8 additive_identity is 82
9 additive_inverse1 is 84
10 additive_inverse2 is 83
13 commutativity_of_add is 92
14 commutativity_of_multiply is 91
20 multiplicative_id1 is 79
21 multiplicative_id2 is 78
22 multiplicative_identity is 85
23 multiplicative_inverse1 is 81
24 multiplicative_inverse2 is 80
26 prove_associativity is 94
28 Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
30 multiply ?5 ?6 =?= multiply ?6 ?5
31 [6, 5] by commutativity_of_multiply ?5 ?6
33 add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
34 [10, 9, 8] by distributivity1 ?8 ?9 ?10
36 add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
37 [14, 13, 12] by distributivity2 ?12 ?13 ?14
39 multiply (add ?16 ?17) ?18
41 add (multiply ?16 ?18) (multiply ?17 ?18)
42 [18, 17, 16] by distributivity3 ?16 ?17 ?18
44 multiply ?20 (add ?21 ?22)
46 add (multiply ?20 ?21) (multiply ?20 ?22)
47 [22, 21, 20] by distributivity4 ?20 ?21 ?22
49 add ?24 (inverse ?24) =>= multiplicative_identity
50 [24] by additive_inverse1 ?24
52 add (inverse ?26) ?26 =>= multiplicative_identity
53 [26] by additive_inverse2 ?26
55 multiply ?28 (inverse ?28) =>= additive_identity
56 [28] by multiplicative_inverse1 ?28
58 multiply (inverse ?30) ?30 =>= additive_identity
59 [30] by multiplicative_inverse2 ?30
61 multiply ?32 multiplicative_identity =>= ?32
62 [32] by multiplicative_id1 ?32
64 multiply multiplicative_identity ?34 =>= ?34
65 [34] by multiplicative_id2 ?34
66 Id : 28, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
67 Id : 30, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
70 multiply a (multiply b c) =<= multiply (multiply a b) c
71 [] by prove_associativity
73 FAILURE in 253 iterations
74 % SZS status Timeout for BOO007-2.p
81 additive_identity is 88
82 additive_inverse1 is 83
85 commutativity_of_add is 92
86 commutativity_of_multiply is 91
90 multiplicative_id1 is 85
91 multiplicative_identity is 86
92 multiplicative_inverse1 is 82
94 prove_associativity is 94
96 Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
98 multiply ?5 ?6 =?= multiply ?6 ?5
99 [6, 5] by commutativity_of_multiply ?5 ?6
101 add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
102 [10, 9, 8] by distributivity1 ?8 ?9 ?10
104 multiply ?12 (add ?13 ?14)
106 add (multiply ?12 ?13) (multiply ?12 ?14)
107 [14, 13, 12] by distributivity2 ?12 ?13 ?14
108 Id : 12, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
110 multiply ?18 multiplicative_identity =>= ?18
111 [18] by multiplicative_id1 ?18
113 add ?20 (inverse ?20) =>= multiplicative_identity
114 [20] by additive_inverse1 ?20
116 multiply ?22 (inverse ?22) =>= additive_identity
117 [22] by multiplicative_inverse1 ?22
120 multiply a (multiply b c) =<= multiply (multiply a b) c
121 [] by prove_associativity
123 FAILURE in 258 iterations
124 % SZS status Timeout for BOO007-4.p
130 additive_inverse is 83
131 associativity_of_add is 80
132 associativity_of_multiply is 79
141 multiplicative_inverse is 81
147 prove_multiply_add_property is 93
150 add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
152 multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
153 [4, 3, 2] by distributivity ?2 ?3 ?4
155 add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
156 [8, 7, 6] by l1 ?6 ?7 ?8
158 add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
159 [12, 11, 10] by l3 ?10 ?11 ?12
161 multiply (add ?14 (inverse ?14)) ?15 =>= ?15
162 [15, 14] by property3 ?14 ?15
164 multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
165 [19, 18, 17] by l2 ?17 ?18 ?19
167 multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
168 [23, 22, 21] by l4 ?21 ?22 ?23
170 add (multiply ?25 (inverse ?25)) ?26 =>= ?26
171 [26, 25] by property3_dual ?25 ?26
172 Id : 18, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
174 multiply ?30 (inverse ?30) =>= n0
175 [30] by multiplicative_inverse ?30
177 add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
178 [34, 33, 32] by associativity_of_add ?32 ?33 ?34
180 multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
181 [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
184 multiply a (add b c) =<= add (multiply b a) (multiply c a)
185 [] by prove_multiply_add_property
187 FAILURE in 221 iterations
188 % SZS status Timeout for BOO031-1.p
203 prove_single_axiom is 89
205 ternary_multiply_1 is 87
206 ternary_multiply_2 is 86
209 multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
211 multiply ?2 ?3 (multiply ?4 ?5 ?6)
212 [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
213 Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
215 multiply ?11 ?11 ?12 =>= ?11
216 [12, 11] by ternary_multiply_2 ?11 ?12
218 multiply (inverse ?14) ?14 ?15 =>= ?15
219 [15, 14] by left_inverse ?14 ?15
221 multiply ?17 ?18 (inverse ?18) =>= ?17
222 [18, 17] by right_inverse ?17 ?18
225 multiply (multiply a (inverse a) b)
226 (inverse (multiply (multiply c d e) f (multiply c d g)))
227 (multiply d (multiply g f e) c)
230 [] by prove_single_axiom
231 Found proof, 2.355821s
232 % SZS status Unsatisfiable for BOO034-1.p
233 % SZS output start CNFRefutation for BOO034-1.p
234 Id : 8, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
235 Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
236 Id : 12, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
237 Id : 10, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
238 Id : 4, {_}: 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
239 Id : 75, {_}: multiply ?212 ?213 ?214 =<= multiply ?212 ?213 (multiply ?215 (multiply ?212 ?213 ?214) ?214) [215, 214, 213, 212] by Super 4 with 6 at 2
240 Id : 84, {_}: multiply ?257 ?258 ?259 =<= multiply ?257 ?258 (multiply ?257 ?258 ?259) [259, 258, 257] by Super 75 with 8 at 3,3
241 Id : 115, {_}: multiply (multiply ?285 ?286 ?288) ?289 (multiply ?285 ?286 ?287) =?= multiply ?285 ?286 (multiply ?288 ?289 (multiply ?285 ?286 ?287)) [287, 289, 288, 286, 285] by Super 4 with 84 at 3,2
242 Id : 298, {_}: multiply ?735 ?736 (multiply ?737 ?738 ?739) =<= multiply ?735 ?736 (multiply ?737 ?738 (multiply ?735 ?736 ?739)) [739, 738, 737, 736, 735] by Demod 115 with 4 at 2
243 Id : 184, {_}: multiply ?446 ?447 ?448 =<= multiply ?446 ?447 (multiply ?448 (multiply ?446 ?447 ?448) ?449) [449, 448, 447, 446] by Super 4 with 8 at 2
244 Id : 189, {_}: multiply ?470 ?471 (inverse ?471) =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Super 184 with 12 at 2,3,3
245 Id : 225, {_}: ?470 =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Demod 189 with 12 at 2
246 Id : 321, {_}: multiply (inverse ?865) ?864 (multiply ?864 ?865 ?866) =>= multiply (inverse ?865) ?864 ?864 [866, 864, 865] by Super 298 with 225 at 3,3
247 Id : 387, {_}: multiply (inverse ?963) ?964 (multiply ?964 ?963 ?965) =>= ?964 [965, 964, 963] by Demod 321 with 6 at 3
248 Id : 389, {_}: multiply (inverse ?974) ?973 ?974 =>= ?973 [973, 974] by Super 387 with 6 at 3,2
249 Id : 437, {_}: ?1071 =<= inverse (inverse ?1071) [1071] by Super 12 with 389 at 2
250 Id : 462, {_}: multiply ?1119 (inverse ?1119) ?1120 =>= ?1120 [1120, 1119] by Super 10 with 437 at 1,2
251 Id : 116, {_}: multiply (multiply ?291 ?292 ?293) ?294 (multiply ?291 ?292 ?295) =?= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Super 4 with 84 at 1,2
252 Id : 12671, {_}: multiply ?19232 ?19233 (multiply ?19234 ?19235 ?19236) =<= multiply ?19232 ?19233 (multiply (multiply ?19232 ?19233 ?19234) ?19235 ?19236) [19236, 19235, 19234, 19233, 19232] by Demod 116 with 4 at 2
253 Id : 80, {_}: multiply ?236 ?237 (inverse ?237) =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Super 75 with 12 at 2,3,3
254 Id : 105, {_}: ?236 =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Demod 80 with 12 at 2
255 Id : 996, {_}: ?2202 =<= multiply ?2202 (inverse ?2203) (multiply ?2204 ?2202 ?2203) [2204, 2203, 2202] by Super 105 with 437 at 3,3,3
256 Id : 1012, {_}: ?2262 =<= multiply ?2262 (inverse (multiply ?2261 ?2263 (inverse ?2262))) ?2263 [2263, 2261, 2262] by Super 996 with 105 at 3,3
257 Id : 459, {_}: ?1109 =<= multiply ?1109 (inverse ?1108) (multiply ?1108 ?1109 ?1110) [1110, 1108, 1109] by Super 225 with 437 at 1,3,3
258 Id : 1017, {_}: inverse ?2283 =<= multiply (inverse ?2283) (inverse (multiply ?2283 ?2285 ?2284)) ?2285 [2284, 2285, 2283] by Super 996 with 459 at 3,3
259 Id : 1909, {_}: ?3987 =<= multiply ?3987 (inverse (inverse ?3985)) (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Super 1012 with 1017 at 1,2,3
260 Id : 1996, {_}: ?3987 =<= multiply ?3987 ?3985 (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Demod 1909 with 437 at 2,3
261 Id : 2510, {_}: ?5132 =<= multiply ?5132 (multiply ?5132 (inverse ?5131) ?5133) ?5131 [5133, 5131, 5132] by Super 105 with 1996 at 3,3
262 Id : 2812, {_}: multiply ?5719 (inverse (inverse ?5721)) ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Super 105 with 2510 at 3,3
263 Id : 2874, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2812 with 437 at 2,2
264 Id : 2875, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 ?5721 ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2874 with 437 at 2,1,3
265 Id : 12777, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =?= multiply ?19864 ?19863 (multiply ?19864 ?19863 ?19862) [19862, 19863, 19864] by Super 12671 with 2875 at 3,3
266 Id : 12993, {_}: multiply ?20226 ?20227 (multiply ?20228 ?20227 ?20226) =>= multiply ?20226 ?20227 ?20228 [20228, 20227, 20226] by Demod 12777 with 84 at 3
267 Id : 19, {_}: multiply ?58 ?59 ?61 =<= multiply ?58 ?59 (multiply ?60 (multiply ?58 ?59 ?61) ?61) [60, 61, 59, 58] by Super 4 with 6 at 2
268 Id : 463, {_}: multiply ?1122 ?1123 (inverse ?1122) =>= ?1123 [1123, 1122] by Super 389 with 437 at 1,2
269 Id : 607, {_}: multiply ?1371 ?1372 (inverse ?1371) =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1372, 1371] by Super 19 with 463 at 2,3,3
270 Id : 625, {_}: ?1372 =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1371, 1372] by Demod 607 with 463 at 2
271 Id : 460, {_}: ?1113 =<= multiply ?1113 (inverse ?1112) (multiply ?1114 ?1113 ?1112) [1114, 1112, 1113] by Super 105 with 437 at 3,3,3
272 Id : 1018, {_}: inverse ?2287 =<= multiply (inverse ?2287) (inverse (multiply ?2288 ?2289 ?2287)) ?2289 [2289, 2288, 2287] by Super 996 with 460 at 3,3
273 Id : 2078, {_}: ?4356 =<= multiply ?4356 (inverse (inverse ?4354)) (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Super 1012 with 1018 at 1,2,3
274 Id : 2124, {_}: ?4356 =<= multiply ?4356 ?4354 (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Demod 2078 with 437 at 2,3
275 Id : 3650, {_}: ?7215 =<= multiply ?7215 (multiply ?7216 (inverse ?7214) ?7215) ?7214 [7214, 7216, 7215] by Super 105 with 2124 at 3,3
276 Id : 4032, {_}: multiply ?7968 (inverse (inverse ?7969)) ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Super 625 with 3650 at 3,3
277 Id : 4103, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Demod 4032 with 437 at 2,2
278 Id : 4104, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 ?7969 ?7967) ?7967 [7967, 7969, 7968] by Demod 4103 with 437 at 2,2,3
279 Id : 13062, {_}: multiply ?20502 (multiply ?20501 ?20503 ?20502) (multiply ?20501 ?20503 ?20502) =>= multiply ?20502 (multiply ?20501 ?20503 ?20502) ?20503 [20503, 20501, 20502] by Super 12993 with 4104 at 3,2
280 Id : 13612, {_}: multiply ?21322 ?21323 ?21324 =<= multiply ?21324 (multiply ?21322 ?21323 ?21324) ?21323 [21324, 21323, 21322] by Demod 13062 with 6 at 2
281 Id : 12903, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =>= multiply ?19864 ?19863 ?19862 [19862, 19863, 19864] by Demod 12777 with 84 at 3
282 Id : 13625, {_}: multiply ?21368 ?21369 (multiply ?21367 ?21369 ?21368) =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Super 13612 with 12903 at 2,3
283 Id : 13783, {_}: multiply ?21368 ?21369 ?21367 =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Demod 13625 with 12903 at 2
284 Id : 34254, {_}: multiply (multiply ?56219 ?56220 ?56221) ?56222 ?56219 =<= multiply ?56219 ?56220 (multiply ?56221 ?56222 (multiply ?56223 ?56219 (inverse ?56220))) [56223, 56222, 56221, 56220, 56219] by Super 4 with 105 at 3,2
285 Id : 34779, {_}: multiply (multiply ?57676 ?57677 ?57678) ?57678 ?57676 =>= multiply ?57676 ?57677 ?57678 [57678, 57677, 57676] by Super 34254 with 8 at 3,3
286 Id : 34856, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =?= multiply ?57993 (multiply ?57992 ?57993 ?57994) ?57994 [57994, 57993, 57992] by Super 34779 with 4104 at 1,2
287 Id : 35127, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =>= multiply ?57992 ?57993 ?57994 [57994, 57993, 57992] by Demod 34856 with 4104 at 3
288 Id : 36341, {_}: multiply (multiply ?60132 ?60133 ?60134) ?60134 ?60133 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Super 13783 with 35127 at 2,3
289 Id : 36698, {_}: multiply ?60132 ?60133 ?60134 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Demod 36341 with 35127 at 2
290 Id : 36699, {_}: multiply ?60132 ?60133 ?60134 =<= multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134) [60134, 60133, 60132] by Demod 36698 with 35127 at 3
291 Id : 136, {_}: multiply ?291 ?292 (multiply ?293 ?294 ?295) =<= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Demod 116 with 4 at 2
292 Id : 2796, {_}: multiply ?5648 (inverse (inverse ?5650)) ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Super 625 with 2510 at 3,3
293 Id : 2887, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Demod 2796 with 437 at 2,2
294 Id : 2888, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 ?5650 ?5649) ?5648 [5649, 5650, 5648] by Demod 2887 with 437 at 2,2,3
295 Id : 34851, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =?= multiply ?57973 (multiply ?57974 ?57973 ?57972) ?57974 [57972, 57973, 57974] by Super 34779 with 2888 at 1,2
296 Id : 35118, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =>= multiply ?57974 ?57973 ?57972 [57972, 57973, 57974] by Demod 34851 with 2888 at 3
297 Id : 35773, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =?= multiply ?59268 ?59269 (multiply ?59268 ?59269 ?59270) [59270, 59269, 59268] by Super 136 with 35118 at 3,3
298 Id : 36062, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =>= multiply ?59268 ?59269 ?59270 [59270, 59269, 59268] by Demod 35773 with 84 at 3
299 Id : 37434, {_}: multiply ?60132 ?60133 ?60134 =?= multiply ?60133 ?60134 ?60132 [60134, 60133, 60132] by Demod 36699 with 36062 at 3
300 Id : 25, {_}: multiply ?84 ?85 ?86 =<= multiply ?84 ?85 (multiply ?86 (multiply ?84 ?85 ?86) ?87) [87, 86, 85, 84] by Super 4 with 8 at 2
301 Id : 317, {_}: multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?848) =?= multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?845) [848, 847, 846, 845] by Super 298 with 25 at 3,3
302 Id : 24761, {_}: multiply ?36657 (multiply ?36658 ?36659 ?36657) (multiply ?36658 ?36659 ?36660) =>= multiply ?36658 ?36659 ?36657 [36660, 36659, 36658, 36657] by Demod 317 with 6 at 3
303 Id : 24766, {_}: multiply ?36681 (multiply ?36682 ?36683 ?36681) ?36682 =>= multiply ?36682 ?36683 ?36681 [36683, 36682, 36681] by Super 24761 with 12 at 3,2
304 Id : 37848, {_}: multiply ?63783 ?63784 (multiply ?63783 ?63785 ?63784) =>= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Super 24766 with 37434 at 2
305 Id : 37799, {_}: multiply ?63587 ?63589 (multiply ?63587 ?63588 ?63589) =>= multiply ?63587 ?63589 ?63588 [63588, 63589, 63587] by Super 12903 with 37434 at 3,2
306 Id : 41410, {_}: multiply ?63783 ?63784 ?63785 =?= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Demod 37848 with 37799 at 2
307 Id : 42482, {_}: b === b [] by Demod 42481 with 12 at 2
308 Id : 42481, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 42480 with 41410 at 3,1,3,2
309 Id : 42480, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 42479 with 41410 at 1,3,2
310 Id : 42479, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 42478 with 41410 at 2,2
311 Id : 42478, {_}: multiply b (multiply d (multiply g f e) c) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 38490 with 41410 at 2
312 Id : 38490, {_}: multiply b (inverse (multiply d (multiply g e f) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38489 with 37434 at 2,1,2,2
313 Id : 38489, {_}: multiply b (inverse (multiply d (multiply f g e) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38488 with 37434 at 2,1,2,2
314 Id : 38488, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 595 with 37434 at 1,2,2
315 Id : 595, {_}: multiply b (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 53 with 462 at 1,2
316 Id : 53, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 2 with 4 at 1,2,2
317 Id : 2, {_}: 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
318 % SZS output end CNFRefutation for BOO034-1.p
331 (add (inverse (add (inverse (add ?2 ?3)) ?4))
333 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
336 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
338 Id : 2, {_}: add b a =>= add a b [] by huntinton_1
339 Found proof, 0.372303s
340 % SZS status Unsatisfiable for BOO072-1.p
