?21) ?22
36037 add (multiply ?20 ?22) (multiply ?21 ?22)
36038 [22, 21, 20] by distribute2 ?20 ?21 ?22
36039 25338: Id : 11, {_}:
36040 add ?24 ?25 =?= add ?25 ?24
36041 [25, 24] by commutativity_for_addition ?24 ?25
36042 25338: Id : 12, {_}:
36043 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
36044 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
36045 25338: Id : 13, {_}:
36046 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
36047 [32, 31] by right_alternative ?31 ?32
36048 25338: Id : 14, {_}:
36049 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
36050 [35, 34] by left_alternative ?34 ?35
36051 25338: Id : 15, {_}:
36052 associator ?37 ?38 ?39
36054 add (multiply (multiply ?37 ?38) ?39)
36055 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
36056 [39, 38, 37] by associator ?37 ?38 ?39
36057 25338: Id : 16, {_}:
36060 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
36061 [42, 41] by commutator ?41 ?42
36063 25338: Id : 1, {_}:
36064 multiply (multiply x y) (multiply z x)
36066 multiply (multiply x (multiply y z)) x
36067 [] by prove_middle_moufang
36071 25338: commutator 1 2 0
36072 25338: associator 1 3 0
36073 25338: additive_inverse 6 1 0
36075 25338: additive_identity 8 0 0
36076 25338: z 2 0 2 1,2,2
36077 25338: multiply 28 2 6 0,2
36078 25338: y 2 0 2 2,1,2
36079 25338: x 4 0 4 1,1,2
36080 NO CLASH, using fixed ground order
36082 25339: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
36083 25339: Id : 3, {_}:
36084 add ?4 additive_identity =>= ?4
36085 [4] by right_additive_identity ?4
36086 25339: Id : 4, {_}:
36087 multiply additive_identity ?6 =>= additive_identity
36088 [6] by left_multiplicative_zero ?6
36089 25339: Id : 5, {_}:
36090 multiply ?8 additive_identity =>= additive_identity
36091 [8] by right_multiplicative_zero ?8
36092 25339: Id : 6, {_}:
36093 add (additive_inverse ?10) ?10 =>= additive_identity
36094 [10] by left_additive_inverse ?10
36095 25339: Id : 7, {_}:
36096 add ?12 (additive_inverse ?12) =>= additive_identity
36097 [12] by right_additive_inverse ?12
36098 25339: Id : 8, {_}:
36099 additive_inverse (additive_inverse ?14) =>= ?14
36100 [14] by additive_inverse_additive_inverse ?14
36101 25339: Id : 9, {_}:
36102 multiply ?16 (add ?17 ?18)
36104 add (multiply ?16 ?17) (multiply ?16 ?18)
36105 [18, 17, 16] by distribute1 ?16 ?17 ?18
36106 25339: Id : 10, {_}:
36107 multiply (add ?20 ?21) ?22
36109 add (multiply ?20 ?22) (multiply ?21 ?22)
36110 [22, 21, 20] by distribute2 ?20 ?21 ?22
36111 25339: Id : 11, {_}:
36112 add ?24 ?25 =?= add ?25 ?24
36113 [25, 24] by commutativity_for_addition ?24 ?25
36114 25339: Id : 12, {_}:
36115 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
36116 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
36117 25339: Id : 13, {_}:
36118 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
36119 [32, 31] by right_alternative ?31 ?32
36120 25339: Id : 14, {_}:
36121 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
36122 [35, 34] by left_alternative ?34 ?35
36123 25339: Id : 15, {_}:
36124 associator ?37 ?38 ?39
36126 add (multiply (multiply ?37 ?38) ?39)
36127 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
36128 [39, 38, 37] by associator ?37 ?38 ?39
36129 25339: Id : 16, {_}:
36132 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
36133 [42, 41] by commutator ?41 ?42
36135 25339: Id : 1, {_}:
36136 multiply (multiply x y) (multiply z x)
36138 multiply (multiply x (multiply y z)) x
36139 [] by prove_middle_moufang
36143 25339: commutator 1 2 0
36144 25339: associator 1 3 0
36145 25339: additive_inverse 6 1 0
36147 25339: additive_identity 8 0 0
36148 25339: z 2 0 2 1,2,2
36149 25339: multiply 28 2 6 0,2
36150 25339: y 2 0 2 2,1,2
36151 25339: x 4 0 4 1,1,2
36152 % SZS status Timeout for RNG029-6.p
36153 NO CLASH, using fixed ground order
36155 25367: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
36156 25367: Id : 3, {_}:
36157 add ?4 additive_identity =>= ?4
36158 [4] by right_additive_identity ?4
36159 25367: Id : 4, {_}:
36160 multiply additive_identity ?6 =>= additive_identity
36161 [6] by left_multiplicative_zero ?6
36162 25367: Id : 5, {_}:
36163 multiply ?8 additive_identity =>= additive_identity
36164 [8] by right_multiplicative_zero ?8
36165 25367: Id : 6, {_}:
36166 add (additive_inverse ?10) ?10 =>= additive_identity
36167 [10] by left_additive_inverse ?10
36168 25367: Id : 7, {_}:
36169 add ?12 (additive_inverse ?12) =>= additive_identity
36170 [12] by right_additive_inverse ?12
36171 25367: Id : 8, {_}:
36172 additive_inverse (additive_inverse ?14) =>= ?14
36173 [14] by additive_inverse_additive_inverse ?14
36174 25367: Id : 9, {_}:
36175 multiply ?16 (add ?17 ?18)
36177 add (multiply ?16 ?17) (multiply ?16 ?18)
36178 [18, 17, 16] by distribute1 ?16 ?17 ?18
36179 25367: Id : 10, {_}:
36180 multiply (add ?20 ?21) ?22
36182 add (multiply ?20 ?22) (multiply ?21 ?22)
36183 [22, 21, 20] by distribute2 ?20 ?21 ?22
36184 25367: Id : 11, {_}:
36185 add ?24 ?25 =?= add ?25 ?24
36186 [25, 24] by commutativity_for_addition ?24 ?25
36187 25367: Id : 12, {_}:
36188 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
36189 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
36190 25367: Id : 13, {_}:
36191 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
36192 [32, 31] by right_alternative ?31 ?32
36193 25367: Id : 14, {_}:
36194 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
36195 [35, 34] by left_alternative ?34 ?35
36196 25367: Id : 15, {_}:
36197 associator ?37 ?38 ?39
36199 add (multiply (multiply ?37 ?38) ?39)
36200 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
36201 [39, 38, 37] by associator ?37 ?38 ?39
36202 25367: Id : 16, {_}:
36205 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
36206 [42, 41] by commutator ?41 ?42
36207 25367: Id : 17, {_}:
36208 multiply (additive_inverse ?44) (additive_inverse ?45)
36211 [45, 44] by product_of_inverses ?44 ?45
36212 25367: Id : 18, {_}:
36213 multiply (additive_inverse ?47) ?48
36215 additive_inverse (multiply ?47 ?48)
36216 [48, 47] by inverse_product1 ?47 ?48
36217 25367: Id : 19, {_}:
36218 multiply ?50 (additive_inverse ?51)
36220 additive_inverse (multiply ?50 ?51)
36221 [51, 50] by inverse_product2 ?50 ?51
36222 25367: Id : 20, {_}:
36223 multiply ?53 (add ?54 (additive_inverse ?55))
36225 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
36226 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
36227 25367: Id : 21, {_}:
36228 multiply (add ?57 (additive_inverse ?58)) ?59
36230 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
36231 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
36232 25367: Id : 22, {_}:
36233 multiply (additive_inverse ?61) (add ?62 ?63)
36235 add (additive_inverse (multiply ?61 ?62))
36236 (additive_inverse (multiply ?61 ?63))
36237 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
36238 25367: Id : 23, {_}:
36239 multiply (add ?65 ?66) (additive_inverse ?67)
36241 add (additive_inverse (multiply ?65 ?67))
36242 (additive_inverse (multiply ?66 ?67))
36243 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
36245 25367: Id : 1, {_}:
36246 multiply (multiply x y) (multiply z x)
36248 multiply (multiply x (multiply y z)) x
36249 [] by prove_middle_moufang
36253 25367: commutator 1 2 0
36254 25367: associator 1 3 0
36255 25367: additive_inverse 22 1 0
36257 25367: additive_identity 8 0 0
36258 25367: z 2 0 2 1,2,2
36259 25367: multiply 46 2 6 0,2
36260 25367: y 2 0 2 2,1,2
36261 25367: x 4 0 4 1,1,2
36262 NO CLASH, using fixed ground order
36264 25368: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
36265 25368: Id : 3, {_}:
36266 add ?4 additive_identity =>= ?4
36267 [4] by right_additive_identity ?4
36268 25368: Id : 4, {_}:
36269 multiply additive_identity ?6 =>= additive_identity
36270 [6] by left_multiplicative_zero ?6
36271 NO CLASH, using fixed ground order
36273 25369: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
36274 25369: Id : 3, {_}:
36275 add ?4 additive_identity =>= ?4
36276 [4] by right_additive_identity ?4
36277 25369: Id : 4, {_}:
36278 multiply additive_identity ?6 =>= additive_identity
36279 [6] by left_multiplicative_zero ?6
36280 25369: Id : 5, {_}:
36281 multiply ?8 additive_identity =>= additive_identity
36282 [8] by right_multiplicative_zero ?8
36283 25369: Id : 6, {_}:
36284 add (additive_inverse ?10) ?10 =>= additive_identity
36285 [10] by left_additive_inverse ?10
36286 25369: Id : 7, {_}:
36287 add ?12 (additive_inverse ?12) =>= additive_identity
36288 [12] by right_additive_inverse ?12
36289 25369: Id : 8, {_}:
36290 additive_inverse (additive_inverse ?14) =>= ?14
36291 [14] by additive_inverse_additive_inverse ?14
36292 25369: Id : 9, {_}:
36293 multiply ?16 (add ?17 ?18)
36295 add (multiply ?16 ?17) (multiply ?16 ?18)
36296 [18, 17, 16] by distribute1 ?16 ?17 ?18
36297 25369: Id : 10, {_}:
36298 multiply (add ?20 ?21) ?22
36300 add (multiply ?20 ?22) (multiply ?21 ?22)
36301 [22, 21, 20] by distribute2 ?20 ?21 ?22
36302 25369: Id : 11, {_}:
36303 add ?24 ?25 =?= add ?25 ?24
36304 [25, 24] by commutativity_for_addition ?24 ?25
36305 25369: Id : 12, {_}:
36306 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
36307 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
36308 25369: Id : 13, {_}:
36309 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
36310 [32, 31] by right_alternative ?31 ?32
36311 25369: Id : 14, {_}:
36312 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
36313 [35, 34] by left_alternative ?34 ?35
36314 25369: Id : 15, {_}:
36315 associator ?37 ?38 ?39
36317 add (multiply (multiply ?37 ?38) ?39)
36318 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
36319 [39, 38, 37] by associator ?37 ?38 ?39
36320 25369: Id : 16, {_}:
36323 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
36324 [42, 41] by commutator ?41 ?42
36325 25369: Id : 17, {_}:
36326 multiply (additive_inverse ?44) (additive_inverse ?45)
36329 [45, 44] by product_of_inverses ?44 ?45
36330 25369: Id : 18, {_}:
36331 multiply (additive_inverse ?47) ?48
36333 additive_inverse (multiply ?47 ?48)
36334 [48, 47] by inverse_product1 ?47 ?48
36335 25369: Id : 19, {_}:
36336 multiply ?50 (additive_inverse ?51)
36338 additive_inverse (multiply ?50 ?51)
36339 [51, 50] by inverse_product2 ?50 ?51
36340 25369: Id : 20, {_}:
36341 multiply ?53 (add ?54 (additive_inverse ?55))
36343 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
36344 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
36345 25369: Id : 21, {_}:
36346 multiply (add ?57 (additive_inverse ?58)) ?59
36348 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
36349 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
36350 25369: Id : 22, {_}:
36351 multiply (additive_inverse ?61) (add ?62 ?63)
36353 add (additive_inverse (multiply ?61 ?62))
36354 (additive_inverse (multiply ?61 ?63))
36355 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
36356 25369: Id : 23, {_}:
36357 multiply (add ?65 ?66) (additive_inverse ?67)
36359 add (additive_inverse (multiply ?65 ?67))
36360 (additive_inverse (multiply ?66 ?67))
36361 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
36363 25369: Id : 1, {_}:
36364 multiply (multiply x y) (multiply z x)
36366 multiply (multiply x (multiply y z)) x
36367 [] by prove_middle_moufang
36371 25369: commutator 1 2 0
36372 25369: associator 1 3 0
36373 25369: additive_inverse 22 1 0
36375 25369: additive_identity 8 0 0
36376 25369: z 2 0 2 1,2,2
36377 25369: multiply 46 2 6 0,2
36378 25369: y 2 0 2 2,1,2
36379 25369: x 4 0 4 1,1,2
36380 25368: Id : 5, {_}:
36381 multiply ?8 additive_identity =>= additive_identity
36382 [8] by right_multiplicative_zero ?8
36383 25368: Id : 6, {_}:
36384 add (additive_inverse ?10) ?10 =>= additive_identity
36385 [10] by left_additive_inverse ?10
36386 25368: Id : 7, {_}:
36387 add ?12 (additive_inverse ?12) =>= additive_identity
36388 [12] by right_additive_inverse ?12
36389 25368: Id : 8, {_}:
36390 additive_inverse (additive_inverse ?14) =>= ?14
36391 [14] by additive_inverse_additive_inverse ?14
36392 25368: Id : 9, {_}:
36393 multiply ?16 (add ?17 ?18)
36395 add (multiply ?16 ?17) (multiply ?16 ?18)
36396 [18, 17, 16] by distribute1 ?16 ?17 ?18
36397 25368: Id : 10, {_}:
36398 multiply (add ?20 ?21) ?22
36400 add (multiply ?20 ?22) (multiply ?21 ?22)
36401 [22, 21, 20] by distribute2 ?20 ?21 ?22
36402 25368: Id : 11, {_}:
36403 add ?24 ?25 =?= add ?25 ?24
36404 [25, 24] by commutativity_for_addition ?24 ?25
36405 25368: Id : 12, {_}:
36406 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
36407 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
36408 25368: Id : 13, {_}:
36409 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
36410 [32, 31] by right_alternative ?31 ?32
36411 25368: Id : 14, {_}:
36412 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
36413 [35, 34] by left_alternative ?34 ?35
36414 25368: Id : 15, {_}:
36415 associator ?37 ?38 ?39
36417 add (multiply (multiply ?37 ?38) ?39)
36418 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
36419 [39, 38, 37] by associator ?37 ?38 ?39
36420 25368: Id : 16, {_}:
36423 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
36424 [42, 41] by commutator ?41 ?42
36425 25368: Id : 17, {_}:
36426 multiply (additive_inverse ?44) (additive_inverse ?45)
36429 [45, 44] by product_of_inverses ?44 ?45
36430 25368: Id : 18, {_}:
36431 multiply (additive_inverse ?47) ?48
36433 additive_inverse (multiply ?47 ?48)
36434 [48, 47] by inverse_product1 ?47 ?48
36435 25368: Id : 19, {_}:
36436 multiply ?50 (additive_inverse ?51)
36438 additive_inverse (multiply ?50 ?51)
36439 [51, 50] by inverse_product2 ?50 ?51
36440 25368: Id : 20, {_}:
36441 multiply ?53 (add ?54 (additive_inverse ?55))
36443 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
36444 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
36445 25368: Id : 21, {_}:
36446 multiply (add ?57 (additive_inverse ?58)) ?59
36448 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
36449 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
36450 25368: Id : 22, {_}:
36451 multiply (additive_inverse ?61) (add ?62 ?63)
36453 add (additive_inverse (multiply ?61 ?62))
36454 (additive_inverse (multiply ?61 ?63))
36455 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
36456 25368: Id : 23, {_}:
36457 multiply (add ?65 ?66) (additive_inverse ?67)
36459 add (additive_inverse (multiply ?65 ?67))
36460 (additive_inverse (multiply ?66 ?67))
36461 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
36463 25368: Id : 1, {_}:
36464 multiply (multiply x y) (multiply z x)
36466 multiply (multiply x (multiply y z)) x
36467 [] by prove_middle_moufang
36471 25368: commutator 1 2 0
36472 25368: associator 1 3 0
36473 25368: additive_inverse 22 1 0
36475 25368: additive_identity 8 0 0
36476 25368: z 2 0 2 1,2,2
36477 25368: multiply 46 2 6 0,2
36478 25368: y 2 0 2 2,1,2
36479 25368: x 4 0 4 1,1,2
36480 % SZS status Timeout for RNG029-7.p
36481 NO CLASH, using fixed ground order
36483 25651: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
36484 25651: Id : 3, {_}:
36485 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
36486 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
36487 25651: Id : 4, {_}:
36488 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
36491 [10, 9] by robbins_axiom ?9 ?10
36492 25651: Id : 5, {_}: add c d =>= d [] by absorbtion
36494 NO CLASH, using fixed ground order
36496 25652: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
36497 25652: Id : 3, {_}:
36498 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
36499 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
36500 25652: Id : 4, {_}:
36501 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
36504 [10, 9] by robbins_axiom ?9 ?10
36505 25652: Id : 5, {_}: add c d =>= d [] by absorbtion
36507 25652: Id : 1, {_}:
36508 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
36511 [] by prove_huntingtons_axiom
36517 25652: add 13 2 3 0,2
36518 25652: negate 9 1 5 0,1,2
36519 25652: b 3 0 3 1,2,1,1,2
36520 25652: a 2 0 2 1,1,1,2
36521 25651: Id : 1, {_}:
36522 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
36525 [] by prove_huntingtons_axiom
36531 25651: add 13 2 3 0,2
36532 25651: negate 9 1 5 0,1,2
36533 25651: b 3 0 3 1,2,1,1,2
36534 25651: a 2 0 2 1,1,1,2
36535 NO CLASH, using fixed ground order
36537 25653: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
36538 25653: Id : 3, {_}:
36539 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
36540 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
36541 25653: Id : 4, {_}:
36542 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
36545 [10, 9] by robbins_axiom ?9 ?10
36546 25653: Id : 5, {_}: add c d =>= d [] by absorbtion
36548 25653: Id : 1, {_}:
36549 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
36552 [] by prove_huntingtons_axiom
36558 25653: add 13 2 3 0,2
36559 25653: negate 9 1 5 0,1,2
36560 25653: b 3 0 3 1,2,1,1,2
36561 25653: a 2 0 2 1,1,1,2
36562 % SZS status Timeout for ROB006-1.p
36563 NO CLASH, using fixed ground order
36565 25684: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
36566 25684: Id : 3, {_}:
36567 add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
36568 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
36569 25684: Id : 4, {_}:
36570 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
36573 [11, 10] by robbins_axiom ?10 ?11
36574 25684: Id : 5, {_}: add c d =>= d [] by absorbtion
36576 25684: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
36582 25684: negate 4 1 0
36583 25684: add 11 2 1 0,2
36584 NO CLASH, using fixed ground order
36586 25685: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
36587 25685: Id : 3, {_}:
36588 add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
36589 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
36590 25685: Id : 4, {_}:
36591 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
36594 [11, 10] by robbins_axiom ?10 ?11
36595 25685: Id : 5, {_}: add c d =>= d [] by absorbtion
36597 25685: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
36603 25685: negate 4 1 0
36604 25685: add 11 2 1 0,2
36605 NO CLASH, using fixed ground order
36607 25686: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
36608 25686: Id : 3, {_}:
36609 add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
36610 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
36611 25686: Id : 4, {_}:
36612 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
36615 [11, 10] by robbins_axiom ?10 ?11
36616 25686: Id : 5, {_}: add c d =>= d [] by absorbtion
36618 25686: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
36624 25686: negate 4 1 0
36625 25686: add 11 2 1 0,2
36626 % SZS status Timeout for ROB006-2.p
36627 NO CLASH, using fixed ground order
36629 25702: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
36630 25702: Id : 3, {_}:
36631 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
36632 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
36633 25702: Id : 4, {_}:
36634 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
36637 [10, 9] by robbins_axiom ?9 ?10
36638 25702: Id : 5, {_}: add c d =>= c [] by identity_constant
36640 25702: Id : 1, {_}:
36641 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
36644 [] by prove_huntingtons_axiom
36650 25702: add 13 2 3 0,2
36651 25702: negate 9 1 5 0,1,2
36652 25702: b 3 0 3 1,2,1,1,2
36653 25702: a 2 0 2 1,1,1,2
36654 NO CLASH, using fixed ground order
36656 25704: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
36657 25704: Id : 3, {_}:
36658 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
36659 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
36660 25704: Id : 4, {_}:
36661 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
36664 [10, 9] by robbins_axiom ?9 ?10
36665 25704: Id : 5, {_}: add c d =>= c [] by identity_constant
36667 25704: Id : 1, {_}:
36668 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
36671 [] by prove_huntingtons_axiom
36677 25704: add 13 2 3 0,2
36678 25704: negate 9 1 5 0,1,2
36679 25704: b 3 0 3 1,2,1,1,2
36680 25704: a 2 0 2 1,1,1,2
36681 NO CLASH, using fixed ground order
36683 25703: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
36684 25703: Id : 3, {_}:
36685 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
36686 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
36687 25703: Id : 4, {_}:
36688 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
36691 [10, 9] by robbins_axiom ?9 ?10
36692 25703: Id : 5, {_}: add c d =>= c [] by identity_constant
36694 25703: Id : 1, {_}:
36695 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
36698 [] by prove_huntingtons_axiom
36704 25703: add 13 2 3 0,2
36705 25703: negate 9 1 5 0,1,2
36706 25703: b 3 0 3 1,2,1,1,2
36707 25703: a 2 0 2 1,1,1,2
36708 % SZS status Timeout for ROB026-1.p
36709 NO CLASH, using fixed ground order
36711 25731: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
36712 25731: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
36713 25731: Id : 4, {_}:
36714 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
36715 [8, 7, 6] by associativity ?6 ?7 ?8
36716 25731: Id : 5, {_}:
36717 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
36718 [11, 10] by symmetry_of_glb ?10 ?11
36719 25731: Id : 6, {_}:
36720 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
36721 [14, 13] by symmetry_of_lub ?13 ?14
36722 25731: Id : 7, {_}:
36723 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
36725 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
36726 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
36727 25731: Id : 8, {_}:
36728 least_upper_bound ?20 (least_upper_bound ?21 ?22)
36730 least_upper_bound (least_upper_bound ?20 ?21) ?22
36731 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
36732 25731: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
36733 25731: Id : 10, {_}:
36734 greatest_lower_bound ?26 ?26 =>= ?26
36735 [26] by idempotence_of_gld ?26
36736 25731: Id : 11, {_}:
36737 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
36738 [29, 28] by lub_absorbtion ?28 ?29
36739 25731: Id : 12, {_}:
36740 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
36741 [32, 31] by glb_absorbtion ?31 ?32
36742 25731: Id : 13, {_}:
36743 multiply ?34 (least_upper_bound ?35 ?36)
36745 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
36746 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
36747 25731: Id : 14, {_}:
36748 multiply ?38 (greatest_lower_bound ?39 ?40)
36750 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
36751 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
36752 25731: Id : 15, {_}:
36753 multiply (least_upper_bound ?42 ?43) ?44
36755 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
36756 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
36757 25731: Id : 16, {_}:
36758 multiply (greatest_lower_bound ?46 ?47) ?48
36760 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
36761 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
36763 25731: Id : 1, {_}:
36764 least_upper_bound a (greatest_lower_bound b c)
36766 greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
36767 [] by prove_distrnu
36771 25731: inverse 1 1 0
36772 25731: multiply 18 2 0
36773 25731: identity 2 0 0
36774 25731: least_upper_bound 16 2 3 0,2
36775 25731: greatest_lower_bound 15 2 2 0,2,2
36776 25731: c 2 0 2 2,2,2
36777 25731: b 2 0 2 1,2,2
36779 NO CLASH, using fixed ground order
36781 25732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
36782 25732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
36783 25732: Id : 4, {_}:
36784 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
36785 [8, 7, 6] by associativity ?6 ?7 ?8
36786 25732: Id : 5, {_}:
36787 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
36788 [11, 10] by symmetry_of_glb ?10 ?11
36789 25732: Id : 6, {_}:
36790 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
36791 [14, 13] by symmetry_of_lub ?13 ?14
36792 25732: Id : 7, {_}:
36793 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
36795 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
36796 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
36797 25732: Id : 8, {_}:
36798 least_upper_bound ?20 (least_upper_bound ?21 ?22)
36800 least_upper_bound (least_upper_bound ?20 ?21) ?22
36801 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
36802 25732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
36803 25732: Id : 10, {_}:
36804 greatest_lower_bound ?26 ?26 =>= ?26
36805 [26] by idempotence_of_gld ?26
36806 25732: Id : 11, {_}:
36807 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
36808 [29, 28] by lub_absorbtion ?28 ?29
36809 25732: Id : 12, {_}:
36810 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
36811 [32, 31] by glb_absorbtion ?31 ?32
36812 25732: Id : 13, {_}:
36813 multiply ?34 (least_upper_bound ?35 ?36)
36815 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
36816 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
36817 25732: Id : 14, {_}:
36818 multiply ?38 (greatest_lower_bound ?39 ?40)
36820 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
36821 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
36822 25732: Id : 15, {_}:
36823 multiply (least_upper_bound ?42 ?43) ?44
36825 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
36826 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
36827 25732: Id : 16, {_}:
36828 multiply (greatest_lower_bound ?46 ?47) ?48
36830 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
36831 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
36833 25732: Id : 1, {_}:
36834 least_upper_bound a (greatest_lower_bound b c)
36836 greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
36837 [] by prove_distrnu
36841 25732: inverse 1 1 0
36842 25732: multiply 18 2 0
36843 25732: identity 2 0 0
36844 25732: least_upper_bound 16 2 3 0,2
36845 25732: greatest_lower_bound 15 2 2 0,2,2
36846 25732: c 2 0 2 2,2,2
36847 25732: b 2 0 2 1,2,2
36849 NO CLASH, using fixed ground order
36851 25733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
36852 25733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
36853 25733: Id : 4, {_}:
36854 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
36855 [8, 7, 6] by associativity ?6 ?7 ?8
36856 25733: Id : 5, {_}:
36857 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
36858 [11, 10] by symmetry_of_glb ?10 ?11
36859 25733: Id : 6, {_}:
36860 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
36861 [14, 13] by symmetry_of_lub ?13 ?14
36862 25733: Id : 7, {_}:
36863 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
36865 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
36866 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
36867 25733: Id : 8, {_}:
36868 least_upper_bound ?20 (least_upper_bound ?21 ?22)
36870 least_upper_bound (least_upper_bound ?20 ?21) ?22
36871 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
36872 25733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
36873 25733: Id : 10, {_}:
36874 greatest_lower_bound ?26 ?26 =>= ?26
36875 [26] by idempotence_of_gld ?26
36876 25733: Id : 11, {_}:
36877 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
36878 [29, 28] by lub_absorbtion ?28 ?29
36879 25733: Id : 12, {_}:
36880 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
36881 [32, 31] by glb_absorbtion ?31 ?32
36882 25733: Id : 13, {_}:
36883 multiply ?34 (least_upper_bound ?35 ?36)
36885 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
36886 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
36887 25733: Id : 14, {_}:
36888 multiply ?38 (greatest_lower_bound ?39 ?40)
36890 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
36891 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
36892 25733: Id : 15, {_}:
36893 multiply (least_upper_bound ?42 ?43) ?44
36895 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
36896 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
36897 25733: Id : 16, {_}:
36898 multiply (greatest_lower_bound ?46 ?47) ?48
36900 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
36901 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
36903 25733: Id : 1, {_}:
36904 least_upper_bound a (greatest_lower_bound b c)
36906 greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
36907 [] by prove_distrnu
36911 25733: inverse 1 1 0
36912 25733: multiply 18 2 0
36913 25733: identity 2 0 0
36914 25733: least_upper_bound 16 2 3 0,2
36915 25733: greatest_lower_bound 15 2 2 0,2,2
36916 25733: c 2 0 2 2,2,2
36917 25733: b 2 0 2 1,2,2
36919 % SZS status Timeout for GRP164-1.p
36920 NO CLASH, using fixed ground order
36922 25749: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
36923 25749: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
36924 25749: Id : 4, {_}:
36925 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
36926 [8, 7, 6] by associativity ?6 ?7 ?8
36927 25749: Id : 5, {_}:
36928 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
36929 [11, 10] by symmetry_of_glb ?10 ?11
36930 25749: Id : 6, {_}:
36931 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
36932 [14, 13] by symmetry_of_lub ?13 ?14
36933 25749: Id : 7, {_}:
36934 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
36936 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
36937 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
36938 25749: Id : 8, {_}:
36939 least_upper_bound ?20 (least_upper_bound ?21 ?22)
36941 least_upper_bound (least_upper_bound ?20 ?21) ?22
36942 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
36943 25749: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
36944 25749: Id : 10, {_}:
36945 greatest_lower_bound ?26 ?26 =>= ?26
36946 [26] by idempotence_of_gld ?26
36947 25749: Id : 11, {_}:
36948 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
36949 [29, 28] by lub_absorbtion ?28 ?29
36950 25749: Id : 12, {_}:
36951 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
36952 [32, 31] by glb_absorbtion ?31 ?32
36953 25749: Id : 13, {_}:
36954 multiply ?34 (least_upper_bound ?35 ?36)
36956 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
36957 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
36958 25749: Id : 14, {_}:
36959 multiply ?38 (greatest_lower_bound ?39 ?40)
36961 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
36962 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
36963 25749: Id : 15, {_}:
36964 multiply (least_upper_bound ?42 ?43) ?44
36966 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
36967 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
36968 25749: Id : 16, {_}:
36969 multiply (greatest_lower_bound ?46 ?47) ?48
36971 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
36972 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
36974 25749: Id : 1, {_}:
36975 greatest_lower_bound a (least_upper_bound b c)
36977 least_upper_bound (greatest_lower_bound a b)
36978 (greatest_lower_bound a c)
36979 [] by prove_distrun
36983 25749: inverse 1 1 0
36984 25749: multiply 18 2 0
36985 25749: identity 2 0 0
36986 25749: greatest_lower_bound 16 2 3 0,2
36987 25749: least_upper_bound 15 2 2 0,2,2
36988 25749: c 2 0 2 2,2,2
36989 25749: b 2 0 2 1,2,2
36991 NO CLASH, using fixed ground order
36993 25750: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
36994 25750: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
36995 25750: Id : 4, {_}:
36996 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
36997 [8, 7, 6] by associativity ?6 ?7 ?8
36998 25750: Id : 5, {_}:
36999 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
37000 [11, 10] by symmetry_of_glb ?10 ?11
37001 25750: Id : 6, {_}:
37002 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
37003 [14, 13] by symmetry_of_lub ?13 ?14
37004 25750: Id : 7, {_}:
37005 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
37007 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
37008 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
37009 25750: Id : 8, {_}:
37010 least_upper_bound ?20 (least_upper_bound ?21 ?22)
37012 least_upper_bound (least_upper_bound ?20 ?21) ?22
37013 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
37014 25750: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
37015 25750: Id : 10, {_}:
37016 greatest_lower_bound ?26 ?26 =>= ?26
37017 [26] by idempotence_of_gld ?26
37018 25750: Id : 11, {_}:
37019 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
37020 [29, 28] by lub_absorbtion ?28 ?29
37021 25750: Id : 12, {_}:
37022 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
37023 [32, 31] by glb_absorbtion ?31 ?32
37024 NO CLASH, using fixed ground order
37026 25751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
37027 25751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
37028 25751: Id : 4, {_}:
37029 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
37030 [8, 7, 6] by associativity ?6 ?7 ?8
37031 25751: Id : 5, {_}:
37032 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
37033 [11, 10] by symmetry_of_glb ?10 ?11
37034 25751: Id : 6, {_}:
37035 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
37036 [14, 13] by symmetry_of_lub ?13 ?14
37037 25751: Id : 7, {_}:
37038 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
37040 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
37041 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
37042 25751: Id : 8, {_}:
37043 least_upper_bound ?20 (least_upper_bound ?21 ?22)
37045 least_upper_bound (least_upper_bound ?20 ?21) ?22
37046 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
37047 25751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
37048 25751: Id : 10, {_}:
37049 greatest_lower_bound ?26 ?26 =>= ?26
37050 [26] by idempotence_of_gld ?26
37051 25751: Id : 11, {_}:
37052 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
37053 [29, 28] by lub_absorbtion ?28 ?29
37054 25751: Id : 12, {_}:
37055 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
37056 [32, 31] by glb_absorbtion ?31 ?32
37057 25751: Id : 13, {_}:
37058 multiply ?34 (least_upper_bound ?35 ?36)
37060 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
37061 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
37062 25751: Id : 14, {_}:
37063 multiply ?38 (greatest_lower_bound ?39 ?40)
37065 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
37066 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
37067 25751: Id : 15, {_}:
37068 multiply (least_upper_bound ?42 ?43) ?44
37070 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
37071 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
37072 25751: Id : 16, {_}:
37073 multiply (greatest_lower_bound ?46 ?47) ?48
37075 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
37076 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
37078 25751: Id : 1, {_}:
37079 greatest_lower_bound a (least_upper_bound b c)
37081 least_upper_bound (greatest_lower_bound a b)
37082 (greatest_lower_bound a c)
37083 [] by prove_distrun
37087 25751: inverse 1 1 0
37088 25751: multiply 18 2 0
37089 25751: identity 2 0 0
37090 25751: greatest_lower_bound 16 2 3 0,2
37091 25751: least_upper_bound 15 2 2 0,2,2
37092 25751: c 2 0 2 2,2,2
37093 25751: b 2 0 2 1,2,2
37095 25750: Id : 13, {_}:
37096 multiply ?34 (least_upper_bound ?35 ?36)
37098 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
37099 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
37100 25750: Id : 14, {_}:
37101 multiply ?38 (greatest_lower_bound ?39 ?40)
37103 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
37104 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
37105 25750: Id : 15, {_}:
37106 multiply (least_upper_bound ?42 ?43) ?44
37108 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
37109 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
37110 25750: Id : 16, {_}:
37111 multiply (greatest_lower_bound ?46 ?47) ?48
37113 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
37114 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
37116 25750: Id : 1, {_}:
37117 greatest_lower_bound a (least_upper_bound b c)
37119 least_upper_bound (greatest_lower_bound a b)
37120 (greatest_lower_bound a c)
37121 [] by prove_distrun
37125 25750: inverse 1 1 0
37126 25750: multiply 18 2 0
37127 25750: identity 2 0 0
37128 25750: greatest_lower_bound 16 2 3 0,2
37129 25750: least_upper_bound 15 2 2 0,2,2
37130 25750: c 2 0 2 2,2,2
37131 25750: b 2 0 2 1,2,2
37133 % SZS status Timeout for GRP164-2.p
37134 NO CLASH, using fixed ground order
37136 25782: Id : 2, {_}:
37137 multiply (multiply ?2 ?3) ?4 =?= multiply ?2 (multiply ?3 ?4)
37138 [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
37139 25782: Id : 3, {_}:
37140 multiply ?6 (multiply ?7 (multiply ?7 ?7))
37142 multiply ?7 (multiply ?7 (multiply ?7 ?6))
37143 [7, 6] by condition ?6 ?7
37145 25782: Id : 1, {_}:
37160 (multiply a (multiply b (multiply a b))))))))))))))))
37176 (multiply b (multiply b (multiply b b))))))))))))))))
37181 25782: multiply 44 2 34 0,2
37182 25782: b 18 0 18 1,2,2
37183 25782: a 18 0 18 1,2
37184 NO CLASH, using fixed ground order
37186 25783: Id : 2, {_}:
37187 multiply (multiply ?2 ?3) ?4 =>= multiply ?2 (multiply ?3 ?4)
37188 [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
37189 25783: Id : 3, {_}:
37190 multiply ?6 (multiply ?7 (multiply ?7 ?7))
37192 multiply ?7 (multiply ?7 (multiply ?7 ?6))
37193 [7, 6] by condition ?6 ?7
37195 25783: Id : 1, {_}:
37210 (multiply a (multiply b (multiply a b))))))))))))))))
37226 (multiply b (multiply b (multiply b b))))))))))))))))
37231 25783: multiply 44 2 34 0,2
37232 25783: b 18 0 18 1,2,2
37233 25783: a 18 0 18 1,2
37234 NO CLASH, using fixed ground order
37235 % SZS status Timeout for GRP196-1.p
37236 NO CLASH, using fixed ground order
37238 25809: Id : 2, {_}:
37239 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
37240 (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
37243 [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
37245 25809: Id : 1, {_}:
37246 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
37247 [] by associativity
37251 25809: f 18 2 8 0,2
37252 25809: c 3 0 3 2,1,2,2
37253 25809: b 4 0 4 1,1,2,2
37255 NO CLASH, using fixed ground order
37257 25810: Id : 2, {_}:
37258 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
37259 (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
37262 [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
37264 25810: Id : 1, {_}:
37265 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
37266 [] by associativity
37270 25810: f 18 2 8 0,2
37271 25810: c 3 0 3 2,1,2,2
37272 25810: b 4 0 4 1,1,2,2
37274 NO CLASH, using fixed ground order
37276 25811: Id : 2, {_}:
37277 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
37278 (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
37281 [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
37283 25811: Id : 1, {_}:
37284 f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
37285 [] by associativity
37289 25811: f 18 2 8 0,2
37290 25811: c 3 0 3 2,1,2,2
37291 25811: b 4 0 4 1,1,2,2
37293 % SZS status Timeout for LAT070-1.p
37294 NO CLASH, using fixed ground order
37295 NO CLASH, using fixed ground order
37297 25843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37298 25843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37299 25843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37300 25843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37301 25843: Id : 6, {_}:
37302 meet ?12 ?13 =?= meet ?13 ?12
37303 [13, 12] by commutativity_of_meet ?12 ?13
37304 25843: Id : 7, {_}:
37305 join ?15 ?16 =?= join ?16 ?15
37306 [16, 15] by commutativity_of_join ?15 ?16
37307 25843: Id : 8, {_}:
37308 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37309 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37310 25843: Id : 9, {_}:
37311 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37312 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37313 25843: Id : 10, {_}:
37314 meet ?26 (join ?27 (meet ?26 ?28))
37318 (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
37319 [28, 27, 26] by equation_H7 ?26 ?27 ?28
37321 25843: Id : 1, {_}:
37322 meet a (join b (meet a c))
37324 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
37329 25843: join 17 2 4 0,2,2
37330 25843: meet 21 2 6 0,2
37331 25843: c 3 0 3 2,2,2,2
37332 25843: b 3 0 3 1,2,2
37334 NO CLASH, using fixed ground order
37336 25844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37337 25844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37338 25844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37339 25844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37340 25844: Id : 6, {_}:
37341 meet ?12 ?13 =?= meet ?13 ?12
37342 [13, 12] by commutativity_of_meet ?12 ?13
37343 25844: Id : 7, {_}:
37344 join ?15 ?16 =?= join ?16 ?15
37345 [16, 15] by commutativity_of_join ?15 ?16
37346 25844: Id : 8, {_}:
37347 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37348 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37349 25844: Id : 9, {_}:
37350 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37351 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37352 25844: Id : 10, {_}:
37353 meet ?26 (join ?27 (meet ?26 ?28))
37357 (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
37358 [28, 27, 26] by equation_H7 ?26 ?27 ?28
37360 25844: Id : 1, {_}:
37361 meet a (join b (meet a c))
37363 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
37368 25844: join 17 2 4 0,2,2
37369 25844: meet 21 2 6 0,2
37370 25844: c 3 0 3 2,2,2,2
37371 25844: b 3 0 3 1,2,2
37374 25842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37375 25842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37376 25842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37377 25842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37378 25842: Id : 6, {_}:
37379 meet ?12 ?13 =?= meet ?13 ?12
37380 [13, 12] by commutativity_of_meet ?12 ?13
37381 25842: Id : 7, {_}:
37382 join ?15 ?16 =?= join ?16 ?15
37383 [16, 15] by commutativity_of_join ?15 ?16
37384 25842: Id : 8, {_}:
37385 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
37386 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37387 25842: Id : 9, {_}:
37388 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
37389 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37390 25842: Id : 10, {_}:
37391 meet ?26 (join ?27 (meet ?26 ?28))
37395 (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
37396 [28, 27, 26] by equation_H7 ?26 ?27 ?28
37398 25842: Id : 1, {_}:
37399 meet a (join b (meet a c))
37401 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
37406 25842: join 17 2 4 0,2,2
37407 25842: meet 21 2 6 0,2
37408 25842: c 3 0 3 2,2,2,2
37409 25842: b 3 0 3 1,2,2
37411 % SZS status Timeout for LAT138-1.p
37412 NO CLASH, using fixed ground order
37414 25866: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37415 25866: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37416 25866: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37417 25866: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37418 25866: Id : 6, {_}:
37419 meet ?12 ?13 =?= meet ?13 ?12
37420 [13, 12] by commutativity_of_meet ?12 ?13
37421 25866: Id : 7, {_}:
37422 join ?15 ?16 =?= join ?16 ?15
37423 [16, 15] by commutativity_of_join ?15 ?16
37424 25866: Id : 8, {_}:
37425 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
37426 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37427 25866: Id : 9, {_}:
37428 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
37429 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37430 25866: Id : 10, {_}:
37431 join (meet ?26 ?27) (meet ?26 ?28)
37434 (join (meet ?27 (join ?26 (meet ?27 ?28)))
37435 (meet ?28 (join ?26 ?27)))
37436 [28, 27, 26] by equation_H21 ?26 ?27 ?28
37438 25866: Id : 1, {_}:
37439 meet a (join b (meet a c))
37441 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
37446 25866: join 17 2 4 0,2,2
37447 25866: meet 21 2 6 0,2
37448 25866: c 4 0 4 2,2,2,2
37449 25866: b 4 0 4 1,2,2
37451 NO CLASH, using fixed ground order
37453 25867: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37454 25867: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37455 25867: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37456 25867: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37457 25867: Id : 6, {_}:
37458 meet ?12 ?13 =?= meet ?13 ?12
37459 [13, 12] by commutativity_of_meet ?12 ?13
37460 25867: Id : 7, {_}:
37461 join ?15 ?16 =?= join ?16 ?15
37462 [16, 15] by commutativity_of_join ?15 ?16
37463 25867: Id : 8, {_}:
37464 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37465 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37466 25867: Id : 9, {_}:
37467 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37468 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37469 25867: Id : 10, {_}:
37470 join (meet ?26 ?27) (meet ?26 ?28)
37473 (join (meet ?27 (join ?26 (meet ?27 ?28)))
37474 (meet ?28 (join ?26 ?27)))
37475 [28, 27, 26] by equation_H21 ?26 ?27 ?28
37477 25867: Id : 1, {_}:
37478 meet a (join b (meet a c))
37480 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
37485 25867: join 17 2 4 0,2,2
37486 25867: meet 21 2 6 0,2
37487 25867: c 4 0 4 2,2,2,2
37488 25867: b 4 0 4 1,2,2
37490 NO CLASH, using fixed ground order
37492 25868: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37493 25868: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37494 25868: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37495 25868: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37496 25868: Id : 6, {_}:
37497 meet ?12 ?13 =?= meet ?13 ?12
37498 [13, 12] by commutativity_of_meet ?12 ?13
37499 25868: Id : 7, {_}:
37500 join ?15 ?16 =?= join ?16 ?15
37501 [16, 15] by commutativity_of_join ?15 ?16
37502 25868: Id : 8, {_}:
37503 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37504 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37505 25868: Id : 9, {_}:
37506 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37507 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37508 25868: Id : 10, {_}:
37509 join (meet ?26 ?27) (meet ?26 ?28)
37512 (join (meet ?27 (join ?26 (meet ?27 ?28)))
37513 (meet ?28 (join ?26 ?27)))
37514 [28, 27, 26] by equation_H21 ?26 ?27 ?28
37516 25868: Id : 1, {_}:
37517 meet a (join b (meet a c))
37519 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
37524 25868: join 17 2 4 0,2,2
37525 25868: meet 21 2 6 0,2
37526 25868: c 4 0 4 2,2,2,2
37527 25868: b 4 0 4 1,2,2
37529 % SZS status Timeout for LAT140-1.p
37530 NO CLASH, using fixed ground order
37532 25928: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37533 25928: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37534 25928: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37535 25928: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37536 25928: Id : 6, {_}:
37537 meet ?12 ?13 =?= meet ?13 ?12
37538 [13, 12] by commutativity_of_meet ?12 ?13
37539 25928: Id : 7, {_}:
37540 join ?15 ?16 =?= join ?16 ?15
37541 [16, 15] by commutativity_of_join ?15 ?16
37542 25928: Id : 8, {_}:
37543 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
37544 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37545 25928: Id : 9, {_}:
37546 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
37547 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37548 25928: Id : 10, {_}:
37549 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
37551 meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
37552 [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
37554 NO CLASH, using fixed ground order
37556 25929: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37557 25929: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37558 25929: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37559 25929: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37560 25929: Id : 6, {_}:
37561 meet ?12 ?13 =?= meet ?13 ?12
37562 [13, 12] by commutativity_of_meet ?12 ?13
37563 25929: Id : 7, {_}:
37564 join ?15 ?16 =?= join ?16 ?15
37565 [16, 15] by commutativity_of_join ?15 ?16
37566 25929: Id : 8, {_}:
37567 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37568 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37569 25929: Id : 9, {_}:
37570 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37571 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37572 25929: Id : 10, {_}:
37573 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
37575 meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
37576 [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
37578 25929: Id : 1, {_}:
37579 meet a (join b (meet a c))
37581 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
37586 25929: join 16 2 4 0,2,2
37587 25929: meet 22 2 6 0,2
37588 25929: c 3 0 3 2,2,2,2
37589 25929: b 3 0 3 1,2,2
37591 25928: Id : 1, {_}:
37592 meet a (join b (meet a c))
37594 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
37599 25928: join 16 2 4 0,2,2
37600 25928: meet 22 2 6 0,2
37601 25928: c 3 0 3 2,2,2,2
37602 25928: b 3 0 3 1,2,2
37604 NO CLASH, using fixed ground order
37606 25930: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37607 25930: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37608 25930: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37609 25930: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37610 25930: Id : 6, {_}:
37611 meet ?12 ?13 =?= meet ?13 ?12
37612 [13, 12] by commutativity_of_meet ?12 ?13
37613 25930: Id : 7, {_}:
37614 join ?15 ?16 =?= join ?16 ?15
37615 [16, 15] by commutativity_of_join ?15 ?16
37616 25930: Id : 8, {_}:
37617 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37618 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37619 25930: Id : 9, {_}:
37620 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37621 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37622 25930: Id : 10, {_}:
37623 meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
37625 meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
37626 [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
37628 25930: Id : 1, {_}:
37629 meet a (join b (meet a c))
37631 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
37636 25930: join 16 2 4 0,2,2
37637 25930: meet 22 2 6 0,2
37638 25930: c 3 0 3 2,2,2,2
37639 25930: b 3 0 3 1,2,2
37641 % SZS status Timeout for LAT145-1.p
37642 NO CLASH, using fixed ground order
37644 25948: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37645 25948: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37646 25948: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37647 25948: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37648 25948: Id : 6, {_}:
37649 meet ?12 ?13 =?= meet ?13 ?12
37650 [13, 12] by commutativity_of_meet ?12 ?13
37651 25948: Id : 7, {_}:
37652 join ?15 ?16 =?= join ?16 ?15
37653 [16, 15] by commutativity_of_join ?15 ?16
37654 25948: Id : 8, {_}:
37655 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
37656 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37657 25948: Id : 9, {_}:
37658 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
37659 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37660 25948: Id : 10, {_}:
37661 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
37663 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
37664 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
37666 25948: Id : 1, {_}:
37667 meet a (join b (meet c (join b d)))
37669 meet a (join b (meet c (join d (meet a (join b d)))))
37674 25948: meet 19 2 5 0,2
37675 25948: join 19 2 5 0,2,2
37676 25948: d 3 0 3 2,2,2,2,2
37677 25948: c 2 0 2 1,2,2,2
37678 25948: b 4 0 4 1,2,2
37680 NO CLASH, using fixed ground order
37682 25949: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37683 25949: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37684 25949: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37685 25949: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37686 25949: Id : 6, {_}:
37687 meet ?12 ?13 =?= meet ?13 ?12
37688 [13, 12] by commutativity_of_meet ?12 ?13
37689 25949: Id : 7, {_}:
37690 join ?15 ?16 =?= join ?16 ?15
37691 [16, 15] by commutativity_of_join ?15 ?16
37692 25949: Id : 8, {_}:
37693 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37694 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37695 25949: Id : 9, {_}:
37696 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37697 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37698 25949: Id : 10, {_}:
37699 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
37701 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
37702 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
37704 25949: Id : 1, {_}:
37705 meet a (join b (meet c (join b d)))
37707 meet a (join b (meet c (join d (meet a (join b d)))))
37712 25949: meet 19 2 5 0,2
37713 25949: join 19 2 5 0,2,2
37714 25949: d 3 0 3 2,2,2,2,2
37715 25949: c 2 0 2 1,2,2,2
37716 25949: b 4 0 4 1,2,2
37718 NO CLASH, using fixed ground order
37720 25950: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37721 25950: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37722 25950: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37723 25950: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37724 25950: Id : 6, {_}:
37725 meet ?12 ?13 =?= meet ?13 ?12
37726 [13, 12] by commutativity_of_meet ?12 ?13
37727 25950: Id : 7, {_}:
37728 join ?15 ?16 =?= join ?16 ?15
37729 [16, 15] by commutativity_of_join ?15 ?16
37730 25950: Id : 8, {_}:
37731 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37732 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37733 25950: Id : 9, {_}:
37734 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37735 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37736 25950: Id : 10, {_}:
37737 meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
37739 meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
37740 [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
37742 25950: Id : 1, {_}:
37743 meet a (join b (meet c (join b d)))
37745 meet a (join b (meet c (join d (meet a (join b d)))))
37750 25950: meet 19 2 5 0,2
37751 25950: join 19 2 5 0,2,2
37752 25950: d 3 0 3 2,2,2,2,2
37753 25950: c 2 0 2 1,2,2,2
37754 25950: b 4 0 4 1,2,2
37756 % SZS status Timeout for LAT149-1.p
37757 NO CLASH, using fixed ground order
37759 26495: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37760 26495: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37761 26495: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37762 26495: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37763 26495: Id : 6, {_}:
37764 meet ?12 ?13 =?= meet ?13 ?12
37765 [13, 12] by commutativity_of_meet ?12 ?13
37766 26495: Id : 7, {_}:
37767 join ?15 ?16 =?= join ?16 ?15
37768 [16, 15] by commutativity_of_join ?15 ?16
37769 26495: Id : 8, {_}:
37770 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
37771 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37772 26495: Id : 9, {_}:
37773 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
37774 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37775 26495: Id : 10, {_}:
37776 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
37778 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
37779 [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
37781 26495: Id : 1, {_}:
37782 meet a (join b (meet a c))
37784 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
37789 26495: join 18 2 4 0,2,2
37790 26495: meet 20 2 6 0,2
37791 26495: c 2 0 2 2,2,2,2
37792 26495: b 4 0 4 1,2,2
37794 NO CLASH, using fixed ground order
37796 26496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37797 26496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37798 26496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37799 26496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37800 26496: Id : 6, {_}:
37801 meet ?12 ?13 =?= meet ?13 ?12
37802 [13, 12] by commutativity_of_meet ?12 ?13
37803 26496: Id : 7, {_}:
37804 join ?15 ?16 =?= join ?16 ?15
37805 [16, 15] by commutativity_of_join ?15 ?16
37806 26496: Id : 8, {_}:
37807 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37808 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37809 26496: Id : 9, {_}:
37810 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37811 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37812 26496: Id : 10, {_}:
37813 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
37815 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
37816 [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
37818 26496: Id : 1, {_}:
37819 meet a (join b (meet a c))
37821 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
37826 26496: join 18 2 4 0,2,2
37827 26496: meet 20 2 6 0,2
37828 26496: c 2 0 2 2,2,2,2
37829 26496: b 4 0 4 1,2,2
37831 NO CLASH, using fixed ground order
37833 26497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37834 26497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37835 26497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37836 26497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37837 26497: Id : 6, {_}:
37838 meet ?12 ?13 =?= meet ?13 ?12
37839 [13, 12] by commutativity_of_meet ?12 ?13
37840 26497: Id : 7, {_}:
37841 join ?15 ?16 =?= join ?16 ?15
37842 [16, 15] by commutativity_of_join ?15 ?16
37843 26497: Id : 8, {_}:
37844 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37845 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37846 26497: Id : 9, {_}:
37847 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37848 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37849 26497: Id : 10, {_}:
37850 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
37852 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
37853 [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
37855 26497: Id : 1, {_}:
37856 meet a (join b (meet a c))
37858 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
37863 26497: join 18 2 4 0,2,2
37864 26497: meet 20 2 6 0,2
37865 26497: c 2 0 2 2,2,2,2
37866 26497: b 4 0 4 1,2,2
37868 % SZS status Timeout for LAT153-1.p
37869 NO CLASH, using fixed ground order
37871 26513: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37872 26513: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37873 26513: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37874 26513: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37875 26513: Id : 6, {_}:
37876 meet ?12 ?13 =?= meet ?13 ?12
37877 [13, 12] by commutativity_of_meet ?12 ?13
37878 26513: Id : 7, {_}:
37879 join ?15 ?16 =?= join ?16 ?15
37880 [16, 15] by commutativity_of_join ?15 ?16
37881 26513: Id : 8, {_}:
37882 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
37883 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37884 26513: Id : 9, {_}:
37885 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
37886 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37887 26513: Id : 10, {_}:
37888 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
37890 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
37891 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
37893 26513: Id : 1, {_}:
37894 meet a (join b (meet a c))
37896 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
37901 26513: join 18 2 4 0,2,2
37902 26513: meet 20 2 6 0,2
37903 26513: c 4 0 4 2,2,2,2
37904 26513: b 4 0 4 1,2,2
37906 NO CLASH, using fixed ground order
37908 26514: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37909 26514: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37910 26514: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37911 26514: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37912 26514: Id : 6, {_}:
37913 meet ?12 ?13 =?= meet ?13 ?12
37914 [13, 12] by commutativity_of_meet ?12 ?13
37915 26514: Id : 7, {_}:
37916 join ?15 ?16 =?= join ?16 ?15
37917 [16, 15] by commutativity_of_join ?15 ?16
37918 26514: Id : 8, {_}:
37919 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37920 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37921 26514: Id : 9, {_}:
37922 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37923 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37924 26514: Id : 10, {_}:
37925 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
37927 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
37928 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
37930 26514: Id : 1, {_}:
37931 meet a (join b (meet a c))
37933 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
37938 26514: join 18 2 4 0,2,2
37939 26514: meet 20 2 6 0,2
37940 26514: c 4 0 4 2,2,2,2
37941 26514: b 4 0 4 1,2,2
37943 NO CLASH, using fixed ground order
37945 26515: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37946 26515: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37947 26515: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37948 26515: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37949 26515: Id : 6, {_}:
37950 meet ?12 ?13 =?= meet ?13 ?12
37951 [13, 12] by commutativity_of_meet ?12 ?13
37952 26515: Id : 7, {_}:
37953 join ?15 ?16 =?= join ?16 ?15
37954 [16, 15] by commutativity_of_join ?15 ?16
37955 26515: Id : 8, {_}:
37956 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
37957 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37958 26515: Id : 9, {_}:
37959 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
37960 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37961 26515: Id : 10, {_}:
37962 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
37964 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
37965 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
37967 26515: Id : 1, {_}:
37968 meet a (join b (meet a c))
37970 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
37975 26515: join 18 2 4 0,2,2
37976 26515: meet 20 2 6 0,2
37977 26515: c 4 0 4 2,2,2,2
37978 26515: b 4 0 4 1,2,2
37980 % SZS status Timeout for LAT157-1.p
37981 NO CLASH, using fixed ground order
37983 26542: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
37984 26542: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
37985 26542: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
37986 26542: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
37987 26542: Id : 6, {_}:
37988 meet ?12 ?13 =?= meet ?13 ?12
37989 [13, 12] by commutativity_of_meet ?12 ?13
37990 26542: Id : 7, {_}:
37991 join ?15 ?16 =?= join ?16 ?15
37992 [16, 15] by commutativity_of_join ?15 ?16
37993 26542: Id : 8, {_}:
37994 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
37995 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
37996 26542: Id : 9, {_}:
37997 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
37998 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
37999 26542: Id : 10, {_}:
38000 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
38002 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
38003 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
38005 26542: Id : 1, {_}:
38006 meet a (join b (meet c (join a d)))
38008 meet a (join b (join (meet a c) (meet c (join b d))))
38013 26542: meet 19 2 5 0,2
38014 26542: join 19 2 5 0,2,2
38015 26542: d 2 0 2 2,2,2,2,2
38016 26542: c 3 0 3 1,2,2,2
38017 26542: b 3 0 3 1,2,2
38019 NO CLASH, using fixed ground order
38021 26543: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38022 26543: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38023 26543: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38024 26543: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38025 26543: Id : 6, {_}:
38026 meet ?12 ?13 =?= meet ?13 ?12
38027 [13, 12] by commutativity_of_meet ?12 ?13
38028 26543: Id : 7, {_}:
38029 join ?15 ?16 =?= join ?16 ?15
38030 [16, 15] by commutativity_of_join ?15 ?16
38031 26543: Id : 8, {_}:
38032 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38033 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38034 26543: Id : 9, {_}:
38035 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38036 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38037 26543: Id : 10, {_}:
38038 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
38040 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
38041 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
38043 26543: Id : 1, {_}:
38044 meet a (join b (meet c (join a d)))
38046 meet a (join b (join (meet a c) (meet c (join b d))))
38051 26543: meet 19 2 5 0,2
38052 26543: join 19 2 5 0,2,2
38053 26543: d 2 0 2 2,2,2,2,2
38054 26543: c 3 0 3 1,2,2,2
38055 26543: b 3 0 3 1,2,2
38057 NO CLASH, using fixed ground order
38059 26544: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38060 26544: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38061 26544: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38062 26544: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38063 26544: Id : 6, {_}:
38064 meet ?12 ?13 =?= meet ?13 ?12
38065 [13, 12] by commutativity_of_meet ?12 ?13
38066 26544: Id : 7, {_}:
38067 join ?15 ?16 =?= join ?16 ?15
38068 [16, 15] by commutativity_of_join ?15 ?16
38069 26544: Id : 8, {_}:
38070 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38071 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38072 26544: Id : 9, {_}:
38073 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38074 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38075 26544: Id : 10, {_}:
38076 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
38078 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
38079 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
38081 26544: Id : 1, {_}:
38082 meet a (join b (meet c (join a d)))
38084 meet a (join b (join (meet a c) (meet c (join b d))))
38089 26544: meet 19 2 5 0,2
38090 26544: join 19 2 5 0,2,2
38091 26544: d 2 0 2 2,2,2,2,2
38092 26544: c 3 0 3 1,2,2,2
38093 26544: b 3 0 3 1,2,2
38095 % SZS status Timeout for LAT158-1.p
38096 NO CLASH, using fixed ground order
38098 26561: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38099 26561: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38100 26561: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38101 26561: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38102 26561: Id : 6, {_}:
38103 meet ?12 ?13 =?= meet ?13 ?12
38104 [13, 12] by commutativity_of_meet ?12 ?13
38105 26561: Id : 7, {_}:
38106 join ?15 ?16 =?= join ?16 ?15
38107 [16, 15] by commutativity_of_join ?15 ?16
38108 26561: Id : 8, {_}:
38109 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38110 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38111 26561: Id : 9, {_}:
38112 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38113 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38114 26561: Id : 10, {_}:
38115 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38117 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
38118 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
38120 26561: Id : 1, {_}:
38121 meet a (join b (meet a (meet c d)))
38123 meet a (join b (meet c (join (meet a d) (meet b d))))
38128 26561: join 16 2 3 0,2,2
38129 26561: meet 21 2 7 0,2
38130 26561: d 3 0 3 2,2,2,2,2
38131 26561: c 2 0 2 1,2,2,2,2
38132 26561: b 3 0 3 1,2,2
38134 NO CLASH, using fixed ground order
38136 26562: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38137 26562: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38138 26562: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38139 26562: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38140 26562: Id : 6, {_}:
38141 meet ?12 ?13 =?= meet ?13 ?12
38142 [13, 12] by commutativity_of_meet ?12 ?13
38143 26562: Id : 7, {_}:
38144 join ?15 ?16 =?= join ?16 ?15
38145 [16, 15] by commutativity_of_join ?15 ?16
38146 26562: Id : 8, {_}:
38147 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38148 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38149 26562: Id : 9, {_}:
38150 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38151 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38152 26562: Id : 10, {_}:
38153 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38155 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
38156 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
38158 26562: Id : 1, {_}:
38159 meet a (join b (meet a (meet c d)))
38161 meet a (join b (meet c (join (meet a d) (meet b d))))
38166 26562: join 16 2 3 0,2,2
38167 26562: meet 21 2 7 0,2
38168 26562: d 3 0 3 2,2,2,2,2
38169 26562: c 2 0 2 1,2,2,2,2
38170 26562: b 3 0 3 1,2,2
38172 NO CLASH, using fixed ground order
38174 26563: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38175 26563: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38176 26563: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38177 26563: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38178 26563: Id : 6, {_}:
38179 meet ?12 ?13 =?= meet ?13 ?12
38180 [13, 12] by commutativity_of_meet ?12 ?13
38181 26563: Id : 7, {_}:
38182 join ?15 ?16 =?= join ?16 ?15
38183 [16, 15] by commutativity_of_join ?15 ?16
38184 26563: Id : 8, {_}:
38185 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38186 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38187 26563: Id : 9, {_}:
38188 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38189 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38190 26563: Id : 10, {_}:
38191 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38193 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
38194 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
38196 26563: Id : 1, {_}:
38197 meet a (join b (meet a (meet c d)))
38199 meet a (join b (meet c (join (meet a d) (meet b d))))
38204 26563: join 16 2 3 0,2,2
38205 26563: meet 21 2 7 0,2
38206 26563: d 3 0 3 2,2,2,2,2
38207 26563: c 2 0 2 1,2,2,2,2
38208 26563: b 3 0 3 1,2,2
38210 % SZS status Timeout for LAT163-1.p
38211 NO CLASH, using fixed ground order
38212 NO CLASH, using fixed ground order
38214 26595: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38215 26595: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38216 26595: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38217 26595: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38218 26595: Id : 6, {_}:
38219 meet ?12 ?13 =?= meet ?13 ?12
38220 [13, 12] by commutativity_of_meet ?12 ?13
38221 26595: Id : 7, {_}:
38222 join ?15 ?16 =?= join ?16 ?15
38223 [16, 15] by commutativity_of_join ?15 ?16
38224 26595: Id : 8, {_}:
38225 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38226 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38227 26595: Id : 9, {_}:
38228 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38229 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38230 26595: Id : 10, {_}:
38231 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38233 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
38234 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
38236 26595: Id : 1, {_}:
38237 meet a (join b (meet c (join b d)))
38239 meet a (join b (meet c (join d (meet a (meet b c)))))
38244 26595: meet 20 2 6 0,2
38245 26595: join 17 2 4 0,2,2
38246 26595: d 2 0 2 2,2,2,2,2
38247 26595: c 3 0 3 1,2,2,2
38248 26595: b 4 0 4 1,2,2
38251 26594: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38252 26594: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38253 26594: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38254 26594: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38255 26594: Id : 6, {_}:
38256 meet ?12 ?13 =?= meet ?13 ?12
38257 [13, 12] by commutativity_of_meet ?12 ?13
38258 26594: Id : 7, {_}:
38259 join ?15 ?16 =?= join ?16 ?15
38260 [16, 15] by commutativity_of_join ?15 ?16
38261 26594: Id : 8, {_}:
38262 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38263 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38264 26594: Id : 9, {_}:
38265 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38266 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38267 26594: Id : 10, {_}:
38268 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38270 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
38271 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
38273 26594: Id : 1, {_}:
38274 meet a (join b (meet c (join b d)))
38276 meet a (join b (meet c (join d (meet a (meet b c)))))
38281 26594: meet 20 2 6 0,2
38282 26594: join 17 2 4 0,2,2
38283 26594: d 2 0 2 2,2,2,2,2
38284 26594: c 3 0 3 1,2,2,2
38285 26594: b 4 0 4 1,2,2
38287 NO CLASH, using fixed ground order
38289 26596: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38290 26596: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38291 26596: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38292 26596: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38293 26596: Id : 6, {_}:
38294 meet ?12 ?13 =?= meet ?13 ?12
38295 [13, 12] by commutativity_of_meet ?12 ?13
38296 26596: Id : 7, {_}:
38297 join ?15 ?16 =?= join ?16 ?15
38298 [16, 15] by commutativity_of_join ?15 ?16
38299 26596: Id : 8, {_}:
38300 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38301 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38302 26596: Id : 9, {_}:
38303 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38304 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38305 26596: Id : 10, {_}:
38306 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38308 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
38309 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
38311 26596: Id : 1, {_}:
38312 meet a (join b (meet c (join b d)))
38314 meet a (join b (meet c (join d (meet a (meet b c)))))
38319 26596: meet 20 2 6 0,2
38320 26596: join 17 2 4 0,2,2
38321 26596: d 2 0 2 2,2,2,2,2
38322 26596: c 3 0 3 1,2,2,2
38323 26596: b 4 0 4 1,2,2
38325 % SZS status Timeout for LAT165-1.p
38326 NO CLASH, using fixed ground order
38328 26645: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38329 26645: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38330 26645: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38331 26645: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38332 26645: Id : 6, {_}:
38333 meet ?12 ?13 =?= meet ?13 ?12
38334 [13, 12] by commutativity_of_meet ?12 ?13
38335 26645: Id : 7, {_}:
38336 join ?15 ?16 =?= join ?16 ?15
38337 [16, 15] by commutativity_of_join ?15 ?16
38338 26645: Id : 8, {_}:
38339 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38340 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38341 26645: Id : 9, {_}:
38342 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38343 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38344 26645: Id : 10, {_}:
38345 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38347 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
38348 [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
38350 26645: Id : 1, {_}:
38351 meet a (join b (meet c (join b d)))
38353 meet a (join b (meet c (join d (meet b (join a d)))))
38358 26645: meet 20 2 5 0,2
38359 26645: join 18 2 5 0,2,2
38360 26645: d 3 0 3 2,2,2,2,2
38361 26645: c 2 0 2 1,2,2,2
38362 26645: b 4 0 4 1,2,2
38364 NO CLASH, using fixed ground order
38366 26646: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38367 26646: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38368 26646: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38369 26646: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38370 26646: Id : 6, {_}:
38371 meet ?12 ?13 =?= meet ?13 ?12
38372 [13, 12] by commutativity_of_meet ?12 ?13
38373 26646: Id : 7, {_}:
38374 join ?15 ?16 =?= join ?16 ?15
38375 [16, 15] by commutativity_of_join ?15 ?16
38376 26646: Id : 8, {_}:
38377 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38378 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38379 26646: Id : 9, {_}:
38380 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38381 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38382 26646: Id : 10, {_}:
38383 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38385 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
38386 [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
38388 26646: Id : 1, {_}:
38389 meet a (join b (meet c (join b d)))
38391 meet a (join b (meet c (join d (meet b (join a d)))))
38396 26646: meet 20 2 5 0,2
38397 26646: join 18 2 5 0,2,2
38398 26646: d 3 0 3 2,2,2,2,2
38399 26646: c 2 0 2 1,2,2,2
38400 26646: b 4 0 4 1,2,2
38402 NO CLASH, using fixed ground order
38404 26647: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38405 26647: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38406 26647: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38407 26647: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38408 26647: Id : 6, {_}:
38409 meet ?12 ?13 =?= meet ?13 ?12
38410 [13, 12] by commutativity_of_meet ?12 ?13
38411 26647: Id : 7, {_}:
38412 join ?15 ?16 =?= join ?16 ?15
38413 [16, 15] by commutativity_of_join ?15 ?16
38414 26647: Id : 8, {_}:
38415 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38416 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38417 26647: Id : 9, {_}:
38418 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38419 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38420 26647: Id : 10, {_}:
38421 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38423 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
38424 [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
38426 26647: Id : 1, {_}:
38427 meet a (join b (meet c (join b d)))
38429 meet a (join b (meet c (join d (meet b (join a d)))))
38434 26647: meet 20 2 5 0,2
38435 26647: join 18 2 5 0,2,2
38436 26647: d 3 0 3 2,2,2,2,2
38437 26647: c 2 0 2 1,2,2,2
38438 26647: b 4 0 4 1,2,2
38440 % SZS status Timeout for LAT166-1.p
38441 NO CLASH, using fixed ground order
38443 26677: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38444 26677: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38445 26677: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38446 26677: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38447 26677: Id : 6, {_}:
38448 meet ?12 ?13 =?= meet ?13 ?12
38449 [13, 12] by commutativity_of_meet ?12 ?13
38450 26677: Id : 7, {_}:
38451 join ?15 ?16 =?= join ?16 ?15
38452 [16, 15] by commutativity_of_join ?15 ?16
38453 26677: Id : 8, {_}:
38454 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38455 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38456 26677: Id : 9, {_}:
38457 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38458 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38459 26677: Id : 10, {_}:
38460 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38462 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
38463 [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
38465 26677: Id : 1, {_}:
38466 meet a (join b (meet c (join b d)))
38468 meet a (join b (meet c (join d (meet a (meet b c)))))
38473 26677: meet 20 2 6 0,2
38474 26677: join 18 2 4 0,2,2
38475 26677: d 2 0 2 2,2,2,2,2
38476 26677: c 3 0 3 1,2,2,2
38477 26677: b 4 0 4 1,2,2
38479 NO CLASH, using fixed ground order
38481 26676: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38482 26676: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38483 26676: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38484 26676: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38485 26676: Id : 6, {_}:
38486 meet ?12 ?13 =?= meet ?13 ?12
38487 [13, 12] by commutativity_of_meet ?12 ?13
38488 26676: Id : 7, {_}:
38489 join ?15 ?16 =?= join ?16 ?15
38490 [16, 15] by commutativity_of_join ?15 ?16
38491 26676: Id : 8, {_}:
38492 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38493 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38494 26676: Id : 9, {_}:
38495 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38496 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38497 26676: Id : 10, {_}:
38498 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38500 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
38501 [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
38503 26676: Id : 1, {_}:
38504 meet a (join b (meet c (join b d)))
38506 meet a (join b (meet c (join d (meet a (meet b c)))))
38511 26676: meet 20 2 6 0,2
38512 26676: join 18 2 4 0,2,2
38513 26676: d 2 0 2 2,2,2,2,2
38514 26676: c 3 0 3 1,2,2,2
38515 26676: b 4 0 4 1,2,2
38517 NO CLASH, using fixed ground order
38519 26678: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38520 26678: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38521 26678: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38522 26678: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38523 26678: Id : 6, {_}:
38524 meet ?12 ?13 =?= meet ?13 ?12
38525 [13, 12] by commutativity_of_meet ?12 ?13
38526 26678: Id : 7, {_}:
38527 join ?15 ?16 =?= join ?16 ?15
38528 [16, 15] by commutativity_of_join ?15 ?16
38529 26678: Id : 8, {_}:
38530 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38531 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38532 26678: Id : 9, {_}:
38533 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38534 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38535 26678: Id : 10, {_}:
38536 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
38538 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
38539 [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
38541 26678: Id : 1, {_}:
38542 meet a (join b (meet c (join b d)))
38544 meet a (join b (meet c (join d (meet a (meet b c)))))
38549 26678: meet 20 2 6 0,2
38550 26678: join 18 2 4 0,2,2
38551 26678: d 2 0 2 2,2,2,2,2
38552 26678: c 3 0 3 1,2,2,2
38553 26678: b 4 0 4 1,2,2
38555 % SZS status Timeout for LAT167-1.p
38556 NO CLASH, using fixed ground order
38558 26697: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38559 26697: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38560 26697: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38561 26697: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38562 26697: Id : 6, {_}:
38563 meet ?12 ?13 =?= meet ?13 ?12
38564 [13, 12] by commutativity_of_meet ?12 ?13
38565 26697: Id : 7, {_}:
38566 join ?15 ?16 =?= join ?16 ?15
38567 [16, 15] by commutativity_of_join ?15 ?16
38568 26697: Id : 8, {_}:
38569 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38570 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38571 26697: Id : 9, {_}:
38572 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38573 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38574 26697: Id : 10, {_}:
38575 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
38577 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
38578 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
38580 26697: Id : 1, {_}:
38581 meet a (join b (meet a (meet c d)))
38583 meet a (join b (meet c (join (meet a d) (meet b d))))
38588 26697: join 17 2 3 0,2,2
38589 26697: meet 20 2 7 0,2
38590 26697: d 3 0 3 2,2,2,2,2
38591 26697: c 2 0 2 1,2,2,2,2
38592 26697: b 3 0 3 1,2,2
38594 NO CLASH, using fixed ground order
38596 26698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38597 26698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38598 26698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38599 26698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38600 26698: Id : 6, {_}:
38601 meet ?12 ?13 =?= meet ?13 ?12
38602 [13, 12] by commutativity_of_meet ?12 ?13
38603 26698: Id : 7, {_}:
38604 join ?15 ?16 =?= join ?16 ?15
38605 [16, 15] by commutativity_of_join ?15 ?16
38606 26698: Id : 8, {_}:
38607 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38608 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38609 26698: Id : 9, {_}:
38610 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38611 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38612 26698: Id : 10, {_}:
38613 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
38615 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
38616 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
38618 26698: Id : 1, {_}:
38619 meet a (join b (meet a (meet c d)))
38621 meet a (join b (meet c (join (meet a d) (meet b d))))
38626 26698: join 17 2 3 0,2,2
38627 26698: meet 20 2 7 0,2
38628 26698: d 3 0 3 2,2,2,2,2
38629 26698: c 2 0 2 1,2,2,2,2
38630 26698: b 3 0 3 1,2,2
38632 NO CLASH, using fixed ground order
38634 26699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38635 26699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38636 26699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38637 26699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38638 26699: Id : 6, {_}:
38639 meet ?12 ?13 =?= meet ?13 ?12
38640 [13, 12] by commutativity_of_meet ?12 ?13
38641 26699: Id : 7, {_}:
38642 join ?15 ?16 =?= join ?16 ?15
38643 [16, 15] by commutativity_of_join ?15 ?16
38644 26699: Id : 8, {_}:
38645 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38646 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38647 26699: Id : 9, {_}:
38648 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38649 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38650 26699: Id : 10, {_}:
38651 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
38653 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
38654 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
38656 26699: Id : 1, {_}:
38657 meet a (join b (meet a (meet c d)))
38659 meet a (join b (meet c (join (meet a d) (meet b d))))
38664 26699: join 17 2 3 0,2,2
38665 26699: meet 20 2 7 0,2
38666 26699: d 3 0 3 2,2,2,2,2
38667 26699: c 2 0 2 1,2,2,2,2
38668 26699: b 3 0 3 1,2,2
38670 % SZS status Timeout for LAT172-1.p
38671 NO CLASH, using fixed ground order
38673 26727: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38674 26727: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38675 26727: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38676 26727: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38677 26727: Id : 6, {_}:
38678 meet ?12 ?13 =?= meet ?13 ?12
38679 [13, 12] by commutativity_of_meet ?12 ?13
38680 26727: Id : 7, {_}:
38681 join ?15 ?16 =?= join ?16 ?15
38682 [16, 15] by commutativity_of_join ?15 ?16
38683 26727: Id : 8, {_}:
38684 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38685 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38686 26727: Id : 9, {_}:
38687 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38688 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38689 26727: Id : 10, {_}:
38690 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
38692 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
38693 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
38695 26727: Id : 1, {_}:
38696 meet a (join b (meet c (join a d)))
38698 meet a (join b (meet c (join d (meet c (join a b)))))
38703 26727: meet 18 2 5 0,2
38704 26727: join 19 2 5 0,2,2
38705 26727: d 2 0 2 2,2,2,2,2
38706 26727: c 3 0 3 1,2,2,2
38707 26727: b 3 0 3 1,2,2
38709 NO CLASH, using fixed ground order
38711 26728: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38712 26728: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38713 26728: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38714 26728: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38715 26728: Id : 6, {_}:
38716 meet ?12 ?13 =?= meet ?13 ?12
38717 [13, 12] by commutativity_of_meet ?12 ?13
38718 26728: Id : 7, {_}:
38719 join ?15 ?16 =?= join ?16 ?15
38720 [16, 15] by commutativity_of_join ?15 ?16
38721 26728: Id : 8, {_}:
38722 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38723 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38724 26728: Id : 9, {_}:
38725 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38726 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38727 26728: Id : 10, {_}:
38728 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
38730 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
38731 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
38733 26728: Id : 1, {_}:
38734 meet a (join b (meet c (join a d)))
38736 meet a (join b (meet c (join d (meet c (join a b)))))
38741 26728: meet 18 2 5 0,2
38742 26728: join 19 2 5 0,2,2
38743 26728: d 2 0 2 2,2,2,2,2
38744 26728: c 3 0 3 1,2,2,2
38745 26728: b 3 0 3 1,2,2
38747 NO CLASH, using fixed ground order
38749 26729: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38750 26729: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38751 26729: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38752 26729: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38753 26729: Id : 6, {_}:
38754 meet ?12 ?13 =?= meet ?13 ?12
38755 [13, 12] by commutativity_of_meet ?12 ?13
38756 26729: Id : 7, {_}:
38757 join ?15 ?16 =?= join ?16 ?15
38758 [16, 15] by commutativity_of_join ?15 ?16
38759 26729: Id : 8, {_}:
38760 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38761 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38762 26729: Id : 9, {_}:
38763 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38764 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38765 26729: Id : 10, {_}:
38766 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
38768 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
38769 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
38771 26729: Id : 1, {_}:
38772 meet a (join b (meet c (join a d)))
38774 meet a (join b (meet c (join d (meet c (join a b)))))
38779 26729: meet 18 2 5 0,2
38780 26729: join 19 2 5 0,2,2
38781 26729: d 2 0 2 2,2,2,2,2
38782 26729: c 3 0 3 1,2,2,2
38783 26729: b 3 0 3 1,2,2
38785 % SZS status Timeout for LAT173-1.p
38786 NO CLASH, using fixed ground order
38788 26747: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38789 26747: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38790 26747: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38791 26747: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38792 26747: Id : 6, {_}:
38793 meet ?12 ?13 =?= meet ?13 ?12
38794 [13, 12] by commutativity_of_meet ?12 ?13
38795 26747: Id : 7, {_}:
38796 join ?15 ?16 =?= join ?16 ?15
38797 [16, 15] by commutativity_of_join ?15 ?16
38798 26747: Id : 8, {_}:
38799 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38800 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38801 26747: Id : 9, {_}:
38802 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38803 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38804 26747: Id : 10, {_}:
38805 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
38807 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
38808 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
38810 26747: Id : 1, {_}:
38811 meet a (join b (meet a (meet c d)))
38813 meet a (join b (meet c (join (meet a d) (meet b d))))
38818 26747: join 18 2 3 0,2,2
38819 26747: meet 20 2 7 0,2
38820 26747: d 3 0 3 2,2,2,2,2
38821 26747: c 2 0 2 1,2,2,2,2
38822 26747: b 3 0 3 1,2,2
38824 NO CLASH, using fixed ground order
38826 26746: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38827 26746: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38828 26746: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38829 26746: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38830 26746: Id : 6, {_}:
38831 meet ?12 ?13 =?= meet ?13 ?12
38832 [13, 12] by commutativity_of_meet ?12 ?13
38833 26746: Id : 7, {_}:
38834 join ?15 ?16 =?= join ?16 ?15
38835 [16, 15] by commutativity_of_join ?15 ?16
38836 26746: Id : 8, {_}:
38837 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38838 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38839 26746: Id : 9, {_}:
38840 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38841 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38842 26746: Id : 10, {_}:
38843 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
38845 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
38846 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
38848 26746: Id : 1, {_}:
38849 meet a (join b (meet a (meet c d)))
38851 meet a (join b (meet c (join (meet a d) (meet b d))))
38856 26746: join 18 2 3 0,2,2
38857 26746: meet 20 2 7 0,2
38858 26746: d 3 0 3 2,2,2,2,2
38859 26746: c 2 0 2 1,2,2,2,2
38860 26746: b 3 0 3 1,2,2
38862 NO CLASH, using fixed ground order
38864 26748: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38865 26748: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38866 26748: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38867 26748: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38868 26748: Id : 6, {_}:
38869 meet ?12 ?13 =?= meet ?13 ?12
38870 [13, 12] by commutativity_of_meet ?12 ?13
38871 26748: Id : 7, {_}:
38872 join ?15 ?16 =?= join ?16 ?15
38873 [16, 15] by commutativity_of_join ?15 ?16
38874 26748: Id : 8, {_}:
38875 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38876 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38877 26748: Id : 9, {_}:
38878 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38879 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38880 26748: Id : 10, {_}:
38881 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
38883 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
38884 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
38886 26748: Id : 1, {_}:
38887 meet a (join b (meet a (meet c d)))
38889 meet a (join b (meet c (join (meet a d) (meet b d))))
38894 26748: join 18 2 3 0,2,2
38895 26748: meet 20 2 7 0,2
38896 26748: d 3 0 3 2,2,2,2,2
38897 26748: c 2 0 2 1,2,2,2,2
38898 26748: b 3 0 3 1,2,2
38900 % SZS status Timeout for LAT175-1.p
38901 NO CLASH, using fixed ground order
38903 26789: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38904 26789: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38905 26789: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38906 26789: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38907 26789: Id : 6, {_}:
38908 meet ?12 ?13 =?= meet ?13 ?12
38909 [13, 12] by commutativity_of_meet ?12 ?13
38910 26789: Id : 7, {_}:
38911 join ?15 ?16 =?= join ?16 ?15
38912 [16, 15] by commutativity_of_join ?15 ?16
38913 26789: Id : 8, {_}:
38914 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
38915 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38916 26789: Id : 9, {_}:
38917 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
38918 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38919 26789: Id : 10, {_}:
38920 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
38922 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
38923 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
38925 26789: Id : 1, {_}:
38926 meet a (join b (meet c (join a d)))
38928 meet a (join b (meet c (join b (join d (meet a c)))))
38933 26789: meet 18 2 5 0,2
38934 26789: join 20 2 5 0,2,2
38935 26789: d 2 0 2 2,2,2,2,2
38936 26789: c 3 0 3 1,2,2,2
38937 26789: b 3 0 3 1,2,2
38939 NO CLASH, using fixed ground order
38941 26790: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38942 26790: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38943 26790: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38944 26790: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38945 26790: Id : 6, {_}:
38946 meet ?12 ?13 =?= meet ?13 ?12
38947 [13, 12] by commutativity_of_meet ?12 ?13
38948 26790: Id : 7, {_}:
38949 join ?15 ?16 =?= join ?16 ?15
38950 [16, 15] by commutativity_of_join ?15 ?16
38951 26790: Id : 8, {_}:
38952 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38953 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38954 26790: Id : 9, {_}:
38955 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38956 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38957 26790: Id : 10, {_}:
38958 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
38960 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
38961 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
38963 26790: Id : 1, {_}:
38964 meet a (join b (meet c (join a d)))
38966 meet a (join b (meet c (join b (join d (meet a c)))))
38971 26790: meet 18 2 5 0,2
38972 26790: join 20 2 5 0,2,2
38973 26790: d 2 0 2 2,2,2,2,2
38974 26790: c 3 0 3 1,2,2,2
38975 26790: b 3 0 3 1,2,2
38977 NO CLASH, using fixed ground order
38979 26791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
38980 26791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
38981 26791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
38982 26791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
38983 26791: Id : 6, {_}:
38984 meet ?12 ?13 =?= meet ?13 ?12
38985 [13, 12] by commutativity_of_meet ?12 ?13
38986 26791: Id : 7, {_}:
38987 join ?15 ?16 =?= join ?16 ?15
38988 [16, 15] by commutativity_of_join ?15 ?16
38989 26791: Id : 8, {_}:
38990 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
38991 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
38992 26791: Id : 9, {_}:
38993 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
38994 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
38995 26791: Id : 10, {_}:
38996 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
38998 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
38999 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
39001 26791: Id : 1, {_}:
39002 meet a (join b (meet c (join a d)))
39004 meet a (join b (meet c (join b (join d (meet a c)))))
39009 26791: meet 18 2 5 0,2
39010 26791: join 20 2 5 0,2,2
39011 26791: d 2 0 2 2,2,2,2,2
39012 26791: c 3 0 3 1,2,2,2
39013 26791: b 3 0 3 1,2,2
39015 % SZS status Timeout for LAT176-1.p
39016 NO CLASH, using fixed ground order
39018 27075: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
39019 27075: Id : 3, {_}:
39020 add ?4 additive_identity =>= ?4
39021 [4] by right_additive_identity ?4
39022 27075: Id : 4, {_}:
39023 add (additive_inverse ?6) ?6 =>= additive_identity
39024 [6] by left_additive_inverse ?6
39025 27075: Id : 5, {_}:
39026 add ?8 (additive_inverse ?8) =>= additive_identity
39027 [8] by right_additive_inverse ?8
39028 27075: Id : 6, {_}:
39029 add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
39030 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
39031 27075: Id : 7, {_}:
39032 add ?14 ?15 =?= add ?15 ?14
39033 [15, 14] by commutativity_for_addition ?14 ?15
39034 27075: Id : 8, {_}:
39035 multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
39036 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
39037 27075: Id : 9, {_}:
39038 multiply ?21 (add ?22 ?23)
39040 add (multiply ?21 ?22) (multiply ?21 ?23)
39041 [23, 22, 21] by distribute1 ?21 ?22 ?23
39042 27075: Id : 10, {_}:
39043 multiply (add ?25 ?26) ?27
39045 add (multiply ?25 ?27) (multiply ?26 ?27)
39046 [27, 26, 25] by distribute2 ?25 ?26 ?27
39047 27075: Id : 11, {_}:
39048 multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
39049 [29] by x_fourthed_is_x ?29
39050 27075: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
39052 27075: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
39056 27075: additive_inverse 2 1 0
39058 27075: additive_identity 4 0 0
39060 27075: multiply 15 2 1 0,2
39063 NO CLASH, using fixed ground order
39065 27077: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
39066 27077: Id : 3, {_}:
39067 add ?4 additive_identity =>= ?4
39068 [4] by right_additive_identity ?4
39069 27077: Id : 4, {_}:
39070 add (additive_inverse ?6) ?6 =>= additive_identity
39071 [6] by left_additive_inverse ?6
39072 27077: Id : 5, {_}:
39073 add ?8 (additive_inverse ?8) =>= additive_identity
39074 [8] by right_additive_inverse ?8
39075 27077: Id : 6, {_}:
39076 add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
39077 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
39078 27077: Id : 7, {_}:
39079 add ?14 ?15 =?= add ?15 ?14
39080 [15, 14] by commutativity_for_addition ?14 ?15
39081 27077: Id : 8, {_}:
39082 multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
39083 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
39084 27077: Id : 9, {_}:
39085 multiply ?21 (add ?22 ?23)
39087 add (multiply ?21 ?22) (multiply ?21 ?23)
39088 [23, 22, 21] by distribute1 ?21 ?22 ?23
39089 27077: Id : 10, {_}:
39090 multiply (add ?25 ?26) ?27
39092 add (multiply ?25 ?27) (multiply ?26 ?27)
39093 [27, 26, 25] by distribute2 ?25 ?26 ?27
39094 27077: Id : 11, {_}:
39095 multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
39096 [29] by x_fourthed_is_x ?29
39097 27077: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
39099 27077: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
39103 27077: additive_inverse 2 1 0
39105 27077: additive_identity 4 0 0
39107 27077: multiply 15 2 1 0,2
39110 NO CLASH, using fixed ground order
39112 27076: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
39113 27076: Id : 3, {_}:
39114 add ?4 additive_identity =>= ?4
39115 [4] by right_additive_identity ?4
39116 27076: Id : 4, {_}:
39117 add (additive_inverse ?6) ?6 =>= additive_identity
39118 [6] by left_additive_inverse ?6
39119 27076: Id : 5, {_}:
39120 add ?8 (additive_inverse ?8) =>= additive_identity
39121 [8] by right_additive_inverse ?8
39122 27076: Id : 6, {_}:
39123 add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
39124 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
39125 27076: Id : 7, {_}:
39126 add ?14 ?15 =?= add ?15 ?14
39127 [15, 14] by commutativity_for_addition ?14 ?15
39128 27076: Id : 8, {_}:
39129 multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
39130 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
39131 27076: Id : 9, {_}:
39132 multiply ?21 (add ?22 ?23)
39134 add (multiply ?21 ?22) (multiply ?21 ?23)
39135 [23, 22, 21] by distribute1 ?21 ?22 ?23
39136 27076: Id : 10, {_}:
39137 multiply (add ?25 ?26) ?27
39139 add (multiply ?25 ?27) (multiply ?26 ?27)
39140 [27, 26, 25] by distribute2 ?25 ?26 ?27
39141 27076: Id : 11, {_}:
39142 multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
39143 [29] by x_fourthed_is_x ?29
39144 27076: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
39146 27076: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
39150 27076: additive_inverse 2 1 0
39152 27076: additive_identity 4 0 0
39154 27076: multiply 15 2 1 0,2
39157 % SZS status Timeout for RNG035-7.p
39158 NO CLASH, using fixed ground order
39160 27109: Id : 2, {_}:
39161 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
39162 [4, 3, 2] by c1 ?2 ?3 ?4
39164 27109: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39168 27109: b 1 0 1 1,2,2
39169 27109: nand 9 2 3 0,2
39170 27109: a 4 0 4 1,1,2
39171 NO CLASH, using fixed ground order
39173 27110: Id : 2, {_}:
39174 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
39175 [4, 3, 2] by c1 ?2 ?3 ?4
39177 27110: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39181 27110: b 1 0 1 1,2,2
39182 27110: nand 9 2 3 0,2
39183 27110: a 4 0 4 1,1,2
39184 NO CLASH, using fixed ground order
39186 27111: Id : 2, {_}:
39187 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
39188 [4, 3, 2] by c1 ?2 ?3 ?4
39190 27111: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39194 27111: b 1 0 1 1,2,2
39195 27111: nand 9 2 3 0,2
39196 27111: a 4 0 4 1,1,2
39197 % SZS status Timeout for BOO077-1.p
39198 NO CLASH, using fixed ground order
39200 27127: Id : 2, {_}:
39201 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
39202 [4, 3, 2] by c1 ?2 ?3 ?4
39204 27127: Id : 1, {_}:
39205 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39206 [] by prove_meredith_2_basis_2
39210 27127: nand 12 2 6 0,2
39211 27127: c 2 0 2 2,2,2,2
39212 27127: b 3 0 3 1,2,2
39214 NO CLASH, using fixed ground order
39216 27128: Id : 2, {_}:
39217 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
39218 [4, 3, 2] by c1 ?2 ?3 ?4
39220 27128: Id : 1, {_}:
39221 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39222 [] by prove_meredith_2_basis_2
39226 27128: nand 12 2 6 0,2
39227 27128: c 2 0 2 2,2,2,2
39228 27128: b 3 0 3 1,2,2
39230 NO CLASH, using fixed ground order
39232 27129: Id : 2, {_}:
39233 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
39234 [4, 3, 2] by c1 ?2 ?3 ?4
39236 27129: Id : 1, {_}:
39237 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39238 [] by prove_meredith_2_basis_2
39242 27129: nand 12 2 6 0,2
39243 27129: c 2 0 2 2,2,2,2
39244 27129: b 3 0 3 1,2,2
39246 % SZS status Timeout for BOO078-1.p
39247 NO CLASH, using fixed ground order
39249 27161: Id : 2, {_}:
39250 nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
39251 [4, 3, 2] by c2 ?2 ?3 ?4
39253 27161: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39257 27161: b 1 0 1 1,2,2
39258 27161: nand 9 2 3 0,2
39259 27161: a 4 0 4 1,1,2
39260 NO CLASH, using fixed ground order
39262 27162: Id : 2, {_}:
39263 nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
39264 [4, 3, 2] by c2 ?2 ?3 ?4
39266 27162: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39270 27162: b 1 0 1 1,2,2
39271 27162: nand 9 2 3 0,2
39272 27162: a 4 0 4 1,1,2
39273 NO CLASH, using fixed ground order
39275 27160: Id : 2, {_}:
39276 nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
39277 [4, 3, 2] by c2 ?2 ?3 ?4
39279 27160: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39283 27160: b 1 0 1 1,2,2
39284 27160: nand 9 2 3 0,2
39285 27160: a 4 0 4 1,1,2
39286 % SZS status Timeout for BOO079-1.p
39287 NO CLASH, using fixed ground order
39289 27178: Id : 2, {_}:
39290 nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
39291 [4, 3, 2] by c2 ?2 ?3 ?4
39293 27178: Id : 1, {_}:
39294 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39295 [] by prove_meredith_2_basis_2
39299 27178: nand 12 2 6 0,2
39300 27178: c 2 0 2 2,2,2,2
39301 27178: b 3 0 3 1,2,2
39303 NO CLASH, using fixed ground order
39305 27179: Id : 2, {_}:
39306 nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
39307 [4, 3, 2] by c2 ?2 ?3 ?4
39309 27179: Id : 1, {_}:
39310 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39311 [] by prove_meredith_2_basis_2
39315 27179: nand 12 2 6 0,2
39316 27179: c 2 0 2 2,2,2,2
39317 27179: b 3 0 3 1,2,2
39319 NO CLASH, using fixed ground order
39321 27180: Id : 2, {_}:
39322 nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
39323 [4, 3, 2] by c2 ?2 ?3 ?4
39325 27180: Id : 1, {_}:
39326 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39327 [] by prove_meredith_2_basis_2
39331 27180: nand 12 2 6 0,2
39332 27180: c 2 0 2 2,2,2,2
39333 27180: b 3 0 3 1,2,2
39335 % SZS status Timeout for BOO080-1.p
39336 NO CLASH, using fixed ground order
39338 27207: Id : 2, {_}:
39339 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39340 [4, 3, 2] by c3 ?2 ?3 ?4
39342 27207: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39346 27207: b 1 0 1 1,2,2
39347 27207: nand 9 2 3 0,2
39348 27207: a 4 0 4 1,1,2
39349 NO CLASH, using fixed ground order
39351 27208: Id : 2, {_}:
39352 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39353 [4, 3, 2] by c3 ?2 ?3 ?4
39355 27208: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39359 27208: b 1 0 1 1,2,2
39360 27208: nand 9 2 3 0,2
39361 27208: a 4 0 4 1,1,2
39362 NO CLASH, using fixed ground order
39364 27209: Id : 2, {_}:
39365 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39366 [4, 3, 2] by c3 ?2 ?3 ?4
39368 27209: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39372 27209: b 1 0 1 1,2,2
39373 27209: nand 9 2 3 0,2
39374 27209: a 4 0 4 1,1,2
39375 % SZS status Timeout for BOO081-1.p
39376 NO CLASH, using fixed ground order
39378 27227: Id : 2, {_}:
39379 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39380 [4, 3, 2] by c3 ?2 ?3 ?4
39382 27227: Id : 1, {_}:
39383 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39384 [] by prove_meredith_2_basis_2
39388 27227: nand 12 2 6 0,2
39389 27227: c 2 0 2 2,2,2,2
39390 27227: b 3 0 3 1,2,2
39392 NO CLASH, using fixed ground order
39394 27228: Id : 2, {_}:
39395 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39396 [4, 3, 2] by c3 ?2 ?3 ?4
39398 27228: Id : 1, {_}:
39399 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39400 [] by prove_meredith_2_basis_2
39404 27228: nand 12 2 6 0,2
39405 27228: c 2 0 2 2,2,2,2
39406 27228: b 3 0 3 1,2,2
39408 NO CLASH, using fixed ground order
39410 27229: Id : 2, {_}:
39411 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39412 [4, 3, 2] by c3 ?2 ?3 ?4
39414 27229: Id : 1, {_}:
39415 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39416 [] by prove_meredith_2_basis_2
39420 27229: nand 12 2 6 0,2
39421 27229: c 2 0 2 2,2,2,2
39422 27229: b 3 0 3 1,2,2
39424 % SZS status Timeout for BOO082-1.p
39425 NO CLASH, using fixed ground order
39427 27257: Id : 2, {_}:
39428 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
39429 [4, 3, 2] by c4 ?2 ?3 ?4
39431 27257: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39435 27257: b 1 0 1 1,2,2
39436 27257: nand 9 2 3 0,2
39437 27257: a 4 0 4 1,1,2
39438 NO CLASH, using fixed ground order
39440 27258: Id : 2, {_}:
39441 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
39442 [4, 3, 2] by c4 ?2 ?3 ?4
39444 27258: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39448 27258: b 1 0 1 1,2,2
39449 27258: nand 9 2 3 0,2
39450 27258: a 4 0 4 1,1,2
39451 NO CLASH, using fixed ground order
39453 27259: Id : 2, {_}:
39454 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
39455 [4, 3, 2] by c4 ?2 ?3 ?4
39457 27259: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39461 27259: b 1 0 1 1,2,2
39462 27259: nand 9 2 3 0,2
39463 27259: a 4 0 4 1,1,2
39464 % SZS status Timeout for BOO083-1.p
39465 NO CLASH, using fixed ground order
39467 27275: Id : 2, {_}:
39468 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
39469 [4, 3, 2] by c4 ?2 ?3 ?4
39471 27275: Id : 1, {_}:
39472 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39473 [] by prove_meredith_2_basis_2
39477 27275: nand 12 2 6 0,2
39478 27275: c 2 0 2 2,2,2,2
39479 27275: b 3 0 3 1,2,2
39481 NO CLASH, using fixed ground order
39483 27276: Id : 2, {_}:
39484 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
39485 [4, 3, 2] by c4 ?2 ?3 ?4
39487 27276: Id : 1, {_}:
39488 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39489 [] by prove_meredith_2_basis_2
39493 27276: nand 12 2 6 0,2
39494 27276: c 2 0 2 2,2,2,2
39495 27276: b 3 0 3 1,2,2
39497 NO CLASH, using fixed ground order
39499 27277: Id : 2, {_}:
39500 nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
39501 [4, 3, 2] by c4 ?2 ?3 ?4
39503 27277: Id : 1, {_}:
39504 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39505 [] by prove_meredith_2_basis_2
39509 27277: nand 12 2 6 0,2
39510 27277: c 2 0 2 2,2,2,2
39511 27277: b 3 0 3 1,2,2
39513 % SZS status Timeout for BOO084-1.p
39514 NO CLASH, using fixed ground order
39516 27304: Id : 2, {_}:
39517 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
39518 [4, 3, 2] by c5 ?2 ?3 ?4
39520 27304: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39524 27304: b 1 0 1 1,2,2
39525 27304: nand 9 2 3 0,2
39526 27304: a 4 0 4 1,1,2
39527 NO CLASH, using fixed ground order
39529 27305: Id : 2, {_}:
39530 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
39531 [4, 3, 2] by c5 ?2 ?3 ?4
39533 27305: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39537 27305: b 1 0 1 1,2,2
39538 27305: nand 9 2 3 0,2
39539 27305: a 4 0 4 1,1,2
39540 NO CLASH, using fixed ground order
39542 27306: Id : 2, {_}:
39543 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
39544 [4, 3, 2] by c5 ?2 ?3 ?4
39546 27306: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39550 27306: b 1 0 1 1,2,2
39551 27306: nand 9 2 3 0,2
39552 27306: a 4 0 4 1,1,2
39553 % SZS status Timeout for BOO085-1.p
39554 NO CLASH, using fixed ground order
39556 27328: Id : 2, {_}:
39557 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
39558 [4, 3, 2] by c5 ?2 ?3 ?4
39560 27328: Id : 1, {_}:
39561 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39562 [] by prove_meredith_2_basis_2
39566 27328: nand 12 2 6 0,2
39567 27328: c 2 0 2 2,2,2,2
39568 27328: b 3 0 3 1,2,2
39570 NO CLASH, using fixed ground order
39572 27331: Id : 2, {_}:
39573 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
39574 [4, 3, 2] by c5 ?2 ?3 ?4
39576 27331: Id : 1, {_}:
39577 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39578 [] by prove_meredith_2_basis_2
39582 27331: nand 12 2 6 0,2
39583 27331: c 2 0 2 2,2,2,2
39584 27331: b 3 0 3 1,2,2
39586 NO CLASH, using fixed ground order
39588 27329: Id : 2, {_}:
39589 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
39590 [4, 3, 2] by c5 ?2 ?3 ?4
39592 27329: Id : 1, {_}:
39593 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39594 [] by prove_meredith_2_basis_2
39598 27329: nand 12 2 6 0,2
39599 27329: c 2 0 2 2,2,2,2
39600 27329: b 3 0 3 1,2,2
39602 % SZS status Timeout for BOO086-1.p
39603 NO CLASH, using fixed ground order
39605 27408: Id : 2, {_}:
39606 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
39607 [4, 3, 2] by c6 ?2 ?3 ?4
39609 27408: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39613 27408: b 1 0 1 1,2,2
39614 27408: nand 9 2 3 0,2
39615 27408: a 4 0 4 1,1,2
39616 NO CLASH, using fixed ground order
39618 27407: Id : 2, {_}:
39619 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
39620 [4, 3, 2] by c6 ?2 ?3 ?4
39622 27407: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39626 27407: b 1 0 1 1,2,2
39627 27407: nand 9 2 3 0,2
39628 27407: a 4 0 4 1,1,2
39629 NO CLASH, using fixed ground order
39631 27409: Id : 2, {_}:
39632 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
39633 [4, 3, 2] by c6 ?2 ?3 ?4
39635 27409: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39639 27409: b 1 0 1 1,2,2
39640 27409: nand 9 2 3 0,2
39641 27409: a 4 0 4 1,1,2
39642 % SZS status Timeout for BOO087-1.p
39643 NO CLASH, using fixed ground order
39645 27425: Id : 2, {_}:
39646 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
39647 [4, 3, 2] by c6 ?2 ?3 ?4
39649 27425: Id : 1, {_}:
39650 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39651 [] by prove_meredith_2_basis_2
39655 27425: nand 12 2 6 0,2
39656 27425: c 2 0 2 2,2,2,2
39657 27425: b 3 0 3 1,2,2
39659 NO CLASH, using fixed ground order
39661 27426: Id : 2, {_}:
39662 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
39663 [4, 3, 2] by c6 ?2 ?3 ?4
39665 27426: Id : 1, {_}:
39666 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39667 [] by prove_meredith_2_basis_2
39671 27426: nand 12 2 6 0,2
39672 27426: c 2 0 2 2,2,2,2
39673 27426: b 3 0 3 1,2,2
39675 NO CLASH, using fixed ground order
39677 27427: Id : 2, {_}:
39678 nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
39679 [4, 3, 2] by c6 ?2 ?3 ?4
39681 27427: Id : 1, {_}:
39682 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39683 [] by prove_meredith_2_basis_2
39687 27427: nand 12 2 6 0,2
39688 27427: c 2 0 2 2,2,2,2
39689 27427: b 3 0 3 1,2,2
39691 % SZS status Timeout for BOO088-1.p
39692 NO CLASH, using fixed ground order
39694 27458: Id : 2, {_}:
39695 nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39696 [4, 3, 2] by c7 ?2 ?3 ?4
39698 27458: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39702 27458: b 1 0 1 1,2,2
39703 27458: nand 9 2 3 0,2
39704 27458: a 4 0 4 1,1,2
39705 NO CLASH, using fixed ground order
39707 27459: Id : 2, {_}:
39708 nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39709 [4, 3, 2] by c7 ?2 ?3 ?4
39711 27459: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39715 27459: b 1 0 1 1,2,2
39716 27459: nand 9 2 3 0,2
39717 27459: a 4 0 4 1,1,2
39718 NO CLASH, using fixed ground order
39720 27460: Id : 2, {_}:
39721 nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39722 [4, 3, 2] by c7 ?2 ?3 ?4
39724 27460: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39728 27460: b 1 0 1 1,2,2
39729 27460: nand 9 2 3 0,2
39730 27460: a 4 0 4 1,1,2
39731 % SZS status Timeout for BOO089-1.p
39732 NO CLASH, using fixed ground order
39734 27496: Id : 2, {_}:
39735 nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39736 [4, 3, 2] by c7 ?2 ?3 ?4
39738 27496: Id : 1, {_}:
39739 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39740 [] by prove_meredith_2_basis_2
39744 27496: nand 12 2 6 0,2
39745 27496: c 2 0 2 2,2,2,2
39746 27496: b 3 0 3 1,2,2
39748 NO CLASH, using fixed ground order
39750 27497: Id : 2, {_}:
39751 nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39752 [4, 3, 2] by c7 ?2 ?3 ?4
39754 27497: Id : 1, {_}:
39755 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39756 [] by prove_meredith_2_basis_2
39760 27497: nand 12 2 6 0,2
39761 27497: c 2 0 2 2,2,2,2
39762 27497: b 3 0 3 1,2,2
39764 NO CLASH, using fixed ground order
39766 27498: Id : 2, {_}:
39767 nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
39768 [4, 3, 2] by c7 ?2 ?3 ?4
39770 27498: Id : 1, {_}:
39771 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39772 [] by prove_meredith_2_basis_2
39776 27498: nand 12 2 6 0,2
39777 27498: c 2 0 2 2,2,2,2
39778 27498: b 3 0 3 1,2,2
39780 % SZS status Timeout for BOO090-1.p
39781 NO CLASH, using fixed ground order
39783 27534: Id : 2, {_}:
39784 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39785 [4, 3, 2] by c8 ?2 ?3 ?4
39787 27534: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39791 27534: b 1 0 1 1,2,2