341 % SZS output start CNFRefutation for BOO072-1.p
342 Id : 5, {_}: 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
343 Id : 4, {_}: 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
344 Id : 17, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?80)) ?81)) ?80)) ?82)) (inverse ?80))) ?80) =>= inverse ?80 [82, 81, 80] by Super 5 with 4 at 2,1,2
345 Id : 22, {_}: inverse (add (inverse (add ?111 (inverse ?111))) ?111) =>= inverse ?111 [111] by Super 17 with 4 at 1,1,1,1,2
346 Id : 36, {_}: inverse (add (inverse ?135) (inverse (add ?135 (inverse (add (inverse ?135) (inverse (add ?135 ?136))))))) =>= ?135 [136, 135] by Super 4 with 22 at 1,1,2
347 Id : 57, {_}: inverse (add (inverse (add (inverse (add ?192 ?193)) ?190)) (inverse (add ?192 ?190))) =>= ?190 [190, 193, 192] by Super 4 with 36 at 2,1,2,1,2
348 Id : 131, {_}: inverse (add (inverse (add (inverse (add ?400 ?401)) ?402)) (inverse (add ?400 ?402))) =>= ?402 [402, 401, 400] by Super 4 with 36 at 2,1,2,1,2
349 Id : 141, {_}: inverse (add (inverse (add ?444 ?446)) (inverse (add (inverse ?444) ?446))) =>= ?446 [446, 444] by Super 131 with 36 at 1,1,1,1,2
350 Id : 175, {_}: inverse (add ?545 (inverse (add ?544 (inverse (add (inverse ?544) ?545))))) =>= inverse (add (inverse ?544) ?545) [544, 545] by Super 57 with 141 at 1,1,2
351 Id : 341, {_}: inverse (add (inverse ?894) (inverse (add ?894 (inverse (add (inverse ?894) (inverse ?894)))))) =>= ?894 [894] by Super 36 with 175 at 2,1,2,1,2
352 Id : 390, {_}: inverse (add (inverse ?894) (inverse ?894)) =>= ?894 [894] by Demod 341 with 175 at 2
353 Id : 176, {_}: inverse (add (inverse (add ?547 ?548)) (inverse (add (inverse ?547) ?548))) =>= ?548 [548, 547] by Super 131 with 36 at 1,1,1,1,2
354 Id : 61, {_}: inverse (add (inverse ?208) (inverse (add ?208 (inverse (add (inverse ?208) (inverse (add ?208 ?209))))))) =>= ?208 [209, 208] by Super 4 with 22 at 1,1,2
355 Id : 70, {_}: inverse (add (inverse ?244) (inverse (add ?244 ?244))) =>= ?244 [244] by Super 61 with 36 at 2,1,2,1,2
356 Id : 189, {_}: inverse (add (inverse (add ?598 (inverse (add ?598 ?598)))) ?598) =>= inverse (add ?598 ?598) [598] by Super 176 with 70 at 2,1,2
357 Id : 209, {_}: inverse (add (inverse (add ?635 ?635)) (inverse (add ?635 ?635))) =>= ?635 [635] by Super 57 with 189 at 1,1,2
358 Id : 418, {_}: add ?635 ?635 =>= ?635 [635] by Demod 209 with 390 at 2
359 Id : 427, {_}: inverse (inverse ?894) =>= ?894 [894] by Demod 390 with 418 at 1,2
360 Id : 434, {_}: inverse (add (inverse (add (inverse ?1049) ?1050)) (inverse (add ?1049 ?1050))) =>= ?1050 [1050, 1049] by Super 141 with 427 at 1,1,2,1,2
361 Id : 1002, {_}: inverse (add ?1872 (inverse (add (inverse ?1871) (inverse (add ?1871 ?1872))))) =>= inverse (add ?1871 ?1872) [1871, 1872] by Super 57 with 434 at 1,1,2
362 Id : 2935, {_}: inverse (inverse (add ?4531 ?4530)) =<= add ?4530 (inverse (add (inverse ?4531) (inverse (add ?4531 ?4530)))) [4530, 4531] by Super 427 with 1002 at 1,2
363 Id : 3025, {_}: add ?4531 ?4530 =<= add ?4530 (inverse (add (inverse ?4531) (inverse (add ?4531 ?4530)))) [4530, 4531] by Demod 2935 with 427 at 2
364 Id : 5776, {_}: inverse (add ?7863 (inverse (add (inverse (add ?7864 ?7865)) (inverse (add ?7864 ?7863))))) =>= inverse (add ?7864 ?7863) [7865, 7864, 7863] by Super 131 with 57 at 1,1,2
365 Id : 441, {_}: inverse (inverse ?1072) =>= ?1072 [1072] by Demod 390 with 418 at 1,2
366 Id : 447, {_}: inverse (inverse (add (inverse ?1092) ?1091)) =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Super 441 with 175 at 1,2
367 Id : 459, {_}: add (inverse ?1092) ?1091 =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Demod 447 with 427 at 2
368 Id : 5835, {_}: inverse (add (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104)))) (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) =>= inverse (add ?8103 (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) [8104, 8103] by Super 5776 with 459 at 1,2,1,2
369 Id : 5988, {_}: inverse (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104)))) =<= inverse (add ?8103 (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) [8104, 8103] by Demod 5835 with 418 at 1,2
370 Id : 5989, {_}: add (inverse ?8103) (inverse (add ?8103 ?8104)) =<= inverse (add ?8103 (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) [8104, 8103] by Demod 5988 with 427 at 2
371 Id : 6002, {_}: inverse (add (inverse ?135) (add (inverse ?135) (inverse (add ?135 ?136)))) =>= ?135 [136, 135] by Demod 36 with 5989 at 2,1,2
372 Id : 8, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?28)) ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Super 5 with 4 at 2,1,2
373 Id : 428, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?28 ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Demod 8 with 427 at 1,1,1,1,1,1,1,1,1,1,2
374 Id : 251, {_}: inverse (add ?739 (inverse (add ?739 (inverse (add ?739 ?739))))) =>= inverse (add ?739 ?739) [739] by Super 57 with 209 at 1,1,2
375 Id : 419, {_}: inverse (add ?739 (inverse (add ?739 (inverse ?739)))) =>= inverse (add ?739 ?739) [739] by Demod 251 with 418 at 1,2,1,2,1,2
376 Id : 420, {_}: inverse (add ?739 (inverse (add ?739 (inverse ?739)))) =>= inverse ?739 [739] by Demod 419 with 418 at 1,3
377 Id : 448, {_}: inverse (inverse ?1094) =<= add ?1094 (inverse (add ?1094 (inverse ?1094))) [1094] by Super 441 with 420 at 1,2
378 Id : 460, {_}: ?1094 =<= add ?1094 (inverse (add ?1094 (inverse ?1094))) [1094] by Demod 448 with 427 at 2
379 Id : 509, {_}: inverse (add (inverse (add (inverse ?1198) (inverse (inverse ?1198)))) (inverse (add ?1198 (inverse (inverse ?1198))))) =>= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Super 175 with 460 at 1,2,1,2,1,2
380 Id : 522, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse (add ?1198 (inverse (inverse ?1198))))) =>= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Demod 509 with 427 at 2,1,1,1,2
381 Id : 523, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse (add ?1198 ?1198))) =?= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Demod 522 with 427 at 2,1,2,1,2
382 Id : 524, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse ?1198)) =<= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Demod 523 with 418 at 1,2,1,2
383 Id : 525, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse ?1198)) =>= inverse (inverse ?1198) [1198] by Demod 524 with 460 at 1,3
384 Id : 526, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse ?1198)) =>= ?1198 [1198] by Demod 525 with 427 at 3
385 Id : 564, {_}: inverse ?1294 =<= add (inverse (add (inverse ?1294) ?1294)) (inverse ?1294) [1294] by Super 427 with 526 at 1,2
386 Id : 633, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?1388)) ?1389)) (inverse (inverse ?1388)))) (inverse ?1388)) =>= inverse (inverse ?1388) [1389, 1388] by Super 428 with 564 at 1,1,1,1,1,1,1,2
387 Id : 653, {_}: inverse (add (inverse (add (inverse (add ?1388 ?1389)) (inverse (inverse ?1388)))) (inverse ?1388)) =>= inverse (inverse ?1388) [1389, 1388] by Demod 633 with 427 at 1,1,1,1,1,1,2
388 Id : 654, {_}: inverse (add (inverse (add (inverse (add ?1388 ?1389)) ?1388)) (inverse ?1388)) =>= inverse (inverse ?1388) [1389, 1388] by Demod 653 with 427 at 2,1,1,1,2
389 Id : 1550, {_}: inverse (add (inverse (add (inverse (add ?2636 ?2637)) ?2636)) (inverse ?2636)) =>= ?2636 [2637, 2636] by Demod 654 with 427 at 3
390 Id : 1579, {_}: inverse (add ?2725 (inverse (inverse (add ?2724 ?2725)))) =>= inverse (add ?2724 ?2725) [2724, 2725] by Super 1550 with 57 at 1,1,2
391 Id : 1654, {_}: inverse (add ?2725 (add ?2724 ?2725)) =>= inverse (add ?2724 ?2725) [2724, 2725] by Demod 1579 with 427 at 2,1,2
392 Id : 1668, {_}: inverse (inverse (add ?2771 ?2770)) =<= add ?2770 (add ?2771 ?2770) [2770, 2771] by Super 427 with 1654 at 1,2
393 Id : 1719, {_}: add ?2771 ?2770 =<= add ?2770 (add ?2771 ?2770) [2770, 2771] by Demod 1668 with 427 at 2
394 Id : 1694, {_}: inverse (add ?2869 (add ?2870 ?2869)) =>= inverse (add ?2870 ?2869) [2870, 2869] by Demod 1579 with 427 at 2,1,2
395 Id : 1011, {_}: inverse ?1910 =<= add (inverse (add (inverse ?1909) ?1910)) (inverse (add ?1909 ?1910)) [1909, 1910] by Super 427 with 434 at 1,2
396 Id : 1703, {_}: inverse (add (inverse (add ?2891 ?2890)) (inverse ?2890)) =<= inverse (add (inverse (add (inverse ?2891) ?2890)) (inverse (add ?2891 ?2890))) [2890, 2891] by Super 1694 with 1011 at 2,1,2
397 Id : 1752, {_}: inverse (add (inverse (add ?2891 ?2890)) (inverse ?2890)) =>= inverse (inverse ?2890) [2890, 2891] by Demod 1703 with 1011 at 1,3
398 Id : 1753, {_}: inverse (add (inverse (add ?2891 ?2890)) (inverse ?2890)) =>= ?2890 [2890, 2891] by Demod 1752 with 427 at 3
399 Id : 1836, {_}: inverse ?3039 =<= add (inverse (add ?3038 ?3039)) (inverse ?3039) [3038, 3039] by Super 427 with 1753 at 1,2
400 Id : 1990, {_}: inverse (add (inverse (inverse ?3259)) (inverse (add ?3260 (inverse ?3259)))) =>= inverse ?3259 [3260, 3259] by Super 57 with 1836 at 1,1,1,2
401 Id : 2039, {_}: inverse (add ?3259 (inverse (add ?3260 (inverse ?3259)))) =>= inverse ?3259 [3260, 3259] by Demod 1990 with 427 at 1,1,2
402 Id : 2119, {_}: inverse (inverse ?3394) =<= add ?3394 (inverse (add ?3395 (inverse ?3394))) [3395, 3394] by Super 427 with 2039 at 1,2
403 Id : 2221, {_}: ?3394 =<= add ?3394 (inverse (add ?3395 (inverse ?3394))) [3395, 3394] by Demod 2119 with 427 at 2
404 Id : 2575, {_}: add ?4058 (inverse (add ?4059 (inverse ?4058))) =?= add (inverse (add ?4059 (inverse ?4058))) ?4058 [4059, 4058] by Super 1719 with 2221 at 2,3
405 Id : 2687, {_}: ?4204 =<= add (inverse (add ?4205 (inverse ?4204))) ?4204 [4205, 4204] by Demod 2575 with 2221 at 2
406 Id : 5192, {_}: add ?7211 (inverse (add (inverse ?7212) (inverse (add ?7212 ?7213)))) =<= add ?7212 (add ?7211 (inverse (add (inverse ?7212) (inverse (add ?7212 ?7213))))) [7213, 7212, 7211] by Super 2687 with 4 at 1,3
407 Id : 2141, {_}: add (inverse ?3482) (inverse (add ?3481 (inverse (inverse ?3482)))) =<= add (inverse (add ?3481 (inverse (inverse ?3482)))) (inverse (add ?3482 (inverse (inverse ?3482)))) [3481, 3482] by Super 459 with 2039 at 2,1,2,3
408 Id : 2187, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =<= add (inverse (add ?3481 (inverse (inverse ?3482)))) (inverse (add ?3482 (inverse (inverse ?3482)))) [3481, 3482] by Demod 2141 with 427 at 2,1,2,2
409 Id : 2188, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =<= add (inverse (add ?3481 ?3482)) (inverse (add ?3482 (inverse (inverse ?3482)))) [3481, 3482] by Demod 2187 with 427 at 2,1,1,3
410 Id : 2189, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =<= add (inverse (add ?3481 ?3482)) (inverse (add ?3482 ?3482)) [3481, 3482] by Demod 2188 with 427 at 2,1,2,3
411 Id : 2190, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =?= add (inverse (add ?3481 ?3482)) (inverse ?3482) [3481, 3482] by Demod 2189 with 418 at 1,2,3
412 Id : 2191, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =>= inverse ?3482 [3481, 3482] by Demod 2190 with 1836 at 3
413 Id : 5228, {_}: add (inverse (inverse (add ?7359 ?7360))) (inverse (add (inverse ?7359) (inverse (add ?7359 ?7360)))) =>= add ?7359 (inverse (inverse (add ?7359 ?7360))) [7360, 7359] by Super 5192 with 2191 at 2,3
414 Id : 5491, {_}: inverse (inverse (add ?7359 ?7360)) =<= add ?7359 (inverse (inverse (add ?7359 ?7360))) [7360, 7359] by Demod 5228 with 2191 at 2
415 Id : 5492, {_}: add ?7359 ?7360 =<= add ?7359 (inverse (inverse (add ?7359 ?7360))) [7360, 7359] by Demod 5491 with 427 at 2
416 Id : 5493, {_}: add ?7359 ?7360 =<= add ?7359 (add ?7359 ?7360) [7360, 7359] by Demod 5492 with 427 at 2,3
417 Id : 6003, {_}: inverse (add (inverse ?135) (inverse (add ?135 ?136))) =>= ?135 [136, 135] by Demod 6002 with 5493 at 1,2
418 Id : 6005, {_}: add ?4531 ?4530 =?= add ?4530 ?4531 [4530, 4531] by Demod 3025 with 6003 at 2,3
419 Id : 6260, {_}: add a b === add a b [] by Demod 2 with 6005 at 2
420 Id : 2, {_}: add b a =>= add a b [] by huntinton_1
421 % SZS output end CNFRefutation for BOO072-1.p
435 (add (inverse (add (inverse (add ?2 ?3)) ?4))
437 (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
440 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
442 Id : 2, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
444 FAILURE in 151 iterations
445 % SZS status Timeout for BOO073-1.p
453 prove_meredith_2_basis_2 is 94
457 nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
458 [4, 3, 2] by sh_1 ?2 ?3 ?4
461 nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
462 [] by prove_meredith_2_basis_2
464 FAILURE in 131 iterations
465 % SZS status Timeout for BOO076-1.p
473 prove_strong_fixed_point is 95
474 strong_fixed_point is 98
479 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
480 [4, 3, 2] by b_definition ?2 ?3 ?4
482 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
483 [7, 6] by w_definition ?6 ?7
487 apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
488 [] by strong_fixed_point
491 apply strong_fixed_point fixed_pt
493 apply fixed_pt (apply strong_fixed_point fixed_pt)
494 [] by prove_strong_fixed_point
496 FAILURE in 376 iterations
497 % SZS status Timeout for COL003-12.p
505 prove_strong_fixed_point is 96
510 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
511 [5, 4, 3] by b_definition ?3 ?4 ?5
513 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
514 [8, 7] by w_definition ?7 ?8
517 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
518 [1] by prove_strong_fixed_point ?1
520 FAILURE in 26 iterations
521 % SZS status Timeout for COL003-1.p
529 prove_strong_fixed_point is 95
530 strong_fixed_point is 98
535 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
536 [4, 3, 2] by b_definition ?2 ?3 ?4
538 apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
539 [7, 6] by w_definition ?6 ?7
543 apply (apply b (apply w w))
544 (apply (apply b (apply b w)) (apply (apply b b) b))
545 [] by strong_fixed_point
548 apply strong_fixed_point fixed_pt
550 apply fixed_pt (apply strong_fixed_point fixed_pt)
551 [] by prove_strong_fixed_point
553 FAILURE in 374 iterations
554 % SZS status Timeout for COL003-20.p
562 prove_strong_fixed_point is 95
565 strong_fixed_point is 98
568 apply (apply (apply s ?2) ?3) ?4
570 apply (apply ?2 ?4) (apply ?3 ?4)
571 [4, 3, 2] by s_definition ?2 ?3 ?4
572 Id : 6, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
579 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
580 (apply (apply s (apply (apply s (apply k s)) k))
582 (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
583 [] by strong_fixed_point
586 apply strong_fixed_point fixed_pt
588 apply fixed_pt (apply strong_fixed_point fixed_pt)
589 [] by prove_strong_fixed_point
591 FAILURE in 425 iterations
592 % SZS status Timeout for COL006-6.p
600 prove_fixed_point is 96
605 apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
606 [4, 3] by o_definition ?3 ?4
608 apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
609 [8, 7, 6] by q1_definition ?6 ?7 ?8
611 Id : 2, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
613 FAILURE in 13 iterations
614 % SZS status Timeout for COL011-1.p
624 prove_fixed_point is 96
629 apply (apply (apply s ?3) ?4) ?5
631 apply (apply ?3 ?5) (apply ?4 ?5)
632 [5, 4, 3] by s_definition ?3 ?4 ?5
634 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
635 [9, 8, 7] by b_definition ?7 ?8 ?9
637 apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
638 [13, 12, 11] by c_definition ?11 ?12 ?13
641 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
642 [1] by prove_fixed_point ?1
644 FAILURE in 27 iterations
645 % SZS status Timeout for COL037-1.p
655 prove_fixed_point is 96
660 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
661 [5, 4, 3] by b_definition ?3 ?4 ?5
662 Id : 6, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
664 apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
665 [11, 10, 9] by v_definition ?9 ?10 ?11
668 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
669 [1] by prove_fixed_point ?1
671 FAILURE in 35 iterations
672 % SZS status Timeout for COL038-1.p
682 prove_strong_fixed_point is 95
683 strong_fixed_point is 98
686 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
687 [4, 3, 2] by b_definition ?2 ?3 ?4
689 apply (apply (apply h ?6) ?7) ?8
691 apply (apply (apply ?6 ?7) ?8) ?7
692 [8, 7, 6] by h_definition ?6 ?7 ?8
702 (apply (apply b (apply (apply b h) (apply b b)))
703 (apply h (apply (apply b h) (apply b b))))) h)) b)) b
704 [] by strong_fixed_point
707 apply strong_fixed_point fixed_pt
709 apply fixed_pt (apply strong_fixed_point fixed_pt)
710 [] by prove_strong_fixed_point
712 FAILURE in 388 iterations
713 % SZS status Timeout for COL043-3.p
723 prove_strong_fixed_point is 95
724 strong_fixed_point is 98
727 apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
728 [4, 3, 2] by b_definition ?2 ?3 ?4
730 apply (apply (apply n ?6) ?7) ?8
732 apply (apply (apply ?6 ?8) ?7) ?8
733 [8, 7, 6] by n_definition ?6 ?7 ?8
744 (apply (apply b (apply b b))