39792 27534: nand 9 2 3 0,2
39793 27534: a 4 0 4 1,1,2
39794 NO CLASH, using fixed ground order
39796 27535: Id : 2, {_}:
39797 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39798 [4, 3, 2] by c8 ?2 ?3 ?4
39800 27535: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39804 27535: b 1 0 1 1,2,2
39805 27535: nand 9 2 3 0,2
39806 27535: a 4 0 4 1,1,2
39807 NO CLASH, using fixed ground order
39809 27536: Id : 2, {_}:
39810 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39811 [4, 3, 2] by c8 ?2 ?3 ?4
39813 27536: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39817 27536: b 1 0 1 1,2,2
39818 27536: nand 9 2 3 0,2
39819 27536: a 4 0 4 1,1,2
39820 % SZS status Timeout for BOO091-1.p
39821 NO CLASH, using fixed ground order
39823 27553: Id : 2, {_}:
39824 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39825 [4, 3, 2] by c8 ?2 ?3 ?4
39827 27553: Id : 1, {_}:
39828 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39829 [] by prove_meredith_2_basis_2
39833 27553: nand 12 2 6 0,2
39834 27553: c 2 0 2 2,2,2,2
39835 27553: b 3 0 3 1,2,2
39837 NO CLASH, using fixed ground order
39839 27554: Id : 2, {_}:
39840 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39841 [4, 3, 2] by c8 ?2 ?3 ?4
39843 27554: Id : 1, {_}:
39844 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39845 [] by prove_meredith_2_basis_2
39849 27554: nand 12 2 6 0,2
39850 27554: c 2 0 2 2,2,2,2
39851 27554: b 3 0 3 1,2,2
39853 NO CLASH, using fixed ground order
39855 27555: Id : 2, {_}:
39856 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39857 [4, 3, 2] by c8 ?2 ?3 ?4
39859 27555: Id : 1, {_}:
39860 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39861 [] by prove_meredith_2_basis_2
39865 27555: nand 12 2 6 0,2
39866 27555: c 2 0 2 2,2,2,2
39867 27555: b 3 0 3 1,2,2
39869 % SZS status Timeout for BOO092-1.p
39870 NO CLASH, using fixed ground order
39872 27585: Id : 2, {_}:
39873 nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39874 [4, 3, 2] by c9 ?2 ?3 ?4
39876 27585: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39880 27585: b 1 0 1 1,2,2
39881 27585: nand 9 2 3 0,2
39882 27585: a 4 0 4 1,1,2
39883 NO CLASH, using fixed ground order
39885 27584: Id : 2, {_}:
39886 nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39887 [4, 3, 2] by c9 ?2 ?3 ?4
39889 27584: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39893 27584: b 1 0 1 1,2,2
39894 27584: nand 9 2 3 0,2
39895 27584: a 4 0 4 1,1,2
39896 NO CLASH, using fixed ground order
39898 27586: Id : 2, {_}:
39899 nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39900 [4, 3, 2] by c9 ?2 ?3 ?4
39902 27586: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39906 27586: b 1 0 1 1,2,2
39907 27586: nand 9 2 3 0,2
39908 27586: a 4 0 4 1,1,2
39909 % SZS status Timeout for BOO093-1.p
39910 NO CLASH, using fixed ground order
39912 27602: Id : 2, {_}:
39913 nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39914 [4, 3, 2] by c9 ?2 ?3 ?4
39916 27602: Id : 1, {_}:
39917 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39918 [] by prove_meredith_2_basis_2
39922 27602: nand 12 2 6 0,2
39923 27602: c 2 0 2 2,2,2,2
39924 27602: b 3 0 3 1,2,2
39926 NO CLASH, using fixed ground order
39928 27603: Id : 2, {_}:
39929 nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39930 [4, 3, 2] by c9 ?2 ?3 ?4
39932 27603: Id : 1, {_}:
39933 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39934 [] by prove_meredith_2_basis_2
39938 27603: nand 12 2 6 0,2
39939 27603: c 2 0 2 2,2,2,2
39940 27603: b 3 0 3 1,2,2
39942 NO CLASH, using fixed ground order
39944 27604: Id : 2, {_}:
39945 nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
39946 [4, 3, 2] by c9 ?2 ?3 ?4
39948 27604: Id : 1, {_}:
39949 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
39950 [] by prove_meredith_2_basis_2
39954 27604: nand 12 2 6 0,2
39955 27604: c 2 0 2 2,2,2,2
39956 27604: b 3 0 3 1,2,2
39958 % SZS status Timeout for BOO094-1.p
39959 NO CLASH, using fixed ground order
39961 27635: Id : 2, {_}:
39962 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
39963 [4, 3, 2] by c10 ?2 ?3 ?4
39965 27635: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39969 27635: b 1 0 1 1,2,2
39970 27635: nand 9 2 3 0,2
39971 27635: a 4 0 4 1,1,2
39972 NO CLASH, using fixed ground order
39974 27636: Id : 2, {_}:
39975 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
39976 [4, 3, 2] by c10 ?2 ?3 ?4
39978 27636: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39982 27636: b 1 0 1 1,2,2
39983 27636: nand 9 2 3 0,2
39984 27636: a 4 0 4 1,1,2
39985 NO CLASH, using fixed ground order
39987 27637: Id : 2, {_}:
39988 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
39989 [4, 3, 2] by c10 ?2 ?3 ?4
39991 27637: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
39995 27637: b 1 0 1 1,2,2
39996 27637: nand 9 2 3 0,2
39997 27637: a 4 0 4 1,1,2
39998 % SZS status Timeout for BOO095-1.p
39999 NO CLASH, using fixed ground order
40001 27662: Id : 2, {_}:
40002 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40003 [4, 3, 2] by c10 ?2 ?3 ?4
40005 27662: Id : 1, {_}:
40006 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40007 [] by prove_meredith_2_basis_2
40011 27662: nand 12 2 6 0,2
40012 27662: c 2 0 2 2,2,2,2
40013 27662: b 3 0 3 1,2,2
40015 NO CLASH, using fixed ground order
40017 27663: Id : 2, {_}:
40018 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40019 [4, 3, 2] by c10 ?2 ?3 ?4
40021 27663: Id : 1, {_}:
40022 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40023 [] by prove_meredith_2_basis_2
40027 27663: nand 12 2 6 0,2
40028 27663: c 2 0 2 2,2,2,2
40029 27663: b 3 0 3 1,2,2
40031 NO CLASH, using fixed ground order
40033 27664: Id : 2, {_}:
40034 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40035 [4, 3, 2] by c10 ?2 ?3 ?4
40037 27664: Id : 1, {_}:
40038 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40039 [] by prove_meredith_2_basis_2
40043 27664: nand 12 2 6 0,2
40044 27664: c 2 0 2 2,2,2,2
40045 27664: b 3 0 3 1,2,2
40047 % SZS status Timeout for BOO096-1.p
40048 NO CLASH, using fixed ground order
40050 27691: Id : 2, {_}:
40051 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
40052 [4, 3, 2] by c11 ?2 ?3 ?4
40054 27691: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40058 27691: b 1 0 1 1,2,2
40059 27691: nand 9 2 3 0,2
40060 27691: a 4 0 4 1,1,2
40061 NO CLASH, using fixed ground order
40063 27692: Id : 2, {_}:
40064 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
40065 [4, 3, 2] by c11 ?2 ?3 ?4
40067 27692: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40071 27692: b 1 0 1 1,2,2
40072 27692: nand 9 2 3 0,2
40073 27692: a 4 0 4 1,1,2
40074 NO CLASH, using fixed ground order
40076 27693: Id : 2, {_}:
40077 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
40078 [4, 3, 2] by c11 ?2 ?3 ?4
40080 27693: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40084 27693: b 1 0 1 1,2,2
40085 27693: nand 9 2 3 0,2
40086 27693: a 4 0 4 1,1,2
40087 % SZS status Timeout for BOO097-1.p
40088 NO CLASH, using fixed ground order
40090 27766: Id : 2, {_}:
40091 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
40092 [4, 3, 2] by c11 ?2 ?3 ?4
40094 27766: Id : 1, {_}:
40095 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40096 [] by prove_meredith_2_basis_2
40100 27766: nand 12 2 6 0,2
40101 27766: c 2 0 2 2,2,2,2
40102 27766: b 3 0 3 1,2,2
40104 NO CLASH, using fixed ground order
40106 27767: Id : 2, {_}:
40107 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
40108 [4, 3, 2] by c11 ?2 ?3 ?4
40110 27767: Id : 1, {_}:
40111 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40112 [] by prove_meredith_2_basis_2
40116 27767: nand 12 2 6 0,2
40117 27767: c 2 0 2 2,2,2,2
40118 27767: b 3 0 3 1,2,2
40120 NO CLASH, using fixed ground order
40122 27768: Id : 2, {_}:
40123 nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
40124 [4, 3, 2] by c11 ?2 ?3 ?4
40126 27768: Id : 1, {_}:
40127 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40128 [] by prove_meredith_2_basis_2
40132 27768: nand 12 2 6 0,2
40133 27768: c 2 0 2 2,2,2,2
40134 27768: b 3 0 3 1,2,2
40136 % SZS status Timeout for BOO098-1.p
40137 NO CLASH, using fixed ground order
40139 27800: Id : 2, {_}:
40140 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40141 [4, 3, 2] by c12 ?2 ?3 ?4
40143 27800: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40147 27800: b 1 0 1 1,2,2
40148 27800: nand 9 2 3 0,2
40149 27800: a 4 0 4 1,1,2
40150 NO CLASH, using fixed ground order
40152 27801: Id : 2, {_}:
40153 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40154 [4, 3, 2] by c12 ?2 ?3 ?4
40156 27801: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40160 27801: b 1 0 1 1,2,2
40161 27801: nand 9 2 3 0,2
40162 27801: a 4 0 4 1,1,2
40163 NO CLASH, using fixed ground order
40165 27802: Id : 2, {_}:
40166 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40167 [4, 3, 2] by c12 ?2 ?3 ?4
40169 27802: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40173 27802: b 1 0 1 1,2,2
40174 27802: nand 9 2 3 0,2
40175 27802: a 4 0 4 1,1,2
40176 % SZS status Timeout for BOO099-1.p
40177 NO CLASH, using fixed ground order
40179 27864: Id : 2, {_}:
40180 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40181 [4, 3, 2] by c12 ?2 ?3 ?4
40183 27864: Id : 1, {_}:
40184 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40185 [] by prove_meredith_2_basis_2
40189 27864: nand 12 2 6 0,2
40190 27864: c 2 0 2 2,2,2,2
40191 27864: b 3 0 3 1,2,2
40193 NO CLASH, using fixed ground order
40195 27865: Id : 2, {_}:
40196 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40197 [4, 3, 2] by c12 ?2 ?3 ?4
40199 27865: Id : 1, {_}:
40200 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40201 [] by prove_meredith_2_basis_2
40205 27865: nand 12 2 6 0,2
40206 27865: c 2 0 2 2,2,2,2
40207 27865: b 3 0 3 1,2,2
40209 NO CLASH, using fixed ground order
40211 27866: Id : 2, {_}:
40212 nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40213 [4, 3, 2] by c12 ?2 ?3 ?4
40215 27866: Id : 1, {_}:
40216 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40217 [] by prove_meredith_2_basis_2
40221 27866: nand 12 2 6 0,2
40222 27866: c 2 0 2 2,2,2,2
40223 27866: b 3 0 3 1,2,2
40225 % SZS status Timeout for BOO100-1.p
40226 NO CLASH, using fixed ground order
40228 27893: Id : 2, {_}:
40229 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
40230 [4, 3, 2] by c13 ?2 ?3 ?4
40232 27893: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40236 27893: b 1 0 1 1,2,2
40237 27893: nand 9 2 3 0,2
40238 27893: a 4 0 4 1,1,2
40239 NO CLASH, using fixed ground order
40241 27894: Id : 2, {_}:
40242 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
40243 [4, 3, 2] by c13 ?2 ?3 ?4
40245 27894: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40249 27894: b 1 0 1 1,2,2
40250 27894: nand 9 2 3 0,2
40251 27894: a 4 0 4 1,1,2
40252 NO CLASH, using fixed ground order
40254 27895: Id : 2, {_}:
40255 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
40256 [4, 3, 2] by c13 ?2 ?3 ?4
40258 27895: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40262 27895: b 1 0 1 1,2,2
40263 27895: nand 9 2 3 0,2
40264 27895: a 4 0 4 1,1,2
40265 % SZS status Timeout for BOO101-1.p
40266 NO CLASH, using fixed ground order
40268 27912: Id : 2, {_}:
40269 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
40270 [4, 3, 2] by c13 ?2 ?3 ?4
40272 27912: Id : 1, {_}:
40273 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40274 [] by prove_meredith_2_basis_2
40278 27912: nand 12 2 6 0,2
40279 27912: c 2 0 2 2,2,2,2
40280 27912: b 3 0 3 1,2,2
40282 NO CLASH, using fixed ground order
40284 27913: Id : 2, {_}:
40285 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
40286 [4, 3, 2] by c13 ?2 ?3 ?4
40288 27913: Id : 1, {_}:
40289 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40290 [] by prove_meredith_2_basis_2
40294 27913: nand 12 2 6 0,2
40295 27913: c 2 0 2 2,2,2,2
40296 27913: b 3 0 3 1,2,2
40298 NO CLASH, using fixed ground order
40300 27914: Id : 2, {_}:
40301 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
40302 [4, 3, 2] by c13 ?2 ?3 ?4
40304 27914: Id : 1, {_}:
40305 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40306 [] by prove_meredith_2_basis_2
40310 27914: nand 12 2 6 0,2
40311 27914: c 2 0 2 2,2,2,2
40312 27914: b 3 0 3 1,2,2
40314 % SZS status Timeout for BOO102-1.p
40315 NO CLASH, using fixed ground order
40317 27942: Id : 2, {_}:
40318 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40319 [4, 3, 2] by c14 ?2 ?3 ?4
40321 27942: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40325 27942: b 1 0 1 1,2,2
40326 27942: nand 9 2 3 0,2
40327 27942: a 4 0 4 1,1,2
40328 NO CLASH, using fixed ground order
40330 27943: Id : 2, {_}:
40331 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40332 [4, 3, 2] by c14 ?2 ?3 ?4
40334 27943: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40338 27943: b 1 0 1 1,2,2
40339 27943: nand 9 2 3 0,2
40340 27943: a 4 0 4 1,1,2
40341 NO CLASH, using fixed ground order
40343 27944: Id : 2, {_}:
40344 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40345 [4, 3, 2] by c14 ?2 ?3 ?4
40347 27944: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40351 27944: b 1 0 1 1,2,2
40352 27944: nand 9 2 3 0,2
40353 27944: a 4 0 4 1,1,2
40354 % SZS status Timeout for BOO103-1.p
40355 NO CLASH, using fixed ground order
40357 27963: Id : 2, {_}:
40358 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40359 [4, 3, 2] by c14 ?2 ?3 ?4
40361 27963: Id : 1, {_}:
40362 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40363 [] by prove_meredith_2_basis_2
40367 27963: nand 12 2 6 0,2
40368 27963: c 2 0 2 2,2,2,2
40369 27963: b 3 0 3 1,2,2
40371 NO CLASH, using fixed ground order
40373 27964: Id : 2, {_}:
40374 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40375 [4, 3, 2] by c14 ?2 ?3 ?4
40377 27964: Id : 1, {_}:
40378 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40379 [] by prove_meredith_2_basis_2
40383 27964: nand 12 2 6 0,2
40384 27964: c 2 0 2 2,2,2,2
40385 27964: b 3 0 3 1,2,2
40387 NO CLASH, using fixed ground order
40389 27965: Id : 2, {_}:
40390 nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
40391 [4, 3, 2] by c14 ?2 ?3 ?4
40393 27965: Id : 1, {_}:
40394 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40395 [] by prove_meredith_2_basis_2
40399 27965: nand 12 2 6 0,2
40400 27965: c 2 0 2 2,2,2,2
40401 27965: b 3 0 3 1,2,2
40403 % SZS status Timeout for BOO104-1.p
40404 NO CLASH, using fixed ground order
40406 27992: Id : 2, {_}:
40407 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
40408 [4, 3, 2] by c15 ?2 ?3 ?4
40410 27992: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40414 27992: b 1 0 1 1,2,2
40415 27992: nand 9 2 3 0,2
40416 27992: a 4 0 4 1,1,2
40417 NO CLASH, using fixed ground order
40419 27993: Id : 2, {_}:
40420 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
40421 [4, 3, 2] by c15 ?2 ?3 ?4
40423 27993: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40427 27993: b 1 0 1 1,2,2
40428 27993: nand 9 2 3 0,2
40429 27993: a 4 0 4 1,1,2
40430 NO CLASH, using fixed ground order
40432 27994: Id : 2, {_}:
40433 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
40434 [4, 3, 2] by c15 ?2 ?3 ?4
40436 27994: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40440 27994: b 1 0 1 1,2,2
40441 27994: nand 9 2 3 0,2
40442 27994: a 4 0 4 1,1,2
40443 % SZS status Timeout for BOO105-1.p
40444 NO CLASH, using fixed ground order
40446 28010: Id : 2, {_}:
40447 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
40448 [4, 3, 2] by c15 ?2 ?3 ?4
40450 28010: Id : 1, {_}:
40451 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40452 [] by prove_meredith_2_basis_2
40456 28010: nand 12 2 6 0,2
40457 28010: c 2 0 2 2,2,2,2
40458 28010: b 3 0 3 1,2,2
40460 NO CLASH, using fixed ground order
40462 28011: Id : 2, {_}:
40463 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
40464 [4, 3, 2] by c15 ?2 ?3 ?4
40466 28011: Id : 1, {_}:
40467 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40468 [] by prove_meredith_2_basis_2
40472 28011: nand 12 2 6 0,2
40473 28011: c 2 0 2 2,2,2,2
40474 28011: b 3 0 3 1,2,2
40476 NO CLASH, using fixed ground order
40478 28012: Id : 2, {_}:
40479 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
40480 [4, 3, 2] by c15 ?2 ?3 ?4
40482 28012: Id : 1, {_}:
40483 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40484 [] by prove_meredith_2_basis_2
40488 28012: nand 12 2 6 0,2
40489 28012: c 2 0 2 2,2,2,2
40490 28012: b 3 0 3 1,2,2
40492 % SZS status Timeout for BOO106-1.p
40493 NO CLASH, using fixed ground order
40495 28046: Id : 2, {_}:
40496 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
40497 [4, 3, 2] by c16 ?2 ?3 ?4
40499 28046: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40503 28046: b 1 0 1 1,2,2
40504 28046: nand 9 2 3 0,2
40505 28046: a 4 0 4 1,1,2
40506 NO CLASH, using fixed ground order
40508 28047: Id : 2, {_}:
40509 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
40510 [4, 3, 2] by c16 ?2 ?3 ?4
40512 28047: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40516 28047: b 1 0 1 1,2,2
40517 28047: nand 9 2 3 0,2
40518 28047: a 4 0 4 1,1,2
40519 NO CLASH, using fixed ground order
40521 28048: Id : 2, {_}:
40522 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
40523 [4, 3, 2] by c16 ?2 ?3 ?4
40525 28048: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
40529 28048: b 1 0 1 1,2,2
40530 28048: nand 9 2 3 0,2
40531 28048: a 4 0 4 1,1,2
40532 % SZS status Timeout for BOO107-1.p
40533 NO CLASH, using fixed ground order
40535 28069: Id : 2, {_}:
40536 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
40537 [4, 3, 2] by c16 ?2 ?3 ?4
40539 28069: Id : 1, {_}:
40540 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40541 [] by prove_meredith_2_basis_2
40545 28069: nand 12 2 6 0,2
40546 28069: c 2 0 2 2,2,2,2
40547 28069: b 3 0 3 1,2,2
40549 NO CLASH, using fixed ground order
40551 28070: Id : 2, {_}:
40552 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
40553 [4, 3, 2] by c16 ?2 ?3 ?4
40555 28070: Id : 1, {_}:
40556 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40557 [] by prove_meredith_2_basis_2
40561 28070: nand 12 2 6 0,2
40562 28070: c 2 0 2 2,2,2,2
40563 28070: b 3 0 3 1,2,2
40565 NO CLASH, using fixed ground order
40567 28071: Id : 2, {_}:
40568 nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
40569 [4, 3, 2] by c16 ?2 ?3 ?4
40571 28071: Id : 1, {_}:
40572 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
40573 [] by prove_meredith_2_basis_2
40577 28071: nand 12 2 6 0,2
40578 28071: c 2 0 2 2,2,2,2
40579 28071: b 3 0 3 1,2,2
40581 % SZS status Timeout for BOO108-1.p
40582 CLASH, statistics insufficient
40584 28456: Id : 2, {_}:
40585 apply (apply (apply s ?3) ?4) ?5
40587 apply (apply ?3 ?5) (apply ?4 ?5)
40588 [5, 4, 3] by s_definition ?3 ?4 ?5
40589 28456: Id : 3, {_}:
40590 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
40591 [9, 8, 7] by b_definition ?7 ?8 ?9
40593 28456: Id : 1, {_}:
40594 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40595 [1] by prove_fixed_point ?1
40601 28456: apply 14 2 3 0,2
40602 28456: f 3 1 3 0,2,2
40603 CLASH, statistics insufficient
40605 28457: Id : 2, {_}:
40606 apply (apply (apply s ?3) ?4) ?5
40608 apply (apply ?3 ?5) (apply ?4 ?5)
40609 [5, 4, 3] by s_definition ?3 ?4 ?5
40610 28457: Id : 3, {_}:
40611 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
40612 [9, 8, 7] by b_definition ?7 ?8 ?9
40614 28457: Id : 1, {_}:
40615 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40616 [1] by prove_fixed_point ?1
40622 28457: apply 14 2 3 0,2
40623 28457: f 3 1 3 0,2,2
40624 CLASH, statistics insufficient
40626 28458: Id : 2, {_}:
40627 apply (apply (apply s ?3) ?4) ?5
40629 apply (apply ?3 ?5) (apply ?4 ?5)
40630 [5, 4, 3] by s_definition ?3 ?4 ?5
40631 28458: Id : 3, {_}:
40632 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
40633 [9, 8, 7] by b_definition ?7 ?8 ?9
40635 28458: Id : 1, {_}:
40636 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40637 [1] by prove_fixed_point ?1
40643 28458: apply 14 2 3 0,2
40644 28458: f 3 1 3 0,2,2
40645 % SZS status Timeout for COL067-1.p
40646 CLASH, statistics insufficient
40648 28873: Id : 2, {_}:
40649 apply (apply (apply s ?3) ?4) ?5
40651 apply (apply ?3 ?5) (apply ?4 ?5)
40652 [5, 4, 3] by s_definition ?3 ?4 ?5
40653 28873: Id : 3, {_}:
40654 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
40655 [9, 8, 7] by b_definition ?7 ?8 ?9
40657 28873: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
40663 28873: apply 12 2 1 0,3
40664 28873: combinator 1 0 1 1,3
40665 CLASH, statistics insufficient
40667 28874: Id : 2, {_}:
40668 apply (apply (apply s ?3) ?4) ?5
40670 apply (apply ?3 ?5) (apply ?4 ?5)
40671 [5, 4, 3] by s_definition ?3 ?4 ?5
40672 28874: Id : 3, {_}:
40673 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
40674 [9, 8, 7] by b_definition ?7 ?8 ?9
40676 28874: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
40682 28874: apply 12 2 1 0,3
40683 28874: combinator 1 0 1 1,3
40684 CLASH, statistics insufficient
40686 28875: Id : 2, {_}:
40687 apply (apply (apply s ?3) ?4) ?5
40689 apply (apply ?3 ?5) (apply ?4 ?5)
40690 [5, 4, 3] by s_definition ?3 ?4 ?5
40691 28875: Id : 3, {_}:
40692 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
40693 [9, 8, 7] by b_definition ?7 ?8 ?9
40695 28875: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
40701 28875: apply 12 2 1 0,3
40702 28875: combinator 1 0 1 1,3
40703 % SZS status Timeout for COL068-1.p
40704 CLASH, statistics insufficient
40706 28902: Id : 2, {_}:
40707 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
40708 [5, 4, 3] by b_definition ?3 ?4 ?5
40709 28902: Id : 3, {_}:
40710 apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
40711 [8, 7] by l_definition ?7 ?8
40713 28902: Id : 1, {_}:
40714 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40715 [1] by prove_fixed_point ?1
40721 28902: apply 12 2 3 0,2
40722 28902: f 3 1 3 0,2,2
40723 CLASH, statistics insufficient
40725 28903: Id : 2, {_}:
40726 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
40727 [5, 4, 3] by b_definition ?3 ?4 ?5
40728 28903: Id : 3, {_}:
40729 apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
40730 [8, 7] by l_definition ?7 ?8
40732 28903: Id : 1, {_}:
40733 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40734 [1] by prove_fixed_point ?1
40740 28903: apply 12 2 3 0,2
40741 28903: f 3 1 3 0,2,2
40742 CLASH, statistics insufficient
40744 28904: Id : 2, {_}:
40745 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
40746 [5, 4, 3] by b_definition ?3 ?4 ?5
40747 28904: Id : 3, {_}:
40748 apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
40749 [8, 7] by l_definition ?7 ?8
40751 28904: Id : 1, {_}:
40752 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40753 [1] by prove_fixed_point ?1
40759 28904: apply 12 2 3 0,2
40760 28904: f 3 1 3 0,2,2
40761 % SZS status Timeout for COL069-1.p
40762 CLASH, statistics insufficient
40764 28921: Id : 2, {_}:
40765 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
40766 [5, 4, 3] by definition_B ?3 ?4 ?5
40767 28921: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
40769 28921: Id : 1, {_}:
40770 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40771 [1] by strong_fixpoint ?1
40777 28921: apply 10 2 3 0,2
40778 28921: f 3 1 3 0,2,2
40779 CLASH, statistics insufficient
40781 28922: Id : 2, {_}:
40782 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
40783 [5, 4, 3] by definition_B ?3 ?4 ?5
40784 28922: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
40786 28922: Id : 1, {_}:
40787 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40788 [1] by strong_fixpoint ?1
40794 28922: apply 10 2 3 0,2
40795 28922: f 3 1 3 0,2,2
40796 CLASH, statistics insufficient
40798 28923: Id : 2, {_}:
40799 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
40800 [5, 4, 3] by definition_B ?3 ?4 ?5
40801 28923: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
40803 28923: Id : 1, {_}:
40804 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
40805 [1] by strong_fixpoint ?1
40811 28923: apply 10 2 3 0,2
40812 28923: f 3 1 3 0,2,2
40813 % SZS status Timeout for COL087-1.p
40814 NO CLASH, using fixed ground order
40816 28951: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
40817 28951: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
40818 28951: Id : 4, {_}:
40819 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
40820 [8, 7, 6] by associativity ?6 ?7 ?8
40821 28951: Id : 5, {_}:
40822 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
40823 [11, 10] by symmetry_of_glb ?10 ?11
40824 28951: Id : 6, {_}:
40825 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
40826 [14, 13] by symmetry_of_lub ?13 ?14
40827 28951: Id : 7, {_}:
40828 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
40830 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
40831 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
40832 28951: Id : 8, {_}:
40833 least_upper_bound ?20 (least_upper_bound ?21 ?22)
40835 least_upper_bound (least_upper_bound ?20 ?21) ?22
40836 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
40837 28951: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
40838 28951: Id : 10, {_}:
40839 greatest_lower_bound ?26 ?26 =>= ?26
40840 [26] by idempotence_of_gld ?26
40841 28951: Id : 11, {_}:
40842 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
40843 [29, 28] by lub_absorbtion ?28 ?29
40844 28951: Id : 12, {_}:
40845 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
40846 [32, 31] by glb_absorbtion ?31 ?32
40847 28951: Id : 13, {_}:
40848 multiply ?34 (least_upper_bound ?35 ?36)
40850 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
40851 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
40852 28951: Id : 14, {_}:
40853 multiply ?38 (greatest_lower_bound ?39 ?40)
40855 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
40856 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
40857 28951: Id : 15, {_}:
40858 multiply (least_upper_bound ?42 ?43) ?44
40860 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
40861 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
40862 28951: Id : 16, {_}:
40863 multiply (greatest_lower_bound ?46 ?47) ?48
40865 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
40866 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
40867 28951: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
40868 28951: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
40869 28951: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
40871 28951: Id : 1, {_}:
40872 least_upper_bound (greatest_lower_bound a (multiply b c))
40873 (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
40875 multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
40880 28951: inverse 1 1 0
40881 28951: identity 5 0 0
40882 28951: least_upper_bound 17 2 1 0,2
40883 28951: greatest_lower_bound 18 2 5 0,1,2
40884 28951: multiply 21 2 3 0,2,1,2
40885 28951: c 5 0 3 2,2,1,2
40886 28951: b 5 0 3 1,2,1,2
40887 28951: a 7 0 5 1,1,2
40888 NO CLASH, using fixed ground order
40890 28952: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
40891 28952: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
40892 28952: Id : 4, {_}:
40893 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
40894 [8, 7, 6] by associativity ?6 ?7 ?8
40895 28952: Id : 5, {_}:
40896 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
40897 [11, 10] by symmetry_of_glb ?10 ?11
40898 28952: Id : 6, {_}:
40899 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
40900 [14, 13] by symmetry_of_lub ?13 ?14
40901 28952: Id : 7, {_}:
40902 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
40904 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
40905 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
40906 28952: Id : 8, {_}:
40907 least_upper_bound ?20 (least_upper_bound ?21 ?22)
40909 least_upper_bound (least_upper_bound ?20 ?21) ?22
40910 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
40911 28952: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
40912 28952: Id : 10, {_}:
40913 greatest_lower_bound ?26 ?26 =>= ?26
40914 [26] by idempotence_of_gld ?26
40915 28952: Id : 11, {_}:
40916 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
40917 [29, 28] by lub_absorbtion ?28 ?29
40918 28952: Id : 12, {_}:
40919 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
40920 [32, 31] by glb_absorbtion ?31 ?32
40921 28952: Id : 13, {_}:
40922 multiply ?34 (least_upper_bound ?35 ?36)
40924 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
40925 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
40926 28952: Id : 14, {_}:
40927 multiply ?38 (greatest_lower_bound ?39 ?40)
40929 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
40930 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
40931 28952: Id : 15, {_}:
40932 multiply (least_upper_bound ?42 ?43) ?44
40934 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
40935 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
40936 28952: Id : 16, {_}:
40937 multiply (greatest_lower_bound ?46 ?47) ?48
40939 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
40940 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
40941 28952: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
40942 28952: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
40943 28952: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
40945 28952: Id : 1, {_}:
40946 least_upper_bound (greatest_lower_bound a (multiply b c))
40947 (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
40949 multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
40954 28952: inverse 1 1 0
40955 28952: identity 5 0 0
40956 28952: least_upper_bound 17 2 1 0,2
40957 28952: greatest_lower_bound 18 2 5 0,1,2
40958 28952: multiply 21 2 3 0,2,1,2
40959 28952: c 5 0 3 2,2,1,2
40960 28952: b 5 0 3 1,2,1,2
40961 28952: a 7 0 5 1,1,2
40962 NO CLASH, using fixed ground order
40964 28953: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
40965 28953: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
40966 28953: Id : 4, {_}:
40967 multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
40968 [8, 7, 6] by associativity ?6 ?7 ?8
40969 28953: Id : 5, {_}:
40970 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
40971 [11, 10] by symmetry_of_glb ?10 ?11
40972 28953: Id : 6, {_}:
40973 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
40974 [14, 13] by symmetry_of_lub ?13 ?14
40975 28953: Id : 7, {_}:
40976 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
40978 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
40979 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
40980 28953: Id : 8, {_}:
40981 least_upper_bound ?20 (least_upper_bound ?21 ?22)
40983 least_upper_bound (least_upper_bound ?20 ?21) ?22
40984 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
40985 28953: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
40986 28953: Id : 10, {_}:
40987 greatest_lower_bound ?26 ?26 =>= ?26
40988 [26] by idempotence_of_gld ?26
40989 28953: Id : 11, {_}:
40990 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
40991 [29, 28] by lub_absorbtion ?28 ?29
40992 28953: Id : 12, {_}:
40993 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
40994 [32, 31] by glb_absorbtion ?31 ?32
40995 28953: Id : 13, {_}:
40996 multiply ?34 (least_upper_bound ?35 ?36)
40998 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
40999 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
41000 28953: Id : 14, {_}:
41001 multiply ?38 (greatest_lower_bound ?39 ?40)
41003 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
41004 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
41005 28953: Id : 15, {_}:
41006 multiply (least_upper_bound ?42 ?43) ?44
41008 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
41009 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
41010 28953: Id : 16, {_}:
41011 multiply (greatest_lower_bound ?46 ?47) ?48
41013 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
41014 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
41015 28953: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
41016 28953: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
41017 28953: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
41019 28953: Id : 1, {_}:
41020 least_upper_bound (greatest_lower_bound a (multiply b c))
41021 (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
41023 multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
41028 28953: inverse 1 1 0
41029 28953: identity 5 0 0
41030 28953: least_upper_bound 17 2 1 0,2
41031 28953: greatest_lower_bound 18 2 5 0,1,2
41032 28953: multiply 21 2 3 0,2,1,2
41033 28953: c 5 0 3 2,2,1,2
41034 28953: b 5 0 3 1,2,1,2
41035 28953: a 7 0 5 1,1,2
41036 % SZS status Timeout for GRP177-1.p
41037 NO CLASH, using fixed ground order
41039 28970: Id : 2, {_}:
41040 f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
41043 [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
41045 28970: Id : 1, {_}:
41046 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41047 [] by associativity
41051 28970: f 17 2 8 0,2
41052 28970: c 3 0 3 2,1,2,2
41053 28970: b 4 0 4 1,1,2,2
41055 NO CLASH, using fixed ground order
41057 28971: Id : 2, {_}:
41058 f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
41061 [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
41063 28971: Id : 1, {_}:
41064 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41065 [] by associativity
41069 28971: f 17 2 8 0,2
41070 28971: c 3 0 3 2,1,2,2
41071 28971: b 4 0 4 1,1,2,2
41073 NO CLASH, using fixed ground order
41075 28972: Id : 2, {_}:
41076 f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
41079 [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
41081 28972: Id : 1, {_}:
41082 f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
41083 [] by associativity
41087 28972: f 17 2 8 0,2
41088 28972: c 3 0 3 2,1,2,2
41089 28972: b 4 0 4 1,1,2,2
41091 % SZS status Timeout for LAT071-1.p
41092 NO CLASH, using fixed ground order
41094 29000: Id : 2, {_}:
41095 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41096 (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
41099 [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
41101 29000: Id : 1, {_}:
41102 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41103 [] by associativity
41107 29000: f 18 2 8 0,2
41108 29000: c 3 0 3 2,1,2,2
41109 29000: b 4 0 4 1,1,2,2
41111 NO CLASH, using fixed ground order
41113 29001: Id : 2, {_}:
41114 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41115 (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
41118 [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
41120 29001: Id : 1, {_}:
41121 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41122 [] by associativity
41126 29001: f 18 2 8 0,2
41127 29001: c 3 0 3 2,1,2,2
41128 29001: b 4 0 4 1,1,2,2
41130 NO CLASH, using fixed ground order
41132 29002: Id : 2, {_}:
41133 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41134 (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
41137 [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
41139 29002: Id : 1, {_}:
41140 f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
41141 [] by associativity
41145 29002: f 18 2 8 0,2
41146 29002: c 3 0 3 2,1,2,2
41147 29002: b 4 0 4 1,1,2,2
41149 % SZS status Timeout for LAT072-1.p
41150 NO CLASH, using fixed ground order
41152 29018: Id : 2, {_}:
41153 f (f (f ?2 (f ?3 ?2)) ?2)
41154 (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
41157 [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
41159 29018: Id : 1, {_}:
41160 f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
41165 29018: f 18 2 8 0,2
41166 29018: c 3 0 3 1,2,2,2,2
41167 29018: b 3 0 3 1,2,2
41169 NO CLASH, using fixed ground order
41171 29019: Id : 2, {_}:
41172 f (f (f ?2 (f ?3 ?2)) ?2)
41173 (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
41176 [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
41178 29019: Id : 1, {_}:
41179 f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
41184 29019: f 18 2 8 0,2
41185 29019: c 3 0 3 1,2,2,2,2
41186 29019: b 3 0 3 1,2,2
41188 NO CLASH, using fixed ground order
41190 29020: Id : 2, {_}:
41191 f (f (f ?2 (f ?3 ?2)) ?2)
41192 (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
41195 [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
41197 29020: Id : 1, {_}:
41198 f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
41203 29020: f 18 2 8 0,2
41204 29020: c 3 0 3 1,2,2,2,2
41205 29020: b 3 0 3 1,2,2
41207 % SZS status Timeout for LAT073-1.p
41208 NO CLASH, using fixed ground order
41210 29047: Id : 2, {_}:
41212 (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
41215 [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
41217 29047: Id : 1, {_}:
41218 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41219 [] by associativity
41223 29047: f 19 2 8 0,2
41224 29047: c 3 0 3 2,1,2,2
41225 29047: b 4 0 4 1,1,2,2
41227 NO CLASH, using fixed ground order
41229 29048: Id : 2, {_}:
41231 (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
41234 [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
41236 29048: Id : 1, {_}:
41237 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41238 [] by associativity
41242 29048: f 19 2 8 0,2
41243 29048: c 3 0 3 2,1,2,2
41244 29048: b 4 0 4 1,1,2,2
41246 NO CLASH, using fixed ground order
41248 29049: Id : 2, {_}:
41250 (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
41253 [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
41255 29049: Id : 1, {_}:
41256 f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
41257 [] by associativity
41261 29049: f 19 2 8 0,2
41262 29049: c 3 0 3 2,1,2,2
41263 29049: b 4 0 4 1,1,2,2
41265 % SZS status Timeout for LAT074-1.p
41266 NO CLASH, using fixed ground order
41268 29065: Id : 2, {_}:
41270 (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
41273 [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
41275 29065: Id : 1, {_}:
41276 f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
41281 29065: f 19 2 8 0,2
41282 29065: c 3 0 3 1,2,2,2,2
41283 29065: b 3 0 3 1,2,2
41285 NO CLASH, using fixed ground order
41287 29066: Id : 2, {_}:
41289 (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
41292 [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
41294 29066: Id : 1, {_}:
41295 f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
41300 29066: f 19 2 8 0,2
41301 29066: c 3 0 3 1,2,2,2,2
41302 29066: b 3 0 3 1,2,2
41304 NO CLASH, using fixed ground order
41306 29067: Id : 2, {_}:
41308 (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
41311 [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
41313 29067: Id : 1, {_}:
41314 f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
41319 29067: f 19 2 8 0,2
41320 29067: c 3 0 3 1,2,2,2,2
41321 29067: b 3 0 3 1,2,2