745 (apply n (apply (apply b b) n))))) n)) b)) b
746 [] by strong_fixed_point
749 apply strong_fixed_point fixed_pt
751 apply fixed_pt (apply strong_fixed_point fixed_pt)
752 [] by prove_strong_fixed_point
754 FAILURE in 339 iterations
755 % SZS status Timeout for COL044-8.p
765 prove_fixed_point is 96
770 apply (apply (apply s ?3) ?4) ?5
772 apply (apply ?3 ?5) (apply ?4 ?5)
773 [5, 4, 3] by s_definition ?3 ?4 ?5
775 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
776 [9, 8, 7] by b_definition ?7 ?8 ?9
777 Id : 8, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
780 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
781 [1] by prove_fixed_point ?1
783 FAILURE in 26 iterations
784 % SZS status Timeout for COL046-1.p
794 prove_strong_fixed_point is 96
799 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
800 [5, 4, 3] by b_definition ?3 ?4 ?5
802 apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
803 [8, 7] by w_definition ?7 ?8
804 Id : 8, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
807 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
808 [1] by prove_strong_fixed_point ?1
810 FAILURE in 26 iterations
811 % SZS status Timeout for COL049-1.p
823 prove_strong_fixed_point is 96
828 apply (apply (apply s ?3) ?4) ?5
830 apply (apply ?3 ?5) (apply ?4 ?5)
831 [5, 4, 3] by s_definition ?3 ?4 ?5
833 apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
834 [9, 8, 7] by b_definition ?7 ?8 ?9
836 apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
837 [13, 12, 11] by c_definition ?11 ?12 ?13
838 Id : 10, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
841 apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
842 [1] by prove_strong_fixed_point ?1
844 FAILURE in 28 iterations
845 % SZS status Timeout for COL057-1.p
855 prove_q_combinator is 94
860 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
861 [5, 4, 3] by b_definition ?3 ?4 ?5
863 apply (apply t ?7) ?8 =>= apply ?8 ?7
864 [8, 7] by t_definition ?7 ?8
867 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
869 apply (g ?1) (apply (f ?1) (h ?1))
870 [1] by prove_q_combinator ?1
872 FAILURE in 44 iterations
873 % SZS status Timeout for COL060-1.p
883 prove_q1_combinator is 94
888 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
889 [5, 4, 3] by b_definition ?3 ?4 ?5
891 apply (apply t ?7) ?8 =>= apply ?8 ?7
892 [8, 7] by t_definition ?7 ?8
895 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
897 apply (f ?1) (apply (h ?1) (g ?1))
898 [1] by prove_q1_combinator ?1
900 FAILURE in 44 iterations
901 % SZS status Timeout for COL061-1.p
911 prove_f_combinator is 94
916 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
917 [5, 4, 3] by b_definition ?3 ?4 ?5
919 apply (apply t ?7) ?8 =>= apply ?8 ?7
920 [8, 7] by t_definition ?7 ?8
923 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
925 apply (apply (h ?1) (g ?1)) (f ?1)
926 [1] by prove_f_combinator ?1
928 FAILURE in 43 iterations
929 % SZS status Timeout for COL063-1.p
939 prove_v_combinator is 94
944 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
945 [5, 4, 3] by b_definition ?3 ?4 ?5
947 apply (apply t ?7) ?8 =>= apply ?8 ?7
948 [8, 7] by t_definition ?7 ?8
951 apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
953 apply (apply (h ?1) (f ?1)) (g ?1)
954 [1] by prove_v_combinator ?1
956 FAILURE in 43 iterations
957 % SZS status Timeout for COL064-1.p
968 prove_g_combinator is 93
973 apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
974 [5, 4, 3] by b_definition ?3 ?4 ?5
976 apply (apply t ?7) ?8 =>= apply ?8 ?7
977 [8, 7] by t_definition ?7 ?8
980 apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
982 apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
983 [1] by prove_g_combinator ?1
985 FAILURE in 41 iterations
986 % SZS status Timeout for COL065-1.p
996 prove_associativity is 94
1003 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
1004 ?5) (inverse (multiply ?3 ?5))))
1007 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
1010 multiply a (multiply b c) =<= multiply (multiply a b) c
1011 [] by prove_associativity
1012 Found proof, 2.278024s
1013 % SZS status Unsatisfiable for GRP014-1.p
1014 % SZS output start CNFRefutation for GRP014-1.p
1015 Id : 4, {_}: 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
1016 Id : 5, {_}: 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
1017 Id : 8, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (inverse (multiply (inverse ?26) (multiply (inverse (inverse (multiply (inverse ?30) (multiply (inverse ?29) ?31)))) ?27))) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 31, 26, 30, 27, 29] by Super 5 with 4 at 1,1,2,2
1018 Id : 7, {_}: multiply ?22 (inverse (multiply (multiply (inverse (multiply (inverse ?23) ?20)) ?24) (inverse (multiply ?23 ?24)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?19) (multiply (inverse (inverse ?22)) ?20))) ?21) (inverse (multiply ?19 ?21))) [21, 19, 24, 20, 23, 22] by Super 5 with 4 at 2,1,1,1,1,2,2
1019 Id : 65, {_}: multiply (inverse ?586) (multiply ?586 (inverse (multiply (multiply (inverse (multiply (inverse ?587) ?588)) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 588, 587, 586] by Super 4 with 7 at 2,2
1020 Id : 66, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?596) (multiply (inverse (inverse ?593)) (multiply (inverse ?593) ?598)))) ?597) (inverse (multiply ?596 ?597))) =>= ?598 [597, 598, 593, 596] by Super 4 with 7 at 2
1021 Id : 285, {_}: multiply (inverse ?2327) (multiply ?2327 ?2328) =?= multiply (inverse (inverse ?2329)) (multiply (inverse ?2329) ?2328) [2329, 2328, 2327] by Super 65 with 66 at 2,2,2
1022 Id : 188, {_}: multiply (inverse ?1696) (multiply ?1696 ?1694) =?= multiply (inverse (inverse ?1693)) (multiply (inverse ?1693) ?1694) [1693, 1694, 1696] by Super 65 with 66 at 2,2,2
1023 Id : 299, {_}: multiply (inverse ?2421) (multiply ?2421 ?2422) =?= multiply (inverse ?2420) (multiply ?2420 ?2422) [2420, 2422, 2421] by Super 285 with 188 at 3
1024 Id : 395, {_}: multiply (inverse ?2916) (multiply ?2916 (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915, 2916] by Super 65 with 299 at 1,1,1,1,2,2,2
1025 Id : 549, {_}: multiply ?3835 (inverse (multiply (multiply (inverse (multiply (inverse ?3836) (multiply ?3836 ?3837))) ?3838) (inverse (multiply (inverse ?3835) ?3838)))) =>= ?3837 [3838, 3837, 3836, 3835] by Super 4 with 299 at 1,1,1,1,2,2
1026 Id : 2606, {_}: multiply ?16468 (inverse (multiply (multiply (inverse (multiply (inverse ?16469) (multiply ?16469 ?16470))) (multiply ?16468 ?16471)) (inverse (multiply (inverse ?16472) (multiply ?16472 ?16471))))) =>= ?16470 [16472, 16471, 16470, 16469, 16468] by Super 549 with 299 at 1,2,1,2,2
1027 Id : 2691, {_}: multiply (multiply (inverse ?17193) (multiply ?17193 ?17194)) (inverse (multiply ?17191 (inverse (multiply (inverse ?17195) (multiply ?17195 (inverse (multiply (multiply (inverse (multiply (inverse ?17190) ?17191)) ?17192) (inverse (multiply ?17190 ?17192))))))))) =>= ?17194 [17192, 17190, 17195, 17191, 17194, 17193] by Super 2606 with 65 at 1,1,2,2
1028 Id : 2733, {_}: multiply (multiply (inverse ?17193) (multiply ?17193 ?17194)) (inverse (multiply ?17191 (inverse ?17191))) =>= ?17194 [17191, 17194, 17193] by Demod 2691 with 65 at 1,2,1,2,2
1029 Id : 2764, {_}: multiply (inverse (multiply (inverse ?17455) (multiply ?17455 ?17456))) ?17456 =?= multiply (inverse (multiply (inverse ?17457) (multiply ?17457 ?17458))) ?17458 [17458, 17457, 17456, 17455] by Super 395 with 2733 at 2,2
1030 Id : 2997, {_}: multiply (inverse (inverse (multiply (inverse ?18879) (multiply ?18879 (inverse (multiply (multiply (inverse (multiply (inverse ?18882) ?18883)) ?18884) (inverse (multiply ?18882 ?18884)))))))) (multiply (inverse (multiply (inverse ?18880) (multiply ?18880 ?18881))) ?18881) =>= ?18883 [18881, 18880, 18884, 18883, 18882, 18879] by Super 65 with 2764 at 2,2
1031 Id : 3188, {_}: multiply (inverse (inverse ?18883)) (multiply (inverse (multiply (inverse ?18880) (multiply ?18880 ?18881))) ?18881) =>= ?18883 [18881, 18880, 18883] by Demod 2997 with 65 at 1,1,1,2
1032 Id : 137, {_}: multiply (inverse ?1284) (multiply ?1284 (inverse (multiply (multiply (inverse (multiply (inverse ?1285) ?1286)) ?1287) (inverse (multiply ?1285 ?1287))))) =>= ?1286 [1287, 1286, 1285, 1284] by Super 4 with 7 at 2,2
1033 Id : 156, {_}: multiply (inverse ?1443) (multiply ?1443 (multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439, 1443] by Super 137 with 7 at 2,2,2
1034 Id : 3268, {_}: multiply (inverse (inverse (inverse ?20656))) ?20656 =?= multiply (inverse (inverse (inverse (multiply (inverse ?20657) (multiply ?20657 (inverse (multiply (multiply (inverse (multiply (inverse ?20658) ?20659)) ?20660) (inverse (multiply ?20658 ?20660))))))))) ?20659 [20660, 20659, 20658, 20657, 20656] by Super 156 with 3188 at 2,2
1035 Id : 3359, {_}: multiply (inverse (inverse (inverse ?20656))) ?20656 =?= multiply (inverse (inverse (inverse ?20659))) ?20659 [20659, 20656] by Demod 3268 with 65 at 1,1,1,1,3
1036 Id : 3543, {_}: multiply (inverse (inverse ?21963)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?21961)))) (multiply (inverse (inverse (inverse ?21962))) ?21962))) ?21961) =>= ?21963 [21962, 21961, 21963] by Super 3188 with 3359 at 2,1,1,2,2
1037 Id : 379, {_}: multiply ?2799 (inverse (multiply (multiply (inverse ?2798) (multiply ?2798 ?2797)) (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797))))) =>= ?2801 [2801, 2800, 2797, 2798, 2799] by Super 4 with 299 at 1,1,2,2
1038 Id : 190, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1706) (multiply (inverse (inverse ?1707)) (multiply (inverse ?1707) ?1708)))) ?1709) (inverse (multiply ?1706 ?1709))) =>= ?1708 [1709, 1708, 1707, 1706] by Super 4 with 7 at 2
1039 Id : 198, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1768) (multiply (inverse (inverse ?1769)) (multiply (inverse ?1769) ?1770)))) ?1771) (inverse (multiply ?1768 ?1771))))) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1771, 1770, 1769, 1768, 1772] by Super 190 with 66 at 1,2,2,1,1,1,1,2
1040 Id : 223, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse ?1770) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1770, 1772] by Demod 198 with 66 at 1,1,2,1,1,1,1,2
1041 Id : 635, {_}: multiply (inverse ?4438) (multiply ?4438 (multiply ?4439 (inverse (multiply (multiply (inverse (multiply (inverse ?4440) ?4441)) ?4442) (inverse (multiply ?4440 ?4442)))))) =>= multiply (inverse (inverse ?4439)) ?4441 [4442, 4441, 4440, 4439, 4438] by Super 137 with 7 at 2,2,2
1042 Id : 668, {_}: multiply (inverse ?4724) (multiply ?4724 (multiply ?4725 ?4723)) =?= multiply (inverse (inverse ?4725)) (multiply (inverse ?4722) (multiply ?4722 ?4723)) [4722, 4723, 4725, 4724] by Super 635 with 223 at 2,2,2,2
1043 Id : 761, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5332) (multiply ?5332 (multiply ?5333 ?5334)))) ?5336) (inverse (multiply (inverse ?5333) ?5336))) =>= ?5334 [5336, 5334, 5333, 5332] by Super 223 with 668 at 1,1,1,1,2
1044 Id : 2971, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18698) (multiply ?18698 ?18699))) ?18699) (inverse (multiply (inverse ?18700) (multiply ?18700 ?18701)))) =>= ?18701 [18701, 18700, 18699, 18698] by Super 761 with 2764 at 1,1,2
1045 Id : 3407, {_}: multiply (multiply (inverse (inverse (inverse (inverse ?21175)))) (multiply (inverse (inverse (inverse ?21176))) ?21176)) (inverse (multiply ?21177 (inverse ?21177))) =>= ?21175 [21177, 21176, 21175] by Super 2733 with 3359 at 2,1,2
1046 Id : 3267, {_}: multiply (inverse ?20652) (multiply ?20652 (multiply ?20653 (inverse (multiply (multiply (inverse ?20649) ?20654) (inverse (multiply (inverse ?20649) ?20654)))))) =?= multiply (inverse (inverse ?20653)) (multiply (inverse (multiply (inverse ?20650) (multiply ?20650 ?20651))) ?20651) [20651, 20650, 20654, 20649, 20653, 20652] by Super 156 with 3188 at 1,1,1,1,2,2,2,2
1047 Id : 5050, {_}: multiply (inverse ?30421) (multiply ?30421 (multiply ?30422 (inverse (multiply (multiply (inverse ?30423) ?30424) (inverse (multiply (inverse ?30423) ?30424)))))) =>= ?30422 [30424, 30423, 30422, 30421] by Demod 3267 with 3188 at 3
1048 Id : 5058, {_}: multiply (inverse ?30488) (multiply ?30488 (multiply ?30489 (inverse (multiply (multiply (inverse ?30490) (inverse (multiply (multiply (inverse (multiply (inverse ?30485) (multiply (inverse (inverse ?30490)) ?30486))) ?30487) (inverse (multiply ?30485 ?30487))))) (inverse ?30486))))) =>= ?30489 [30487, 30486, 30485, 30490, 30489, 30488] by Super 5050 with 4 at 1,2,1,2,2,2,2
1049 Id : 5182, {_}: multiply (inverse ?30488) (multiply ?30488 (multiply ?30489 (inverse (multiply ?30486 (inverse ?30486))))) =>= ?30489 [30486, 30489, 30488] by Demod 5058 with 4 at 1,1,2,2,2,2
1050 Id : 5242, {_}: multiply ?31236 (inverse (multiply ?31238 (inverse ?31238))) =?= multiply ?31236 (inverse (multiply ?31237 (inverse ?31237))) [31237, 31238, 31236] by Super 3407 with 5182 at 1,2
1051 Id : 5880, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?34514) (multiply ?34514 ?34515))) ?34515) (inverse (multiply (inverse ?34511) (multiply ?34511 (inverse (multiply ?34513 (inverse ?34513))))))) =?= inverse (multiply ?34512 (inverse ?34512)) [34512, 34513, 34511, 34515, 34514] by Super 2971 with 5242 at 2,1,2,1,2
1052 Id : 5941, {_}: inverse (multiply ?34513 (inverse ?34513)) =?= inverse (multiply ?34512 (inverse ?34512)) [34512, 34513] by Demod 5880 with 2971 at 2
1053 Id : 6233, {_}: multiply (inverse (inverse (multiply ?36082 (inverse ?36082)))) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?36083)))) (multiply (inverse (inverse (inverse ?36084))) ?36084))) ?36083) =?= multiply ?36081 (inverse ?36081) [36081, 36084, 36083, 36082] by Super 3543 with 5941 at 1,1,2
1054 Id : 6294, {_}: multiply ?36082 (inverse ?36082) =?= multiply ?36081 (inverse ?36081) [36081, 36082] by Demod 6233 with 3543 at 2
1055 Id : 6354, {_}: multiply (multiply (inverse ?36480) (multiply ?36481 (inverse ?36481))) (inverse (multiply ?36482 (inverse ?36482))) =>= inverse ?36480 [36482, 36481, 36480] by Super 2733 with 6294 at 2,1,2
1056 Id : 6918, {_}: multiply ?39301 (inverse (multiply (multiply (inverse ?39302) (multiply ?39302 (inverse (multiply ?39300 (inverse ?39300))))) (inverse (multiply ?39299 (inverse ?39299))))) =>= inverse (inverse ?39301) [39299, 39300, 39302, 39301] by Super 379 with 6354 at 2,1,2,1,2,2
1057 Id : 6993, {_}: multiply ?39301 (inverse (inverse (multiply ?39300 (inverse ?39300)))) =>= inverse (inverse ?39301) [39300, 39301] by Demod 6918 with 2733 at 1,2,2
1058 Id : 7034, {_}: multiply (inverse (inverse ?39791)) (multiply (inverse (multiply (inverse ?39789) (inverse (inverse ?39789)))) (inverse (inverse (multiply ?39790 (inverse ?39790))))) =>= ?39791 [39790, 39789, 39791] by Super 3188 with 6993 at 2,1,1,2,2
1059 Id : 7801, {_}: multiply (inverse (inverse ?42915)) (inverse (inverse (inverse (multiply (inverse ?42916) (inverse (inverse ?42916)))))) =>= ?42915 [42916, 42915] by Demod 7034 with 6993 at 2,2
1060 Id : 7116, {_}: multiply ?40237 (inverse ?40237) =?= inverse (inverse (inverse (multiply ?40236 (inverse ?40236)))) [40236, 40237] by Super 6294 with 6993 at 3
1061 Id : 7831, {_}: multiply (inverse (inverse ?43066)) (multiply ?43065 (inverse ?43065)) =>= ?43066 [43065, 43066] by Super 7801 with 7116 at 2,2
1062 Id : 7980, {_}: multiply ?43590 (inverse (multiply ?43591 (inverse ?43591))) =>= inverse (inverse ?43590) [43591, 43590] by Super 2733 with 7831 at 1,2
1063 Id : 8167, {_}: multiply (inverse (inverse ?44390)) (inverse (inverse (inverse (multiply (inverse (inverse (inverse (inverse (inverse (multiply ?44389 (inverse ?44389))))))) (multiply (inverse (inverse (inverse ?44391))) ?44391))))) =>= ?44390 [44391, 44389, 44390] by Super 3543 with 7980 at 2,2
1064 Id : 8053, {_}: inverse (inverse (multiply (inverse (inverse (inverse (inverse ?21175)))) (multiply (inverse (inverse (inverse ?21176))) ?21176))) =>= ?21175 [21176, 21175] by Demod 3407 with 7980 at 2
1065 Id : 8222, {_}: multiply (inverse (inverse ?44390)) (inverse (inverse (multiply ?44389 (inverse ?44389)))) =>= ?44390 [44389, 44390] by Demod 8167 with 8053 at 1,2,2
1066 Id : 8223, {_}: inverse (inverse (inverse (inverse ?44390))) =>= ?44390 [44390] by Demod 8222 with 6993 at 2
1067 Id : 905, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?6097) (multiply ?6097 (multiply ?6098 ?6099)))) ?6100) (inverse (multiply (inverse ?6098) ?6100))) =>= ?6099 [6100, 6099, 6098, 6097] by Super 223 with 668 at 1,1,1,1,2
1068 Id : 926, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?6262) (multiply ?6262 (multiply (inverse ?6261) (multiply ?6261 ?6260))))) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260, 6261, 6262] by Super 905 with 299 at 2,2,1,1,1,1,2
1069 Id : 8054, {_}: multiply (inverse ?30488) (multiply ?30488 (inverse (inverse ?30489))) =>= ?30489 [30489, 30488] by Demod 5182 with 7980 at 2,2,2