41323 % SZS status Timeout for LAT075-1.p
41324 NO CLASH, using fixed ground order
41326 29098: Id : 2, {_}:
41327 f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
41328 (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
41331 [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
41333 29098: Id : 1, {_}:
41334 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41335 [] by associativity
41339 29098: f 20 2 8 0,2
41340 29098: c 3 0 3 2,1,2,2
41341 29098: b 4 0 4 1,1,2,2
41343 NO CLASH, using fixed ground order
41345 29099: Id : 2, {_}:
41346 f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
41347 (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
41350 [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
41352 29099: Id : 1, {_}:
41353 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41354 [] by associativity
41358 29099: f 20 2 8 0,2
41359 29099: c 3 0 3 2,1,2,2
41360 29099: b 4 0 4 1,1,2,2
41362 NO CLASH, using fixed ground order
41364 29100: Id : 2, {_}:
41365 f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
41366 (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
41369 [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
41371 29100: Id : 1, {_}:
41372 f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
41373 [] by associativity
41377 29100: f 20 2 8 0,2
41378 29100: c 3 0 3 2,1,2,2
41379 29100: b 4 0 4 1,1,2,2
41381 % SZS status Timeout for LAT076-1.p
41382 NO CLASH, using fixed ground order
41384 NO CLASH, using fixed ground order
41386 29162: Id : 2, {_}:
41387 f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
41388 (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
41391 [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
41393 29162: Id : 1, {_}:
41394 f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
41399 29162: f 20 2 8 0,2
41400 29162: c 3 0 3 1,2,2,2,2
41401 29162: b 3 0 3 1,2,2
41403 29161: Id : 2, {_}:
41404 f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
41405 (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
41408 [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
41410 29161: Id : 1, {_}:
41411 f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
41416 29161: f 20 2 8 0,2
41417 29161: c 3 0 3 1,2,2,2,2
41418 29161: b 3 0 3 1,2,2
41420 NO CLASH, using fixed ground order
41422 29163: Id : 2, {_}:
41423 f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
41424 (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
41427 [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
41429 29163: Id : 1, {_}:
41430 f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
41435 29163: f 20 2 8 0,2
41436 29163: c 3 0 3 1,2,2,2,2
41437 29163: b 3 0 3 1,2,2
41439 % SZS status Timeout for LAT077-1.p
41440 NO CLASH, using fixed ground order
41442 29191: Id : 2, {_}:
41443 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41444 (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
41447 [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
41449 29191: Id : 1, {_}:
41450 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41451 [] by associativity
41455 29191: f 20 2 8 0,2
41456 29191: c 3 0 3 2,1,2,2
41457 29191: b 4 0 4 1,1,2,2
41459 NO CLASH, using fixed ground order
41461 29192: Id : 2, {_}:
41462 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41463 (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
41466 [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
41468 29192: Id : 1, {_}:
41469 f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
41470 [] by associativity
41474 29192: f 20 2 8 0,2
41475 29192: c 3 0 3 2,1,2,2
41476 29192: b 4 0 4 1,1,2,2
41478 NO CLASH, using fixed ground order
41480 29193: Id : 2, {_}:
41481 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41482 (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
41485 [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
41487 29193: Id : 1, {_}:
41488 f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
41489 [] by associativity
41493 29193: f 20 2 8 0,2
41494 29193: c 3 0 3 2,1,2,2
41495 29193: b 4 0 4 1,1,2,2
41497 % SZS status Timeout for LAT078-1.p
41498 NO CLASH, using fixed ground order
41500 29210: Id : 2, {_}:
41501 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41502 (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
41505 [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
41507 29210: Id : 1, {_}:
41508 f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
41513 29210: f 20 2 8 0,2
41514 29210: c 3 0 3 1,2,2,2,2
41515 29210: b 3 0 3 1,2,2
41517 NO CLASH, using fixed ground order
41519 29211: Id : 2, {_}:
41520 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41521 (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
41524 [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
41526 29211: Id : 1, {_}:
41527 f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
41532 29211: f 20 2 8 0,2
41533 29211: c 3 0 3 1,2,2,2,2
41534 29211: b 3 0 3 1,2,2
41536 NO CLASH, using fixed ground order
41538 29212: Id : 2, {_}:
41539 f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
41540 (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
41543 [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
41545 29212: Id : 1, {_}:
41546 f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
41551 29212: f 20 2 8 0,2
41552 29212: c 3 0 3 1,2,2,2,2
41553 29212: b 3 0 3 1,2,2
41555 % SZS status Timeout for LAT079-1.p
41556 NO CLASH, using fixed ground order
41558 29240: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41559 29240: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41560 29240: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41561 29240: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41562 29240: Id : 6, {_}:
41563 meet ?12 ?13 =?= meet ?13 ?12
41564 [13, 12] by commutativity_of_meet ?12 ?13
41565 29240: Id : 7, {_}:
41566 join ?15 ?16 =?= join ?16 ?15
41567 [16, 15] by commutativity_of_join ?15 ?16
41568 29240: Id : 8, {_}:
41569 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
41570 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41571 29240: Id : 9, {_}:
41572 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
41573 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41574 29240: Id : 10, {_}:
41575 meet ?26 (join ?27 (meet ?26 ?28))
41579 (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
41580 [28, 27, 26] by equation_H11 ?26 ?27 ?28
41582 29240: Id : 1, {_}:
41583 meet a (join b (meet a c))
41585 meet a (join b (meet c (join a (meet b c))))
41590 29240: join 16 2 3 0,2,2
41591 29240: meet 20 2 5 0,2
41592 29240: c 3 0 3 2,2,2,2
41593 29240: b 3 0 3 1,2,2
41595 NO CLASH, using fixed ground order
41597 29241: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41598 29241: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41599 29241: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41600 29241: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41601 29241: Id : 6, {_}:
41602 meet ?12 ?13 =?= meet ?13 ?12
41603 [13, 12] by commutativity_of_meet ?12 ?13
41604 29241: Id : 7, {_}:
41605 join ?15 ?16 =?= join ?16 ?15
41606 [16, 15] by commutativity_of_join ?15 ?16
41607 29241: Id : 8, {_}:
41608 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41609 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41610 29241: Id : 9, {_}:
41611 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41612 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41613 29241: Id : 10, {_}:
41614 meet ?26 (join ?27 (meet ?26 ?28))
41618 (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
41619 [28, 27, 26] by equation_H11 ?26 ?27 ?28
41621 29241: Id : 1, {_}:
41622 meet a (join b (meet a c))
41624 meet a (join b (meet c (join a (meet b c))))
41629 29241: join 16 2 3 0,2,2
41630 29241: meet 20 2 5 0,2
41631 29241: c 3 0 3 2,2,2,2
41632 29241: b 3 0 3 1,2,2
41634 NO CLASH, using fixed ground order
41636 29242: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41637 29242: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41638 29242: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41639 29242: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41640 29242: Id : 6, {_}:
41641 meet ?12 ?13 =?= meet ?13 ?12
41642 [13, 12] by commutativity_of_meet ?12 ?13
41643 29242: Id : 7, {_}:
41644 join ?15 ?16 =?= join ?16 ?15
41645 [16, 15] by commutativity_of_join ?15 ?16
41646 29242: Id : 8, {_}:
41647 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41648 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41649 29242: Id : 9, {_}:
41650 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41651 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41652 29242: Id : 10, {_}:
41653 meet ?26 (join ?27 (meet ?26 ?28))
41657 (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
41658 [28, 27, 26] by equation_H11 ?26 ?27 ?28
41660 29242: Id : 1, {_}:
41661 meet a (join b (meet a c))
41663 meet a (join b (meet c (join a (meet b c))))
41668 29242: join 16 2 3 0,2,2
41669 29242: meet 20 2 5 0,2
41670 29242: c 3 0 3 2,2,2,2
41671 29242: b 3 0 3 1,2,2
41673 % SZS status Timeout for LAT139-1.p
41674 NO CLASH, using fixed ground order
41676 29258: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41677 29258: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41678 29258: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41679 29258: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41680 29258: Id : 6, {_}:
41681 meet ?12 ?13 =?= meet ?13 ?12
41682 [13, 12] by commutativity_of_meet ?12 ?13
41683 29258: Id : 7, {_}:
41684 join ?15 ?16 =?= join ?16 ?15
41685 [16, 15] by commutativity_of_join ?15 ?16
41686 29258: Id : 8, {_}:
41687 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
41688 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41689 29258: Id : 9, {_}:
41690 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
41691 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41692 29258: Id : 10, {_}:
41693 join (meet ?26 ?27) (meet ?26 ?28)
41696 (join (meet ?27 (join ?26 (meet ?27 ?28)))
41697 (meet ?28 (join ?26 ?27)))
41698 [28, 27, 26] by equation_H21 ?26 ?27 ?28
41700 29258: Id : 1, {_}:
41701 meet a (join b (meet a c))
41703 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
41708 29258: join 17 2 4 0,2,2
41709 29258: meet 21 2 6 0,2
41710 29258: c 3 0 3 2,2,2,2
41711 29258: b 3 0 3 1,2,2
41713 NO CLASH, using fixed ground order
41715 29259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41716 29259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41717 29259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41718 29259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41719 29259: Id : 6, {_}:
41720 meet ?12 ?13 =?= meet ?13 ?12
41721 [13, 12] by commutativity_of_meet ?12 ?13
41722 29259: Id : 7, {_}:
41723 join ?15 ?16 =?= join ?16 ?15
41724 [16, 15] by commutativity_of_join ?15 ?16
41725 29259: Id : 8, {_}:
41726 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41727 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41728 29259: Id : 9, {_}:
41729 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41730 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41731 29259: Id : 10, {_}:
41732 join (meet ?26 ?27) (meet ?26 ?28)
41735 (join (meet ?27 (join ?26 (meet ?27 ?28)))
41736 (meet ?28 (join ?26 ?27)))
41737 [28, 27, 26] by equation_H21 ?26 ?27 ?28
41739 29259: Id : 1, {_}:
41740 meet a (join b (meet a c))
41742 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
41747 29259: join 17 2 4 0,2,2
41748 29259: meet 21 2 6 0,2
41749 29259: c 3 0 3 2,2,2,2
41750 NO CLASH, using fixed ground order
41752 29260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41753 29260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41754 29260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41755 29260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41756 29260: Id : 6, {_}:
41757 meet ?12 ?13 =?= meet ?13 ?12
41758 [13, 12] by commutativity_of_meet ?12 ?13
41759 29260: Id : 7, {_}:
41760 join ?15 ?16 =?= join ?16 ?15
41761 [16, 15] by commutativity_of_join ?15 ?16
41762 29260: Id : 8, {_}:
41763 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41764 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41765 29260: Id : 9, {_}:
41766 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41767 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41768 29260: Id : 10, {_}:
41769 join (meet ?26 ?27) (meet ?26 ?28)
41772 (join (meet ?27 (join ?26 (meet ?27 ?28)))
41773 (meet ?28 (join ?26 ?27)))
41774 [28, 27, 26] by equation_H21 ?26 ?27 ?28
41776 29260: Id : 1, {_}:
41777 meet a (join b (meet a c))
41779 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
41784 29260: join 17 2 4 0,2,2
41785 29260: meet 21 2 6 0,2
41786 29260: c 3 0 3 2,2,2,2
41787 29260: b 3 0 3 1,2,2
41789 29259: b 3 0 3 1,2,2
41791 % SZS status Timeout for LAT141-1.p
41792 NO CLASH, using fixed ground order
41793 NO CLASH, using fixed ground order
41795 29297: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41796 29297: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41797 29297: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41798 29297: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41799 29297: Id : 6, {_}:
41800 meet ?12 ?13 =?= meet ?13 ?12
41801 [13, 12] by commutativity_of_meet ?12 ?13
41802 29297: Id : 7, {_}:
41803 join ?15 ?16 =?= join ?16 ?15
41804 [16, 15] by commutativity_of_join ?15 ?16
41805 29297: Id : 8, {_}:
41806 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41807 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41808 29297: Id : 9, {_}:
41809 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41810 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41811 29297: Id : 10, {_}:
41812 meet ?26 (join ?27 ?28)
41814 meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
41815 [28, 27, 26] by equation_H58 ?26 ?27 ?28
41817 29297: Id : 1, {_}:
41818 meet a (meet (join b c) (join b d))
41820 meet a (join b (meet (join b d) (join c (meet a b))))
41825 29297: meet 18 2 5 0,2
41826 29297: d 2 0 2 2,2,2,2
41827 29297: join 18 2 5 0,1,2,2
41828 29297: c 2 0 2 2,1,2,2
41829 29297: b 5 0 5 1,1,2,2
41832 29296: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41833 29296: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41834 29296: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41835 29296: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41836 29296: Id : 6, {_}:
41837 meet ?12 ?13 =?= meet ?13 ?12
41838 [13, 12] by commutativity_of_meet ?12 ?13
41839 29296: Id : 7, {_}:
41840 join ?15 ?16 =?= join ?16 ?15
41841 [16, 15] by commutativity_of_join ?15 ?16
41842 29296: Id : 8, {_}:
41843 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
41844 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41845 29296: Id : 9, {_}:
41846 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
41847 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41848 29296: Id : 10, {_}:
41849 meet ?26 (join ?27 ?28)
41851 meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
41852 [28, 27, 26] by equation_H58 ?26 ?27 ?28
41854 29296: Id : 1, {_}:
41855 meet a (meet (join b c) (join b d))
41857 meet a (join b (meet (join b d) (join c (meet a b))))
41862 29296: meet 18 2 5 0,2
41863 29296: d 2 0 2 2,2,2,2
41864 29296: join 18 2 5 0,1,2,2
41865 29296: c 2 0 2 2,1,2,2
41866 29296: b 5 0 5 1,1,2,2
41868 NO CLASH, using fixed ground order
41870 29298: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41871 29298: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41872 29298: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41873 29298: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41874 29298: Id : 6, {_}:
41875 meet ?12 ?13 =?= meet ?13 ?12
41876 [13, 12] by commutativity_of_meet ?12 ?13
41877 29298: Id : 7, {_}:
41878 join ?15 ?16 =?= join ?16 ?15
41879 [16, 15] by commutativity_of_join ?15 ?16
41880 29298: Id : 8, {_}:
41881 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41882 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41883 29298: Id : 9, {_}:
41884 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41885 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41886 29298: Id : 10, {_}:
41887 meet ?26 (join ?27 ?28)
41889 meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
41890 [28, 27, 26] by equation_H58 ?26 ?27 ?28
41892 29298: Id : 1, {_}:
41893 meet a (meet (join b c) (join b d))
41895 meet a (join b (meet (join b d) (join c (meet a b))))
41900 29298: meet 18 2 5 0,2
41901 29298: d 2 0 2 2,2,2,2
41902 29298: join 18 2 5 0,1,2,2
41903 29298: c 2 0 2 2,1,2,2
41904 29298: b 5 0 5 1,1,2,2
41906 % SZS status Timeout for LAT161-1.p
41907 NO CLASH, using fixed ground order
41909 29316: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41910 29316: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41911 29316: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41912 29316: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41913 29316: Id : 6, {_}:
41914 meet ?12 ?13 =?= meet ?13 ?12
41915 [13, 12] by commutativity_of_meet ?12 ?13
41916 29316: Id : 7, {_}:
41917 join ?15 ?16 =?= join ?16 ?15
41918 [16, 15] by commutativity_of_join ?15 ?16
41919 29316: Id : 8, {_}:
41920 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
41921 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41922 29316: Id : 9, {_}:
41923 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
41924 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41925 29316: Id : 10, {_}:
41926 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
41928 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
41929 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
41931 29316: Id : 1, {_}:
41932 meet a (join b (meet a c))
41934 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
41939 29316: join 19 2 4 0,2,2
41940 29316: meet 19 2 6 0,2
41941 29316: c 3 0 3 2,2,2,2
41942 29316: b 3 0 3 1,2,2
41944 NO CLASH, using fixed ground order
41946 29317: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41947 29317: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41948 29317: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41949 29317: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41950 29317: Id : 6, {_}:
41951 meet ?12 ?13 =?= meet ?13 ?12
41952 [13, 12] by commutativity_of_meet ?12 ?13
41953 29317: Id : 7, {_}:
41954 join ?15 ?16 =?= join ?16 ?15
41955 [16, 15] by commutativity_of_join ?15 ?16
41956 29317: Id : 8, {_}:
41957 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41958 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41959 29317: Id : 9, {_}:
41960 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41961 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41962 29317: Id : 10, {_}:
41963 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
41965 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
41966 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
41968 29317: Id : 1, {_}:
41969 meet a (join b (meet a c))
41971 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
41976 29317: join 19 2 4 0,2,2
41977 29317: meet 19 2 6 0,2
41978 29317: c 3 0 3 2,2,2,2
41979 29317: b 3 0 3 1,2,2
41981 NO CLASH, using fixed ground order
41983 29318: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
41984 29318: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
41985 29318: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
41986 29318: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
41987 29318: Id : 6, {_}:
41988 meet ?12 ?13 =?= meet ?13 ?12
41989 [13, 12] by commutativity_of_meet ?12 ?13
41990 29318: Id : 7, {_}:
41991 join ?15 ?16 =?= join ?16 ?15
41992 [16, 15] by commutativity_of_join ?15 ?16
41993 29318: Id : 8, {_}:
41994 meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
41995 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
41996 29318: Id : 9, {_}:
41997 join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
41998 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
41999 29318: Id : 10, {_}:
42000 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
42002 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
42003 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
42005 29318: Id : 1, {_}:
42006 meet a (join b (meet a c))
42008 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
42013 29318: join 19 2 4 0,2,2
42014 29318: meet 19 2 6 0,2
42015 29318: c 3 0 3 2,2,2,2
42016 29318: b 3 0 3 1,2,2
42018 % SZS status Timeout for LAT177-1.p
42019 NO CLASH, using fixed ground order
42021 29346: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
42022 29346: Id : 3, {_}:
42023 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
42024 [7, 6, 5] by associative_addition ?5 ?6 ?7
42025 NO CLASH, using fixed ground order
42027 29347: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
42028 29347: Id : 3, {_}:
42029 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
42030 [7, 6, 5] by associative_addition ?5 ?6 ?7
42031 29347: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
42032 29347: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
42033 29347: Id : 6, {_}:
42034 add ?13 (additive_inverse ?13) =>= additive_identity
42035 [13] by right_additive_inverse ?13
42036 29347: Id : 7, {_}:
42037 add (additive_inverse ?15) ?15 =>= additive_identity
42038 [15] by left_additive_inverse ?15
42039 29347: Id : 8, {_}:
42040 additive_inverse additive_identity =>= additive_identity
42041 [] by additive_inverse_identity
42042 29347: Id : 9, {_}:
42043 add ?18 (add (additive_inverse ?18) ?19) =>= ?19
42044 [19, 18] by property_of_inverse_and_add ?18 ?19
42045 29347: Id : 10, {_}:
42046 additive_inverse (add ?21 ?22)
42048 add (additive_inverse ?21) (additive_inverse ?22)
42049 [22, 21] by distribute_additive_inverse ?21 ?22
42050 29347: Id : 11, {_}:
42051 additive_inverse (additive_inverse ?24) =>= ?24
42052 [24] by additive_inverse_additive_inverse ?24
42053 29347: Id : 12, {_}:
42054 multiply ?26 additive_identity =>= additive_identity
42055 [26] by multiply_additive_id1 ?26
42056 29347: Id : 13, {_}:
42057 multiply additive_identity ?28 =>= additive_identity
42058 [28] by multiply_additive_id2 ?28
42059 29347: Id : 14, {_}:
42060 multiply (additive_inverse ?30) (additive_inverse ?31)
42063 [31, 30] by product_of_inverse ?30 ?31
42064 NO CLASH, using fixed ground order
42065 29346: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
42066 29346: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
42067 29346: Id : 6, {_}:
42068 add ?13 (additive_inverse ?13) =>= additive_identity
42069 [13] by right_additive_inverse ?13
42070 29346: Id : 7, {_}:
42071 add (additive_inverse ?15) ?15 =>= additive_identity
42072 [15] by left_additive_inverse ?15
42073 29346: Id : 8, {_}:
42074 additive_inverse additive_identity =>= additive_identity
42075 [] by additive_inverse_identity
42077 29346: Id : 9, {_}:
42078 add ?18 (add (additive_inverse ?18) ?19) =>= ?19
42079 [19, 18] by property_of_inverse_and_add ?18 ?19
42080 29346: Id : 10, {_}:
42081 additive_inverse (add ?21 ?22)
42083 add (additive_inverse ?21) (additive_inverse ?22)
42084 [22, 21] by distribute_additive_inverse ?21 ?22
42085 29345: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
42086 29345: Id : 3, {_}:
42087 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
42088 [7, 6, 5] by associative_addition ?5 ?6 ?7
42089 29346: Id : 11, {_}:
42090 additive_inverse (additive_inverse ?24) =>= ?24
42091 [24] by additive_inverse_additive_inverse ?24
42092 29345: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
42093 29346: Id : 12, {_}:
42094 multiply ?26 additive_identity =>= additive_identity
42095 [26] by multiply_additive_id1 ?26
42096 29345: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
42097 29346: Id : 13, {_}:
42098 multiply additive_identity ?28 =>= additive_identity
42099 [28] by multiply_additive_id2 ?28
42100 29346: Id : 14, {_}:
42101 multiply (additive_inverse ?30) (additive_inverse ?31)
42104 [31, 30] by product_of_inverse ?30 ?31
42105 29346: Id : 15, {_}:
42106 multiply ?33 (additive_inverse ?34)
42108 additive_inverse (multiply ?33 ?34)
42109 [34, 33] by multiply_additive_inverse1 ?33 ?34
42110 29345: Id : 6, {_}:
42111 add ?13 (additive_inverse ?13) =>= additive_identity
42112 [13] by right_additive_inverse ?13
42113 29345: Id : 7, {_}:
42114 add (additive_inverse ?15) ?15 =>= additive_identity
42115 [15] by left_additive_inverse ?15
42116 29345: Id : 8, {_}:
42117 additive_inverse additive_identity =>= additive_identity
42118 [] by additive_inverse_identity
42119 29346: Id : 16, {_}:
42120 multiply (additive_inverse ?36) ?37
42122 additive_inverse (multiply ?36 ?37)
42123 [37, 36] by multiply_additive_inverse2 ?36 ?37
42124 29345: Id : 9, {_}:
42125 add ?18 (add (additive_inverse ?18) ?19) =>= ?19
42126 [19, 18] by property_of_inverse_and_add ?18 ?19
42127 29346: Id : 17, {_}:
42128 multiply ?39 (add ?40 ?41)
42130 add (multiply ?39 ?40) (multiply ?39 ?41)
42131 [41, 40, 39] by distribute1 ?39 ?40 ?41
42132 29345: Id : 10, {_}:
42133 additive_inverse (add ?21 ?22)
42135 add (additive_inverse ?21) (additive_inverse ?22)
42136 [22, 21] by distribute_additive_inverse ?21 ?22
42137 29346: Id : 18, {_}:
42138 multiply (add ?43 ?44) ?45
42140 add (multiply ?43 ?45) (multiply ?44 ?45)
42141 [45, 44, 43] by distribute2 ?43 ?44 ?45
42142 29345: Id : 11, {_}:
42143 additive_inverse (additive_inverse ?24) =>= ?24
42144 [24] by additive_inverse_additive_inverse ?24
42145 29345: Id : 12, {_}:
42146 multiply ?26 additive_identity =>= additive_identity
42147 [26] by multiply_additive_id1 ?26
42148 29345: Id : 13, {_}:
42149 multiply additive_identity ?28 =>= additive_identity
42150 [28] by multiply_additive_id2 ?28
42151 29345: Id : 14, {_}:
42152 multiply (additive_inverse ?30) (additive_inverse ?31)
42155 [31, 30] by product_of_inverse ?30 ?31
42156 29345: Id : 15, {_}:
42157 multiply ?33 (additive_inverse ?34)
42159 additive_inverse (multiply ?33 ?34)
42160 [34, 33] by multiply_additive_inverse1 ?33 ?34
42161 29345: Id : 16, {_}:
42162 multiply (additive_inverse ?36) ?37
42164 additive_inverse (multiply ?36 ?37)
42165 [37, 36] by multiply_additive_inverse2 ?36 ?37
42166 29345: Id : 17, {_}:
42167 multiply ?39 (add ?40 ?41)
42169 add (multiply ?39 ?40) (multiply ?39 ?41)
42170 [41, 40, 39] by distribute1 ?39 ?40 ?41
42171 29345: Id : 18, {_}:
42172 multiply (add ?43 ?44) ?45
42174 add (multiply ?43 ?45) (multiply ?44 ?45)
42175 [45, 44, 43] by distribute2 ?43 ?44 ?45
42176 29345: Id : 19, {_}:
42177 multiply (multiply ?47 ?48) ?48 =?= multiply ?47 (multiply ?48 ?48)
42178 [48, 47] by right_alternative ?47 ?48
42179 29347: Id : 15, {_}:
42180 multiply ?33 (additive_inverse ?34)
42182 additive_inverse (multiply ?33 ?34)
42183 [34, 33] by multiply_additive_inverse1 ?33 ?34
42184 29345: Id : 20, {_}:
42185 associator ?50 ?51 ?52
42187 add (multiply (multiply ?50 ?51) ?52)
42188 (additive_inverse (multiply ?50 (multiply ?51 ?52)))
42189 [52, 51, 50] by associator ?50 ?51 ?52
42190 29345: Id : 21, {_}:
42193 add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
42194 [55, 54] by commutator ?54 ?55
42195 29347: Id : 16, {_}:
42196 multiply (additive_inverse ?36) ?37
42198 additive_inverse (multiply ?36 ?37)
42199 [37, 36] by multiply_additive_inverse2 ?36 ?37
42200 29347: Id : 17, {_}:
42201 multiply ?39 (add ?40 ?41)
42203 add (multiply ?39 ?40) (multiply ?39 ?41)
42204 [41, 40, 39] by distribute1 ?39 ?40 ?41
42205 29347: Id : 18, {_}:
42206 multiply (add ?43 ?44) ?45
42208 add (multiply ?43 ?45) (multiply ?44 ?45)
42209 [45, 44, 43] by distribute2 ?43 ?44 ?45
42210 29347: Id : 19, {_}:
42211 multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
42212 [48, 47] by right_alternative ?47 ?48
42213 29347: Id : 20, {_}:
42214 associator ?50 ?51 ?52
42216 add (multiply (multiply ?50 ?51) ?52)
42217 (additive_inverse (multiply ?50 (multiply ?51 ?52)))
42218 [52, 51, 50] by associator ?50 ?51 ?52
42219 29347: Id : 21, {_}:
42222 add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
42223 [55, 54] by commutator ?54 ?55
42224 29347: Id : 22, {_}:
42225 multiply (multiply (associator ?57 ?57 ?58) ?57)
42226 (associator ?57 ?57 ?58)
42229 [58, 57] by middle_associator ?57 ?58
42230 29347: Id : 23, {_}:
42231 multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
42232 [61, 60] by left_alternative ?60 ?61
42233 29347: Id : 24, {_}:
42237 (add (associator (multiply ?63 ?64) ?65 ?66)
42238 (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
42239 (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
42240 [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
42241 29347: Id : 25, {_}:
42242 multiply ?68 (multiply ?69 (multiply ?70 ?69))
42244 multiply (multiply (multiply ?68 ?69) ?70) ?69
42245 [70, 69, 68] by right_moufang ?68 ?69 ?70
42246 29347: Id : 26, {_}:
42247 multiply (multiply ?72 (multiply ?73 ?72)) ?74
42249 multiply ?72 (multiply ?73 (multiply ?72 ?74))
42250 [74, 73, 72] by left_moufang ?72 ?73 ?74
42251 29347: Id : 27, {_}:
42252 multiply (multiply ?76 ?77) (multiply ?78 ?76)
42254 multiply (multiply ?76 (multiply ?77 ?78)) ?76
42255 [78, 77, 76] by middle_moufang ?76 ?77 ?78
42257 29347: Id : 1, {_}:
42258 s a b c d =>= additive_inverse (s b a c d)
42259 [] by prove_skew_symmetry
42263 29347: commutator 1 2 0
42264 29347: associator 6 3 0
42265 29347: multiply 51 2 0
42266 29347: additive_identity 11 0 0
42268 29347: additive_inverse 20 1 1 0,3
42274 29346: Id : 19, {_}:
42275 multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
42276 [48, 47] by right_alternative ?47 ?48
42277 29345: Id : 22, {_}:
42278 multiply (multiply (associator ?57 ?57 ?58) ?57)
42279 (associator ?57 ?57 ?58)
42282 [58, 57] by middle_associator ?57 ?58
42283 29345: Id : 23, {_}:
42284 multiply (multiply ?60 ?60) ?61 =?= multiply ?60 (multiply ?60 ?61)
42285 [61, 60] by left_alternative ?60 ?61
42286 29345: Id : 24, {_}:
42290 (add (associator (multiply ?63 ?64) ?65 ?66)
42291 (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
42292 (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
42293 [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
42294 29345: Id : 25, {_}:
42295 multiply ?68 (multiply ?69 (multiply ?70 ?69))
42297 multiply (multiply (multiply ?68 ?69) ?70) ?69
42298 [70, 69, 68] by right_moufang ?68 ?69 ?70
42299 29345: Id : 26, {_}:
42300 multiply (multiply ?72 (multiply ?73 ?72)) ?74
42302 multiply ?72 (multiply ?73 (multiply ?72 ?74))
42303 [74, 73, 72] by left_moufang ?72 ?73 ?74
42304 29345: Id : 27, {_}:
42305 multiply (multiply ?76 ?77) (multiply ?78 ?76)
42307 multiply (multiply ?76 (multiply ?77 ?78)) ?76
42308 [78, 77, 76] by middle_moufang ?76 ?77 ?78
42310 29345: Id : 1, {_}:
42311 s a b c d =<= additive_inverse (s b a c d)
42312 [] by prove_skew_symmetry
42316 29345: commutator 1 2 0
42317 29345: associator 6 3 0
42318 29345: multiply 51 2 0
42319 29345: additive_identity 11 0 0
42321 29345: additive_inverse 20 1 1 0,3
42327 29346: Id : 20, {_}:
42328 associator ?50 ?51 ?52
42330 add (multiply (multiply ?50 ?51) ?52)
42331 (additive_inverse (multiply ?50 (multiply ?51 ?52)))
42332 [52, 51, 50] by associator ?50 ?51 ?52
42333 29346: Id : 21, {_}:
42336 add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
42337 [55, 54] by commutator ?54 ?55
42338 29346: Id : 22, {_}:
42339 multiply (multiply (associator ?57 ?57 ?58) ?57)
42340 (associator ?57 ?57 ?58)
42343 [58, 57] by middle_associator ?57 ?58
42344 29346: Id : 23, {_}:
42345 multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
42346 [61, 60] by left_alternative ?60 ?61
42347 29346: Id : 24, {_}:
42351 (add (associator (multiply ?63 ?64) ?65 ?66)
42352 (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
42353 (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
42354 [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
42355 29346: Id : 25, {_}:
42356 multiply ?68 (multiply ?69 (multiply ?70 ?69))
42358 multiply (multiply (multiply ?68 ?69) ?70) ?69
42359 [70, 69, 68] by right_moufang ?68 ?69 ?70
42360 29346: Id : 26, {_}:
42361 multiply (multiply ?72 (multiply ?73 ?72)) ?74
42363 multiply ?72 (multiply ?73 (multiply ?72 ?74))
42364 [74, 73, 72] by left_moufang ?72 ?73 ?74
42365 29346: Id : 27, {_}:
42366 multiply (multiply ?76 ?77) (multiply ?78 ?76)
42368 multiply (multiply ?76 (multiply ?77 ?78)) ?76
42369 [78, 77, 76] by middle_moufang ?76 ?77 ?78
42371 29346: Id : 1, {_}:
42372 s a b c d =<= additive_inverse (s b a c d)
42373 [] by prove_skew_symmetry
42377 29346: commutator 1 2 0
42378 29346: associator 6 3 0
42379 29346: multiply 51 2 0
42380 29346: additive_identity 11 0 0
42382 29346: additive_inverse 20 1 1 0,3
42388 % SZS status Timeout for RNG010-5.p
42389 NO CLASH, using fixed ground order
42391 29364: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
42392 29364: Id : 3, {_}:
42393 add ?4 additive_identity =>= ?4
42394 [4] by right_additive_identity ?4
42395 29364: Id : 4, {_}:
42396 multiply additive_identity ?6 =>= additive_identity
42397 [6] by left_multiplicative_zero ?6
42398 29364: Id : 5, {_}:
42399 multiply ?8 additive_identity =>= additive_identity
42400 [8] by right_multiplicative_zero ?8
42401 29364: Id : 6, {_}:
42402 add (additive_inverse ?10) ?10 =>= additive_identity
42403 [10] by left_additive_inverse ?10
42404 29364: Id : 7, {_}:
42405 add ?12 (additive_inverse ?12) =>= additive_identity
42406 [12] by right_additive_inverse ?12
42407 29364: Id : 8, {_}:
42408 additive_inverse (additive_inverse ?14) =>= ?14
42409 [14] by additive_inverse_additive_inverse ?14
42410 29364: Id : 9, {_}:
42411 multiply ?16 (add ?17 ?18)
42413 add (multiply ?16 ?17) (multiply ?16 ?18)
42414 [18, 17, 16] by distribute1 ?16 ?17 ?18
42415 29364: Id : 10, {_}:
42416 multiply (add ?20 ?21) ?22
42418 add (multiply ?20 ?22) (multiply ?21 ?22)
42419 [22, 21, 20] by distribute2 ?20 ?21 ?22
42420 29364: Id : 11, {_}:
42421 add ?24 ?25 =?= add ?25 ?24
42422 [25, 24] by commutativity_for_addition ?24 ?25
42423 29364: Id : 12, {_}:
42424 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
42425 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
42426 29364: Id : 13, {_}:
42427 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
42428 [32, 31] by right_alternative ?31 ?32
42429 29364: Id : 14, {_}:
42430 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
42431 [35, 34] by left_alternative ?34 ?35
42432 29364: Id : 15, {_}:
42433 associator ?37 ?38 ?39
42435 add (multiply (multiply ?37 ?38) ?39)
42436 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
42437 [39, 38, 37] by associator ?37 ?38 ?39
42438 29364: Id : 16, {_}:
42441 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
42442 [42, 41] by commutator ?41 ?42
42443 29364: Id : 17, {_}:
42447 (add (associator (multiply ?44 ?45) ?46 ?47)
42448 (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
42449 (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
42450 [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
42451 29364: Id : 18, {_}:
42452 multiply ?49 (multiply ?50 (multiply ?51 ?50))
42454 multiply (multiply (multiply ?49 ?50) ?51) ?50
42455 [51, 50, 49] by right_moufang ?49 ?50 ?51
42456 29364: Id : 19, {_}:
42457 multiply (multiply ?53 (multiply ?54 ?53)) ?55
42459 multiply ?53 (multiply ?54 (multiply ?53 ?55))
42460 [55, 54, 53] by left_moufang ?53 ?54 ?55
42461 29364: Id : 20, {_}:
42462 multiply (multiply ?57 ?58) (multiply ?59 ?57)
42464 multiply (multiply ?57 (multiply ?58 ?59)) ?57
42465 [59, 58, 57] by middle_moufang ?57 ?58 ?59
42467 29364: Id : 1, {_}:
42468 s a b c d =<= additive_inverse (s b a c d)
42469 [] by prove_skew_symmetry
42473 29364: commutator 1 2 0
42474 29364: associator 4 3 0
42475 29364: multiply 43 2 0
42477 29364: additive_identity 8 0 0
42478 29364: additive_inverse 9 1 1 0,3
42484 NO CLASH, using fixed ground order
42486 29363: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
42487 29363: Id : 3, {_}:
42488 add ?4 additive_identity =>= ?4
42489 [4] by right_additive_identity ?4
42490 29363: Id : 4, {_}:
42491 multiply additive_identity ?6 =>= additive_identity
42492 [6] by left_multiplicative_zero ?6
42493 29363: Id : 5, {_}:
42494 multiply ?8 additive_identity =>= additive_identity
42495 [8] by right_multiplicative_zero ?8
42496 29363: Id : 6, {_}:
42497 add (additive_inverse ?10) ?10 =>= additive_identity
42498 [10] by left_additive_inverse ?10
42499 29363: Id : 7, {_}:
42500 add ?12 (additive_inverse ?12) =>= additive_identity
42501 [12] by right_additive_inverse ?12
42502 29363: Id : 8, {_}:
42503 additive_inverse (additive_inverse ?14) =>= ?14
42504 [14] by additive_inverse_additive_inverse ?14
42505 29363: Id : 9, {_}:
42506 multiply ?16 (add ?17 ?18)
42508 add (multiply ?16 ?17) (multiply ?16 ?18)
42509 [18, 17, 16] by distribute1 ?16 ?17 ?18
42510 29363: Id : 10, {_}:
42511 multiply (add ?20 ?21) ?22
42513 add (multiply ?20 ?22) (multiply ?21 ?22)
42514 [22, 21, 20] by distribute2 ?20 ?21 ?22
42515 29363: Id : 11, {_}:
42516 add ?24 ?25 =?= add ?25 ?24
42517 [25, 24] by commutativity_for_addition ?24 ?25
42518 29363: Id : 12, {_}:
42519 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
42520 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
42521 29363: Id : 13, {_}:
42522 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
42523 [32, 31] by right_alternative ?31 ?32
42524 29363: Id : 14, {_}:
42525 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
42526 [35, 34] by left_alternative ?34 ?35
42527 29363: Id : 15, {_}:
42528 associator ?37 ?38 ?39
42530 add (multiply (multiply ?37 ?38) ?39)
42531 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
42532 [39, 38, 37] by associator ?37 ?38 ?39
42533 29363: Id : 16, {_}:
42536 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
42537 [42, 41] by commutator ?41 ?42
42538 29363: Id : 17, {_}:
42542 (add (associator (multiply ?44 ?45) ?46 ?47)
42543 (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
42544 (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
42545 [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
42546 29363: Id : 18, {_}:
42547 multiply ?49 (multiply ?50 (multiply ?51 ?50))
42549 multiply (multiply (multiply ?49 ?50) ?51) ?50
42550 [51, 50, 49] by right_moufang ?49 ?50 ?51
42551 29363: Id : 19, {_}:
42552 multiply (multiply ?53 (multiply ?54 ?53)) ?55
42554 multiply ?53 (multiply ?54 (multiply ?53 ?55))
42555 [55, 54, 53] by left_moufang ?53 ?54 ?55
42556 29363: Id : 20, {_}:
42557 multiply (multiply ?57 ?58) (multiply ?59 ?57)
42559 multiply (multiply ?57 (multiply ?58 ?59)) ?57
42560 [59, 58, 57] by middle_moufang ?57 ?58 ?59
42562 29363: Id : 1, {_}:
42563 s a b c d =<= additive_inverse (s b a c d)
42564 [] by prove_skew_symmetry
42568 29363: commutator 1 2 0
42569 29363: associator 4 3 0
42570 29363: multiply 43 2 0
42572 29363: additive_identity 8 0 0
42573 29363: additive_inverse 9 1 1 0,3
42579 NO CLASH, using fixed ground order
42581 29365: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
42582 29365: Id : 3, {_}:
42583 add ?4 additive_identity =>= ?4
42584 [4] by right_additive_identity ?4
42585 29365: Id : 4, {_}:
42586 multiply additive_identity ?6 =>= additive_identity
42587 [6] by left_multiplicative_zero ?6
42588 29365: Id : 5, {_}:
42589 multiply ?8 additive_identity =>= additive_identity
42590 [8] by right_multiplicative_zero ?8
42591 29365: Id : 6, {_}:
42592 add (additive_inverse ?10) ?10 =>= additive_identity
42593 [10] by left_additive_inverse ?10
42594 29365: Id : 7, {_}:
42595 add ?12 (additive_inverse ?12) =>= additive_identity
42596 [12] by right_additive_inverse ?12
42597 29365: Id : 8, {_}:
42598 additive_inverse (additive_inverse ?14) =>= ?14
42599 [14] by additive_inverse_additive_inverse ?14
42600 29365: Id : 9, {_}:
42601 multiply ?16 (add ?17 ?18)
42603 add (multiply ?16 ?17) (multiply ?16 ?18)
42604 [18, 17, 16] by distribute1 ?16 ?17 ?18
42605 29365: Id : 10, {_}:
42606 multiply (add ?20 ?21) ?22
42608 add (multiply ?20 ?22) (multiply ?21 ?22)
42609 [22, 21, 20] by distribute2 ?20 ?21 ?22
42610 29365: Id : 11, {_}:
42611 add ?24 ?25 =?= add ?25 ?24
42612 [25, 24] by commutativity_for_addition ?24 ?25
42613 29365: Id : 12, {_}:
42614 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
42615 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
42616 29365: Id : 13, {_}:
42617 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
42618 [32, 31] by right_alternative ?31 ?32
42619 29365: Id : 14, {_}:
42620 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
42621 [35, 34] by left_alternative ?34 ?35
42622 29365: Id : 15, {_}:
42623 associator ?37 ?38 ?39
42625 add (multiply (multiply ?37 ?38) ?39)
42626 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
42627 [39, 38, 37] by associator ?37 ?38 ?39
42628 29365: Id : 16, {_}:
42631 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
42632 [42, 41] by commutator ?41 ?42
42633 29365: Id : 17, {_}:
42637 (add (associator (multiply ?44 ?45) ?46 ?47)
42638 (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
42639 (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
42640 [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
42641 29365: Id : 18, {_}:
42642 multiply ?49 (multiply ?50 (multiply ?51 ?50))
42644 multiply (multiply (multiply ?49 ?50) ?51) ?50
42645 [51, 50, 49] by right_moufang ?49 ?50 ?51
42646 29365: Id : 19, {_}:
42647 multiply (multiply ?53 (multiply ?54 ?53)) ?55
42649 multiply ?53 (multiply ?54 (multiply ?53 ?55))
42650 [55, 54, 53] by left_moufang ?53 ?54 ?55
42651 29365: Id : 20, {_}:
42652 multiply (multiply ?57 ?58) (multiply ?59 ?57)
42654 multiply (multiply ?57 (multiply ?58 ?59)) ?57
42655 [59, 58, 57] by middle_moufang ?57 ?58 ?59
42657 29365: Id : 1, {_}:
42658 s a b c d =>= additive_inverse (s b a c d)
42659 [] by prove_skew_symmetry
42663 29365: commutator 1 2 0
42664 29365: associator 4 3 0
42665 29365: multiply 43 2 0
42667 29365: additive_identity 8 0 0
42668 29365: additive_inverse 9 1 1 0,3
42674 % SZS status Timeout for RNG010-6.p
42675 NO CLASH, using fixed ground order
42677 29396: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
42678 29396: Id : 3, {_}:
42679 add ?4 additive_identity =>= ?4
42680 [4] by right_additive_identity ?4
42681 29396: Id : 4, {_}:
42682 multiply additive_identity ?6 =>= additive_identity
42683 [6] by left_multiplicative_zero ?6
42684 29396: Id : 5, {_}:
42685 multiply ?8 additive_identity =>= additive_identity
42686 [8] by right_multiplicative_zero ?8
42687 29396: Id : 6, {_}:
42688 add (additive_inverse ?10) ?10 =>= additive_identity
42689 [10] by left_additive_inverse ?10
42690 29396: Id : 7, {_}:
42691 add ?12 (additive_inverse ?12) =>= additive_identity
42692 [12] by right_additive_inverse ?12
42693 29396: Id : 8, {_}:
42694 additive_inverse (additive_inverse ?14) =>= ?14
42695 [14] by additive_inverse_additive_inverse ?14
42696 29396: Id : 9, {_}:
42697 multiply ?16 (add ?17 ?18)
42699 add (multiply ?16 ?17) (multiply ?16 ?18)
42700 [18, 17, 16] by distribute1 ?16 ?17 ?18
42701 29396: Id : 10, {_}:
42702 multiply (add ?20 ?21) ?22
42704 add (multiply ?20 ?22) (multiply ?21 ?22)
42705 [22, 21, 20] by distribute2 ?20 ?21 ?22
42706 29396: Id : 11, {_}:
42707 add ?24 ?25 =?= add ?25 ?24
42708 [25, 24] by commutativity_for_addition ?24 ?25
42709 29396: Id : 12, {_}:
42710 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
42711 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
42712 29396: Id : 13, {_}:
42713 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
42714 [32, 31] by right_alternative ?31 ?32
42715 29396: Id : 14, {_}:
42716 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
42717 [35, 34] by left_alternative ?34 ?35
42718 29396: Id : 15, {_}:
42719 associator ?37 ?38 ?39
42721 add (multiply (multiply ?37 ?38) ?39)
42722 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
42723 [39, 38, 37] by associator ?37 ?38 ?39
42724 29396: Id : 16, {_}:
42727 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
42728 [42, 41] by commutator ?41 ?42
42729 29396: Id : 17, {_}:
42730 multiply (additive_inverse ?44) (additive_inverse ?45)
42733 [45, 44] by product_of_inverses ?44 ?45
42734 29396: Id : 18, {_}:
42735 multiply (additive_inverse ?47) ?48
42737 additive_inverse (multiply ?47 ?48)
42738 [48, 47] by inverse_product1 ?47 ?48
42739 29396: Id : 19, {_}:
42740 multiply ?50 (additive_inverse ?51)
42742 additive_inverse (multiply ?50 ?51)
42743 [51, 50] by inverse_product2 ?50 ?51
42744 29396: Id : 20, {_}:
42745 multiply ?53 (add ?54 (additive_inverse ?55))
42747 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
42748 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
42749 29396: Id : 21, {_}:
42750 multiply (add ?57 (additive_inverse ?58)) ?59
42752 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
42753 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
42754 29396: Id : 22, {_}:
42755 multiply (additive_inverse ?61) (add ?62 ?63)
42757 add (additive_inverse (multiply ?61 ?62))
42758 (additive_inverse (multiply ?61 ?63))
42759 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
42760 29396: Id : 23, {_}:
42761 multiply (add ?65 ?66) (additive_inverse ?67)
42763 add (additive_inverse (multiply ?65 ?67))
42764 (additive_inverse (multiply ?66 ?67))
42765 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
42766 29396: Id : 24, {_}:
42770 (add (associator (multiply ?69 ?70) ?71 ?72)
42771 (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
42772 (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
42773 [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
42774 29396: Id : 25, {_}:
42775 multiply ?74 (multiply ?75 (multiply ?76 ?75))
42777 multiply (multiply (multiply ?74 ?75) ?76) ?75
42778 [76, 75, 74] by right_moufang ?74 ?75 ?76
42779 29396: Id : 26, {_}:
42780 multiply (multiply ?78 (multiply ?79 ?78)) ?80
42782 multiply ?78 (multiply ?79 (multiply ?78 ?80))
42783 [80, 79, 78] by left_moufang ?78 ?79 ?80
42784 29396: Id : 27, {_}:
42785 multiply (multiply ?82 ?83) (multiply ?84 ?82)
42787 multiply (multiply ?82 (multiply ?83 ?84)) ?82
42788 [84, 83, 82] by middle_moufang ?82 ?83 ?84
42790 29396: Id : 1, {_}:
42791 s a b c d =<= additive_inverse (s b a c d)
42792 [] by prove_skew_symmetry
42796 29396: commutator 1 2 0
42797 29396: associator 4 3 0
42798 29396: multiply 61 2 0
42800 29396: additive_identity 8 0 0
42801 29396: additive_inverse 25 1 1 0,3
42807 NO CLASH, using fixed ground order
42809 29397: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
42810 29397: Id : 3, {_}:
42811 add ?4 additive_identity =>= ?4
42812 [4] by right_additive_identity ?4
42813 29397: Id : 4, {_}:
42814 multiply additive_identity ?6 =>= additive_identity
42815 [6] by left_multiplicative_zero ?6
42816 29397: Id : 5, {_}:
42817 multiply ?8 additive_identity =>= additive_identity
42818 [8] by right_multiplicative_zero ?8
42819 29397: Id : 6, {_}:
42820 add (additive_inverse ?10) ?10 =>= additive_identity
42821 [10] by left_additive_inverse ?10
42822 29397: Id : 7, {_}:
42823 add ?12 (additive_inverse ?12) =>= additive_identity
42824 [12] by right_additive_inverse ?12
42825 29397: Id : 8, {_}:
42826 additive_inverse (additive_inverse ?14) =>= ?14
42827 [14] by additive_inverse_additive_inverse ?14
42828 29397: Id : 9, {_}:
42829 multiply ?16 (add ?17 ?18)
42831 add (multiply ?16 ?17) (multiply ?16 ?18)
42832 [18, 17, 16] by distribute1 ?16 ?17 ?18
42833 29397: Id : 10, {_}:
42834 multiply (add ?20 ?21) ?22
42836 add (multiply ?20 ?22) (multiply ?21 ?22)
42837 [22, 21, 20] by distribute2 ?20 ?21 ?22
42838 29397: Id : 11, {_}:
42839 add ?24 ?25 =?= add ?25 ?24
42840 [25, 24] by commutativity_for_addition ?24 ?25
42841 29397: Id : 12, {_}:
42842 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
42843 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
42844 29397: Id : 13, {_}:
42845 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
42846 [32, 31] by right_alternative ?31 ?32
42847 29397: Id : 14, {_}:
42848 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
42849 [35, 34] by left_alternative ?34 ?35
42850 29397: Id : 15, {_}:
42851 associator ?37 ?38 ?39
42853 add (multiply (multiply ?37 ?38) ?39)
42854 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
42855 [39, 38, 37] by associator ?37 ?38 ?39
42856 29397: Id : 16, {_}:
42859 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
42860 [42, 41] by commutator ?41 ?42
42861 29397: Id : 17, {_}:
42862 multiply (additive_inverse ?44) (additive_inverse ?45)
42865 [45, 44] by product_of_inverses ?44 ?45
42866 29397: Id : 18, {_}:
42867 multiply (additive_inverse ?47) ?48
42869 additive_inverse (multiply ?47 ?48)
42870 [48, 47] by inverse_product1 ?47 ?48
42871 29397: Id : 19, {_}:
42872 multiply ?50 (additive_inverse ?51)
42874 additive_inverse (multiply ?50 ?51)
42875 [51, 50] by inverse_product2 ?50 ?51
42876 29397: Id : 20, {_}:
42877 multiply ?53 (add ?54 (additive_inverse ?55))
42879 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
42880 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
42881 29397: Id : 21, {_}:
42882 multiply (add ?57 (additive_inverse ?58)) ?59
42884 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
42885 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
42886 29397: Id : 22, {_}:
42887 multiply (additive_inverse ?61) (add ?62 ?63)
42889 add (additive_inverse (multiply ?61 ?62))
42890 (additive_inverse (multiply ?61 ?63))
42891 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
42892 29397: Id : 23, {_}:
42893 multiply (add ?65 ?66) (additive_inverse ?67)
42895 add (additive_inverse (multiply ?65 ?67))
42896 (additive_inverse (multiply ?66 ?67))
42897 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
42898 29397: Id : 24, {_}:
42902 (add (associator (multiply ?69 ?70) ?71 ?72)
42903 (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
42904 (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
42905 [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
42906 29397: Id : 25, {_}:
42907 multiply ?74 (multiply ?75 (multiply ?76 ?75))
42909 multiply (multiply (multiply ?74 ?75) ?76) ?75
42910 [76, 75, 74] by right_moufang ?74 ?75 ?76
42911 29397: Id : 26, {_}:
42912 multiply (multiply ?78 (multiply ?79 ?78)) ?80
42914 multiply ?78 (multiply ?79 (multiply ?78 ?80))
42915 [80, 79, 78] by left_moufang ?78 ?79 ?80
42916 29397: Id : 27, {_}:
42917 multiply (multiply ?82 ?83) (multiply ?84 ?82)
42919 multiply (multiply ?82 (multiply ?83 ?84)) ?82
42920 [84, 83, 82] by middle_moufang ?82 ?83 ?84
42922 29397: Id : 1, {_}:
42923 s a b c d =<= additive_inverse (s b a c d)
42924 [] by prove_skew_symmetry
42928 29397: commutator 1 2 0
42929 29397: associator 4 3 0
42930 29397: multiply 61 2 0
42932 29397: additive_identity 8 0 0
42933 29397: additive_inverse 25 1 1 0,3
42939 NO CLASH, using fixed ground order
42941 29398: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
42942 29398: Id : 3, {_}:
42943 add ?4 additive_identity =>= ?4
42944 [4] by right_additive_identity ?4
42945 29398: Id : 4, {_}:
42946 multiply additive_identity ?6 =>= additive_identity
42947 [6] by left_multiplicative_zero ?6
42948 29398: Id : 5, {_}:
42949 multiply ?8 additive_identity =>= additive_identity
42950 [8] by right_multiplicative_zero ?8
42951 29398: Id : 6, {_}:
42952 add (additive_inverse ?10) ?10 =>= additive_identity
42953 [10] by left_additive_inverse ?10
42954 29398: Id : 7, {_}:
42955 add ?12 (additive_inverse ?12) =>= additive_identity
42956 [12] by right_additive_inverse ?12
42957 29398: Id : 8, {_}:
42958 additive_inverse (additive_inverse ?14) =>= ?14
42959 [14] by additive_inverse_additive_inverse ?14
42960 29398: Id : 9, {_}:
42961 multiply ?16 (add ?17 ?18)
42963 add (multiply ?16 ?17) (multiply ?16 ?18)
42964 [18, 17, 16] by distribute1 ?16 ?17 ?18
42965 29398: Id : 10, {_}:
42966 multiply (add ?20 ?21) ?22
42968 add (multiply ?20 ?22) (multiply ?21 ?22)
42969 [22, 21, 20] by distribute2 ?20 ?21 ?22
42970 29398: Id : 11, {_}:
42971 add ?24 ?25 =?= add ?25 ?24
42972 [25, 24] by commutativity_for_addition ?24 ?25
42973 29398: Id : 12, {_}:
42974 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
42975 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
42976 29398: Id : 13, {_}:
42977 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
42978 [32, 31] by right_alternative ?31 ?32
42979 29398: Id : 14, {_}:
42980 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
42981 [35, 34] by left_alternative ?34 ?35
42982 29398: Id : 15, {_}:
42983 associator ?37 ?38 ?39
42985 add (multiply (multiply ?37 ?38) ?39)
42986 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
42987 [39, 38, 37] by associator ?37 ?38 ?39
42988 29398: Id : 16, {_}:
42991 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
42992 [42, 41] by commutator ?41 ?42
42993 29398: Id : 17, {_}:
42994 multiply (additive_inverse ?44) (additive_inverse ?45)
42997 [45, 44] by product_of_inverses ?44 ?45
42998 29398: Id : 18, {_}:
42999 multiply (additive_inverse ?47) ?48
43001 additive_inverse (multiply ?47 ?48)
43002 [48, 47] by inverse_product1 ?47 ?48
43003 29398: Id : 19, {_}:
43004 multiply ?50 (additive_inverse ?51)
43006 additive_inverse (multiply ?50 ?51)
43007 [51, 50] by inverse_product2 ?50 ?51
43008 29398: Id : 20, {_}:
43009 multiply ?53 (add ?54 (additive_inverse ?55))
43011 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
43012 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
43013 29398: Id : 21, {_}:
43014 multiply (add ?57 (additive_inverse ?58)) ?59
43016 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
43017 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
43018 29398: Id : 22, {_}:
43019 multiply (additive_inverse ?61) (add ?62 ?63)
43021 add (additive_inverse (multiply ?61 ?62))
43022 (additive_inverse (multiply ?61 ?63))
43023 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
43024 29398: Id : 23, {_}:
43025 multiply (add ?65 ?66) (additive_inverse ?67)
43027 add (additive_inverse (multiply ?65 ?67))
43028 (additive_inverse (multiply ?66 ?67))
43029 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
43030 29398: Id : 24, {_}:
43034 (add (associator (multiply ?69 ?70) ?71 ?72)
43035 (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
43036 (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
43037 [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
43038 29398: Id : 25, {_}:
43039 multiply ?74 (multiply ?75 (multiply ?76 ?75))
43041 multiply (multiply (multiply ?74 ?75) ?76) ?75
43042 [76, 75, 74] by right_moufang ?74 ?75 ?76
43043 29398: Id : 26, {_}:
43044 multiply (multiply ?78 (multiply ?79 ?78)) ?80
43046 multiply ?78 (multiply ?79 (multiply ?78 ?80))
43047 [80, 79, 78] by left_moufang ?78 ?79 ?80
43048 29398: Id : 27, {_}:
43049 multiply (multiply ?82 ?83) (multiply ?84 ?82)
43051 multiply (multiply ?82 (multiply ?83 ?84)) ?82
43052 [84, 83, 82] by middle_moufang ?82 ?83 ?84
43054 29398: Id : 1, {_}:
43055 s a b c d =>= additive_inverse (s b a c d)
43056 [] by prove_skew_symmetry
43060 29398: commutator 1 2 0
43061 29398: associator 4 3 0
43062 29398: multiply 61 2 0
43064 29398: additive_identity 8 0 0
43065 29398: additive_inverse 25 1 1 0,3
43071 % SZS status Timeout for RNG010-7.p
43072 NO CLASH, using fixed ground order
43074 29437: Id : 2, {_}:
43075 add ?2 ?3 =?= add ?3 ?2
43076 [3, 2] by commutativity_for_addition ?2 ?3
43077 29437: Id : 3, {_}:
43078 add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
43079 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
43080 29437: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
43081 29437: Id : 5, {_}:
43082 add ?11 additive_identity =>= ?11
43083 [11] by right_additive_identity ?11
43084 29437: Id : 6, {_}:
43085 multiply additive_identity ?13 =>= additive_identity
43086 [13] by left_multiplicative_zero ?13
43087 29437: Id : 7, {_}:
43088 multiply ?15 additive_identity =>= additive_identity
43089 [15] by right_multiplicative_zero ?15
43090 29437: Id : 8, {_}:
43091 add (additive_inverse ?17) ?17 =>= additive_identity
43092 [17] by left_additive_inverse ?17
43093 29437: Id : 9, {_}:
43094 add ?19 (additive_inverse ?19) =>= additive_identity
43095 [19] by right_additive_inverse ?19
43096 29437: Id : 10, {_}:
43097 multiply ?21 (add ?22 ?23)
43099 add (multiply ?21 ?22) (multiply ?21 ?23)
43100 [23, 22, 21] by distribute1 ?21 ?22 ?23
43101 29437: Id : 11, {_}:
43102 multiply (add ?25 ?26) ?27
43104 add (multiply ?25 ?27) (multiply ?26 ?27)
43105 [27, 26, 25] by distribute2 ?25 ?26 ?27
43106 29437: Id : 12, {_}:
43107 additive_inverse (additive_inverse ?29) =>= ?29
43108 [29] by additive_inverse_additive_inverse ?29
43109 29437: Id : 13, {_}:
43110 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
43111 [32, 31] by right_alternative ?31 ?32
43112 29437: Id : 14, {_}:
43113 associator ?34 ?35 ?36
43115 add (multiply (multiply ?34 ?35) ?36)
43116 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
43117 [36, 35, 34] by associator ?34 ?35 ?36
43118 29437: Id : 15, {_}:
43121 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
43122 [39, 38] by commutator ?38 ?39
43124 29437: Id : 1, {_}:
43126 (multiply (associator x x y)
43127 (multiply (associator x x y) (associator x x y)))
43128 (multiply (associator x x y)
43129 (multiply (associator x x y) (associator x x y)))
43132 [] by prove_conjecture_1
43136 29437: commutator 1 2 0
43137 29437: additive_inverse 6 1 0
43138 29437: additive_identity 9 0 1 3
43139 29437: add 17 2 1 0,2
43140 29437: multiply 22 2 4 0,1,2
43141 29437: associator 7 3 6 0,1,1,2
43142 29437: y 6 0 6 3,1,1,2
43143 29437: x 12 0 12 1,1,1,2
43144 NO CLASH, using fixed ground order
43146 29438: Id : 2, {_}:
43147 add ?2 ?3 =?= add ?3 ?2
43148 [3, 2] by commutativity_for_addition ?2 ?3
43149 29438: Id : 3, {_}:
43150 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
43151 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
43152 29438: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
43153 29438: Id : 5, {_}:
43154 add ?11 additive_identity =>= ?11
43155 [11] by right_additive_identity ?11
43156 29438: Id : 6, {_}:
43157 multiply additive_identity ?13 =>= additive_identity
43158 [13] by left_multiplicative_zero ?13
43159 29438: Id : 7, {_}:
43160 multiply ?15 additive_identity =>= additive_identity
43161 [15] by right_multiplicative_zero ?15
43162 29438: Id : 8, {_}:
43163 add (additive_inverse ?17) ?17 =>= additive_identity
43164 [17] by left_additive_inverse ?17
43165 29438: Id : 9, {_}:
43166 add ?19 (additive_inverse ?19) =>= additive_identity
43167 [19] by right_additive_inverse ?19
43168 29438: Id : 10, {_}:
43169 multiply ?21 (add ?22 ?23)
43171 add (multiply ?21 ?22) (multiply ?21 ?23)
43172 [23, 22, 21] by distribute1 ?21 ?22 ?23
43173 29438: Id : 11, {_}:
43174 multiply (add ?25 ?26) ?27
43176 add (multiply ?25 ?27) (multiply ?26 ?27)
43177 [27, 26, 25] by distribute2 ?25 ?26 ?27
43178 29438: Id : 12, {_}:
43179 additive_inverse (additive_inverse ?29) =>= ?29
43180 [29] by additive_inverse_additive_inverse ?29
43181 29438: Id : 13, {_}:
43182 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
43183 [32, 31] by right_alternative ?31 ?32
43184 29438: Id : 14, {_}:
43185 associator ?34 ?35 ?36
43187 add (multiply (multiply ?34 ?35) ?36)
43188 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
43189 [36, 35, 34] by associator ?34 ?35 ?36
43190 29438: Id : 15, {_}:
43193 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
43194 [39, 38] by commutator ?38 ?39
43196 29438: Id : 1, {_}:
43198 (multiply (associator x x y)
43199 (multiply (associator x x y) (associator x x y)))
43200 (multiply (associator x x y)
43201 (multiply (associator x x y) (associator x x y)))
43204 [] by prove_conjecture_1
43208 29438: commutator 1 2 0
43209 29438: additive_inverse 6 1 0
43210 29438: additive_identity 9 0 1 3
43211 29438: add 17 2 1 0,2
43212 29438: multiply 22 2 4 0,1,2
43213 29438: associator 7 3 6 0,1,1,2
43214 29438: y 6 0 6 3,1,1,2
43215 29438: x 12 0 12 1,1,1,2
43216 NO CLASH, using fixed ground order
43218 29439: Id : 2, {_}:
43219 add ?2 ?3 =?= add ?3 ?2
43220 [3, 2] by commutativity_for_addition ?2 ?3
43221 29439: Id : 3, {_}:
43222 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
43223 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
43224 29439: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
43225 29439: Id : 5, {_}:
43226 add ?11 additive_identity =>= ?11
43227 [11] by right_additive_identity ?11
43228 29439: Id : 6, {_}:
43229 multiply additive_identity ?13 =>= additive_identity
43230 [13] by left_multiplicative_zero ?13
43231 29439: Id : 7, {_}:
43232 multiply ?15 additive_identity =>= additive_identity
43233 [15] by right_multiplicative_zero ?15
43234 29439: Id : 8, {_}:
43235 add (additive_inverse ?17) ?17 =>= additive_identity
43236 [17] by left_additive_inverse ?17
43237 29439: Id : 9, {_}:
43238 add ?19 (additive_inverse ?19) =>= additive_identity
43239 [19] by right_additive_inverse ?19
43240 29439: Id : 10, {_}:
43241 multiply ?21 (add ?22 ?23)
43243 add (multiply ?21 ?22) (multiply ?21 ?23)
43244 [23, 22, 21] by distribute1 ?21 ?22 ?23
43245 29439: Id : 11, {_}:
43246 multiply (add ?25 ?26) ?27
43248 add (multiply ?25 ?27) (multiply ?26 ?27)
43249 [27, 26, 25] by distribute2 ?25 ?26 ?27
43250 29439: Id : 12, {_}:
43251 additive_inverse (additive_inverse ?29) =>= ?29
43252 [29] by additive_inverse_additive_inverse ?29
43253 29439: Id : 13, {_}:
43254 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
43255 [32, 31] by right_alternative ?31 ?32
43256 29439: Id : 14, {_}:
43257 associator ?34 ?35 ?36
43259 add (multiply (multiply ?34 ?35) ?36)
43260 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
43261 [36, 35, 34] by associator ?34 ?35 ?36
43262 29439: Id : 15, {_}:
43265 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
43266 [39, 38] by commutator ?38 ?39
43268 29439: Id : 1, {_}:
43270 (multiply (associator x x y)
43271 (multiply (associator x x y) (associator x x y)))
43272 (multiply (associator x x y)
43273 (multiply (associator x x y) (associator x x y)))
43276 [] by prove_conjecture_1
43280 29439: commutator 1 2 0
43281 29439: additive_inverse 6 1 0
43282 29439: additive_identity 9 0 1 3
43283 29439: add 17 2 1 0,2
43284 29439: multiply 22 2 4 0,1,2
43285 29439: associator 7 3 6 0,1,1,2
43286 29439: y 6 0 6 3,1,1,2
43287 29439: x 12 0 12 1,1,1,2
43288 % SZS status Timeout for RNG030-6.p
43289 NO CLASH, using fixed ground order
43291 29722: Id : 2, {_}:
43292 multiply (additive_inverse ?2) (additive_inverse ?3)
43295 [3, 2] by product_of_inverses ?2 ?3
43296 29722: Id : 3, {_}:
43297 multiply (additive_inverse ?5) ?6
43299 additive_inverse (multiply ?5 ?6)
43300 [6, 5] by inverse_product1 ?5 ?6
43301 29722: Id : 4, {_}:
43302 multiply ?8 (additive_inverse ?9)
43304 additive_inverse (multiply ?8 ?9)
43305 [9, 8] by inverse_product2 ?8 ?9
43306 29722: Id : 5, {_}:
43307 multiply ?11 (add ?12 (additive_inverse ?13))
43309 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
43310 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
43311 29722: Id : 6, {_}:
43312 multiply (add ?15 (additive_inverse ?16)) ?17
43314 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
43315 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
43316 29722: Id : 7, {_}:
43317 multiply (additive_inverse ?19) (add ?20 ?21)
43319 add (additive_inverse (multiply ?19 ?20))
43320 (additive_inverse (multiply ?19 ?21))
43321 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
43322 29722: Id : 8, {_}:
43323 multiply (add ?23 ?24) (additive_inverse ?25)
43325 add (additive_inverse (multiply ?23 ?25))
43326 (additive_inverse (multiply ?24 ?25))
43327 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
43328 29722: Id : 9, {_}:
43329 add ?27 ?28 =?= add ?28 ?27
43330 [28, 27] by commutativity_for_addition ?27 ?28
43331 29722: Id : 10, {_}:
43332 add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
43333 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
43334 29722: Id : 11, {_}:
43335 add additive_identity ?34 =>= ?34
43336 [34] by left_additive_identity ?34
43337 29722: Id : 12, {_}:
43338 add ?36 additive_identity =>= ?36
43339 [36] by right_additive_identity ?36
43340 29722: Id : 13, {_}:
43341 multiply additive_identity ?38 =>= additive_identity
43342 [38] by left_multiplicative_zero ?38
43343 29722: Id : 14, {_}:
43344 multiply ?40 additive_identity =>= additive_identity
43345 [40] by right_multiplicative_zero ?40
43346 29722: Id : 15, {_}:
43347 add (additive_inverse ?42) ?42 =>= additive_identity
43348 [42] by left_additive_inverse ?42
43349 29722: Id : 16, {_}:
43350 add ?44 (additive_inverse ?44) =>= additive_identity
43351 [44] by right_additive_inverse ?44
43352 29722: Id : 17, {_}:
43353 multiply ?46 (add ?47 ?48)
43355 add (multiply ?46 ?47) (multiply ?46 ?48)
43356 [48, 47, 46] by distribute1 ?46 ?47 ?48
43357 29722: Id : 18, {_}:
43358 multiply (add ?50 ?51) ?52
43360 add (multiply ?50 ?52) (multiply ?51 ?52)
43361 [52, 51, 50] by distribute2 ?50 ?51 ?52
43362 29722: Id : 19, {_}:
43363 additive_inverse (additive_inverse ?54) =>= ?54
43364 [54] by additive_inverse_additive_inverse ?54
43365 29722: Id : 20, {_}:
43366 multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
43367 [57, 56] by right_alternative ?56 ?57
43368 29722: Id : 21, {_}:
43369 associator ?59 ?60 ?61
43371 add (multiply (multiply ?59 ?60) ?61)
43372 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
43373 [61, 60, 59] by associator ?59 ?60 ?61
43374 29722: Id : 22, {_}:
43377 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
43378 [64, 63] by commutator ?63 ?64
43380 29722: Id : 1, {_}:
43382 (multiply (associator x x y)
43383 (multiply (associator x x y) (associator x x y)))
43384 (multiply (associator x x y)
43385 (multiply (associator x x y) (associator x x y)))
43388 [] by prove_conjecture_1
43392 29722: commutator 1 2 0
43393 29722: additive_inverse 22 1 0
43394 29722: additive_identity 9 0 1 3
43395 29722: add 25 2 1 0,2
43396 29722: multiply 40 2 4 0,1,2add
43397 29722: associator 7 3 6 0,1,1,2
43398 29722: y 6 0 6 3,1,1,2
43399 29722: x 12 0 12 1,1,1,2
43400 NO CLASH, using fixed ground order
43402 29723: Id : 2, {_}:
43403 multiply (additive_inverse ?2) (additive_inverse ?3)
43406 [3, 2] by product_of_inverses ?2 ?3
43407 29723: Id : 3, {_}:
43408 multiply (additive_inverse ?5) ?6
43410 additive_inverse (multiply ?5 ?6)
43411 [6, 5] by inverse_product1 ?5 ?6
43412 29723: Id : 4, {_}:
43413 multiply ?8 (additive_inverse ?9)
43415 additive_inverse (multiply ?8 ?9)
43416 [9, 8] by inverse_product2 ?8 ?9
43417 29723: Id : 5, {_}:
43418 multiply ?11 (add ?12 (additive_inverse ?13))
43420 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
43421 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
43422 29723: Id : 6, {_}:
43423 multiply (add ?15 (additive_inverse ?16)) ?17
43425 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
43426 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
43427 29723: Id : 7, {_}:
43428 multiply (additive_inverse ?19) (add ?20 ?21)
43430 add (additive_inverse (multiply ?19 ?20))
43431 (additive_inverse (multiply ?19 ?21))
43432 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
43433 29723: Id : 8, {_}:
43434 multiply (add ?23 ?24) (additive_inverse ?25)
43436 add (additive_inverse (multiply ?23 ?25))
43437 (additive_inverse (multiply ?24 ?25))
43438 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
43439 29723: Id : 9, {_}:
43440 add ?27 ?28 =?= add ?28 ?27
43441 [28, 27] by commutativity_for_addition ?27 ?28
43442 29723: Id : 10, {_}:
43443 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
43444 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
43445 29723: Id : 11, {_}:
43446 add additive_identity ?34 =>= ?34
43447 [34] by left_additive_identity ?34
43448 29723: Id : 12, {_}:
43449 add ?36 additive_identity =>= ?36
43450 [36] by right_additive_identity ?36
43451 29723: Id : 13, {_}:
43452 multiply additive_identity ?38 =>= additive_identity
43453 [38] by left_multiplicative_zero ?38
43454 29723: Id : 14, {_}:
43455 multiply ?40 additive_identity =>= additive_identity
43456 [40] by right_multiplicative_zero ?40
43457 29723: Id : 15, {_}:
43458 add (additive_inverse ?42) ?42 =>= additive_identity
43459 [42] by left_additive_inverse ?42
43460 29723: Id : 16, {_}:
43461 add ?44 (additive_inverse ?44) =>= additive_identity
43462 [44] by right_additive_inverse ?44
43463 29723: Id : 17, {_}:
43464 multiply ?46 (add ?47 ?48)
43466 add (multiply ?46 ?47) (multiply ?46 ?48)
43467 [48, 47, 46] by distribute1 ?46 ?47 ?48
43468 29723: Id : 18, {_}:
43469 multiply (add ?50 ?51) ?52
43471 add (multiply ?50 ?52) (multiply ?51 ?52)
43472 [52, 51, 50] by distribute2 ?50 ?51 ?52
43473 29723: Id : 19, {_}:
43474 additive_inverse (additive_inverse ?54) =>= ?54
43475 [54] by additive_inverse_additive_inverse ?54
43476 29723: Id : 20, {_}:
43477 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
43478 [57, 56] by right_alternative ?56 ?57
43479 29723: Id : 21, {_}:
43480 associator ?59 ?60 ?61
43482 add (multiply (multiply ?59 ?60) ?61)
43483 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
43484 [61, 60, 59] by associator ?59 ?60 ?61
43485 29723: Id : 22, {_}:
43488 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
43489 [64, 63] by commutator ?63 ?64
43491 29723: Id : 1, {_}:
43493 (multiply (associator x x y)
43494 (multiply (associator x x y) (associator x x y)))
43495 (multiply (associator x x y)
43496 (multiply (associator x x y) (associator x x y)))
43499 [] by prove_conjecture_1
43503 29723: commutator 1 2 0
43504 29723: additive_inverse 22 1 0
43505 29723: additive_identity 9 0 1 3
43506 29723: add 25 2 1 0,2
43507 29723: multiply 40 2 4 0,1,2add
43508 29723: associator 7 3 6 0,1,1,2
43509 29723: y 6 0 6 3,1,1,2
43510 29723: x 12 0 12 1,1,1,2
43511 NO CLASH, using fixed ground order
43513 29724: Id : 2, {_}:
43514 multiply (additive_inverse ?2) (additive_inverse ?3)
43517 [3, 2] by product_of_inverses ?2 ?3
43518 29724: Id : 3, {_}:
43519 multiply (additive_inverse ?5) ?6
43521 additive_inverse (multiply ?5 ?6)
43522 [6, 5] by inverse_product1 ?5 ?6
43523 29724: Id : 4, {_}:
43524 multiply ?8 (additive_inverse ?9)
43526 additive_inverse (multiply ?8 ?9)
43527 [9, 8] by inverse_product2 ?8 ?9
43528 29724: Id : 5, {_}:
43529 multiply ?11 (add ?12 (additive_inverse ?13))
43531 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
43532 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
43533 29724: Id : 6, {_}:
43534 multiply (add ?15 (additive_inverse ?16)) ?17
43536 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
43537 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
43538 29724: Id : 7, {_}:
43539 multiply (additive_inverse ?19) (add ?20 ?21)
43541 add (additive_inverse (multiply ?19 ?20))
43542 (additive_inverse (multiply ?19 ?21))
43543 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
43544 29724: Id : 8, {_}:
43545 multiply (add ?23 ?24) (additive_inverse ?25)
43547 add (additive_inverse (multiply ?23 ?25))
43548 (additive_inverse (multiply ?24 ?25))
43549 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
43550 29724: Id : 9, {_}:
43551 add ?27 ?28 =?= add ?28 ?27
43552 [28, 27] by commutativity_for_addition ?27 ?28
43553 29724: Id : 10, {_}:
43554 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
43555 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
43556 29724: Id : 11, {_}:
43557 add additive_identity ?34 =>= ?34
43558 [34] by left_additive_identity ?34
43559 29724: Id : 12, {_}:
43560 add ?36 additive_identity =>= ?36
43561 [36] by right_additive_identity ?36
43562 29724: Id : 13, {_}:
43563 multiply additive_identity ?38 =>= additive_identity
43564 [38] by left_multiplicative_zero ?38
43565 29724: Id : 14, {_}:
43566 multiply ?40 additive_identity =>= additive_identity
43567 [40] by right_multiplicative_zero ?40
43568 29724: Id : 15, {_}:
43569 add (additive_inverse ?42) ?42 =>= additive_identity
43570 [42] by left_additive_inverse ?42
43571 29724: Id : 16, {_}:
43572 add ?44 (additive_inverse ?44) =>= additive_identity
43573 [44] by right_additive_inverse ?44
43574 29724: Id : 17, {_}:
43575 multiply ?46 (add ?47 ?48)
43577 add (multiply ?46 ?47) (multiply ?46 ?48)
43578 [48, 47, 46] by distribute1 ?46 ?47 ?48
43579 29724: Id : 18, {_}:
43580 multiply (add ?50 ?51) ?52
43582 add (multiply ?50 ?52) (multiply ?51 ?52)
43583 [52, 51, 50] by distribute2 ?50 ?51 ?52
43584 29724: Id : 19, {_}:
43585 additive_inverse (additive_inverse ?54) =>= ?54
43586 [54] by additive_inverse_additive_inverse ?54
43587 29724: Id : 20, {_}:
43588 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
43589 [57, 56] by right_alternative ?56 ?57
43590 29724: Id : 21, {_}:
43591 associator ?59 ?60 ?61
43593 add (multiply (multiply ?59 ?60) ?61)
43594 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
43595 [61, 60, 59] by associator ?59 ?60 ?61
43596 29724: Id : 22, {_}:
43599 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
43600 [64, 63] by commutator ?63 ?64
43602 29724: Id : 1, {_}:
43604 (multiply (associator x x y)
43605 (multiply (associator x x y) (associator x x y)))
43606 (multiply (associator x x y)
43607 (multiply (associator x x y) (associator x x y)))
43610 [] by prove_conjecture_1
43614 29724: commutator 1 2 0
43615 29724: additive_inverse 22 1 0
43616 29724: additive_identity 9 0 1 3
43617 29724: add 25 2 1 0,2
43618 29724: multiply 40 2 4 0,1,2add
43619 29724: associator 7 3 6 0,1,1,2
43620 29724: y 6 0 6 3,1,1,2
43621 29724: x 12 0 12 1,1,1,2
43622 % SZS status Timeout for RNG030-7.p
43623 NO CLASH, using fixed ground order
43625 29762: Id : 2, {_}:
43626 add ?2 ?3 =?= add ?3 ?2
43627 [3, 2] by commutativity_for_addition ?2 ?3
43628 29762: Id : 3, {_}:
43629 add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
43630 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
43631 29762: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
43632 29762: Id : 5, {_}:
43633 add ?11 additive_identity =>= ?11
43634 [11] by right_additive_identity ?11
43635 29762: Id : 6, {_}:
43636 multiply additive_identity ?13 =>= additive_identity
43637 [13] by left_multiplicative_zero ?13
43638 29762: Id : 7, {_}:
43639 multiply ?15 additive_identity =>= additive_identity
43640 [15] by right_multiplicative_zero ?15
43641 29762: Id : 8, {_}:
43642 add (additive_inverse ?17) ?17 =>= additive_identity
43643 [17] by left_additive_inverse ?17
43644 29762: Id : 9, {_}:
43645 add ?19 (additive_inverse ?19) =>= additive_identity
43646 [19] by right_additive_inverse ?19
43647 29762: Id : 10, {_}:
43648 multiply ?21 (add ?22 ?23)
43650 add (multiply ?21 ?22) (multiply ?21 ?23)
43651 [23, 22, 21] by distribute1 ?21 ?22 ?23
43652 29762: Id : 11, {_}:
43653 multiply (add ?25 ?26) ?27
43655 add (multiply ?25 ?27) (multiply ?26 ?27)
43656 [27, 26, 25] by distribute2 ?25 ?26 ?27
43657 29762: Id : 12, {_}:
43658 additive_inverse (additive_inverse ?29) =>= ?29
43659 [29] by additive_inverse_additive_inverse ?29
43660 29762: Id : 13, {_}:
43661 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
43662 [32, 31] by right_alternative ?31 ?32
43663 29762: Id : 14, {_}:
43664 associator ?34 ?35 ?36
43666 add (multiply (multiply ?34 ?35) ?36)
43667 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
43668 [36, 35, 34] by associator ?34 ?35 ?36
43669 29762: Id : 15, {_}:
43672 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
43673 [39, 38] by commutator ?38 ?39
43675 29762: Id : 1, {_}:
43681 (multiply (associator x x y)
43682 (multiply (associator x x y) (associator x x y)))
43683 (multiply (associator x x y)
43684 (multiply (associator x x y) (associator x x y))))
43685 (multiply (associator x x y)
43686 (multiply (associator x x y) (associator x x y))))
43687 (multiply (associator x x y)
43688 (multiply (associator x x y) (associator x x y))))
43689 (multiply (associator x x y)
43690 (multiply (associator x x y) (associator x x y))))
43691 (multiply (associator x x y)
43692 (multiply (associator x x y) (associator x x y)))
43695 [] by prove_conjecture_3
43699 29762: commutator 1 2 0
43700 29762: additive_inverse 6 1 0
43701 29762: additive_identity 9 0 1 3
43702 29762: add 21 2 5 0,2
43703 29762: multiply 30 2 12 0,1,1,1,1,1,2
43704 29762: associator 19 3 18 0,1,1,1,1,1,1,2
43705 29762: y 18 0 18 3,1,1,1,1,1,1,2
43706 29762: x 36 0 36 1,1,1,1,1,1,1,2
43707 NO CLASH, using fixed ground order
43709 29763: Id : 2, {_}:
43710 add ?2 ?3 =?= add ?3 ?2
43711 [3, 2] by commutativity_for_addition ?2 ?3
43712 29763: Id : 3, {_}:
43713 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
43714 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
43715 29763: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
43716 29763: Id : 5, {_}:
43717 add ?11 additive_identity =>= ?11
43718 [11] by right_additive_identity ?11
43719 29763: Id : 6, {_}:
43720 multiply additive_identity ?13 =>= additive_identity
43721 [13] by left_multiplicative_zero ?13
43722 29763: Id : 7, {_}:
43723 multiply ?15 additive_identity =>= additive_identity
43724 [15] by right_multiplicative_zero ?15
43725 29763: Id : 8, {_}:
43726 add (additive_inverse ?17) ?17 =>= additive_identity
43727 [17] by left_additive_inverse ?17
43728 NO CLASH, using fixed ground order
43730 29764: Id : 2, {_}:
43731 add ?2 ?3 =?= add ?3 ?2
43732 [3, 2] by commutativity_for_addition ?2 ?3
43733 29764: Id : 3, {_}:
43734 add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
43735 [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
43736 29764: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
43737 29764: Id : 5, {_}:
43738 add ?11 additive_identity =>= ?11
43739 [11] by right_additive_identity ?11
43740 29764: Id : 6, {_}:
43741 multiply additive_identity ?13 =>= additive_identity