1070 Id : 8447, {_}: multiply (inverse ?45106) (multiply ?45106 ?45105) =>= inverse (inverse ?45105) [45105, 45106] by Super 8054 with 8223 at 2,2,2
1071 Id : 8864, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?6261) (multiply ?6261 ?6260))))) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260, 6261] by Demod 926 with 8447 at 1,1,1,1,2
1072 Id : 8865, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?6260))))) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260] by Demod 8864 with 8447 at 1,1,1,1,1,1,2
1073 Id : 8898, {_}: inverse (multiply (multiply (inverse ?6260) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260] by Demod 8865 with 8223 at 1,1,1,2
1074 Id : 8350, {_}: multiply ?44637 (inverse (multiply (inverse (inverse (inverse ?44636))) ?44636)) =>= inverse (inverse ?44637) [44636, 44637] by Super 7980 with 8223 at 2,1,2,2
1075 Id : 9047, {_}: inverse (inverse (inverse (multiply (inverse ?46455) ?46454))) =>= multiply (inverse ?46454) ?46455 [46454, 46455] by Super 8898 with 8350 at 1,2
1076 Id : 9341, {_}: inverse (multiply (inverse ?47101) ?47100) =>= multiply (inverse ?47100) ?47101 [47100, 47101] by Super 8223 with 9047 at 1,2
1077 Id : 9509, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?30) (multiply (inverse ?29) ?31)))) ?27)) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 8 with 9341 at 1,1,1,2,1,2,1,2,2
1078 Id : 9510, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?30) (multiply (inverse ?29) ?31)))) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 9509 with 9341 at 1,1,1,1,2,1,2,1,2,2
1079 Id : 9511, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?29) ?31)) ?30)) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 9510 with 9341 at 2,1,1,1,1,2,1,2,1,2,2
1080 Id : 9512, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?31) ?29) ?30)) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 9511 with 9341 at 1,2,1,1,1,1,2,1,2,1,2,2
1081 Id : 8876, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915] by Demod 395 with 8447 at 2
1082 Id : 8877, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 8876 with 8447 at 1,1,1,1,1,1,2
1083 Id : 9058, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?46500))) ?46499))))) =>= multiply (inverse (inverse (inverse ?46499))) ?46500 [46499, 46500] by Super 8877 with 8350 at 1,1,1,2
1084 Id : 9242, {_}: inverse (multiply (inverse (inverse (inverse ?46500))) ?46499) =>= multiply (inverse (inverse (inverse ?46499))) ?46500 [46499, 46500] by Demod 9058 with 8223 at 2
1085 Id : 9696, {_}: multiply (inverse ?46499) (inverse (inverse ?46500)) =?= multiply (inverse (inverse (inverse ?46499))) ?46500 [46500, 46499] by Demod 9242 with 9341 at 2
1086 Id : 9788, {_}: multiply (inverse ?48461) (inverse (inverse (multiply (inverse (inverse ?48461)) ?48462))) =>= inverse (inverse ?48462) [48462, 48461] by Super 8447 with 9696 at 2
1087 Id : 9936, {_}: multiply (inverse ?48461) (inverse (multiply (inverse ?48462) (inverse ?48461))) =>= inverse (inverse ?48462) [48462, 48461] by Demod 9788 with 9341 at 1,2,2
1088 Id : 9937, {_}: multiply (inverse ?48461) (multiply (inverse (inverse ?48461)) ?48462) =>= inverse (inverse ?48462) [48462, 48461] by Demod 9936 with 9341 at 2,2
1089 Id : 8881, {_}: multiply ?2799 (inverse (multiply (inverse (inverse ?2797)) (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797))))) =>= ?2801 [2801, 2800, 2797, 2799] by Demod 379 with 8447 at 1,1,2,2
1090 Id : 9499, {_}: multiply ?2799 (multiply (inverse (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797)))) (inverse ?2797)) =>= ?2801 [2797, 2801, 2800, 2799] by Demod 8881 with 9341 at 2,2
1091 Id : 397, {_}: multiply (inverse ?2927) (multiply ?2927 (inverse (multiply (multiply (inverse ?2926) (multiply ?2926 ?2925)) (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))))) =>= ?2929 [2929, 2928, 2925, 2926, 2927] by Super 65 with 299 at 1,1,2,2,2
1092 Id : 8862, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2926) (multiply ?2926 ?2925)) (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))))) =>= ?2929 [2929, 2928, 2925, 2926] by Demod 397 with 8447 at 2
1093 Id : 8863, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2925)) (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))))) =>= ?2929 [2929, 2928, 2925] by Demod 8862 with 8447 at 1,1,1,1,2
1094 Id : 9311, {_}: multiply (inverse (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))) (inverse ?2925) =>= ?2929 [2925, 2929, 2928] by Demod 8863 with 9047 at 2
1095 Id : 9517, {_}: multiply ?2799 (multiply (inverse ?2799) ?2801) =>= ?2801 [2801, 2799] by Demod 9499 with 9311 at 2,2
1096 Id : 9938, {_}: ?48462 =<= inverse (inverse ?48462) [48462] by Demod 9937 with 9517 at 2
1097 Id : 10374, {_}: inverse (multiply ?49383 ?49384) =<= multiply (inverse ?49384) (inverse ?49383) [49384, 49383] by Super 9341 with 9938 at 1,1,2
1098 Id : 10391, {_}: inverse (multiply ?49456 (inverse ?49455)) =>= multiply ?49455 (inverse ?49456) [49455, 49456] by Super 10374 with 9938 at 1,3
1099 Id : 10496, {_}: multiply ?29 (multiply (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?31) ?29) ?30)) ?26) ?28) (inverse (multiply ?26 ?28))))) (inverse ?27)) =>= ?31 [28, 26, 31, 27, 30, 29] by Demod 9512 with 10391 at 2,2
1100 Id : 10497, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?31) ?29) ?30)) ?26) ?28)))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 10496 with 10391 at 2,1,2,2
1101 Id : 10262, {_}: inverse (multiply ?49016 ?49017) =<= multiply (inverse ?49017) (inverse ?49016) [49017, 49016] by Super 9341 with 9938 at 1,1,2
1102 Id : 10628, {_}: multiply ?49899 (inverse (multiply ?49900 ?49899)) =>= inverse ?49900 [49900, 49899] by Super 9517 with 10262 at 2,2
1103 Id : 10356, {_}: multiply ?49320 (inverse (multiply ?49319 ?49320)) =>= inverse ?49319 [49319, 49320] by Super 9517 with 10262 at 2,2
1104 Id : 10637, {_}: multiply (inverse (multiply ?49929 ?49930)) (inverse (inverse ?49929)) =>= inverse ?49930 [49930, 49929] by Super 10628 with 10356 at 1,2,2
1105 Id : 10710, {_}: inverse (multiply (inverse ?49929) (multiply ?49929 ?49930)) =>= inverse ?49930 [49930, 49929] by Demod 10637 with 10262 at 2
1106 Id : 10949, {_}: multiply (inverse (multiply ?50486 ?50487)) ?50486 =>= inverse ?50487 [50487, 50486] by Demod 10710 with 9341 at 2
1107 Id : 8870, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?587) ?588)) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 588, 587] by Demod 65 with 8447 at 2
1108 Id : 9498, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?588) ?587) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 587, 588] by Demod 8870 with 9341 at 1,1,1,1,1,2
1109 Id : 10246, {_}: inverse (multiply (multiply (multiply (inverse ?588) ?587) ?589) (inverse (multiply ?587 ?589))) =>= ?588 [589, 587, 588] by Demod 9498 with 9938 at 2
1110 Id : 10500, {_}: multiply (multiply ?587 ?589) (inverse (multiply (multiply (inverse ?588) ?587) ?589)) =>= ?588 [588, 589, 587] by Demod 10246 with 10391 at 2
1111 Id : 10962, {_}: multiply (inverse ?50540) (multiply ?50538 ?50539) =<= inverse (inverse (multiply (multiply (inverse ?50540) ?50538) ?50539)) [50539, 50538, 50540] by Super 10949 with 10500 at 1,1,2
1112 Id : 11025, {_}: multiply (inverse ?50540) (multiply ?50538 ?50539) =<= multiply (multiply (inverse ?50540) ?50538) ?50539 [50539, 50538, 50540] by Demod 10962 with 9938 at 3
1113 Id : 11420, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?31) ?29) ?30) ?26)) ?28)))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 10497 with 11025 at 1,1,2,2,1,2,2
1114 Id : 11421, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?31) ?29) ?30) ?26) ?28))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11420 with 11025 at 1,2,2,1,2,2
1115 Id : 11422, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?31) (multiply ?29 ?30)) ?26) ?28))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11421 with 11025 at 1,1,2,1,2,2,1,2,2
1116 Id : 11423, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?31) (multiply (multiply ?29 ?30) ?26)) ?28))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11422 with 11025 at 1,2,1,2,2,1,2,2
1117 Id : 11424, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (inverse ?31) (multiply (multiply (multiply ?29 ?30) ?26) ?28)))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11423 with 11025 at 2,1,2,2,1,2,2
1118 Id : 11441, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (multiply (inverse (multiply (inverse ?31) (multiply (multiply (multiply ?29 ?30) ?26) ?28))) ?27))) (inverse ?27)) =>= ?31 [27, 31, 28, 26, 30, 29] by Demod 11424 with 9341 at 2,2,1,2,2
1119 Id : 11442, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (multiply (multiply (inverse (multiply (multiply (multiply ?29 ?30) ?26) ?28)) ?31) ?27))) (inverse ?27)) =>= ?31 [27, 31, 28, 26, 30, 29] by Demod 11441 with 9341 at 1,2,2,1,2,2
1120 Id : 11443, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (multiply (inverse (multiply (multiply (multiply ?29 ?30) ?26) ?28)) (multiply ?31 ?27)))) (inverse ?27)) =>= ?31 [27, 31, 28, 26, 30, 29] by Demod 11442 with 11025 at 2,2,1,2,2
1121 Id : 3545, {_}: multiply (inverse (inverse (inverse ?21969))) ?21969 =?= inverse (multiply (inverse (multiply (inverse ?21970) (multiply ?21970 ?21971))) ?21971) [21971, 21970, 21969] by Super 3188 with 3359 at 2
1122 Id : 8885, {_}: multiply (inverse (inverse (inverse ?21969))) ?21969 =?= inverse (multiply (inverse (inverse (inverse ?21971))) ?21971) [21971, 21969] by Demod 3545 with 8447 at 1,1,1,3
1123 Id : 9513, {_}: multiply (inverse (inverse (inverse ?21969))) ?21969 =?= multiply (inverse ?21971) (inverse (inverse ?21971)) [21971, 21969] by Demod 8885 with 9341 at 3
1124 Id : 10244, {_}: multiply (inverse ?21969) ?21969 =?= multiply (inverse ?21971) (inverse (inverse ?21971)) [21971, 21969] by Demod 9513 with 9938 at 1,2
1125 Id : 10245, {_}: multiply (inverse ?21969) ?21969 =?= multiply (inverse ?21971) ?21971 [21971, 21969] by Demod 10244 with 9938 at 2,3
1126 Id : 10259, {_}: multiply (inverse ?49007) ?49007 =?= multiply ?49006 (inverse ?49006) [49006, 49007] by Super 10245 with 9938 at 1,3
1127 Id : 12679, {_}: multiply ?53137 (multiply (multiply ?53138 (multiply (multiply ?53139 ?53140) (multiply ?53136 (inverse ?53136)))) (inverse ?53140)) =>= multiply (multiply ?53137 ?53138) ?53139 [53136, 53140, 53139, 53138, 53137] by Super 11443 with 10259 at 2,2,1,2,2
1128 Id : 8358, {_}: multiply ?44663 (multiply ?44664 (inverse ?44664)) =>= inverse (inverse ?44663) [44664, 44663] by Super 7831 with 8223 at 1,2
1129 Id : 10234, {_}: multiply ?44663 (multiply ?44664 (inverse ?44664)) =>= ?44663 [44664, 44663] by Demod 8358 with 9938 at 3
1130 Id : 12924, {_}: multiply ?53137 (multiply (multiply ?53138 (multiply ?53139 ?53140)) (inverse ?53140)) =>= multiply (multiply ?53137 ?53138) ?53139 [53140, 53139, 53138, 53137] by Demod 12679 with 10234 at 2,1,2,2
1131 Id : 10222, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 8877 with 9938 at 2
1132 Id : 10223, {_}: inverse (multiply (multiply (inverse ?2914) ?2917) (inverse (multiply ?2913 ?2917))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 10222 with 9938 at 1,1,1,2
1133 Id : 10502, {_}: multiply (multiply ?2913 ?2917) (inverse (multiply (inverse ?2914) ?2917)) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 10223 with 10391 at 2
1134 Id : 10503, {_}: multiply (multiply ?2913 ?2917) (multiply (inverse ?2917) ?2914) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 10502 with 9341 at 2,2
1135 Id : 10711, {_}: multiply (inverse (multiply ?49929 ?49930)) ?49929 =>= inverse ?49930 [49930, 49929] by Demod 10710 with 9341 at 2
1136 Id : 10940, {_}: multiply (multiply ?50443 (multiply ?50441 ?50442)) (inverse ?50442) =>= multiply ?50443 ?50441 [50442, 50441, 50443] by Super 10503 with 10711 at 2,2
1137 Id : 22401, {_}: multiply ?53137 (multiply ?53138 ?53139) =?= multiply (multiply ?53137 ?53138) ?53139 [53139, 53138, 53137] by Demod 12924 with 10940 at 2,2
1138 Id : 22896, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 2 with 22401 at 3
1139 Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
1140 % SZS output end CNFRefutation for GRP014-1.p
1146 associativity_of_commutator is 86
1158 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1159 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1161 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
1162 [8, 7, 6] by associativity ?6 ?7 ?8
1166 multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
1167 [11, 10] by name ?10 ?11
1169 commutator (commutator ?13 ?14) ?15
1171 commutator ?13 (commutator ?14 ?15)
1172 [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
1175 multiply a (commutator b c) =<= multiply (commutator b c) a
1178 FAILURE in 254 iterations
1179 % SZS status Timeout for GRP024-5.p
1187 intersection_associative is 79
1188 intersection_commutative is 81
1189 intersection_idempotent is 84
1190 intersection_union_absorbtion is 76
1192 inverse_involution is 87
1193 inverse_of_identity is 88
1194 inverse_product_lemma is 86
1198 multiply_intersection1 is 74
1199 multiply_intersection2 is 72
1200 multiply_union1 is 75
1201 multiply_union2 is 73
1206 union_associative is 78
1207 union_commutative is 80
1208 union_idempotent is 82
1209 union_intersection_absorbtion is 77
1211 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1212 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1214 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
1215 [8, 7, 6] by associativity ?6 ?7 ?8
1216 Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
1217 Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
1219 inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
1220 [14, 13] by inverse_product_lemma ?13 ?14
1221 Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
1222 Id : 18, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
1224 intersection ?20 ?21 =?= intersection ?21 ?20
1225 [21, 20] by intersection_commutative ?20 ?21
1227 union ?23 ?24 =?= union ?24 ?23
1228 [24, 23] by union_commutative ?23 ?24
1230 intersection ?26 (intersection ?27 ?28)
1232 intersection (intersection ?26 ?27) ?28
1233 [28, 27, 26] by intersection_associative ?26 ?27 ?28
1235 union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
1236 [32, 31, 30] by union_associative ?30 ?31 ?32
1238 union (intersection ?34 ?35) ?35 =>= ?35
1239 [35, 34] by union_intersection_absorbtion ?34 ?35
1241 intersection (union ?37 ?38) ?38 =>= ?38
1242 [38, 37] by intersection_union_absorbtion ?37 ?38
1244 multiply ?40 (union ?41 ?42)
1246 union (multiply ?40 ?41) (multiply ?40 ?42)
1247 [42, 41, 40] by multiply_union1 ?40 ?41 ?42
1249 multiply ?44 (intersection ?45 ?46)
1251 intersection (multiply ?44 ?45) (multiply ?44 ?46)
1252 [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
1254 multiply (union ?48 ?49) ?50
1256 union (multiply ?48 ?50) (multiply ?49 ?50)
1257 [50, 49, 48] by multiply_union2 ?48 ?49 ?50
1259 multiply (intersection ?52 ?53) ?54
1261 intersection (multiply ?52 ?54) (multiply ?53 ?54)
1262 [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
1264 positive_part ?56 =<= union ?56 identity
1265 [56] by positive_part ?56
1267 negative_part ?58 =<= intersection ?58 identity
1268 [58] by negative_part ?58
1271 multiply (positive_part a) (negative_part a) =>= a
1273 Found proof, 2.362992s
1274 % SZS status Unsatisfiable for GRP114-1.p
1275 % SZS output start CNFRefutation for GRP114-1.p
1276 Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
1277 Id : 24, {_}: intersection ?26 (intersection ?27 ?28) =?= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
1278 Id : 34, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
1279 Id : 28, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
1280 Id : 26, {_}: union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
1281 Id : 267, {_}: multiply (union ?680 ?681) ?682 =<= union (multiply ?680 ?682) (multiply ?681 ?682) [682, 681, 680] by multiply_union2 ?680 ?681 ?682
1282 Id : 30, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
1283 Id : 230, {_}: multiply ?593 (intersection ?594 ?595) =<= intersection (multiply ?593 ?594) (multiply ?593 ?595) [595, 594, 593] by multiply_intersection1 ?593 ?594 ?595
1284 Id : 42, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
1285 Id : 20, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
1286 Id : 303, {_}: multiply (intersection ?770 ?771) ?772 =<= intersection (multiply ?770 ?772) (multiply ?771 ?772) [772, 771, 770] by multiply_intersection2 ?770 ?771 ?772
1287 Id : 14, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14
1288 Id : 22, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
1289 Id : 40, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
1290 Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
1291 Id : 32, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
1292 Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
1293 Id : 79, {_}: inverse (multiply ?142 ?143) =<= multiply (inverse ?143) (inverse ?142) [143, 142] by inverse_product_lemma ?142 ?143
1294 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1295 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1296 Id : 47, {_}: multiply (multiply ?68 ?69) ?70 =?= multiply ?68 (multiply ?69 ?70) [70, 69, 68] by associativity ?68 ?69 ?70
1297 Id : 56, {_}: multiply identity ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Super 47 with 6 at 1,2
1298 Id : 8878, {_}: ?10861 =<= multiply (inverse ?10862) (multiply ?10862 ?10861) [10862, 10861] by Demod 56 with 4 at 2
1299 Id : 81, {_}: inverse (multiply (inverse ?147) ?148) =>= multiply (inverse ?148) ?147 [148, 147] by Super 79 with 12 at 2,3
1300 Id : 80, {_}: inverse (multiply identity ?145) =<= multiply (inverse ?145) identity [145] by Super 79 with 10 at 2,3
1301 Id : 450, {_}: inverse ?990 =<= multiply (inverse ?990) identity [990] by Demod 80 with 4 at 1,2
1302 Id : 452, {_}: inverse (inverse ?993) =<= multiply ?993 identity [993] by Super 450 with 12 at 1,3
1303 Id : 467, {_}: ?993 =<= multiply ?993 identity [993] by Demod 452 with 12 at 2
1304 Id : 472, {_}: multiply ?1004 (union ?1005 identity) =?= union (multiply ?1004 ?1005) ?1004 [1005, 1004] by Super 32 with 467 at 2,3
1305 Id : 3150, {_}: multiply ?4224 (positive_part ?4225) =<= union (multiply ?4224 ?4225) ?4224 [4225, 4224] by Demod 472 with 40 at 2,2
1306 Id : 3152, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= union identity (inverse ?4229) [4229] by Super 3150 with 6 at 1,3
1307 Id : 336, {_}: union identity ?835 =>= positive_part ?835 [835] by Super 22 with 40 at 3
1308 Id : 3189, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= positive_part (inverse ?4229) [4229] by Demod 3152 with 336 at 3
1309 Id : 3219, {_}: inverse (positive_part (inverse ?4304)) =<= multiply (inverse (positive_part ?4304)) ?4304 [4304] by Super 81 with 3189 at 1,2
1310 Id : 8893, {_}: ?10899 =<= multiply (inverse (inverse (positive_part ?10899))) (inverse (positive_part (inverse ?10899))) [10899] by Super 8878 with 3219 at 2,3
1311 Id : 8928, {_}: ?10899 =<= inverse (multiply (positive_part (inverse ?10899)) (inverse (positive_part ?10899))) [10899] by Demod 8893 with 14 at 3
1312 Id : 83, {_}: inverse (multiply ?153 (inverse ?152)) =>= multiply ?152 (inverse ?153) [152, 153] by Super 79 with 12 at 1,3
1313 Id : 8929, {_}: ?10899 =<= multiply (positive_part ?10899) (inverse (positive_part (inverse ?10899))) [10899] by Demod 8928 with 83 at 3
1314 Id : 310, {_}: multiply (intersection (inverse ?798) ?797) ?798 =>= intersection identity (multiply ?797 ?798) [797, 798] by Super 303 with 6 at 1,3
1315 Id : 355, {_}: intersection identity ?867 =>= negative_part ?867 [867] by Super 20 with 42 at 3
1316 Id : 15914, {_}: multiply (intersection (inverse ?16735) ?16736) ?16735 =>= negative_part (multiply ?16736 ?16735) [16736, 16735] by Demod 310 with 355 at 3
1317 Id : 15939, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part (multiply identity ?16817) [16817] by Super 15914 with 42 at 1,2
1318 Id : 15984, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15939 with 4 at 1,3
1319 Id : 237, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= intersection identity (multiply (inverse ?620) ?621) [621, 620] by Super 230 with 6 at 1,3
1320 Id : 9377, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= negative_part (multiply (inverse ?620) ?621) [621, 620] by Demod 237 with 355 at 3
1321 Id : 387, {_}: intersection (positive_part ?915) ?915 =>= ?915 [915] by Super 30 with 336 at 1,2
1322 Id : 274, {_}: multiply (union (inverse ?708) ?707) ?708 =>= union identity (multiply ?707 ?708) [707, 708] by Super 267 with 6 at 1,3
1323 Id : 9854, {_}: multiply (union (inverse ?12356) ?12357) ?12356 =>= positive_part (multiply ?12357 ?12356) [12357, 12356] by Demod 274 with 336 at 3
1324 Id : 384, {_}: union identity (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Super 26 with 336 at 1,3
1325 Id : 394, {_}: positive_part (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Demod 384 with 336 at 2
1326 Id : 339, {_}: union ?842 (union ?843 identity) =>= positive_part (union ?842 ?843) [843, 842] by Super 26 with 40 at 3
1327 Id : 350, {_}: union ?842 (positive_part ?843) =<= positive_part (union ?842 ?843) [843, 842] by Demod 339 with 40 at 2,2
1328 Id : 667, {_}: union ?906 (positive_part ?907) =?= union (positive_part ?906) ?907 [907, 906] by Demod 394 with 350 at 2
1329 Id : 414, {_}: union (negative_part ?942) ?942 =>= ?942 [942] by Super 28 with 355 at 1,2
1330 Id : 479, {_}: multiply ?1021 (intersection ?1022 identity) =?= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Super 34 with 467 at 2,3
1331 Id : 2571, {_}: multiply ?3618 (negative_part ?3619) =<= intersection (multiply ?3618 ?3619) ?3618 [3619, 3618] by Demod 479 with 42 at 2,2
1332 Id : 2573, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= intersection identity (inverse ?3623) [3623] by Super 2571 with 6 at 1,3
1333 Id : 2624, {_}: multiply (inverse ?3692) (negative_part ?3692) =>= negative_part (inverse ?3692) [3692] by Demod 2573 with 355 at 3
1334 Id : 358, {_}: intersection ?874 (intersection ?875 identity) =>= negative_part (intersection ?874 ?875) [875, 874] by Super 24 with 42 at 3
1335 Id : 603, {_}: intersection ?1157 (negative_part ?1158) =<= negative_part (intersection ?1157 ?1158) [1158, 1157] by Demod 358 with 42 at 2,2
1336 Id : 613, {_}: intersection ?1189 (negative_part identity) =>= negative_part (negative_part ?1189) [1189] by Super 603 with 42 at 1,3
1337 Id : 354, {_}: negative_part identity =>= identity [] by Super 16 with 42 at 2
1338 Id : 624, {_}: intersection ?1189 identity =<= negative_part (negative_part ?1189) [1189] by Demod 613 with 354 at 2,2
1339 Id : 625, {_}: negative_part ?1189 =<= negative_part (negative_part ?1189) [1189] by Demod 624 with 42 at 2
1340 Id : 2630, {_}: multiply (inverse (negative_part ?3706)) (negative_part ?3706) =>= negative_part (inverse (negative_part ?3706)) [3706] by Super 2624 with 625 at 2,2
1341 Id : 2650, {_}: identity =<= negative_part (inverse (negative_part ?3706)) [3706] by Demod 2630 with 6 at 2
1342 Id : 2720, {_}: union identity (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Super 414 with 2650 at 1,2
1343 Id : 2757, {_}: positive_part (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Demod 2720 with 336 at 2
1344 Id : 2867, {_}: union (inverse (negative_part ?3906)) (positive_part ?3907) =>= union (inverse (negative_part ?3906)) ?3907 [3907, 3906] by Super 667 with 2757 at 1,3
1345 Id : 9877, {_}: multiply (union (inverse (negative_part ?12432)) ?12433) (negative_part ?12432) =>= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12433, 12432] by Super 9854 with 2867 at 1,2
1346 Id : 9834, {_}: multiply (union (inverse ?708) ?707) ?708 =>= positive_part (multiply ?707 ?708) [707, 708] by Demod 274 with 336 at 3
1347 Id : 9911, {_}: positive_part (multiply ?12433 (negative_part ?12432)) =<= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12432, 12433] by Demod 9877 with 9834 at 2
1348 Id : 492, {_}: multiply ?1021 (negative_part ?1022) =<= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Demod 479 with 42 at 2,2
1349 Id : 9880, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part (multiply identity ?12441) [12441] by Super 9854 with 40 at 1,2
1350 Id : 9914, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part ?12441 [12441] by Demod 9880 with 4 at 1,3
1351 Id : 9937, {_}: multiply (positive_part (inverse ?12495)) (negative_part ?12495) =>= intersection (positive_part ?12495) (positive_part (inverse ?12495)) [12495] by Super 492 with 9914 at 1,3
1352 Id : 10764, {_}: positive_part (multiply (inverse ?13313) (negative_part ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Super 9911 with 9937 at 1,3
1353 Id : 2601, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= negative_part (inverse ?3623) [3623] by Demod 2573 with 355 at 3
1354 Id : 10802, {_}: positive_part (negative_part (inverse ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10764 with 2601 at 1,2
1355 Id : 334, {_}: positive_part (intersection ?832 identity) =>= identity [832] by Super 28 with 40 at 2
1356 Id : 507, {_}: positive_part (negative_part ?832) =>= identity [832] by Demod 334 with 42 at 1,2
1357 Id : 10803, {_}: identity =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10802 with 507 at 2
1358 Id : 51479, {_}: intersection identity (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Super 387 with 10803 at 1,2
1359 Id : 51786, {_}: negative_part (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51479 with 355 at 2
1360 Id : 369, {_}: intersection ?874 (negative_part ?875) =<= negative_part (intersection ?874 ?875) [875, 874] by Demod 358 with 42 at 2,2
1361 Id : 51787, {_}: intersection (positive_part ?50477) (negative_part (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51786 with 369 at 2
1362 Id : 51788, {_}: intersection (negative_part (positive_part (inverse ?50477))) (positive_part ?50477) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51787 with 20 at 2
1363 Id : 411, {_}: intersection identity (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Super 24 with 355 at 1,3
1364 Id : 421, {_}: negative_part (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Demod 411 with 355 at 2
1365 Id : 795, {_}: intersection ?1452 (negative_part ?1453) =?= intersection (negative_part ?1452) ?1453 [1453, 1452] by Demod 421 with 369 at 2
1366 Id : 353, {_}: negative_part (union ?864 identity) =>= identity [864] by Super 30 with 42 at 2
1367 Id : 371, {_}: negative_part (positive_part ?864) =>= identity [864] by Demod 353 with 40 at 1,2
1368 Id : 797, {_}: intersection (positive_part ?1457) (negative_part ?1458) =>= intersection identity ?1458 [1458, 1457] by Super 795 with 371 at 1,3
1369 Id : 834, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= intersection identity ?1458 [1457, 1458] by Demod 797 with 20 at 2
1370 Id : 835, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= negative_part ?1458 [1457, 1458] by Demod 834 with 355 at 3
1371 Id : 51789, {_}: negative_part (positive_part (inverse ?50477)) =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51788 with 835 at 2
1372 Id : 51790, {_}: identity =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51789 with 371 at 2
1373 Id : 52162, {_}: multiply (inverse (positive_part ?50853)) identity =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Super 9377 with 51790 at 2,2
1374 Id : 52250, {_}: inverse (positive_part ?50853) =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Demod 52162 with 467 at 2
1375 Id : 65, {_}: ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Demod 56 with 4 at 2
1376 Id : 9942, {_}: multiply (positive_part (inverse ?12505)) ?12505 =>= positive_part ?12505 [12505] by Demod 9880 with 4 at 1,3
1377 Id : 9944, {_}: multiply (positive_part ?12508) (inverse ?12508) =>= positive_part (inverse ?12508) [12508] by Super 9942 with 12 at 1,1,2
1378 Id : 10037, {_}: inverse ?12562 =<= multiply (inverse (positive_part ?12562)) (positive_part (inverse ?12562)) [12562] by Super 65 with 9944 at 2,3
1379 Id : 52251, {_}: inverse (positive_part ?50853) =<= negative_part (inverse ?50853) [50853] by Demod 52250 with 10037 at 1,3
1380 Id : 52520, {_}: multiply (inverse (positive_part ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15984 with 52251 at 1,2
1381 Id : 52551, {_}: inverse (positive_part (inverse ?16817)) =>= negative_part ?16817 [16817] by Demod 52520 with 3219 at 2
1382 Id : 52560, {_}: ?10899 =<= multiply (positive_part ?10899) (negative_part ?10899) [10899] by Demod 8929 with 52551 at 2,3
1383 Id : 52939, {_}: a === a [] by Demod 2 with 52560 at 2
1384 Id : 2, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
1385 % SZS output end CNFRefutation for GRP114-1.p
1391 associativity_of_glb is 84
1392 associativity_of_lub is 83
1395 glb_absorbtion is 79
1396 greatest_lower_bound is 94
1397 idempotence_of_gld is 81
1398 idempotence_of_lub is 82
1401 least_upper_bound is 95
1404 lub_absorbtion is 80
1411 symmetry_of_glb is 86
1412 symmetry_of_lub is 85
1414 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1415 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1417 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
1418 [8, 7, 6] by associativity ?6 ?7 ?8
1420 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
1421 [11, 10] by symmetry_of_glb ?10 ?11
1423 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
1424 [14, 13] by symmetry_of_lub ?13 ?14
1426 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
1428 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
1429 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
1431 least_upper_bound ?20 (least_upper_bound ?21 ?22)
1433 least_upper_bound (least_upper_bound ?20 ?21) ?22
1434 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
1435 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
1437 greatest_lower_bound ?26 ?26 =>= ?26
1438 [26] by idempotence_of_gld ?26
1440 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
1441 [29, 28] by lub_absorbtion ?28 ?29
1443 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
1444 [32, 31] by glb_absorbtion ?31 ?32
1446 multiply ?34 (least_upper_bound ?35 ?36)
1448 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
1449 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
1451 multiply ?38 (greatest_lower_bound ?39 ?40)
1453 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
1454 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
1456 multiply (least_upper_bound ?42 ?43) ?44
1458 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
1459 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
1461 multiply (greatest_lower_bound ?46 ?47) ?48
1463 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
1464 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
1467 greatest_lower_bound a (least_upper_bound b c)
1469 least_upper_bound (greatest_lower_bound a b)
1470 (greatest_lower_bound a c)
1473 FAILURE in 345 iterations
1474 % SZS status Timeout for GRP164-2.p
1480 associativity_of_glb is 84
1481 associativity_of_lub is 83
1482 glb_absorbtion is 79
1483 greatest_lower_bound is 88
1484 idempotence_of_gld is 81
1485 idempotence_of_lub is 82
1492 least_upper_bound is 86
1495 lub_absorbtion is 80
1504 symmetry_of_glb is 87
1505 symmetry_of_lub is 85
1507 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1508 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1510 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
1511 [8, 7, 6] by associativity ?6 ?7 ?8
1513 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
1514 [11, 10] by symmetry_of_glb ?10 ?11
1516 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
1517 [14, 13] by symmetry_of_lub ?13 ?14
1519 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
1521 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
1522 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
1524 least_upper_bound ?20 (least_upper_bound ?21 ?22)
1526 least_upper_bound (least_upper_bound ?20 ?21) ?22
1527 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
1528 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
1530 greatest_lower_bound ?26 ?26 =>= ?26
1531 [26] by idempotence_of_gld ?26
1533 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
1534 [29, 28] by lub_absorbtion ?28 ?29
1536 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
1537 [32, 31] by glb_absorbtion ?31 ?32
1539 multiply ?34 (least_upper_bound ?35 ?36)
1541 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
1542 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
1544 multiply ?38 (greatest_lower_bound ?39 ?40)
1546 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
1547 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
1549 multiply (least_upper_bound ?42 ?43) ?44
1551 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
1552 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
1554 multiply (greatest_lower_bound ?46 ?47) ?48
1556 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
1557 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
1559 positive_part ?50 =<= least_upper_bound ?50 identity
1562 negative_part ?52 =<= greatest_lower_bound ?52 identity
1565 least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
1567 greatest_lower_bound (least_upper_bound ?54 ?55)
1568 (least_upper_bound ?54 ?56)
1569 [56, 55, 54] by lat4_3 ?54 ?55 ?56
1571 greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
1573 least_upper_bound (greatest_lower_bound ?58 ?59)
1574 (greatest_lower_bound ?58 ?60)
1575 [60, 59, 58] by lat4_4 ?58 ?59 ?60
1578 a =<= multiply (positive_part a) (negative_part a)
1580 Found proof, 4.088951s
1581 % SZS status Unsatisfiable for GRP167-1.p
1582 % SZS output start CNFRefutation for GRP167-1.p
1583 Id : 202, {_}: multiply ?551 (greatest_lower_bound ?552 ?553) =<= greatest_lower_bound (multiply ?551 ?552) (multiply ?551 ?553) [553, 552, 551] by monotony_glb1 ?551 ?552 ?553