43742 [13] by left_multiplicative_zero ?13
43743 29764: Id : 7, {_}:
43744 multiply ?15 additive_identity =>= additive_identity
43745 [15] by right_multiplicative_zero ?15
43746 29764: Id : 8, {_}:
43747 add (additive_inverse ?17) ?17 =>= additive_identity
43748 [17] by left_additive_inverse ?17
43749 29764: Id : 9, {_}:
43750 add ?19 (additive_inverse ?19) =>= additive_identity
43751 [19] by right_additive_inverse ?19
43752 29764: Id : 10, {_}:
43753 multiply ?21 (add ?22 ?23)
43755 add (multiply ?21 ?22) (multiply ?21 ?23)
43756 [23, 22, 21] by distribute1 ?21 ?22 ?23
43757 29764: Id : 11, {_}:
43758 multiply (add ?25 ?26) ?27
43760 add (multiply ?25 ?27) (multiply ?26 ?27)
43761 [27, 26, 25] by distribute2 ?25 ?26 ?27
43762 29764: Id : 12, {_}:
43763 additive_inverse (additive_inverse ?29) =>= ?29
43764 [29] by additive_inverse_additive_inverse ?29
43765 29764: Id : 13, {_}:
43766 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
43767 [32, 31] by right_alternative ?31 ?32
43768 29764: Id : 14, {_}:
43769 associator ?34 ?35 ?36
43771 add (multiply (multiply ?34 ?35) ?36)
43772 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
43773 [36, 35, 34] by associator ?34 ?35 ?36
43774 29764: Id : 15, {_}:
43777 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
43778 [39, 38] by commutator ?38 ?39
43780 29764: Id : 1, {_}:
43786 (multiply (associator x x y)
43787 (multiply (associator x x y) (associator x x y)))
43788 (multiply (associator x x y)
43789 (multiply (associator x x y) (associator x x y))))
43790 (multiply (associator x x y)
43791 (multiply (associator x x y) (associator x x y))))
43792 (multiply (associator x x y)
43793 (multiply (associator x x y) (associator x x y))))
43794 (multiply (associator x x y)
43795 (multiply (associator x x y) (associator x x y))))
43796 (multiply (associator x x y)
43797 (multiply (associator x x y) (associator x x y)))
43800 [] by prove_conjecture_3
43804 29764: commutator 1 2 0
43805 29764: additive_inverse 6 1 0
43806 29764: additive_identity 9 0 1 3
43807 29764: add 21 2 5 0,2
43808 29764: multiply 30 2 12 0,1,1,1,1,1,2
43809 29764: associator 19 3 18 0,1,1,1,1,1,1,2
43810 29764: y 18 0 18 3,1,1,1,1,1,1,2
43811 29764: x 36 0 36 1,1,1,1,1,1,1,2
43812 29763: Id : 9, {_}:
43813 add ?19 (additive_inverse ?19) =>= additive_identity
43814 [19] by right_additive_inverse ?19
43815 29763: Id : 10, {_}:
43816 multiply ?21 (add ?22 ?23)
43818 add (multiply ?21 ?22) (multiply ?21 ?23)
43819 [23, 22, 21] by distribute1 ?21 ?22 ?23
43820 29763: Id : 11, {_}:
43821 multiply (add ?25 ?26) ?27
43823 add (multiply ?25 ?27) (multiply ?26 ?27)
43824 [27, 26, 25] by distribute2 ?25 ?26 ?27
43825 29763: Id : 12, {_}:
43826 additive_inverse (additive_inverse ?29) =>= ?29
43827 [29] by additive_inverse_additive_inverse ?29
43828 29763: Id : 13, {_}:
43829 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
43830 [32, 31] by right_alternative ?31 ?32
43831 29763: Id : 14, {_}:
43832 associator ?34 ?35 ?36
43834 add (multiply (multiply ?34 ?35) ?36)
43835 (additive_inverse (multiply ?34 (multiply ?35 ?36)))
43836 [36, 35, 34] by associator ?34 ?35 ?36
43837 29763: Id : 15, {_}:
43840 add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
43841 [39, 38] by commutator ?38 ?39
43843 29763: Id : 1, {_}:
43849 (multiply (associator x x y)
43850 (multiply (associator x x y) (associator x x y)))
43851 (multiply (associator x x y)
43852 (multiply (associator x x y) (associator x x y))))
43853 (multiply (associator x x y)
43854 (multiply (associator x x y) (associator x x y))))
43855 (multiply (associator x x y)
43856 (multiply (associator x x y) (associator x x y))))
43857 (multiply (associator x x y)
43858 (multiply (associator x x y) (associator x x y))))
43859 (multiply (associator x x y)
43860 (multiply (associator x x y) (associator x x y)))
43863 [] by prove_conjecture_3
43867 29763: commutator 1 2 0
43868 29763: additive_inverse 6 1 0
43869 29763: additive_identity 9 0 1 3
43870 29763: add 21 2 5 0,2
43871 29763: multiply 30 2 12 0,1,1,1,1,1,2
43872 29763: associator 19 3 18 0,1,1,1,1,1,1,2
43873 29763: y 18 0 18 3,1,1,1,1,1,1,2
43874 29763: x 36 0 36 1,1,1,1,1,1,1,2
43875 % SZS status Timeout for RNG032-6.p
43876 NO CLASH, using fixed ground order
43878 29792: Id : 2, {_}:
43879 multiply (additive_inverse ?2) (additive_inverse ?3)
43882 [3, 2] by product_of_inverses ?2 ?3
43883 29792: Id : 3, {_}:
43884 multiply (additive_inverse ?5) ?6
43886 additive_inverse (multiply ?5 ?6)
43887 [6, 5] by inverse_product1 ?5 ?6
43888 29792: Id : 4, {_}:
43889 multiply ?8 (additive_inverse ?9)
43891 additive_inverse (multiply ?8 ?9)
43892 [9, 8] by inverse_product2 ?8 ?9
43893 29792: Id : 5, {_}:
43894 multiply ?11 (add ?12 (additive_inverse ?13))
43896 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
43897 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
43898 29792: Id : 6, {_}:
43899 multiply (add ?15 (additive_inverse ?16)) ?17
43901 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
43902 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
43903 29792: Id : 7, {_}:
43904 multiply (additive_inverse ?19) (add ?20 ?21)
43906 add (additive_inverse (multiply ?19 ?20))
43907 (additive_inverse (multiply ?19 ?21))
43908 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
43909 29792: Id : 8, {_}:
43910 multiply (add ?23 ?24) (additive_inverse ?25)
43912 add (additive_inverse (multiply ?23 ?25))
43913 (additive_inverse (multiply ?24 ?25))
43914 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
43915 29792: Id : 9, {_}:
43916 add ?27 ?28 =?= add ?28 ?27
43917 [28, 27] by commutativity_for_addition ?27 ?28
43918 29792: Id : 10, {_}:
43919 add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
43920 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
43921 29792: Id : 11, {_}:
43922 add additive_identity ?34 =>= ?34
43923 [34] by left_additive_identity ?34
43924 29792: Id : 12, {_}:
43925 add ?36 additive_identity =>= ?36
43926 [36] by right_additive_identity ?36
43927 29792: Id : 13, {_}:
43928 multiply additive_identity ?38 =>= additive_identity
43929 [38] by left_multiplicative_zero ?38
43930 29792: Id : 14, {_}:
43931 multiply ?40 additive_identity =>= additive_identity
43932 [40] by right_multiplicative_zero ?40
43933 29792: Id : 15, {_}:
43934 add (additive_inverse ?42) ?42 =>= additive_identity
43935 [42] by left_additive_inverse ?42
43936 29792: Id : 16, {_}:
43937 add ?44 (additive_inverse ?44) =>= additive_identity
43938 [44] by right_additive_inverse ?44
43939 29792: Id : 17, {_}:
43940 multiply ?46 (add ?47 ?48)
43942 add (multiply ?46 ?47) (multiply ?46 ?48)
43943 [48, 47, 46] by distribute1 ?46 ?47 ?48
43944 29792: Id : 18, {_}:
43945 multiply (add ?50 ?51) ?52
43947 add (multiply ?50 ?52) (multiply ?51 ?52)
43948 [52, 51, 50] by distribute2 ?50 ?51 ?52
43949 29792: Id : 19, {_}:
43950 additive_inverse (additive_inverse ?54) =>= ?54
43951 [54] by additive_inverse_additive_inverse ?54
43952 29792: Id : 20, {_}:
43953 multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
43954 [57, 56] by right_alternative ?56 ?57
43955 29792: Id : 21, {_}:
43956 associator ?59 ?60 ?61
43958 add (multiply (multiply ?59 ?60) ?61)
43959 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
43960 [61, 60, 59] by associator ?59 ?60 ?61
43961 29792: Id : 22, {_}:
43964 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
43965 [64, 63] by commutator ?63 ?64
43967 29792: Id : 1, {_}:
43973 (multiply (associator x x y)
43974 (multiply (associator x x y) (associator x x y)))
43975 (multiply (associator x x y)
43976 (multiply (associator x x y) (associator x x y))))
43977 (multiply (associator x x y)
43978 (multiply (associator x x y) (associator x x y))))
43979 (multiply (associator x x y)
43980 (multiply (associator x x y) (associator x x y))))
43981 (multiply (associator x x y)
43982 (multiply (associator x x y) (associator x x y))))
43983 (multiply (associator x x y)
43984 (multiply (associator x x y) (associator x x y)))
43987 [] by prove_conjecture_3
43991 29792: commutator 1 2 0
43992 29792: additive_inverse 22 1 0
43993 29792: additive_identity 9 0 1 3
43994 29792: add 29 2 5 0,2
43995 29792: multiply 48 2 12 0,1,1,1,1,1,2add
43996 29792: associator 19 3 18 0,1,1,1,1,1,1,2
43997 29792: y 18 0 18 3,1,1,1,1,1,1,2
43998 29792: x 36 0 36 1,1,1,1,1,1,1,2
43999 NO CLASH, using fixed ground order
44001 29793: Id : 2, {_}:
44002 multiply (additive_inverse ?2) (additive_inverse ?3)
44005 [3, 2] by product_of_inverses ?2 ?3
44006 29793: Id : 3, {_}:
44007 multiply (additive_inverse ?5) ?6
44009 additive_inverse (multiply ?5 ?6)
44010 [6, 5] by inverse_product1 ?5 ?6
44011 29793: Id : 4, {_}:
44012 multiply ?8 (additive_inverse ?9)
44014 additive_inverse (multiply ?8 ?9)
44015 [9, 8] by inverse_product2 ?8 ?9
44016 29793: Id : 5, {_}:
44017 multiply ?11 (add ?12 (additive_inverse ?13))
44019 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
44020 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
44021 29793: Id : 6, {_}:
44022 multiply (add ?15 (additive_inverse ?16)) ?17
44024 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
44025 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
44026 29793: Id : 7, {_}:
44027 multiply (additive_inverse ?19) (add ?20 ?21)
44029 add (additive_inverse (multiply ?19 ?20))
44030 (additive_inverse (multiply ?19 ?21))
44031 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
44032 29793: Id : 8, {_}:
44033 multiply (add ?23 ?24) (additive_inverse ?25)
44035 add (additive_inverse (multiply ?23 ?25))
44036 (additive_inverse (multiply ?24 ?25))
44037 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
44038 29793: Id : 9, {_}:
44039 add ?27 ?28 =?= add ?28 ?27
44040 [28, 27] by commutativity_for_addition ?27 ?28
44041 29793: Id : 10, {_}:
44042 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
44043 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
44044 29793: Id : 11, {_}:
44045 add additive_identity ?34 =>= ?34
44046 [34] by left_additive_identity ?34
44047 29793: Id : 12, {_}:
44048 add ?36 additive_identity =>= ?36
44049 [36] by right_additive_identity ?36
44050 29793: Id : 13, {_}:
44051 multiply additive_identity ?38 =>= additive_identity
44052 [38] by left_multiplicative_zero ?38
44053 29793: Id : 14, {_}:
44054 multiply ?40 additive_identity =>= additive_identity
44055 [40] by right_multiplicative_zero ?40
44056 29793: Id : 15, {_}:
44057 add (additive_inverse ?42) ?42 =>= additive_identity
44058 [42] by left_additive_inverse ?42
44059 29793: Id : 16, {_}:
44060 add ?44 (additive_inverse ?44) =>= additive_identity
44061 [44] by right_additive_inverse ?44
44062 29793: Id : 17, {_}:
44063 multiply ?46 (add ?47 ?48)
44065 add (multiply ?46 ?47) (multiply ?46 ?48)
44066 [48, 47, 46] by distribute1 ?46 ?47 ?48
44067 29793: Id : 18, {_}:
44068 multiply (add ?50 ?51) ?52
44070 add (multiply ?50 ?52) (multiply ?51 ?52)
44071 [52, 51, 50] by distribute2 ?50 ?51 ?52
44072 29793: Id : 19, {_}:
44073 additive_inverse (additive_inverse ?54) =>= ?54
44074 [54] by additive_inverse_additive_inverse ?54
44075 29793: Id : 20, {_}:
44076 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
44077 [57, 56] by right_alternative ?56 ?57
44078 29793: Id : 21, {_}:
44079 associator ?59 ?60 ?61
44081 add (multiply (multiply ?59 ?60) ?61)
44082 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
44083 [61, 60, 59] by associator ?59 ?60 ?61
44084 29793: Id : 22, {_}:
44087 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
44088 [64, 63] by commutator ?63 ?64
44090 29793: Id : 1, {_}:
44096 (multiply (associator x x y)
44097 (multiply (associator x x y) (associator x x y)))
44098 (multiply (associator x x y)
44099 (multiply (associator x x y) (associator x x y))))
44100 (multiply (associator x x y)
44101 (multiply (associator x x y) (associator x x y))))
44102 (multiply (associator x x y)
44103 (multiply (associator x x y) (associator x x y))))
44104 (multiply (associator x x y)
44105 (multiply (associator x x y) (associator x x y))))
44106 (multiply (associator x x y)
44107 (multiply (associator x x y) (associator x x y)))
44110 [] by prove_conjecture_3
44114 29793: commutator 1 2 0
44115 29793: additive_inverse 22 1 0
44116 29793: additive_identity 9 0 1 3
44117 29793: add 29 2 5 0,2
44118 29793: multiply 48 2 12 0,1,1,1,1,1,2add
44119 29793: associator 19 3 18 0,1,1,1,1,1,1,2
44120 29793: y 18 0 18 3,1,1,1,1,1,1,2
44121 29793: x 36 0 36 1,1,1,1,1,1,1,2
44122 NO CLASH, using fixed ground order
44124 29794: Id : 2, {_}:
44125 multiply (additive_inverse ?2) (additive_inverse ?3)
44128 [3, 2] by product_of_inverses ?2 ?3
44129 29794: Id : 3, {_}:
44130 multiply (additive_inverse ?5) ?6
44132 additive_inverse (multiply ?5 ?6)
44133 [6, 5] by inverse_product1 ?5 ?6
44134 29794: Id : 4, {_}:
44135 multiply ?8 (additive_inverse ?9)
44137 additive_inverse (multiply ?8 ?9)
44138 [9, 8] by inverse_product2 ?8 ?9
44139 29794: Id : 5, {_}:
44140 multiply ?11 (add ?12 (additive_inverse ?13))
44142 add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
44143 [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
44144 29794: Id : 6, {_}:
44145 multiply (add ?15 (additive_inverse ?16)) ?17
44147 add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
44148 [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
44149 29794: Id : 7, {_}:
44150 multiply (additive_inverse ?19) (add ?20 ?21)
44152 add (additive_inverse (multiply ?19 ?20))
44153 (additive_inverse (multiply ?19 ?21))
44154 [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
44155 29794: Id : 8, {_}:
44156 multiply (add ?23 ?24) (additive_inverse ?25)
44158 add (additive_inverse (multiply ?23 ?25))
44159 (additive_inverse (multiply ?24 ?25))
44160 [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
44161 29794: Id : 9, {_}:
44162 add ?27 ?28 =?= add ?28 ?27
44163 [28, 27] by commutativity_for_addition ?27 ?28
44164 29794: Id : 10, {_}:
44165 add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
44166 [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
44167 29794: Id : 11, {_}:
44168 add additive_identity ?34 =>= ?34
44169 [34] by left_additive_identity ?34
44170 29794: Id : 12, {_}:
44171 add ?36 additive_identity =>= ?36
44172 [36] by right_additive_identity ?36
44173 29794: Id : 13, {_}:
44174 multiply additive_identity ?38 =>= additive_identity
44175 [38] by left_multiplicative_zero ?38
44176 29794: Id : 14, {_}:
44177 multiply ?40 additive_identity =>= additive_identity
44178 [40] by right_multiplicative_zero ?40
44179 29794: Id : 15, {_}:
44180 add (additive_inverse ?42) ?42 =>= additive_identity
44181 [42] by left_additive_inverse ?42
44182 29794: Id : 16, {_}:
44183 add ?44 (additive_inverse ?44) =>= additive_identity
44184 [44] by right_additive_inverse ?44
44185 29794: Id : 17, {_}:
44186 multiply ?46 (add ?47 ?48)
44188 add (multiply ?46 ?47) (multiply ?46 ?48)
44189 [48, 47, 46] by distribute1 ?46 ?47 ?48
44190 29794: Id : 18, {_}:
44191 multiply (add ?50 ?51) ?52
44193 add (multiply ?50 ?52) (multiply ?51 ?52)
44194 [52, 51, 50] by distribute2 ?50 ?51 ?52
44195 29794: Id : 19, {_}:
44196 additive_inverse (additive_inverse ?54) =>= ?54
44197 [54] by additive_inverse_additive_inverse ?54
44198 29794: Id : 20, {_}:
44199 multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
44200 [57, 56] by right_alternative ?56 ?57
44201 29794: Id : 21, {_}:
44202 associator ?59 ?60 ?61
44204 add (multiply (multiply ?59 ?60) ?61)
44205 (additive_inverse (multiply ?59 (multiply ?60 ?61)))
44206 [61, 60, 59] by associator ?59 ?60 ?61
44207 29794: Id : 22, {_}:
44210 add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
44211 [64, 63] by commutator ?63 ?64
44213 29794: Id : 1, {_}:
44219 (multiply (associator x x y)
44220 (multiply (associator x x y) (associator x x y)))
44221 (multiply (associator x x y)
44222 (multiply (associator x x y) (associator x x y))))
44223 (multiply (associator x x y)
44224 (multiply (associator x x y) (associator x x y))))
44225 (multiply (associator x x y)
44226 (multiply (associator x x y) (associator x x y))))
44227 (multiply (associator x x y)
44228 (multiply (associator x x y) (associator x x y))))
44229 (multiply (associator x x y)
44230 (multiply (associator x x y) (associator x x y)))
44233 [] by prove_conjecture_3
44237 29794: commutator 1 2 0
44238 29794: additive_inverse 22 1 0
44239 29794: additive_identity 9 0 1 3
44240 29794: add 29 2 5 0,2
44241 29794: multiply 48 2 12 0,1,1,1,1,1,2add
44242 29794: associator 19 3 18 0,1,1,1,1,1,1,2
44243 29794: y 18 0 18 3,1,1,1,1,1,1,2
44244 29794: x 36 0 36 1,1,1,1,1,1,1,2
44245 % SZS status Timeout for RNG032-7.p
44246 NO CLASH, using fixed ground order
44248 29810: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44249 29810: Id : 3, {_}:
44250 add ?4 additive_identity =>= ?4
44251 [4] by right_additive_identity ?4
44252 29810: Id : 4, {_}:
44253 multiply additive_identity ?6 =>= additive_identity
44254 [6] by left_multiplicative_zero ?6
44255 29810: Id : 5, {_}:
44256 multiply ?8 additive_identity =>= additive_identity
44257 [8] by right_multiplicative_zero ?8
44258 29810: Id : 6, {_}:
44259 add (additive_inverse ?10) ?10 =>= additive_identity
44260 [10] by left_additive_inverse ?10
44261 29810: Id : 7, {_}:
44262 add ?12 (additive_inverse ?12) =>= additive_identity
44263 [12] by right_additive_inverse ?12
44264 29810: Id : 8, {_}:
44265 additive_inverse (additive_inverse ?14) =>= ?14
44266 [14] by additive_inverse_additive_inverse ?14
44267 29810: Id : 9, {_}:
44268 multiply ?16 (add ?17 ?18)
44270 add (multiply ?16 ?17) (multiply ?16 ?18)
44271 [18, 17, 16] by distribute1 ?16 ?17 ?18
44272 29810: Id : 10, {_}:
44273 multiply (add ?20 ?21) ?22
44275 add (multiply ?20 ?22) (multiply ?21 ?22)
44276 [22, 21, 20] by distribute2 ?20 ?21 ?22
44277 29810: Id : 11, {_}:
44278 add ?24 ?25 =?= add ?25 ?24
44279 [25, 24] by commutativity_for_addition ?24 ?25
44280 29810: Id : 12, {_}:
44281 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
44282 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44283 29810: Id : 13, {_}:
44284 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
44285 [32, 31] by right_alternative ?31 ?32
44286 29810: Id : 14, {_}:
44287 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
44288 [35, 34] by left_alternative ?34 ?35
44289 29810: Id : 15, {_}:
44290 associator ?37 ?38 ?39
44292 add (multiply (multiply ?37 ?38) ?39)
44293 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44294 [39, 38, 37] by associator ?37 ?38 ?39
44295 29810: Id : 16, {_}:
44298 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44299 [42, 41] by commutator ?41 ?42
44301 29810: Id : 1, {_}:
44302 add (associator (multiply x y) z w) (associator x y (commutator z w))
44304 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44305 [] by prove_challenge
44309 29810: additive_inverse 6 1 0
44310 29810: additive_identity 8 0 0
44311 29810: add 18 2 2 0,2
44312 29810: commutator 2 2 1 0,3,2,2
44313 29810: associator 5 3 4 0,1,2
44314 29810: w 4 0 4 3,1,2
44315 29810: z 4 0 4 2,1,2
44316 29810: multiply 25 2 3 0,1,1,2
44317 29810: y 4 0 4 2,1,1,2
44318 29810: x 4 0 4 1,1,1,2
44319 NO CLASH, using fixed ground order
44321 29811: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44322 29811: Id : 3, {_}:
44323 add ?4 additive_identity =>= ?4
44324 [4] by right_additive_identity ?4
44325 29811: Id : 4, {_}:
44326 multiply additive_identity ?6 =>= additive_identity
44327 [6] by left_multiplicative_zero ?6
44328 29811: Id : 5, {_}:
44329 multiply ?8 additive_identity =>= additive_identity
44330 [8] by right_multiplicative_zero ?8
44331 29811: Id : 6, {_}:
44332 add (additive_inverse ?10) ?10 =>= additive_identity
44333 [10] by left_additive_inverse ?10
44334 29811: Id : 7, {_}:
44335 add ?12 (additive_inverse ?12) =>= additive_identity
44336 [12] by right_additive_inverse ?12
44337 29811: Id : 8, {_}:
44338 additive_inverse (additive_inverse ?14) =>= ?14
44339 [14] by additive_inverse_additive_inverse ?14
44340 29811: Id : 9, {_}:
44341 multiply ?16 (add ?17 ?18)
44343 add (multiply ?16 ?17) (multiply ?16 ?18)
44344 [18, 17, 16] by distribute1 ?16 ?17 ?18
44345 29811: Id : 10, {_}:
44346 multiply (add ?20 ?21) ?22
44348 add (multiply ?20 ?22) (multiply ?21 ?22)
44349 [22, 21, 20] by distribute2 ?20 ?21 ?22
44350 29811: Id : 11, {_}:
44351 add ?24 ?25 =?= add ?25 ?24
44352 [25, 24] by commutativity_for_addition ?24 ?25
44353 29811: Id : 12, {_}:
44354 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
44355 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44356 29811: Id : 13, {_}:
44357 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
44358 [32, 31] by right_alternative ?31 ?32
44359 29811: Id : 14, {_}:
44360 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
44361 [35, 34] by left_alternative ?34 ?35
44362 29811: Id : 15, {_}:
44363 associator ?37 ?38 ?39
44365 add (multiply (multiply ?37 ?38) ?39)
44366 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44367 [39, 38, 37] by associator ?37 ?38 ?39
44368 29811: Id : 16, {_}:
44371 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44372 [42, 41] by commutator ?41 ?42
44374 29811: Id : 1, {_}:
44375 add (associator (multiply x y) z w) (associator x y (commutator z w))
44377 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44378 [] by prove_challenge
44382 29811: additive_inverse 6 1 0
44383 29811: additive_identity 8 0 0
44384 29811: add 18 2 2 0,2
44385 29811: commutator 2 2 1 0,3,2,2
44386 29811: associator 5 3 4 0,1,2
44387 29811: w 4 0 4 3,1,2
44388 29811: z 4 0 4 2,1,2
44389 29811: multiply 25 2 3 0,1,1,2
44390 29811: y 4 0 4 2,1,1,2
44391 29811: x 4 0 4 1,1,1,2
44392 NO CLASH, using fixed ground order
44394 29812: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44395 29812: Id : 3, {_}:
44396 add ?4 additive_identity =>= ?4
44397 [4] by right_additive_identity ?4
44398 29812: Id : 4, {_}:
44399 multiply additive_identity ?6 =>= additive_identity
44400 [6] by left_multiplicative_zero ?6
44401 29812: Id : 5, {_}:
44402 multiply ?8 additive_identity =>= additive_identity
44403 [8] by right_multiplicative_zero ?8
44404 29812: Id : 6, {_}:
44405 add (additive_inverse ?10) ?10 =>= additive_identity
44406 [10] by left_additive_inverse ?10
44407 29812: Id : 7, {_}:
44408 add ?12 (additive_inverse ?12) =>= additive_identity
44409 [12] by right_additive_inverse ?12
44410 29812: Id : 8, {_}:
44411 additive_inverse (additive_inverse ?14) =>= ?14
44412 [14] by additive_inverse_additive_inverse ?14
44413 29812: Id : 9, {_}:
44414 multiply ?16 (add ?17 ?18)
44416 add (multiply ?16 ?17) (multiply ?16 ?18)
44417 [18, 17, 16] by distribute1 ?16 ?17 ?18
44418 29812: Id : 10, {_}:
44419 multiply (add ?20 ?21) ?22
44421 add (multiply ?20 ?22) (multiply ?21 ?22)
44422 [22, 21, 20] by distribute2 ?20 ?21 ?22
44423 29812: Id : 11, {_}:
44424 add ?24 ?25 =?= add ?25 ?24
44425 [25, 24] by commutativity_for_addition ?24 ?25
44426 29812: Id : 12, {_}:
44427 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
44428 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44429 29812: Id : 13, {_}:
44430 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
44431 [32, 31] by right_alternative ?31 ?32
44432 29812: Id : 14, {_}:
44433 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
44434 [35, 34] by left_alternative ?34 ?35
44435 29812: Id : 15, {_}:
44436 associator ?37 ?38 ?39
44438 add (multiply (multiply ?37 ?38) ?39)
44439 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44440 [39, 38, 37] by associator ?37 ?38 ?39
44441 29812: Id : 16, {_}:
44444 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44445 [42, 41] by commutator ?41 ?42
44447 29812: Id : 1, {_}:
44448 add (associator (multiply x y) z w) (associator x y (commutator z w))
44450 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44451 [] by prove_challenge
44455 29812: additive_inverse 6 1 0
44456 29812: additive_identity 8 0 0
44457 29812: add 18 2 2 0,2
44458 29812: commutator 2 2 1 0,3,2,2
44459 29812: associator 5 3 4 0,1,2
44460 29812: w 4 0 4 3,1,2
44461 29812: z 4 0 4 2,1,2
44462 29812: multiply 25 2 3 0,1,1,2
44463 29812: y 4 0 4 2,1,1,2
44464 29812: x 4 0 4 1,1,1,2
44465 % SZS status Timeout for RNG033-6.p
44466 NO CLASH, using fixed ground order
44468 29844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44469 29844: Id : 3, {_}:
44470 add ?4 additive_identity =>= ?4
44471 [4] by right_additive_identity ?4
44472 29844: Id : 4, {_}:
44473 multiply additive_identity ?6 =>= additive_identity
44474 [6] by left_multiplicative_zero ?6
44475 29844: Id : 5, {_}:
44476 multiply ?8 additive_identity =>= additive_identity
44477 [8] by right_multiplicative_zero ?8
44478 29844: Id : 6, {_}:
44479 add (additive_inverse ?10) ?10 =>= additive_identity
44480 [10] by left_additive_inverse ?10
44481 29844: Id : 7, {_}:
44482 add ?12 (additive_inverse ?12) =>= additive_identity
44483 [12] by right_additive_inverse ?12
44484 29844: Id : 8, {_}:
44485 additive_inverse (additive_inverse ?14) =>= ?14
44486 [14] by additive_inverse_additive_inverse ?14
44487 29844: Id : 9, {_}:
44488 multiply ?16 (add ?17 ?18)
44490 add (multiply ?16 ?17) (multiply ?16 ?18)
44491 [18, 17, 16] by distribute1 ?16 ?17 ?18
44492 29844: Id : 10, {_}:
44493 multiply (add ?20 ?21) ?22
44495 add (multiply ?20 ?22) (multiply ?21 ?22)
44496 [22, 21, 20] by distribute2 ?20 ?21 ?22
44497 29844: Id : 11, {_}:
44498 add ?24 ?25 =?= add ?25 ?24
44499 [25, 24] by commutativity_for_addition ?24 ?25
44500 29844: Id : 12, {_}:
44501 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
44502 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44503 29844: Id : 13, {_}:
44504 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
44505 [32, 31] by right_alternative ?31 ?32
44506 29844: Id : 14, {_}:
44507 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
44508 [35, 34] by left_alternative ?34 ?35
44509 29844: Id : 15, {_}:
44510 associator ?37 ?38 ?39
44512 add (multiply (multiply ?37 ?38) ?39)
44513 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44514 [39, 38, 37] by associator ?37 ?38 ?39
44515 29844: Id : 16, {_}:
44518 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44519 [42, 41] by commutator ?41 ?42
44520 29844: Id : 17, {_}:
44521 multiply (additive_inverse ?44) (additive_inverse ?45)
44524 [45, 44] by product_of_inverses ?44 ?45
44525 29844: Id : 18, {_}:
44526 multiply (additive_inverse ?47) ?48
44528 additive_inverse (multiply ?47 ?48)
44529 [48, 47] by inverse_product1 ?47 ?48
44530 29844: Id : 19, {_}:
44531 multiply ?50 (additive_inverse ?51)
44533 additive_inverse (multiply ?50 ?51)
44534 [51, 50] by inverse_product2 ?50 ?51
44535 29844: Id : 20, {_}:
44536 multiply ?53 (add ?54 (additive_inverse ?55))
44538 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
44539 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
44540 29844: Id : 21, {_}:
44541 multiply (add ?57 (additive_inverse ?58)) ?59
44543 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
44544 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
44545 29844: Id : 22, {_}:
44546 multiply (additive_inverse ?61) (add ?62 ?63)
44548 add (additive_inverse (multiply ?61 ?62))
44549 (additive_inverse (multiply ?61 ?63))
44550 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
44551 29844: Id : 23, {_}:
44552 multiply (add ?65 ?66) (additive_inverse ?67)
44554 add (additive_inverse (multiply ?65 ?67))
44555 (additive_inverse (multiply ?66 ?67))
44556 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
44558 29844: Id : 1, {_}:
44559 add (associator (multiply x y) z w) (associator x y (commutator z w))
44561 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44562 [] by prove_challenge
44566 29844: additive_inverse 22 1 0
44567 29844: additive_identity 8 0 0
44568 29844: add 26 2 2 0,2
44569 29844: commutator 2 2 1 0,3,2,2
44570 29844: associator 5 3 4 0,1,2
44571 29844: w 4 0 4 3,1,2
44572 29844: z 4 0 4 2,1,2
44573 29844: multiply 43 2 3 0,1,1,2
44574 29844: y 4 0 4 2,1,1,2
44575 29844: x 4 0 4 1,1,1,2
44576 NO CLASH, using fixed ground order
44578 29846: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44579 29846: Id : 3, {_}:
44580 add ?4 additive_identity =>= ?4
44581 [4] by right_additive_identity ?4
44582 29846: Id : 4, {_}:
44583 multiply additive_identity ?6 =>= additive_identity
44584 [6] by left_multiplicative_zero ?6
44585 29846: Id : 5, {_}:
44586 multiply ?8 additive_identity =>= additive_identity
44587 [8] by right_multiplicative_zero ?8
44588 29846: Id : 6, {_}:
44589 add (additive_inverse ?10) ?10 =>= additive_identity
44590 [10] by left_additive_inverse ?10
44591 29846: Id : 7, {_}:
44592 add ?12 (additive_inverse ?12) =>= additive_identity
44593 [12] by right_additive_inverse ?12
44594 29846: Id : 8, {_}:
44595 additive_inverse (additive_inverse ?14) =>= ?14
44596 [14] by additive_inverse_additive_inverse ?14
44597 29846: Id : 9, {_}:
44598 multiply ?16 (add ?17 ?18)
44600 add (multiply ?16 ?17) (multiply ?16 ?18)
44601 [18, 17, 16] by distribute1 ?16 ?17 ?18
44602 29846: Id : 10, {_}:
44603 multiply (add ?20 ?21) ?22
44605 add (multiply ?20 ?22) (multiply ?21 ?22)
44606 [22, 21, 20] by distribute2 ?20 ?21 ?22
44607 29846: Id : 11, {_}:
44608 add ?24 ?25 =?= add ?25 ?24
44609 [25, 24] by commutativity_for_addition ?24 ?25
44610 29846: Id : 12, {_}:
44611 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
44612 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44613 29846: Id : 13, {_}:
44614 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
44615 [32, 31] by right_alternative ?31 ?32
44616 29846: Id : 14, {_}:
44617 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
44618 [35, 34] by left_alternative ?34 ?35
44619 29846: Id : 15, {_}:
44620 associator ?37 ?38 ?39
44622 add (multiply (multiply ?37 ?38) ?39)
44623 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44624 [39, 38, 37] by associator ?37 ?38 ?39
44625 29846: Id : 16, {_}:
44628 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44629 [42, 41] by commutator ?41 ?42
44630 29846: Id : 17, {_}:
44631 multiply (additive_inverse ?44) (additive_inverse ?45)
44634 [45, 44] by product_of_inverses ?44 ?45
44635 29846: Id : 18, {_}:
44636 multiply (additive_inverse ?47) ?48
44638 additive_inverse (multiply ?47 ?48)
44639 [48, 47] by inverse_product1 ?47 ?48
44640 29846: Id : 19, {_}:
44641 multiply ?50 (additive_inverse ?51)
44643 additive_inverse (multiply ?50 ?51)
44644 [51, 50] by inverse_product2 ?50 ?51
44645 29846: Id : 20, {_}:
44646 multiply ?53 (add ?54 (additive_inverse ?55))
44648 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
44649 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
44650 29846: Id : 21, {_}:
44651 multiply (add ?57 (additive_inverse ?58)) ?59
44653 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
44654 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
44655 29846: Id : 22, {_}:
44656 multiply (additive_inverse ?61) (add ?62 ?63)
44658 add (additive_inverse (multiply ?61 ?62))
44659 (additive_inverse (multiply ?61 ?63))
44660 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
44661 29846: Id : 23, {_}:
44662 multiply (add ?65 ?66) (additive_inverse ?67)
44664 add (additive_inverse (multiply ?65 ?67))
44665 (additive_inverse (multiply ?66 ?67))
44666 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
44668 29846: Id : 1, {_}:
44669 add (associator (multiply x y) z w) (associator x y (commutator z w))
44671 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44672 [] by prove_challenge
44676 29846: additive_inverse 22 1 0
44677 29846: additive_identity 8 0 0
44678 29846: add 26 2 2 0,2
44679 29846: commutator 2 2 1 0,3,2,2
44680 29846: associator 5 3 4 0,1,2
44681 29846: w 4 0 4 3,1,2
44682 29846: z 4 0 4 2,1,2
44683 29846: multiply 43 2 3 0,1,1,2
44684 29846: y 4 0 4 2,1,1,2
44685 29846: x 4 0 4 1,1,1,2
44686 NO CLASH, using fixed ground order
44688 29845: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44689 29845: Id : 3, {_}:
44690 add ?4 additive_identity =>= ?4
44691 [4] by right_additive_identity ?4
44692 29845: Id : 4, {_}:
44693 multiply additive_identity ?6 =>= additive_identity
44694 [6] by left_multiplicative_zero ?6
44695 29845: Id : 5, {_}:
44696 multiply ?8 additive_identity =>= additive_identity
44697 [8] by right_multiplicative_zero ?8
44698 29845: Id : 6, {_}:
44699 add (additive_inverse ?10) ?10 =>= additive_identity
44700 [10] by left_additive_inverse ?10
44701 29845: Id : 7, {_}:
44702 add ?12 (additive_inverse ?12) =>= additive_identity
44703 [12] by right_additive_inverse ?12
44704 29845: Id : 8, {_}:
44705 additive_inverse (additive_inverse ?14) =>= ?14
44706 [14] by additive_inverse_additive_inverse ?14
44707 29845: Id : 9, {_}:
44708 multiply ?16 (add ?17 ?18)
44710 add (multiply ?16 ?17) (multiply ?16 ?18)
44711 [18, 17, 16] by distribute1 ?16 ?17 ?18
44712 29845: Id : 10, {_}:
44713 multiply (add ?20 ?21) ?22
44715 add (multiply ?20 ?22) (multiply ?21 ?22)
44716 [22, 21, 20] by distribute2 ?20 ?21 ?22
44717 29845: Id : 11, {_}:
44718 add ?24 ?25 =?= add ?25 ?24
44719 [25, 24] by commutativity_for_addition ?24 ?25
44720 29845: Id : 12, {_}:
44721 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
44722 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44723 29845: Id : 13, {_}:
44724 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
44725 [32, 31] by right_alternative ?31 ?32
44726 29845: Id : 14, {_}:
44727 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
44728 [35, 34] by left_alternative ?34 ?35
44729 29845: Id : 15, {_}:
44730 associator ?37 ?38 ?39
44732 add (multiply (multiply ?37 ?38) ?39)
44733 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44734 [39, 38, 37] by associator ?37 ?38 ?39
44735 29845: Id : 16, {_}:
44738 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44739 [42, 41] by commutator ?41 ?42
44740 29845: Id : 17, {_}:
44741 multiply (additive_inverse ?44) (additive_inverse ?45)
44744 [45, 44] by product_of_inverses ?44 ?45
44745 29845: Id : 18, {_}:
44746 multiply (additive_inverse ?47) ?48
44748 additive_inverse (multiply ?47 ?48)
44749 [48, 47] by inverse_product1 ?47 ?48
44750 29845: Id : 19, {_}:
44751 multiply ?50 (additive_inverse ?51)
44753 additive_inverse (multiply ?50 ?51)
44754 [51, 50] by inverse_product2 ?50 ?51
44755 29845: Id : 20, {_}:
44756 multiply ?53 (add ?54 (additive_inverse ?55))
44758 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
44759 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
44760 29845: Id : 21, {_}:
44761 multiply (add ?57 (additive_inverse ?58)) ?59
44763 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
44764 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
44765 29845: Id : 22, {_}:
44766 multiply (additive_inverse ?61) (add ?62 ?63)
44768 add (additive_inverse (multiply ?61 ?62))
44769 (additive_inverse (multiply ?61 ?63))
44770 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
44771 29845: Id : 23, {_}:
44772 multiply (add ?65 ?66) (additive_inverse ?67)
44774 add (additive_inverse (multiply ?65 ?67))
44775 (additive_inverse (multiply ?66 ?67))
44776 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
44778 29845: Id : 1, {_}:
44779 add (associator (multiply x y) z w) (associator x y (commutator z w))
44781 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44782 [] by prove_challenge
44786 29845: additive_inverse 22 1 0
44787 29845: additive_identity 8 0 0
44788 29845: add 26 2 2 0,2
44789 29845: commutator 2 2 1 0,3,2,2
44790 29845: associator 5 3 4 0,1,2
44791 29845: w 4 0 4 3,1,2
44792 29845: z 4 0 4 2,1,2
44793 29845: multiply 43 2 3 0,1,1,2
44794 29845: y 4 0 4 2,1,1,2
44795 29845: x 4 0 4 1,1,1,2
44796 % SZS status Timeout for RNG033-7.p
44797 NO CLASH, using fixed ground order
44799 29862: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44800 29862: Id : 3, {_}:
44801 add ?4 additive_identity =>= ?4
44802 [4] by right_additive_identity ?4
44803 29862: Id : 4, {_}:
44804 multiply additive_identity ?6 =>= additive_identity
44805 [6] by left_multiplicative_zero ?6
44806 29862: Id : 5, {_}:
44807 multiply ?8 additive_identity =>= additive_identity
44808 [8] by right_multiplicative_zero ?8
44809 29862: Id : 6, {_}:
44810 add (additive_inverse ?10) ?10 =>= additive_identity
44811 [10] by left_additive_inverse ?10
44812 29862: Id : 7, {_}:
44813 add ?12 (additive_inverse ?12) =>= additive_identity
44814 [12] by right_additive_inverse ?12
44815 29862: Id : 8, {_}:
44816 additive_inverse (additive_inverse ?14) =>= ?14
44817 [14] by additive_inverse_additive_inverse ?14
44818 29862: Id : 9, {_}:
44819 multiply ?16 (add ?17 ?18)
44821 add (multiply ?16 ?17) (multiply ?16 ?18)
44822 [18, 17, 16] by distribute1 ?16 ?17 ?18
44823 29862: Id : 10, {_}:
44824 multiply (add ?20 ?21) ?22
44826 add (multiply ?20 ?22) (multiply ?21 ?22)
44827 [22, 21, 20] by distribute2 ?20 ?21 ?22
44828 29862: Id : 11, {_}:
44829 add ?24 ?25 =?= add ?25 ?24
44830 [25, 24] by commutativity_for_addition ?24 ?25
44831 29862: Id : 12, {_}:
44832 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
44833 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44834 29862: Id : 13, {_}:
44835 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
44836 [32, 31] by right_alternative ?31 ?32
44837 29862: Id : 14, {_}:
44838 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
44839 [35, 34] by left_alternative ?34 ?35
44840 29862: Id : 15, {_}:
44841 associator ?37 ?38 ?39
44843 add (multiply (multiply ?37 ?38) ?39)
44844 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44845 [39, 38, 37] by associator ?37 ?38 ?39
44846 29862: Id : 16, {_}:
44849 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44850 [42, 41] by commutator ?41 ?42
44851 29862: Id : 17, {_}:
44852 multiply ?44 (multiply ?45 (multiply ?46 ?45))
44854 multiply (multiply (multiply ?44 ?45) ?46) ?45
44855 [46, 45, 44] by right_moufang ?44 ?45 ?46
44857 29862: Id : 1, {_}:
44858 add (associator (multiply x y) z w) (associator x y (commutator z w))
44860 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44861 [] by prove_challenge
44865 29862: additive_inverse 6 1 0
44866 29862: additive_identity 8 0 0
44867 29862: add 18 2 2 0,2
44868 29862: commutator 2 2 1 0,3,2,2
44869 29862: associator 5 3 4 0,1,2
44870 29862: w 4 0 4 3,1,2
44871 29862: z 4 0 4 2,1,2
44872 29862: multiply 31 2 3 0,1,1,2
44873 29862: y 4 0 4 2,1,1,2
44874 29862: x 4 0 4 1,1,1,2
44875 NO CLASH, using fixed ground order
44877 29863: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44878 29863: Id : 3, {_}:
44879 add ?4 additive_identity =>= ?4
44880 [4] by right_additive_identity ?4
44881 29863: Id : 4, {_}:
44882 multiply additive_identity ?6 =>= additive_identity
44883 [6] by left_multiplicative_zero ?6
44884 29863: Id : 5, {_}:
44885 multiply ?8 additive_identity =>= additive_identity
44886 [8] by right_multiplicative_zero ?8
44887 29863: Id : 6, {_}:
44888 add (additive_inverse ?10) ?10 =>= additive_identity
44889 [10] by left_additive_inverse ?10
44890 29863: Id : 7, {_}:
44891 add ?12 (additive_inverse ?12) =>= additive_identity
44892 [12] by right_additive_inverse ?12
44893 29863: Id : 8, {_}:
44894 additive_inverse (additive_inverse ?14) =>= ?14
44895 [14] by additive_inverse_additive_inverse ?14
44896 29863: Id : 9, {_}:
44897 multiply ?16 (add ?17 ?18)
44899 add (multiply ?16 ?17) (multiply ?16 ?18)
44900 [18, 17, 16] by distribute1 ?16 ?17 ?18
44901 29863: Id : 10, {_}:
44902 multiply (add ?20 ?21) ?22
44904 add (multiply ?20 ?22) (multiply ?21 ?22)
44905 [22, 21, 20] by distribute2 ?20 ?21 ?22
44906 29863: Id : 11, {_}:
44907 add ?24 ?25 =?= add ?25 ?24
44908 [25, 24] by commutativity_for_addition ?24 ?25
44909 29863: Id : 12, {_}:
44910 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
44911 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44912 29863: Id : 13, {_}:
44913 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
44914 [32, 31] by right_alternative ?31 ?32
44915 29863: Id : 14, {_}:
44916 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
44917 [35, 34] by left_alternative ?34 ?35
44918 29863: Id : 15, {_}:
44919 associator ?37 ?38 ?39
44921 add (multiply (multiply ?37 ?38) ?39)
44922 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
44923 [39, 38, 37] by associator ?37 ?38 ?39
44924 29863: Id : 16, {_}:
44927 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
44928 [42, 41] by commutator ?41 ?42
44929 29863: Id : 17, {_}:
44930 multiply ?44 (multiply ?45 (multiply ?46 ?45))
44932 multiply (multiply (multiply ?44 ?45) ?46) ?45
44933 [46, 45, 44] by right_moufang ?44 ?45 ?46
44935 29863: Id : 1, {_}:
44936 add (associator (multiply x y) z w) (associator x y (commutator z w))
44938 add (multiply x (associator y z w)) (multiply (associator x z w) y)
44939 [] by prove_challenge
44943 29863: additive_inverse 6 1 0
44944 29863: additive_identity 8 0 0
44945 29863: add 18 2 2 0,2
44946 29863: commutator 2 2 1 0,3,2,2
44947 29863: associator 5 3 4 0,1,2
44948 29863: w 4 0 4 3,1,2
44949 29863: z 4 0 4 2,1,2
44950 29863: multiply 31 2 3 0,1,1,2
44951 29863: y 4 0 4 2,1,1,2
44952 29863: x 4 0 4 1,1,1,2
44953 NO CLASH, using fixed ground order
44955 29864: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
44956 29864: Id : 3, {_}:
44957 add ?4 additive_identity =>= ?4
44958 [4] by right_additive_identity ?4
44959 29864: Id : 4, {_}:
44960 multiply additive_identity ?6 =>= additive_identity
44961 [6] by left_multiplicative_zero ?6
44962 29864: Id : 5, {_}:
44963 multiply ?8 additive_identity =>= additive_identity
44964 [8] by right_multiplicative_zero ?8
44965 29864: Id : 6, {_}:
44966 add (additive_inverse ?10) ?10 =>= additive_identity
44967 [10] by left_additive_inverse ?10
44968 29864: Id : 7, {_}:
44969 add ?12 (additive_inverse ?12) =>= additive_identity
44970 [12] by right_additive_inverse ?12
44971 29864: Id : 8, {_}:
44972 additive_inverse (additive_inverse ?14) =>= ?14
44973 [14] by additive_inverse_additive_inverse ?14
44974 29864: Id : 9, {_}:
44975 multiply ?16 (add ?17 ?18)
44977 add (multiply ?16 ?17) (multiply ?16 ?18)
44978 [18, 17, 16] by distribute1 ?16 ?17 ?18
44979 29864: Id : 10, {_}:
44980 multiply (add ?20 ?21) ?22
44982 add (multiply ?20 ?22) (multiply ?21 ?22)
44983 [22, 21, 20] by distribute2 ?20 ?21 ?22
44984 29864: Id : 11, {_}:
44985 add ?24 ?25 =?= add ?25 ?24
44986 [25, 24] by commutativity_for_addition ?24 ?25
44987 29864: Id : 12, {_}:
44988 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
44989 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
44990 29864: Id : 13, {_}:
44991 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
44992 [32, 31] by right_alternative ?31 ?32
44993 29864: Id : 14, {_}:
44994 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
44995 [35, 34] by left_alternative ?34 ?35
44996 29864: Id : 15, {_}:
44997 associator ?37 ?38 ?39
44999 add (multiply (multiply ?37 ?38) ?39)
45000 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
45001 [39, 38, 37] by associator ?37 ?38 ?39
45002 29864: Id : 16, {_}:
45005 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
45006 [42, 41] by commutator ?41 ?42
45007 29864: Id : 17, {_}:
45008 multiply ?44 (multiply ?45 (multiply ?46 ?45))
45010 multiply (multiply (multiply ?44 ?45) ?46) ?45
45011 [46, 45, 44] by right_moufang ?44 ?45 ?46
45013 29864: Id : 1, {_}:
45014 add (associator (multiply x y) z w) (associator x y (commutator z w))
45016 add (multiply x (associator y z w)) (multiply (associator x z w) y)
45017 [] by prove_challenge
45021 29864: additive_inverse 6 1 0
45022 29864: additive_identity 8 0 0
45023 29864: add 18 2 2 0,2
45024 29864: commutator 2 2 1 0,3,2,2
45025 29864: associator 5 3 4 0,1,2
45026 29864: w 4 0 4 3,1,2
45027 29864: z 4 0 4 2,1,2
45028 29864: multiply 31 2 3 0,1,1,2
45029 29864: y 4 0 4 2,1,1,2
45030 29864: x 4 0 4 1,1,1,2
45031 % SZS status Timeout for RNG033-8.p
45032 NO CLASH, using fixed ground order
45034 29900: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
45035 29900: Id : 3, {_}:
45036 add ?4 additive_identity =>= ?4
45037 [4] by right_additive_identity ?4
45038 29900: Id : 4, {_}:
45039 multiply additive_identity ?6 =>= additive_identity
45040 [6] by left_multiplicative_zero ?6
45041 29900: Id : 5, {_}:
45042 multiply ?8 additive_identity =>= additive_identity
45043 [8] by right_multiplicative_zero ?8
45044 29900: Id : 6, {_}:
45045 add (additive_inverse ?10) ?10 =>= additive_identity
45046 [10] by left_additive_inverse ?10
45047 29900: Id : 7, {_}:
45048 add ?12 (additive_inverse ?12) =>= additive_identity
45049 [12] by right_additive_inverse ?12
45050 29900: Id : 8, {_}:
45051 additive_inverse (additive_inverse ?14) =>= ?14
45052 [14] by additive_inverse_additive_inverse ?14
45053 29900: Id : 9, {_}:
45054 multiply ?16 (add ?17 ?18)
45056 add (multiply ?16 ?17) (multiply ?16 ?18)
45057 [18, 17, 16] by distribute1 ?16 ?17 ?18
45058 29900: Id : 10, {_}:
45059 multiply (add ?20 ?21) ?22
45061 add (multiply ?20 ?22) (multiply ?21 ?22)
45062 [22, 21, 20] by distribute2 ?20 ?21 ?22
45063 29900: Id : 11, {_}:
45064 add ?24 ?25 =?= add ?25 ?24
45065 [25, 24] by commutativity_for_addition ?24 ?25
45066 29900: Id : 12, {_}:
45067 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
45068 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
45069 29900: Id : 13, {_}:
45070 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
45071 [32, 31] by right_alternative ?31 ?32
45072 29900: Id : 14, {_}:
45073 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
45074 [35, 34] by left_alternative ?34 ?35
45075 29900: Id : 15, {_}:
45076 associator ?37 ?38 ?39
45078 add (multiply (multiply ?37 ?38) ?39)
45079 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
45080 [39, 38, 37] by associator ?37 ?38 ?39
45081 29900: Id : 16, {_}:
45084 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
45085 [42, 41] by commutator ?41 ?42
45086 29900: Id : 17, {_}:
45087 multiply (additive_inverse ?44) (additive_inverse ?45)
45090 [45, 44] by product_of_inverses ?44 ?45
45091 29900: Id : 18, {_}:
45092 multiply (additive_inverse ?47) ?48
45094 additive_inverse (multiply ?47 ?48)
45095 [48, 47] by inverse_product1 ?47 ?48
45096 29900: Id : 19, {_}:
45097 multiply ?50 (additive_inverse ?51)
45099 additive_inverse (multiply ?50 ?51)
45100 [51, 50] by inverse_product2 ?50 ?51
45101 29900: Id : 20, {_}:
45102 multiply ?53 (add ?54 (additive_inverse ?55))
45104 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
45105 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
45106 29900: Id : 21, {_}:
45107 multiply (add ?57 (additive_inverse ?58)) ?59
45109 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
45110 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
45111 29900: Id : 22, {_}:
45112 multiply (additive_inverse ?61) (add ?62 ?63)
45114 add (additive_inverse (multiply ?61 ?62))
45115 (additive_inverse (multiply ?61 ?63))
45116 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
45117 29900: Id : 23, {_}:
45118 multiply (add ?65 ?66) (additive_inverse ?67)
45120 add (additive_inverse (multiply ?65 ?67))
45121 (additive_inverse (multiply ?66 ?67))
45122 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
45123 29900: Id : 24, {_}:
45124 multiply ?69 (multiply ?70 (multiply ?71 ?70))
45126 multiply (multiply (multiply ?69 ?70) ?71) ?70
45127 [71, 70, 69] by right_moufang ?69 ?70 ?71
45129 29900: Id : 1, {_}:
45130 add (associator (multiply x y) z w) (associator x y (commutator z w))
45132 add (multiply x (associator y z w)) (multiply (associator x z w) y)
45133 [] by prove_challenge
45137 29900: additive_inverse 22 1 0
45138 29900: additive_identity 8 0 0
45139 29900: add 26 2 2 0,2
45140 29900: commutator 2 2 1 0,3,2,2
45141 29900: associator 5 3 4 0,1,2
45142 29900: w 4 0 4 3,1,2
45143 29900: z 4 0 4 2,1,2
45144 29900: multiply 49 2 3 0,1,1,2
45145 29900: y 4 0 4 2,1,1,2
45146 29900: x 4 0 4 1,1,1,2
45147 NO CLASH, using fixed ground order
45149 29901: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
45150 29901: Id : 3, {_}:
45151 add ?4 additive_identity =>= ?4
45152 [4] by right_additive_identity ?4
45153 29901: Id : 4, {_}:
45154 multiply additive_identity ?6 =>= additive_identity
45155 [6] by left_multiplicative_zero ?6
45156 29901: Id : 5, {_}:
45157 multiply ?8 additive_identity =>= additive_identity
45158 [8] by right_multiplicative_zero ?8
45159 29901: Id : 6, {_}:
45160 add (additive_inverse ?10) ?10 =>= additive_identity
45161 [10] by left_additive_inverse ?10
45162 29901: Id : 7, {_}:
45163 add ?12 (additive_inverse ?12) =>= additive_identity
45164 [12] by right_additive_inverse ?12
45165 29901: Id : 8, {_}:
45166 additive_inverse (additive_inverse ?14) =>= ?14
45167 [14] by additive_inverse_additive_inverse ?14
45168 29901: Id : 9, {_}:
45169 multiply ?16 (add ?17 ?18)
45171 add (multiply ?16 ?17) (multiply ?16 ?18)
45172 [18, 17, 16] by distribute1 ?16 ?17 ?18
45173 29901: Id : 10, {_}:
45174 multiply (add ?20 ?21) ?22
45176 add (multiply ?20 ?22) (multiply ?21 ?22)
45177 [22, 21, 20] by distribute2 ?20 ?21 ?22
45178 29901: Id : 11, {_}:
45179 add ?24 ?25 =?= add ?25 ?24
45180 [25, 24] by commutativity_for_addition ?24 ?25
45181 29901: Id : 12, {_}:
45182 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
45183 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
45184 29901: Id : 13, {_}:
45185 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
45186 [32, 31] by right_alternative ?31 ?32
45187 29901: Id : 14, {_}:
45188 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
45189 [35, 34] by left_alternative ?34 ?35
45190 29901: Id : 15, {_}:
45191 associator ?37 ?38 ?39
45193 add (multiply (multiply ?37 ?38) ?39)
45194 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
45195 [39, 38, 37] by associator ?37 ?38 ?39
45196 29901: Id : 16, {_}:
45199 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
45200 [42, 41] by commutator ?41 ?42
45201 29901: Id : 17, {_}:
45202 multiply (additive_inverse ?44) (additive_inverse ?45)
45205 [45, 44] by product_of_inverses ?44 ?45
45206 29901: Id : 18, {_}:
45207 multiply (additive_inverse ?47) ?48
45209 additive_inverse (multiply ?47 ?48)
45210 [48, 47] by inverse_product1 ?47 ?48
45211 29901: Id : 19, {_}:
45212 multiply ?50 (additive_inverse ?51)
45214 additive_inverse (multiply ?50 ?51)
45215 [51, 50] by inverse_product2 ?50 ?51
45216 29901: Id : 20, {_}:
45217 multiply ?53 (add ?54 (additive_inverse ?55))
45219 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
45220 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
45221 29901: Id : 21, {_}:
45222 multiply (add ?57 (additive_inverse ?58)) ?59
45224 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
45225 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
45226 29901: Id : 22, {_}:
45227 multiply (additive_inverse ?61) (add ?62 ?63)
45229 add (additive_inverse (multiply ?61 ?62))
45230 (additive_inverse (multiply ?61 ?63))
45231 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
45232 29901: Id : 23, {_}:
45233 multiply (add ?65 ?66) (additive_inverse ?67)
45235 add (additive_inverse (multiply ?65 ?67))
45236 (additive_inverse (multiply ?66 ?67))
45237 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
45238 29901: Id : 24, {_}:
45239 multiply ?69 (multiply ?70 (multiply ?71 ?70))
45241 multiply (multiply (multiply ?69 ?70) ?71) ?70
45242 [71, 70, 69] by right_moufang ?69 ?70 ?71
45244 29901: Id : 1, {_}:
45245 add (associator (multiply x y) z w) (associator x y (commutator z w))
45247 add (multiply x (associator y z w)) (multiply (associator x z w) y)
45248 [] by prove_challenge
45252 29901: additive_inverse 22 1 0
45253 29901: additive_identity 8 0 0
45254 29901: add 26 2 2 0,2
45255 29901: commutator 2 2 1 0,3,2,2
45256 29901: associator 5 3 4 0,1,2
45257 29901: w 4 0 4 3,1,2
45258 29901: z 4 0 4 2,1,2
45259 29901: multiply 49 2 3 0,1,1,2
45260 29901: y 4 0 4 2,1,1,2
45261 29901: x 4 0 4 1,1,1,2
45262 NO CLASH, using fixed ground order
45264 29902: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
45265 29902: Id : 3, {_}:
45266 add ?4 additive_identity =>= ?4
45267 [4] by right_additive_identity ?4
45268 29902: Id : 4, {_}:
45269 multiply additive_identity ?6 =>= additive_identity
45270 [6] by left_multiplicative_zero ?6
45271 29902: Id : 5, {_}:
45272 multiply ?8 additive_identity =>= additive_identity
45273 [8] by right_multiplicative_zero ?8
45274 29902: Id : 6, {_}:
45275 add (additive_inverse ?10) ?10 =>= additive_identity
45276 [10] by left_additive_inverse ?10
45277 29902: Id : 7, {_}:
45278 add ?12 (additive_inverse ?12) =>= additive_identity
45279 [12] by right_additive_inverse ?12
45280 29902: Id : 8, {_}:
45281 additive_inverse (additive_inverse ?14) =>= ?14
45282 [14] by additive_inverse_additive_inverse ?14
45283 29902: Id : 9, {_}:
45284 multiply ?16 (add ?17 ?18)
45286 add (multiply ?16 ?17) (multiply ?16 ?18)
45287 [18, 17, 16] by distribute1 ?16 ?17 ?18
45288 29902: Id : 10, {_}:
45289 multiply (add ?20 ?21) ?22
45291 add (multiply ?20 ?22) (multiply ?21 ?22)
45292 [22, 21, 20] by distribute2 ?20 ?21 ?22
45293 29902: Id : 11, {_}:
45294 add ?24 ?25 =?= add ?25 ?24
45295 [25, 24] by commutativity_for_addition ?24 ?25
45296 29902: Id : 12, {_}:
45297 add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
45298 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
45299 29902: Id : 13, {_}:
45300 multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
45301 [32, 31] by right_alternative ?31 ?32
45302 29902: Id : 14, {_}:
45303 multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
45304 [35, 34] by left_alternative ?34 ?35
45305 29902: Id : 15, {_}:
45306 associator ?37 ?38 ?39
45308 add (multiply (multiply ?37 ?38) ?39)
45309 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
45310 [39, 38, 37] by associator ?37 ?38 ?39
45311 29902: Id : 16, {_}:
45314 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
45315 [42, 41] by commutator ?41 ?42
45316 29902: Id : 17, {_}:
45317 multiply (additive_inverse ?44) (additive_inverse ?45)
45320 [45, 44] by product_of_inverses ?44 ?45
45321 29902: Id : 18, {_}:
45322 multiply (additive_inverse ?47) ?48
45324 additive_inverse (multiply ?47 ?48)
45325 [48, 47] by inverse_product1 ?47 ?48
45326 29902: Id : 19, {_}:
45327 multiply ?50 (additive_inverse ?51)
45329 additive_inverse (multiply ?50 ?51)
45330 [51, 50] by inverse_product2 ?50 ?51
45331 29902: Id : 20, {_}:
45332 multiply ?53 (add ?54 (additive_inverse ?55))
45334 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
45335 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
45336 29902: Id : 21, {_}:
45337 multiply (add ?57 (additive_inverse ?58)) ?59
45339 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
45340 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
45341 29902: Id : 22, {_}:
45342 multiply (additive_inverse ?61) (add ?62 ?63)
45344 add (additive_inverse (multiply ?61 ?62))
45345 (additive_inverse (multiply ?61 ?63))
45346 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
45347 29902: Id : 23, {_}:
45348 multiply (add ?65 ?66) (additive_inverse ?67)
45350 add (additive_inverse (multiply ?65 ?67))
45351 (additive_inverse (multiply ?66 ?67))
45352 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
45353 29902: Id : 24, {_}:
45354 multiply ?69 (multiply ?70 (multiply ?71 ?70))
45356 multiply (multiply (multiply ?69 ?70) ?71) ?70
45357 [71, 70, 69] by right_moufang ?69 ?70 ?71
45359 29902: Id : 1, {_}:
45360 add (associator (multiply x y) z w) (associator x y (commutator z w))
45362 add (multiply x (associator y z w)) (multiply (associator x z w) y)
45363 [] by prove_challenge
45367 29902: additive_inverse 22 1 0
45368 29902: additive_identity 8 0 0
45369 29902: add 26 2 2 0,2
45370 29902: commutator 2 2 1 0,3,2,2
45371 29902: associator 5 3 4 0,1,2
45372 29902: w 4 0 4 3,1,2
45373 29902: z 4 0 4 2,1,2
45374 29902: multiply 49 2 3 0,1,1,2
45375 29902: y 4 0 4 2,1,1,2
45376 29902: x 4 0 4 1,1,1,2
45377 % SZS status Timeout for RNG033-9.p
45378 NO CLASH, using fixed ground order
45380 29918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
45381 29918: Id : 3, {_}:
45382 add ?4 additive_identity =>= ?4
45383 [4] by right_additive_identity ?4
45384 29918: Id : 4, {_}:
45385 add (additive_inverse ?6) ?6 =>= additive_identity
45386 [6] by left_additive_inverse ?6
45387 29918: Id : 5, {_}:
45388 add ?8 (additive_inverse ?8) =>= additive_identity
45389 [8] by right_additive_inverse ?8
45390 29918: Id : 6, {_}:
45391 add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
45392 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
45393 29918: Id : 7, {_}:
45394 add ?14 ?15 =?= add ?15 ?14
45395 [15, 14] by commutativity_for_addition ?14 ?15
45396 29918: Id : 8, {_}:
45397 multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
45398 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
45399 29918: Id : 9, {_}:
45400 multiply ?21 (add ?22 ?23)
45402 add (multiply ?21 ?22) (multiply ?21 ?23)
45403 [23, 22, 21] by distribute1 ?21 ?22 ?23
45404 29918: Id : 10, {_}:
45405 multiply (add ?25 ?26) ?27
45407 add (multiply ?25 ?27) (multiply ?26 ?27)
45408 [27, 26, 25] by distribute2 ?25 ?26 ?27
45409 29918: Id : 11, {_}:
45410 multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
45411 [29] by x_fifthed_is_x ?29
45412 29918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
45414 29918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
45418 29918: additive_inverse 2 1 0
45420 29918: additive_identity 4 0 0
45422 29918: multiply 16 2 1 0,2
45425 NO CLASH, using fixed ground order
45427 29919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
45428 29919: Id : 3, {_}:
45429 add ?4 additive_identity =>= ?4
45430 [4] by right_additive_identity ?4
45431 29919: Id : 4, {_}:
45432 add (additive_inverse ?6) ?6 =>= additive_identity
45433 [6] by left_additive_inverse ?6
45434 29919: Id : 5, {_}:
45435 add ?8 (additive_inverse ?8) =>= additive_identity
45436 [8] by right_additive_inverse ?8
45437 29919: Id : 6, {_}:
45438 add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
45439 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
45440 29919: Id : 7, {_}:
45441 add ?14 ?15 =?= add ?15 ?14
45442 [15, 14] by commutativity_for_addition ?14 ?15
45443 29919: Id : 8, {_}:
45444 multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
45445 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
45446 29919: Id : 9, {_}:
45447 multiply ?21 (add ?22 ?23)
45449 add (multiply ?21 ?22) (multiply ?21 ?23)
45450 [23, 22, 21] by distribute1 ?21 ?22 ?23
45451 29919: Id : 10, {_}:
45452 multiply (add ?25 ?26) ?27
45454 add (multiply ?25 ?27) (multiply ?26 ?27)
45455 [27, 26, 25] by distribute2 ?25 ?26 ?27
45456 29919: Id : 11, {_}:
45457 multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
45458 [29] by x_fifthed_is_x ?29
45459 29919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
45461 29919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
45465 29919: additive_inverse 2 1 0
45467 29919: additive_identity 4 0 0
45468 NO CLASH, using fixed ground order
45470 29920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
45471 29920: Id : 3, {_}:
45472 add ?4 additive_identity =>= ?4
45473 [4] by right_additive_identity ?4
45474 29920: Id : 4, {_}:
45475 add (additive_inverse ?6) ?6 =>= additive_identity
45476 [6] by left_additive_inverse ?6
45477 29920: Id : 5, {_}:
45478 add ?8 (additive_inverse ?8) =>= additive_identity
45479 [8] by right_additive_inverse ?8
45480 29920: Id : 6, {_}:
45481 add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
45482 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
45483 29920: Id : 7, {_}:
45484 add ?14 ?15 =?= add ?15 ?14
45485 [15, 14] by commutativity_for_addition ?14 ?15
45486 29920: Id : 8, {_}:
45487 multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
45488 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
45489 29920: Id : 9, {_}:
45490 multiply ?21 (add ?22 ?23)
45492 add (multiply ?21 ?22) (multiply ?21 ?23)
45493 [23, 22, 21] by distribute1 ?21 ?22 ?23
45494 29920: Id : 10, {_}:
45495 multiply (add ?25 ?26) ?27
45497 add (multiply ?25 ?27) (multiply ?26 ?27)
45498 [27, 26, 25] by distribute2 ?25 ?26 ?27
45499 29920: Id : 11, {_}:
45500 multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
45501 [29] by x_fifthed_is_x ?29
45502 29920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
45504 29920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
45508 29920: additive_inverse 2 1 0
45510 29920: additive_identity 4 0 0
45512 29920: multiply 16 2 1 0,2
45516 29919: multiply 16 2 1 0,2
45519 % SZS status Timeout for RNG036-7.p
45520 NO CLASH, using fixed ground order
45522 29951: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45523 29951: Id : 3, {_}:
45524 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
45525 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45526 29951: Id : 4, {_}:
45527 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45530 [10, 9] by robbins_axiom ?9 ?10
45532 29951: Id : 1, {_}:
45533 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45536 [] by prove_huntingtons_axiom
45540 29951: add 12 2 3 0,2
45541 29951: negate 9 1 5 0,1,2
45542 29951: b 3 0 3 1,2,1,1,2
45543 29951: a 2 0 2 1,1,1,2
45544 NO CLASH, using fixed ground order
45546 29952: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45547 29952: Id : 3, {_}:
45548 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45549 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45550 29952: Id : 4, {_}:
45551 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45554 [10, 9] by robbins_axiom ?9 ?10
45556 29952: Id : 1, {_}:
45557 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45560 [] by prove_huntingtons_axiom
45564 29952: add 12 2 3 0,2
45565 29952: negate 9 1 5 0,1,2
45566 29952: b 3 0 3 1,2,1,1,2
45567 29952: a 2 0 2 1,1,1,2
45568 NO CLASH, using fixed ground order
45570 29953: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45571 29953: Id : 3, {_}:
45572 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45573 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45574 29953: Id : 4, {_}:
45575 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45578 [10, 9] by robbins_axiom ?9 ?10
45580 29953: Id : 1, {_}:
45581 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45584 [] by prove_huntingtons_axiom
45588 29953: add 12 2 3 0,2
45589 29953: negate 9 1 5 0,1,2
45590 29953: b 3 0 3 1,2,1,1,2
45591 29953: a 2 0 2 1,1,1,2
45592 % SZS status Timeout for ROB001-1.p
45593 NO CLASH, using fixed ground order
45595 29969: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45596 29969: Id : 3, {_}:
45597 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
45598 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45599 29969: Id : 4, {_}:
45600 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45603 [10, 9] by robbins_axiom ?9 ?10
45604 29969: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
45606 29969: Id : 1, {_}:
45607 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45610 [] by prove_huntingtons_axiom
45614 29969: add 13 2 3 0,2
45615 29969: negate 11 1 5 0,1,2
45616 29969: b 5 0 3 1,2,1,1,2
45617 29969: a 3 0 2 1,1,1,2
45618 NO CLASH, using fixed ground order
45620 29970: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45621 29970: Id : 3, {_}:
45622 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45623 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45624 29970: Id : 4, {_}:
45625 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45628 [10, 9] by robbins_axiom ?9 ?10
45629 29970: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
45631 29970: Id : 1, {_}:
45632 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45635 [] by prove_huntingtons_axiom
45639 29970: add 13 2 3 0,2
45640 29970: negate 11 1 5 0,1,2
45641 29970: b 5 0 3 1,2,1,1,2
45642 29970: a 3 0 2 1,1,1,2
45643 NO CLASH, using fixed ground order
45645 29971: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45646 29971: Id : 3, {_}:
45647 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45648 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45649 29971: Id : 4, {_}:
45650 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45653 [10, 9] by robbins_axiom ?9 ?10
45654 29971: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
45656 29971: Id : 1, {_}:
45657 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45660 [] by prove_huntingtons_axiom
45664 29971: add 13 2 3 0,2
45665 29971: negate 11 1 5 0,1,2
45666 29971: b 5 0 3 1,2,1,1,2
45667 29971: a 3 0 2 1,1,1,2
45668 % SZS status Timeout for ROB007-1.p
45669 NO CLASH, using fixed ground order
45671 29998: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
45672 29998: Id : 3, {_}:
45673 add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
45674 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
45675 29998: Id : 4, {_}:
45676 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
45679 [11, 10] by robbins_axiom ?10 ?11
45680 29998: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
45682 29998: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
45688 29998: negate 6 1 0
45689 29998: add 11 2 1 0,2
45690 NO CLASH, using fixed ground order
45692 29999: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
45693 29999: Id : 3, {_}:
45694 add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
45695 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
45696 29999: Id : 4, {_}:
45697 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
45700 [11, 10] by robbins_axiom ?10 ?11
45701 29999: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
45703 29999: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
45709 29999: negate 6 1 0
45710 29999: add 11 2 1 0,2
45711 NO CLASH, using fixed ground order
45713 30000: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
45714 30000: Id : 3, {_}:
45715 add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
45716 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
45717 30000: Id : 4, {_}:
45718 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
45721 [11, 10] by robbins_axiom ?10 ?11
45722 30000: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
45724 30000: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
45730 30000: negate 6 1 0
45731 30000: add 11 2 1 0,2
45732 % SZS status Timeout for ROB007-2.p
45733 NO CLASH, using fixed ground order
45735 30074: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45736 NO CLASH, using fixed ground order
45738 30075: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45739 30075: Id : 3, {_}:
45740 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45741 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45742 30075: Id : 4, {_}:
45743 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45746 [10, 9] by robbins_axiom ?9 ?10
45747 30075: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
45749 30075: Id : 1, {_}:
45750 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45753 [] by prove_huntingtons_axiom
45757 30075: add 13 2 3 0,2
45758 30075: negate 11 1 5 0,1,2
45759 30075: b 5 0 3 1,2,1,1,2
45760 30075: a 3 0 2 1,1,1,2
45761 30074: Id : 3, {_}:
45762 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
45763 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45764 30074: Id : 4, {_}:
45765 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45768 [10, 9] by robbins_axiom ?9 ?10
45769 30074: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
45771 30074: Id : 1, {_}:
45772 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45775 [] by prove_huntingtons_axiom
45779 30074: add 13 2 3 0,2
45780 30074: negate 11 1 5 0,1,2
45781 30074: b 5 0 3 1,2,1,1,2
45782 30074: a 3 0 2 1,1,1,2
45783 NO CLASH, using fixed ground order
45785 30076: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45786 30076: Id : 3, {_}:
45787 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45788 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45789 30076: Id : 4, {_}:
45790 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45793 [10, 9] by robbins_axiom ?9 ?10
45794 30076: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
45796 30076: Id : 1, {_}:
45797 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45800 [] by prove_huntingtons_axiom
45804 30076: add 13 2 3 0,2
45805 30076: negate 11 1 5 0,1,2
45806 30076: b 5 0 3 1,2,1,1,2
45807 30076: a 3 0 2 1,1,1,2
45808 % SZS status Timeout for ROB020-1.p
45809 NO CLASH, using fixed ground order
45811 30104: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
45812 30104: Id : 3, {_}:
45813 add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
45814 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
45815 30104: Id : 4, {_}:
45816 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
45819 [11, 10] by robbins_axiom ?10 ?11
45820 30104: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
45822 30104: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
45828 30104: negate 6 1 0
45829 30104: add 11 2 1 0,2
45830 NO CLASH, using fixed ground order
45832 30105: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
45833 30105: Id : 3, {_}:
45834 add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
45835 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
45836 30105: Id : 4, {_}:
45837 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
45840 [11, 10] by robbins_axiom ?10 ?11
45841 30105: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
45843 30105: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
45849 30105: negate 6 1 0
45850 30105: add 11 2 1 0,2
45851 NO CLASH, using fixed ground order
45853 30106: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
45854 30106: Id : 3, {_}:
45855 add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
45856 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
45857 30106: Id : 4, {_}:
45858 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
45861 [11, 10] by robbins_axiom ?10 ?11
45862 30106: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
45864 30106: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
45870 30106: negate 6 1 0
45871 30106: add 11 2 1 0,2
45872 % SZS status Timeout for ROB020-2.p
45873 NO CLASH, using fixed ground order
45875 30123: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45876 30123: Id : 3, {_}:
45877 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
45878 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45879 30123: Id : 4, {_}:
45880 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45883 [10, 9] by robbins_axiom ?9 ?10
45884 30123: Id : 5, {_}:
45885 negate (add (negate (add a (add a b))) (negate (add a (negate b))))
45888 [] by the_condition
45890 30123: Id : 1, {_}:
45891 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45894 [] by prove_huntingtons_axiom
45898 30123: add 16 2 3 0,2
45899 30123: negate 13 1 5 0,1,2
45900 30123: b 5 0 3 1,2,1,1,2
45901 30123: a 6 0 2 1,1,1,2
45902 NO CLASH, using fixed ground order
45904 30124: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45905 30124: Id : 3, {_}:
45906 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45907 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45908 30124: Id : 4, {_}:
45909 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45912 [10, 9] by robbins_axiom ?9 ?10
45913 30124: Id : 5, {_}:
45914 negate (add (negate (add a (add a b))) (negate (add a (negate b))))
45917 [] by the_condition
45919 30124: Id : 1, {_}:
45920 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45923 [] by prove_huntingtons_axiom
45927 30124: add 16 2 3 0,2
45928 30124: negate 13 1 5 0,1,2
45929 30124: b 5 0 3 1,2,1,1,2
45930 30124: a 6 0 2 1,1,1,2
45931 NO CLASH, using fixed ground order
45933 30125: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45934 30125: Id : 3, {_}:
45935 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45936 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45937 30125: Id : 4, {_}:
45938 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45941 [10, 9] by robbins_axiom ?9 ?10
45942 30125: Id : 5, {_}:
45943 negate (add (negate (add a (add a b))) (negate (add a (negate b))))
45946 [] by the_condition
45948 30125: Id : 1, {_}:
45949 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45952 [] by prove_huntingtons_axiom
45956 30125: add 16 2 3 0,2
45957 30125: negate 13 1 5 0,1,2
45958 30125: b 5 0 3 1,2,1,1,2
45959 30125: a 6 0 2 1,1,1,2
45960 % SZS status Timeout for ROB024-1.p
45961 NO CLASH, using fixed ground order
45963 30152: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45964 30152: Id : 3, {_}:
45965 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
45966 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45967 30152: Id : 4, {_}:
45968 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45971 [10, 9] by robbins_axiom ?9 ?10
45972 30152: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
45974 30152: Id : 1, {_}:
45975 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
45978 [] by prove_huntingtons_axiom
45983 30152: add 12 2 3 0,2
45984 30152: negate 11 1 5 0,1,2
45985 30152: b 3 0 3 1,2,1,1,2
45986 30152: a 2 0 2 1,1,1,2
45987 NO CLASH, using fixed ground order
45989 30153: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
45990 30153: Id : 3, {_}:
45991 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
45992 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
45993 30153: Id : 4, {_}:
45994 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
45997 [10, 9] by robbins_axiom ?9 ?10
45998 30153: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
46000 30153: Id : 1, {_}:
46001 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
46004 [] by prove_huntingtons_axiom
46009 30153: add 12 2 3 0,2
46010 30153: negate 11 1 5 0,1,2
46011 30153: b 3 0 3 1,2,1,1,2
46012 30153: a 2 0 2 1,1,1,2
46013 NO CLASH, using fixed ground order
46015 30154: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
46016 30154: Id : 3, {_}:
46017 add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
46018 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
46019 30154: Id : 4, {_}:
46020 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
46023 [10, 9] by robbins_axiom ?9 ?10
46024 30154: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
46026 30154: Id : 1, {_}:
46027 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
46030 [] by prove_huntingtons_axiom
46035 30154: add 12 2 3 0,2
46036 30154: negate 11 1 5 0,1,2
46037 30154: b 3 0 3 1,2,1,1,2
46038 30154: a 2 0 2 1,1,1,2
46039 % SZS status Timeout for ROB027-1.p
46040 NO CLASH, using fixed ground order
46042 30170: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
46043 30170: Id : 3, {_}:
46044 add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
46045 [9, 8, 7] by associativity_of_add ?7 ?8 ?9
46046 30170: Id : 4, {_}:
46047 negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
46050 [12, 11] by robbins_axiom ?11 ?12
46052 30170: Id : 1, {_}:
46053 negate (add ?1 ?2) =>= negate ?2
46054 [2, 1] by prove_absorption_within_negation ?1 ?2
46058 30170: negate 6 1 2 0,2
46059 30170: add 10 2 1 0,1,2
46060 NO CLASH, using fixed ground order
46062 30171: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
46063 30171: Id : 3, {_}:
46064 add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
46065 [9, 8, 7] by associativity_of_add ?7 ?8 ?9
46066 30171: Id : 4, {_}:
46067 negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
46070 [12, 11] by robbins_axiom ?11 ?12
46072 30171: Id : 1, {_}:
46073 negate (add ?1 ?2) =>= negate ?2
46074 [2, 1] by prove_absorption_within_negation ?1 ?2
46078 30171: negate 6 1 2 0,2
46079 30171: add 10 2 1 0,1,2
46080 NO CLASH, using fixed ground order
46082 30172: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
46083 30172: Id : 3, {_}:
46084 add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
46085 [9, 8, 7] by associativity_of_add ?7 ?8 ?9
46086 30172: Id : 4, {_}:
46087 negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
46090 [12, 11] by robbins_axiom ?11 ?12
46092 30172: Id : 1, {_}:
46093 negate (add ?1 ?2) =>= negate ?2
46094 [2, 1] by prove_absorption_within_negation ?1 ?2
46098 30172: negate 6 1 2 0,2
46099 30172: add 10 2 1 0,1,2
46100 % SZS status Timeout for ROB031-1.p
46101 NO CLASH, using fixed ground order
46103 30204: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
46104 NO CLASH, using fixed ground order
46106 30205: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
46107 30205: Id : 3, {_}:
46108 add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
46109 [9, 8, 7] by associativity_of_add ?7 ?8 ?9
46110 30205: Id : 4, {_}:
46111 negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
46114 [12, 11] by robbins_axiom ?11 ?12
46116 30205: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
46120 30205: negate 4 1 0
46121 30205: add 10 2 1 0,2
46122 30204: Id : 3, {_}:
46123 add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
46124 [9, 8, 7] by associativity_of_add ?7 ?8 ?9
46125 30204: Id : 4, {_}:
46126 negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
46129 [12, 11] by robbins_axiom ?11 ?12
46131 30204: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
46135 30204: negate 4 1 0
46136 30204: add 10 2 1 0,2
46137 NO CLASH, using fixed ground order
46139 30206: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
46140 30206: Id : 3, {_}:
46141 add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
46142 [9, 8, 7] by associativity_of_add ?7 ?8 ?9
46143 30206: Id : 4, {_}:
46144 negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
46147 [12, 11] by robbins_axiom ?11 ?12
46149 30206: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
46153 30206: negate 4 1 0
46154 30206: add 10 2 1 0,2
46155 % SZS status Timeout for ROB032-1.p