1584 Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
1585 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
1586 Id : 16, {_}: 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
1587 Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
1588 Id : 171, {_}: multiply ?475 (least_upper_bound ?476 ?477) =<= least_upper_bound (multiply ?475 ?476) (multiply ?475 ?477) [477, 476, 475] by monotony_lub1 ?475 ?476 ?477
1589 Id : 14, {_}: 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
1590 Id : 32, {_}: 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
1591 Id : 384, {_}: greatest_lower_bound ?977 (least_upper_bound ?978 ?979) =<= least_upper_bound (greatest_lower_bound ?977 ?978) (greatest_lower_bound ?977 ?979) [979, 978, 977] by lat4_4 ?977 ?978 ?979
1592 Id : 34, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
1593 Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
1594 Id : 236, {_}: multiply (least_upper_bound ?630 ?631) ?632 =<= least_upper_bound (multiply ?630 ?632) (multiply ?631 ?632) [632, 631, 630] by monotony_lub2 ?630 ?631 ?632
1595 Id : 36, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
1596 Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
1597 Id : 269, {_}: multiply (greatest_lower_bound ?712 ?713) ?714 =<= greatest_lower_bound (multiply ?712 ?714) (multiply ?713 ?714) [714, 713, 712] by monotony_glb2 ?712 ?713 ?714
1598 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1599 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1600 Id : 45, {_}: multiply (multiply ?70 ?71) ?72 =?= multiply ?70 (multiply ?71 ?72) [72, 71, 70] by associativity ?70 ?71 ?72
1601 Id : 54, {_}: multiply identity ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Super 45 with 6 at 1,2
1602 Id : 63, {_}: ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Demod 54 with 4 at 2
1603 Id : 275, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= greatest_lower_bound identity (multiply ?735 ?736) [735, 736] by Super 269 with 6 at 1,3
1604 Id : 314, {_}: greatest_lower_bound identity ?795 =>= negative_part ?795 [795] by Super 10 with 36 at 3
1605 Id : 16387, {_}: multiply (greatest_lower_bound (inverse ?19768) ?19769) ?19768 =>= negative_part (multiply ?19769 ?19768) [19769, 19768] by Demod 275 with 314 at 3
1606 Id : 16411, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part (multiply identity ?19845) [19845] by Super 16387 with 36 at 1,2
1607 Id : 16448, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part ?19845 [19845] by Demod 16411 with 4 at 1,3
1608 Id : 16459, {_}: ?19856 =<= multiply (inverse (negative_part (inverse ?19856))) (negative_part ?19856) [19856] by Super 63 with 16448 at 2,3
1609 Id : 242, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= least_upper_bound identity (multiply ?653 ?654) [653, 654] by Super 236 with 6 at 1,3
1610 Id : 298, {_}: least_upper_bound identity ?767 =>= positive_part ?767 [767] by Super 12 with 34 at 3
1611 Id : 14211, {_}: multiply (least_upper_bound (inverse ?17599) ?17600) ?17599 =>= positive_part (multiply ?17600 ?17599) [17600, 17599] by Demod 242 with 298 at 3
1612 Id : 14234, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part (multiply identity ?17673) [17673] by Super 14211 with 34 at 1,2
1613 Id : 14264, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14234 with 4 at 1,3
1614 Id : 14196, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= positive_part (multiply ?653 ?654) [653, 654] by Demod 242 with 298 at 3
1615 Id : 393, {_}: greatest_lower_bound ?1016 (least_upper_bound ?1017 identity) =<= least_upper_bound (greatest_lower_bound ?1016 ?1017) (negative_part ?1016) [1017, 1016] by Super 384 with 36 at 2,3
1616 Id : 17840, {_}: greatest_lower_bound ?21384 (positive_part ?21385) =<= least_upper_bound (greatest_lower_bound ?21384 ?21385) (negative_part ?21384) [21385, 21384] by Demod 393 with 34 at 2,2
1617 Id : 17869, {_}: greatest_lower_bound ?21489 (positive_part ?21490) =<= least_upper_bound (greatest_lower_bound ?21490 ?21489) (negative_part ?21489) [21490, 21489] by Super 17840 with 10 at 1,3
1618 Id : 16471, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19889)) ?19890) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Super 32 with 16448 at 1,3
1619 Id : 480, {_}: greatest_lower_bound identity (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Super 14 with 314 at 1,3
1620 Id : 492, {_}: negative_part (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 480 with 314 at 2
1621 Id : 317, {_}: greatest_lower_bound ?802 (greatest_lower_bound ?803 identity) =>= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Super 14 with 36 at 3
1622 Id : 326, {_}: greatest_lower_bound ?802 (negative_part ?803) =<= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Demod 317 with 36 at 2,2
1623 Id : 770, {_}: greatest_lower_bound ?1137 (negative_part ?1138) =?= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 492 with 326 at 2
1624 Id : 16499, {_}: multiply (greatest_lower_bound (inverse ?19889) (negative_part ?19890)) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Demod 16471 with 770 at 1,2
1625 Id : 16372, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= negative_part (multiply ?735 ?736) [735, 736] by Demod 275 with 314 at 3
1626 Id : 16500, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19889, 19890] by Demod 16499 with 16372 at 2
1627 Id : 16501, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (multiply ?19890 ?19889) (negative_part ?19889) [19889, 19890] by Demod 16500 with 10 at 3
1628 Id : 47, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= multiply ?77 identity [78, 77] by Super 45 with 6 at 2,3
1629 Id : 4534, {_}: multiply (multiply ?6403 (inverse ?6404)) ?6404 =>= multiply ?6403 identity [6404, 6403] by Super 45 with 6 at 2,3
1630 Id : 4537, {_}: multiply identity ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Super 4534 with 6 at 1,2
1631 Id : 4552, {_}: ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Demod 4537 with 4 at 2
1632 Id : 46, {_}: multiply (multiply ?74 identity) ?75 =>= multiply ?74 ?75 [75, 74] by Super 45 with 4 at 2,3
1633 Id : 4557, {_}: multiply ?6432 ?6433 =<= multiply (inverse (inverse ?6432)) ?6433 [6433, 6432] by Super 46 with 4552 at 1,2
1634 Id : 4577, {_}: ?6410 =<= multiply ?6410 identity [6410] by Demod 4552 with 4557 at 3
1635 Id : 4578, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= ?77 [78, 77] by Demod 47 with 4577 at 3
1636 Id : 4593, {_}: inverse (inverse ?6519) =<= multiply ?6519 identity [6519] by Super 4577 with 4557 at 3
1637 Id : 4599, {_}: inverse (inverse ?6519) =>= ?6519 [6519] by Demod 4593 with 4577 at 3
1638 Id : 4627, {_}: multiply (multiply ?6536 ?6535) (inverse ?6535) =>= ?6536 [6535, 6536] by Super 4578 with 4599 at 2,1,2
1639 Id : 62767, {_}: inverse ?65768 =<= multiply (inverse (multiply ?65769 ?65768)) ?65769 [65769, 65768] by Super 63 with 4627 at 2,3
1640 Id : 177, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= least_upper_bound identity (multiply (inverse ?498) ?499) [499, 498] by Super 171 with 6 at 1,3
1641 Id : 4718, {_}: multiply (inverse ?6711) (least_upper_bound ?6711 ?6712) =>= positive_part (multiply (inverse ?6711) ?6712) [6712, 6711] by Demod 177 with 298 at 3
1642 Id : 4741, {_}: multiply (inverse ?6778) (positive_part ?6778) =?= positive_part (multiply (inverse ?6778) identity) [6778] by Super 4718 with 34 at 2,2
1643 Id : 4789, {_}: multiply (inverse ?6833) (positive_part ?6833) =>= positive_part (inverse ?6833) [6833] by Demod 4741 with 4577 at 1,3
1644 Id : 4801, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part (inverse (inverse ?6862)) [6862] by Super 4789 with 4599 at 1,2
1645 Id : 4820, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part ?6862 [6862] by Demod 4801 with 4599 at 1,3
1646 Id : 62784, {_}: inverse (positive_part (inverse ?65816)) =<= multiply (inverse (positive_part ?65816)) ?65816 [65816] by Super 62767 with 4820 at 1,1,3
1647 Id : 63204, {_}: negative_part (multiply (negative_part (inverse (positive_part ?66345))) ?66345) =>= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Super 16501 with 62784 at 1,3
1648 Id : 303, {_}: greatest_lower_bound ?780 (positive_part ?780) =>= ?780 [780] by Super 24 with 34 at 2,2
1649 Id : 535, {_}: greatest_lower_bound (positive_part ?1185) ?1185 =>= ?1185 [1185] by Super 10 with 303 at 3
1650 Id : 301, {_}: least_upper_bound ?774 (least_upper_bound ?775 identity) =>= positive_part (least_upper_bound ?774 ?775) [775, 774] by Super 16 with 34 at 3
1651 Id : 566, {_}: least_upper_bound ?1228 (positive_part ?1229) =<= positive_part (least_upper_bound ?1228 ?1229) [1229, 1228] by Demod 301 with 34 at 2,2
1652 Id : 576, {_}: least_upper_bound ?1260 (positive_part identity) =>= positive_part (positive_part ?1260) [1260] by Super 566 with 34 at 1,3
1653 Id : 297, {_}: positive_part identity =>= identity [] by Super 18 with 34 at 2
1654 Id : 590, {_}: least_upper_bound ?1260 identity =<= positive_part (positive_part ?1260) [1260] by Demod 576 with 297 at 2,2
1655 Id : 591, {_}: positive_part ?1260 =<= positive_part (positive_part ?1260) [1260] by Demod 590 with 34 at 2
1656 Id : 4798, {_}: multiply (inverse (positive_part ?6856)) (positive_part ?6856) =>= positive_part (inverse (positive_part ?6856)) [6856] by Super 4789 with 591 at 2,2
1657 Id : 4815, {_}: identity =<= positive_part (inverse (positive_part ?6856)) [6856] by Demod 4798 with 6 at 2
1658 Id : 4901, {_}: greatest_lower_bound identity (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Super 535 with 4815 at 1,2
1659 Id : 4948, {_}: negative_part (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Demod 4901 with 314 at 2
1660 Id : 63301, {_}: negative_part (multiply (inverse (positive_part ?66345)) ?66345) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63204 with 4948 at 1,1,2
1661 Id : 63302, {_}: negative_part (inverse (positive_part (inverse ?66345))) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63301 with 62784 at 1,2
1662 Id : 63303, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63302 with 4948 at 2
1663 Id : 5093, {_}: greatest_lower_bound (inverse (positive_part ?7140)) (negative_part ?7141) =>= greatest_lower_bound (inverse (positive_part ?7140)) ?7141 [7141, 7140] by Super 770 with 4948 at 1,3
1664 Id : 63304, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) ?66345 [66345] by Demod 63303 with 5093 at 3
1665 Id : 63811, {_}: greatest_lower_bound ?66966 (positive_part (inverse (positive_part (inverse ?66966)))) =>= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Super 17869 with 63304 at 1,3
1666 Id : 64079, {_}: greatest_lower_bound ?66966 identity =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 63811 with 4815 at 2,2
1667 Id : 64080, {_}: negative_part ?66966 =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 64079 with 36 at 2
1668 Id : 81148, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (positive_part (inverse ?80770))) [80770] by Super 14196 with 64080 at 1,2
1669 Id : 4706, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= positive_part (multiply (inverse ?498) ?499) [499, 498] by Demod 177 with 298 at 3
1670 Id : 444, {_}: least_upper_bound identity (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Super 16 with 298 at 1,3
1671 Id : 455, {_}: positive_part (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 444 with 298 at 2
1672 Id : 310, {_}: least_upper_bound ?774 (positive_part ?775) =<= positive_part (least_upper_bound ?774 ?775) [775, 774] by Demod 301 with 34 at 2,2
1673 Id : 677, {_}: least_upper_bound ?1100 (positive_part ?1101) =?= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 455 with 310 at 2
1674 Id : 483, {_}: least_upper_bound identity (negative_part ?1146) =>= identity [1146] by Super 22 with 314 at 2,2
1675 Id : 491, {_}: positive_part (negative_part ?1146) =>= identity [1146] by Demod 483 with 298 at 2
1676 Id : 4791, {_}: multiply (inverse (negative_part ?6836)) identity =>= positive_part (inverse (negative_part ?6836)) [6836] by Super 4789 with 491 at 2,2
1677 Id : 4812, {_}: inverse (negative_part ?6836) =<= positive_part (inverse (negative_part ?6836)) [6836] by Demod 4791 with 4577 at 2
1678 Id : 4834, {_}: least_upper_bound (inverse (negative_part ?6900)) (positive_part ?6901) =>= least_upper_bound (inverse (negative_part ?6900)) ?6901 [6901, 6900] by Super 677 with 4812 at 1,3
1679 Id : 6361, {_}: multiply (inverse (inverse (negative_part ?8525))) (least_upper_bound (inverse (negative_part ?8525)) ?8526) =>= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Super 4706 with 4834 at 2,2
1680 Id : 6399, {_}: positive_part (multiply (inverse (inverse (negative_part ?8525))) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6361 with 4706 at 2
1681 Id : 6400, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6399 with 4599 at 1,1,2
1682 Id : 6401, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (negative_part ?8525) (positive_part ?8526)) [8526, 8525] by Demod 6400 with 4599 at 1,1,3
1683 Id : 81268, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (inverse ?80770)) [80770] by Demod 81148 with 6401 at 3
1684 Id : 16474, {_}: multiply (negative_part (inverse ?19896)) ?19896 =>= negative_part ?19896 [19896] by Demod 16411 with 4 at 1,3
1685 Id : 16476, {_}: multiply (negative_part ?19899) (inverse ?19899) =>= negative_part (inverse ?19899) [19899] by Super 16474 with 4599 at 1,1,2
1686 Id : 81269, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= positive_part (negative_part (inverse ?80770)) [80770] by Demod 81268 with 16476 at 1,3
1687 Id : 81270, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= identity [80770] by Demod 81269 with 491 at 3
1688 Id : 81595, {_}: positive_part (inverse ?81005) =<= multiply (inverse (negative_part ?81005)) identity [81005] by Super 63 with 81270 at 2,3
1689 Id : 81710, {_}: positive_part (inverse ?81005) =>= inverse (negative_part ?81005) [81005] by Demod 81595 with 4577 at 3
1690 Id : 81898, {_}: multiply (inverse (negative_part ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14264 with 81710 at 1,2
1691 Id : 208, {_}: multiply (inverse ?574) (greatest_lower_bound ?574 ?575) =>= greatest_lower_bound identity (multiply (inverse ?574) ?575) [575, 574] by Super 202 with 6 at 1,3
1692 Id : 13514, {_}: multiply (inverse ?16653) (greatest_lower_bound ?16653 ?16654) =>= negative_part (multiply (inverse ?16653) ?16654) [16654, 16653] by Demod 208 with 314 at 3
1693 Id : 13540, {_}: multiply (inverse ?16729) (negative_part ?16729) =?= negative_part (multiply (inverse ?16729) identity) [16729] by Super 13514 with 36 at 2,2
1694 Id : 13620, {_}: multiply (inverse ?16816) (negative_part ?16816) =>= negative_part (inverse ?16816) [16816] by Demod 13540 with 4577 at 1,3
1695 Id : 13647, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part (inverse (inverse ?16885)) [16885] by Super 13620 with 4599 at 1,2
1696 Id : 13709, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part ?16885 [16885] by Demod 13647 with 4599 at 1,3
1697 Id : 62788, {_}: inverse (negative_part (inverse ?65826)) =<= multiply (inverse (negative_part ?65826)) ?65826 [65826] by Super 62767 with 13709 at 1,1,3
1698 Id : 81922, {_}: inverse (negative_part (inverse ?17673)) =>= positive_part ?17673 [17673] by Demod 81898 with 62788 at 2
1699 Id : 81929, {_}: ?19856 =<= multiply (positive_part ?19856) (negative_part ?19856) [19856] by Demod 16459 with 81922 at 1,3
1700 Id : 82398, {_}: a === a [] by Demod 2 with 81929 at 3
1701 Id : 2, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
1702 % SZS output end CNFRefutation for GRP167-1.p
1708 associativity_of_glb is 84
1709 associativity_of_lub is 83
1712 glb_absorbtion is 79
1713 greatest_lower_bound is 94
1714 idempotence_of_gld is 81
1715 idempotence_of_lub is 82
1718 least_upper_bound is 86
1721 lub_absorbtion is 80
1732 symmetry_of_glb is 87
1733 symmetry_of_lub is 85
1735 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1736 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1738 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
1739 [8, 7, 6] by associativity ?6 ?7 ?8
1741 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
1742 [11, 10] by symmetry_of_glb ?10 ?11
1744 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
1745 [14, 13] by symmetry_of_lub ?13 ?14
1747 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
1749 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
1750 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
1752 least_upper_bound ?20 (least_upper_bound ?21 ?22)
1754 least_upper_bound (least_upper_bound ?20 ?21) ?22
1755 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
1756 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
1758 greatest_lower_bound ?26 ?26 =>= ?26
1759 [26] by idempotence_of_gld ?26
1761 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
1762 [29, 28] by lub_absorbtion ?28 ?29
1764 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
1765 [32, 31] by glb_absorbtion ?31 ?32
1767 multiply ?34 (least_upper_bound ?35 ?36)
1769 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
1770 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
1772 multiply ?38 (greatest_lower_bound ?39 ?40)
1774 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
1775 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
1777 multiply (least_upper_bound ?42 ?43) ?44
1779 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
1780 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
1782 multiply (greatest_lower_bound ?46 ?47) ?48
1784 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
1785 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
1786 Id : 34, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
1787 Id : 36, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
1788 Id : 38, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
1789 Id : 40, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
1792 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
1795 FAILURE in 993 iterations
1796 % SZS status Timeout for GRP178-2.p
1802 associativity_of_glb is 85
1803 associativity_of_lub is 84
1806 glb_absorbtion is 80
1807 greatest_lower_bound is 89
1808 idempotence_of_gld is 82
1809 idempotence_of_lub is 83
1812 least_upper_bound is 87
1815 lub_absorbtion is 81
1829 symmetry_of_glb is 88
1830 symmetry_of_lub is 86
1832 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1833 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1835 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
1836 [8, 7, 6] by associativity ?6 ?7 ?8
1838 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
1839 [11, 10] by symmetry_of_glb ?10 ?11
1841 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
1842 [14, 13] by symmetry_of_lub ?13 ?14
1844 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
1846 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
1847 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
1849 least_upper_bound ?20 (least_upper_bound ?21 ?22)
1851 least_upper_bound (least_upper_bound ?20 ?21) ?22
1852 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
1853 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
1855 greatest_lower_bound ?26 ?26 =>= ?26
1856 [26] by idempotence_of_gld ?26
1858 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
1859 [29, 28] by lub_absorbtion ?28 ?29
1861 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
1862 [32, 31] by glb_absorbtion ?31 ?32
1864 multiply ?34 (least_upper_bound ?35 ?36)
1866 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
1867 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
1869 multiply ?38 (greatest_lower_bound ?39 ?40)
1871 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
1872 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
1874 multiply (least_upper_bound ?42 ?43) ?44
1876 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
1877 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
1879 multiply (greatest_lower_bound ?46 ?47) ?48
1881 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
1882 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
1883 Id : 34, {_}: inverse identity =>= identity [] by p12x_1
1884 Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
1886 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
1887 [54, 53] by p12x_3 ?53 ?54
1889 greatest_lower_bound a c =>= greatest_lower_bound b c
1891 Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
1893 inverse (greatest_lower_bound ?58 ?59)
1895 least_upper_bound (inverse ?58) (inverse ?59)
1896 [59, 58] by p12x_6 ?58 ?59
1898 inverse (least_upper_bound ?61 ?62)
1900 greatest_lower_bound (inverse ?61) (inverse ?62)
1901 [62, 61] by p12x_7 ?61 ?62
1903 Id : 2, {_}: a =>= b [] by prove_p12x
1904 Found proof, 6.988612s
1905 % SZS status Unsatisfiable for GRP181-4.p
1906 % SZS output start CNFRefutation for GRP181-4.p
1907 Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
1908 Id : 30, {_}: 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
1909 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
1910 Id : 40, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
1911 Id : 32, {_}: 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
1912 Id : 14, {_}: 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
1913 Id : 16, {_}: 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
1914 Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
1915 Id : 44, {_}: inverse (greatest_lower_bound ?58 ?59) =<= least_upper_bound (inverse ?58) (inverse ?59) [59, 58] by p12x_6 ?58 ?59
1916 Id : 375, {_}: inverse (greatest_lower_bound ?877 ?878) =<= least_upper_bound (inverse ?877) (inverse ?878) [878, 877] by p12x_6 ?877 ?878
1917 Id : 398, {_}: inverse (least_upper_bound ?920 ?921) =<= greatest_lower_bound (inverse ?920) (inverse ?921) [921, 920] by p12x_7 ?920 ?921
1918 Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
1919 Id : 208, {_}: multiply ?553 (greatest_lower_bound ?554 ?555) =<= greatest_lower_bound (multiply ?553 ?554) (multiply ?553 ?555) [555, 554, 553] by monotony_glb1 ?553 ?554 ?555
1920 Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
1921 Id : 38, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
1922 Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
1923 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
1924 Id : 34, {_}: inverse identity =>= identity [] by p12x_1
1925 Id : 324, {_}: inverse (multiply ?822 ?823) =<= multiply (inverse ?823) (inverse ?822) [823, 822] by p12x_3 ?822 ?823
1926 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
1927 Id : 51, {_}: multiply (multiply ?72 ?73) ?74 =?= multiply ?72 (multiply ?73 ?74) [74, 73, 72] by associativity ?72 ?73 ?74
1928 Id : 53, {_}: multiply (multiply ?79 (inverse ?80)) ?80 =>= multiply ?79 identity [80, 79] by Super 51 with 6 at 2,3
1929 Id : 325, {_}: inverse (multiply identity ?825) =<= multiply (inverse ?825) identity [825] by Super 324 with 34 at 2,3
1930 Id : 428, {_}: inverse ?975 =<= multiply (inverse ?975) identity [975] by Demod 325 with 4 at 1,2
1931 Id : 430, {_}: inverse (inverse ?978) =<= multiply ?978 identity [978] by Super 428 with 36 at 1,3
1932 Id : 441, {_}: ?978 =<= multiply ?978 identity [978] by Demod 430 with 36 at 2
1933 Id : 20385, {_}: multiply (multiply ?15306 (inverse ?15307)) ?15307 =>= ?15306 [15307, 15306] by Demod 53 with 441 at 3
1934 Id : 20408, {_}: multiply (inverse (multiply ?15383 ?15382)) ?15383 =>= inverse ?15382 [15382, 15383] by Super 20385 with 38 at 1,2
1935 Id : 307, {_}: multiply ?771 (inverse ?771) =>= identity [771] by Super 6 with 36 at 1,2
1936 Id : 598, {_}: multiply (multiply ?1178 ?1177) (inverse ?1177) =>= multiply ?1178 identity [1177, 1178] by Super 8 with 307 at 2,3
1937 Id : 32025, {_}: multiply (multiply ?27293 ?27294) (inverse ?27294) =>= ?27293 [27294, 27293] by Demod 598 with 441 at 3
1938 Id : 210, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound (multiply (inverse ?561) ?560) identity [560, 561] by Super 208 with 6 at 2,3
1939 Id : 229, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound identity (multiply (inverse ?561) ?560) [560, 561] by Demod 210 with 10 at 3
1940 Id : 401, {_}: inverse (least_upper_bound identity ?928) =>= greatest_lower_bound identity (inverse ?928) [928] by Super 398 with 34 at 1,3
1941 Id : 534, {_}: inverse (multiply (least_upper_bound identity ?1106) ?1107) =<= multiply (inverse ?1107) (greatest_lower_bound identity (inverse ?1106)) [1107, 1106] by Super 38 with 401 at 2,3
1942 Id : 25730, {_}: inverse (multiply (least_upper_bound identity ?21145) (inverse ?21145)) =>= greatest_lower_bound identity (multiply (inverse (inverse ?21145)) identity) [21145] by Super 229 with 534 at 2
1943 Id : 328, {_}: inverse (multiply ?833 (inverse ?832)) =>= multiply ?832 (inverse ?833) [832, 833] by Super 324 with 36 at 1,3
1944 Id : 25792, {_}: multiply ?21145 (inverse (least_upper_bound identity ?21145)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?21145)) identity) [21145] by Demod 25730 with 328 at 2
1945 Id : 25793, {_}: multiply ?21145 (greatest_lower_bound identity (inverse ?21145)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?21145)) identity) [21145] by Demod 25792 with 401 at 2,2
1946 Id : 25794, {_}: multiply ?21145 (greatest_lower_bound identity (inverse ?21145)) =>= greatest_lower_bound identity (inverse (inverse ?21145)) [21145] by Demod 25793 with 441 at 2,3
1947 Id : 25795, {_}: multiply ?21145 (greatest_lower_bound identity (inverse ?21145)) =>= greatest_lower_bound identity ?21145 [21145] by Demod 25794 with 36 at 2,3
1948 Id : 32085, {_}: multiply (greatest_lower_bound identity ?27496) (inverse (greatest_lower_bound identity (inverse ?27496))) =>= ?27496 [27496] by Super 32025 with 25795 at 1,2
1949 Id : 377, {_}: inverse (greatest_lower_bound ?883 (inverse ?882)) =>= least_upper_bound (inverse ?883) ?882 [882, 883] by Super 375 with 36 at 2,3
1950 Id : 32119, {_}: multiply (greatest_lower_bound identity ?27496) (least_upper_bound (inverse identity) ?27496) =>= ?27496 [27496] by Demod 32085 with 377 at 2,2
1951 Id : 82952, {_}: multiply (greatest_lower_bound identity ?64096) (least_upper_bound identity ?64096) =>= ?64096 [64096] by Demod 32119 with 34 at 1,2,2
1952 Id : 376, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound (inverse ?880) identity [880] by Super 375 with 34 at 2,3
1953 Id : 388, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound identity (inverse ?880) [880] by Demod 376 with 12 at 3
1954 Id : 509, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (inverse ?1077) (least_upper_bound identity (inverse ?1076)) [1076, 1077] by Super 44 with 388 at 2,3
1955 Id : 519, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (least_upper_bound identity (inverse ?1076)) (inverse ?1077) [1076, 1077] by Demod 509 with 12 at 3
1956 Id : 520, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound identity (least_upper_bound (inverse ?1076) (inverse ?1077)) [1076, 1077] by Demod 519 with 16 at 3
1957 Id : 521, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 520 with 44 at 2,3
1958 Id : 512, {_}: inverse (greatest_lower_bound ?1083 identity) =>= least_upper_bound identity (inverse ?1083) [1083] by Demod 376 with 12 at 3
1959 Id : 516, {_}: inverse (greatest_lower_bound ?1090 (greatest_lower_bound ?1091 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1090 ?1091)) [1091, 1090] by Super 512 with 14 at 1,2
1960 Id : 2139, {_}: least_upper_bound identity (inverse (greatest_lower_bound ?1077 ?1076)) =?= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 521 with 516 at 2
1961 Id : 28172, {_}: multiply (greatest_lower_bound ?24454 ?24455) (inverse ?24454) =>= greatest_lower_bound identity (multiply ?24455 (inverse ?24454)) [24455, 24454] by Super 32 with 307 at 1,3
1962 Id : 337, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 40 with 10 at 2
1963 Id : 338, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 337 with 10 at 3
1964 Id : 28217, {_}: multiply (greatest_lower_bound c b) (inverse c) =>= greatest_lower_bound identity (multiply a (inverse c)) [] by Super 28172 with 338 at 1,2
1965 Id : 595, {_}: multiply (greatest_lower_bound ?1168 ?1169) (inverse ?1168) =>= greatest_lower_bound identity (multiply ?1169 (inverse ?1168)) [1169, 1168] by Super 32 with 307 at 1,3
1966 Id : 28364, {_}: greatest_lower_bound identity (multiply b (inverse c)) =<= greatest_lower_bound identity (multiply a (inverse c)) [] by Demod 28217 with 595 at 2
1967 Id : 28527, {_}: least_upper_bound identity (inverse (greatest_lower_bound (multiply a (inverse c)) identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Super 2139 with 28364 at 1,2,3
1968 Id : 28562, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity (multiply a (inverse c)))) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28527 with 2139 at 2
1969 Id : 378, {_}: inverse (greatest_lower_bound identity ?885) =>= least_upper_bound identity (inverse ?885) [885] by Super 375 with 34 at 1,3
1970 Id : 28563, {_}: least_upper_bound identity (least_upper_bound identity (inverse (multiply a (inverse c)))) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28562 with 378 at 2,2
1971 Id : 112, {_}: least_upper_bound ?298 (least_upper_bound ?298 ?299) =>= least_upper_bound ?298 ?299 [299, 298] by Super 16 with 18 at 1,3
1972 Id : 28564, {_}: least_upper_bound identity (inverse (multiply a (inverse c))) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28563 with 112 at 2
1973 Id : 28565, {_}: least_upper_bound identity (multiply c (inverse a)) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28564 with 328 at 2,2
1974 Id : 28566, {_}: least_upper_bound identity (multiply c (inverse a)) =<= least_upper_bound identity (least_upper_bound identity (inverse (multiply b (inverse c)))) [] by Demod 28565 with 378 at 2,3
1975 Id : 28567, {_}: least_upper_bound identity (multiply c (inverse a)) =<= least_upper_bound identity (inverse (multiply b (inverse c))) [] by Demod 28566 with 112 at 3
1976 Id : 28568, {_}: least_upper_bound identity (multiply c (inverse a)) =>= least_upper_bound identity (multiply c (inverse b)) [] by Demod 28567 with 328 at 2,3
1977 Id : 82970, {_}: multiply (greatest_lower_bound identity (multiply c (inverse a))) (least_upper_bound identity (multiply c (inverse b))) =>= multiply c (inverse a) [] by Super 82952 with 28568 at 2,2
1978 Id : 29872, {_}: multiply (least_upper_bound ?25739 ?25740) (inverse ?25739) =>= least_upper_bound identity (multiply ?25740 (inverse ?25739)) [25740, 25739] by Super 30 with 307 at 1,3
1979 Id : 353, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 42 with 12 at 2
1980 Id : 354, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 353 with 12 at 3
1981 Id : 29917, {_}: multiply (least_upper_bound c b) (inverse c) =>= least_upper_bound identity (multiply a (inverse c)) [] by Super 29872 with 354 at 1,2
1982 Id : 605, {_}: multiply (least_upper_bound ?1196 ?1197) (inverse ?1196) =>= least_upper_bound identity (multiply ?1197 (inverse ?1196)) [1197, 1196] by Super 30 with 307 at 1,3
1983 Id : 30072, {_}: least_upper_bound identity (multiply b (inverse c)) =<= least_upper_bound identity (multiply a (inverse c)) [] by Demod 29917 with 605 at 2
1984 Id : 30292, {_}: inverse (least_upper_bound identity (multiply b (inverse c))) =>= greatest_lower_bound identity (inverse (multiply a (inverse c))) [] by Super 401 with 30072 at 1,2
1985 Id : 30345, {_}: greatest_lower_bound identity (inverse (multiply b (inverse c))) =<= greatest_lower_bound identity (inverse (multiply a (inverse c))) [] by Demod 30292 with 401 at 2
1986 Id : 30346, {_}: greatest_lower_bound identity (multiply c (inverse b)) =<= greatest_lower_bound identity (inverse (multiply a (inverse c))) [] by Demod 30345 with 328 at 2,2
1987 Id : 30347, {_}: greatest_lower_bound identity (multiply c (inverse b)) =<= greatest_lower_bound identity (multiply c (inverse a)) [] by Demod 30346 with 328 at 2,3
1988 Id : 83131, {_}: multiply (greatest_lower_bound identity (multiply c (inverse b))) (least_upper_bound identity (multiply c (inverse b))) =>= multiply c (inverse a) [] by Demod 82970 with 30347 at 1,2
1989 Id : 32120, {_}: multiply (greatest_lower_bound identity ?27496) (least_upper_bound identity ?27496) =>= ?27496 [27496] by Demod 32119 with 34 at 1,2,2
1990 Id : 83132, {_}: multiply c (inverse b) =<= multiply c (inverse a) [] by Demod 83131 with 32120 at 2
1991 Id : 83209, {_}: multiply (inverse (multiply c (inverse b))) c =>= inverse (inverse a) [] by Super 20408 with 83132 at 1,1,2
1992 Id : 83212, {_}: inverse (inverse b) =<= inverse (inverse a) [] by Demod 83209 with 20408 at 2
1993 Id : 83213, {_}: b =<= inverse (inverse a) [] by Demod 83212 with 36 at 2
1994 Id : 83214, {_}: b =<= a [] by Demod 83213 with 36 at 3
1995 Id : 83672, {_}: b === b [] by Demod 2 with 83214 at 2
1996 Id : 2, {_}: a =>= b [] by prove_p12x
1997 % SZS output end CNFRefutation for GRP181-4.p
2003 associativity_of_glb is 86
2004 associativity_of_lub is 85
2005 glb_absorbtion is 81
2006 greatest_lower_bound is 94
2007 idempotence_of_gld is 83
2008 idempotence_of_lub is 84
2011 least_upper_bound is 96
2014 lub_absorbtion is 82
2023 symmetry_of_glb is 88
2024 symmetry_of_lub is 87
2026 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2027 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2029 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2030 [8, 7, 6] by associativity ?6 ?7 ?8
2032 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2033 [11, 10] by symmetry_of_glb ?10 ?11
2035 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2036 [14, 13] by symmetry_of_lub ?13 ?14
2038 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2040 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2041 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2043 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2045 least_upper_bound (least_upper_bound ?20 ?21) ?22
2046 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2047 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2049 greatest_lower_bound ?26 ?26 =>= ?26
2050 [26] by idempotence_of_gld ?26
2052 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2053 [29, 28] by lub_absorbtion ?28 ?29
2055 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2056 [32, 31] by glb_absorbtion ?31 ?32
2058 multiply ?34 (least_upper_bound ?35 ?36)
2060 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2061 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2063 multiply ?38 (greatest_lower_bound ?39 ?40)
2065 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2066 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2068 multiply (least_upper_bound ?42 ?43) ?44
2070 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2071 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2073 multiply (greatest_lower_bound ?46 ?47) ?48
2075 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2076 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2077 Id : 34, {_}: inverse identity =>= identity [] by p20x_1
2078 Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
2080 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
2081 [54, 53] by p20x_3 ?53 ?54
2084 greatest_lower_bound (least_upper_bound a identity)
2085 (least_upper_bound (inverse a) identity)
2090 FAILURE in 339 iterations
2091 % SZS status Timeout for GRP183-4.p
2097 associativity_of_glb is 86
2098 associativity_of_lub is 85
2099 glb_absorbtion is 81
2100 greatest_lower_bound is 95
2101 idempotence_of_gld is 83
2102 idempotence_of_lub is 84
2105 least_upper_bound is 96
2108 lub_absorbtion is 82
2115 symmetry_of_glb is 88
2116 symmetry_of_lub is 87
2118 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2119 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2121 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2122 [8, 7, 6] by associativity ?6 ?7 ?8
2124 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2125 [11, 10] by symmetry_of_glb ?10 ?11
2127 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2128 [14, 13] by symmetry_of_lub ?13 ?14
2130 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2132 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2133 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2135 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2137 least_upper_bound (least_upper_bound ?20 ?21) ?22
2138 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2139 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2141 greatest_lower_bound ?26 ?26 =>= ?26
2142 [26] by idempotence_of_gld ?26
2144 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2145 [29, 28] by lub_absorbtion ?28 ?29
2147 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2148 [32, 31] by glb_absorbtion ?31 ?32
2150 multiply ?34 (least_upper_bound ?35 ?36)
2152 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2153 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2155 multiply ?38 (greatest_lower_bound ?39 ?40)
2157 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2158 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2160 multiply (least_upper_bound ?42 ?43) ?44
2162 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2163 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2165 multiply (greatest_lower_bound ?46 ?47) ?48
2167 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2168 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2171 multiply (least_upper_bound a identity)
2172 (inverse (greatest_lower_bound a identity))
2174 multiply (inverse (greatest_lower_bound a identity))
2175 (least_upper_bound a identity)
2178 FAILURE in 344 iterations
2179 % SZS status Timeout for GRP184-1.p
2185 associativity_of_glb is 86
2186 associativity_of_lub is 85
2187 glb_absorbtion is 81
2188 greatest_lower_bound is 95
2189 idempotence_of_gld is 83
2190 idempotence_of_lub is 84
2193 least_upper_bound is 96
2196 lub_absorbtion is 82
2203 symmetry_of_glb is 88
2204 symmetry_of_lub is 87
2206 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2207 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2209 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2210 [8, 7, 6] by associativity ?6 ?7 ?8
2212 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2213 [11, 10] by symmetry_of_glb ?10 ?11
2215 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2216 [14, 13] by symmetry_of_lub ?13 ?14
2218 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2220 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2221 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2223 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2225 least_upper_bound (least_upper_bound ?20 ?21) ?22
2226 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2227 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2229 greatest_lower_bound ?26 ?26 =>= ?26
2230 [26] by idempotence_of_gld ?26
2232 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2233 [29, 28] by lub_absorbtion ?28 ?29
2235 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2236 [32, 31] by glb_absorbtion ?31 ?32
2238 multiply ?34 (least_upper_bound ?35 ?36)
2240 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2241 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2243 multiply ?38 (greatest_lower_bound ?39 ?40)
2245 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2246 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2248 multiply (least_upper_bound ?42 ?43) ?44
2250 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2251 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2253 multiply (greatest_lower_bound ?46 ?47) ?48
2255 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2256 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2259 multiply (least_upper_bound a identity)
2260 (inverse (greatest_lower_bound a identity))
2262 multiply (inverse (greatest_lower_bound a identity))
2263 (least_upper_bound a identity)
2266 FAILURE in 343 iterations
2267 % SZS status Timeout for GRP184-3.p
2273 associativity_of_glb is 85
2274 associativity_of_lub is 84
2276 glb_absorbtion is 80
2277 greatest_lower_bound is 88
2278 idempotence_of_gld is 82
2279 idempotence_of_lub is 83
2282 least_upper_bound is 94
2285 lub_absorbtion is 81
2295 symmetry_of_glb is 87
2296 symmetry_of_lub is 86
2298 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2299 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2301 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2302 [8, 7, 6] by associativity ?6 ?7 ?8
2304 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2305 [11, 10] by symmetry_of_glb ?10 ?11
2307 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2308 [14, 13] by symmetry_of_lub ?13 ?14
2310 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2312 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2313 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2315 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2317 least_upper_bound (least_upper_bound ?20 ?21) ?22
2318 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2319 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2321 greatest_lower_bound ?26 ?26 =>= ?26
2322 [26] by idempotence_of_gld ?26
2324 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2325 [29, 28] by lub_absorbtion ?28 ?29
2327 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2328 [32, 31] by glb_absorbtion ?31 ?32
2330 multiply ?34 (least_upper_bound ?35 ?36)
2332 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2333 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2335 multiply ?38 (greatest_lower_bound ?39 ?40)
2337 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2338 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2340 multiply (least_upper_bound ?42 ?43) ?44
2342 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2343 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2345 multiply (greatest_lower_bound ?46 ?47) ?48
2347 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2348 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2349 Id : 34, {_}: inverse identity =>= identity [] by p22a_1
2350 Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
2352 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
2353 [54, 53] by p22a_3 ?53 ?54
2356 least_upper_bound (least_upper_bound (multiply a b) identity)
2357 (multiply (least_upper_bound a identity)
2358 (least_upper_bound b identity))
2360 multiply (least_upper_bound a identity)
2361 (least_upper_bound b identity)
2364 FAILURE in 339 iterations
2365 % SZS status Timeout for GRP185-2.p
2371 associativity_of_glb is 85
2372 associativity_of_lub is 84
2374 glb_absorbtion is 80
2375 greatest_lower_bound is 93
2376 idempotence_of_gld is 82
2377 idempotence_of_lub is 83
2380 least_upper_bound is 94
2383 lub_absorbtion is 81
2390 symmetry_of_glb is 87
2391 symmetry_of_lub is 86
2393 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2394 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2396 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2397 [8, 7, 6] by associativity ?6 ?7 ?8
2399 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2400 [11, 10] by symmetry_of_glb ?10 ?11
2402 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2403 [14, 13] by symmetry_of_lub ?13 ?14
2405 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2407 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2408 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2410 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2412 least_upper_bound (least_upper_bound ?20 ?21) ?22
2413 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2414 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2416 greatest_lower_bound ?26 ?26 =>= ?26
2417 [26] by idempotence_of_gld ?26
2419 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2420 [29, 28] by lub_absorbtion ?28 ?29
2422 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2423 [32, 31] by glb_absorbtion ?31 ?32
2425 multiply ?34 (least_upper_bound ?35 ?36)
2427 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2428 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2430 multiply ?38 (greatest_lower_bound ?39 ?40)
2432 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2433 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2435 multiply (least_upper_bound ?42 ?43) ?44
2437 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2438 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2440 multiply (greatest_lower_bound ?46 ?47) ?48
2442 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2443 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2446 greatest_lower_bound (least_upper_bound (multiply a b) identity)
2447 (multiply (least_upper_bound a identity)
2448 (least_upper_bound b identity))
2450 least_upper_bound (multiply a b) identity
2453 FAILURE in 352 iterations
2454 % SZS status Timeout for GRP185-3.p
2460 associativity_of_glb is 85
2461 associativity_of_lub is 84
2463 glb_absorbtion is 80
2464 greatest_lower_bound is 92
2465 idempotence_of_gld is 82
2466 idempotence_of_lub is 83
2469 least_upper_bound is 94
2472 lub_absorbtion is 81
2479 symmetry_of_glb is 87
2480 symmetry_of_lub is 86
2482 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2483 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2485 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2486 [8, 7, 6] by associativity ?6 ?7 ?8
2488 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2489 [11, 10] by symmetry_of_glb ?10 ?11
2491 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2492 [14, 13] by symmetry_of_lub ?13 ?14
2494 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2496 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2497 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2499 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2501 least_upper_bound (least_upper_bound ?20 ?21) ?22
2502 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2503 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2505 greatest_lower_bound ?26 ?26 =>= ?26
2506 [26] by idempotence_of_gld ?26
2508 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2509 [29, 28] by lub_absorbtion ?28 ?29
2511 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2512 [32, 31] by glb_absorbtion ?31 ?32
2514 multiply ?34 (least_upper_bound ?35 ?36)
2516 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2517 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2519 multiply ?38 (greatest_lower_bound ?39 ?40)
2521 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2522 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2524 multiply (least_upper_bound ?42 ?43) ?44
2526 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2527 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2529 multiply (greatest_lower_bound ?46 ?47) ?48
2531 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2532 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2535 least_upper_bound (multiply a b) identity
2537 multiply a (inverse (greatest_lower_bound a (inverse b)))
2540 FAILURE in 343 iterations
2541 % SZS status Timeout for GRP186-1.p
2547 associativity_of_glb is 85
2548 associativity_of_lub is 84
2550 glb_absorbtion is 80
2551 greatest_lower_bound is 92
2552 idempotence_of_gld is 82
2553 idempotence_of_lub is 83
2556 least_upper_bound is 94
2559 lub_absorbtion is 81
2569 symmetry_of_glb is 87
2570 symmetry_of_lub is 86
2572 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2573 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2575 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2576 [8, 7, 6] by associativity ?6 ?7 ?8
2578 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2579 [11, 10] by symmetry_of_glb ?10 ?11
2581 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2582 [14, 13] by symmetry_of_lub ?13 ?14
2584 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2586 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2587 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2589 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2591 least_upper_bound (least_upper_bound ?20 ?21) ?22
2592 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2593 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2595 greatest_lower_bound ?26 ?26 =>= ?26
2596 [26] by idempotence_of_gld ?26
2598 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2599 [29, 28] by lub_absorbtion ?28 ?29
2601 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2602 [32, 31] by glb_absorbtion ?31 ?32
2604 multiply ?34 (least_upper_bound ?35 ?36)
2606 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2607 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2609 multiply ?38 (greatest_lower_bound ?39 ?40)
2611 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2612 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2614 multiply (least_upper_bound ?42 ?43) ?44
2616 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2617 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2619 multiply (greatest_lower_bound ?46 ?47) ?48
2621 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2622 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2623 Id : 34, {_}: inverse identity =>= identity [] by p23_1
2624 Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
2626 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
2627 [54, 53] by p23_3 ?53 ?54
2630 least_upper_bound (multiply a b) identity
2632 multiply a (inverse (greatest_lower_bound a (inverse b)))
2635 FAILURE in 341 iterations
2636 % SZS status Timeout for GRP186-2.p
2642 associativity_of_glb is 85
2643 associativity_of_lub is 84
2645 glb_absorbtion is 80
2646 greatest_lower_bound is 89
2647 idempotence_of_gld is 82
2648 idempotence_of_lub is 83
2651 least_upper_bound is 87
2654 lub_absorbtion is 81
2662 symmetry_of_glb is 88
2663 symmetry_of_lub is 86
2665 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2666 Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
2668 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
2669 [8, 7, 6] by associativity ?6 ?7 ?8
2671 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
2672 [11, 10] by symmetry_of_glb ?10 ?11
2674 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
2675 [14, 13] by symmetry_of_lub ?13 ?14
2677 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
2679 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
2680 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
2682 least_upper_bound ?20 (least_upper_bound ?21 ?22)
2684 least_upper_bound (least_upper_bound ?20 ?21) ?22
2685 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
2686 Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
2688 greatest_lower_bound ?26 ?26 =>= ?26
2689 [26] by idempotence_of_gld ?26
2691 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
2692 [29, 28] by lub_absorbtion ?28 ?29
2694 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
2695 [32, 31] by glb_absorbtion ?31 ?32
2697 multiply ?34 (least_upper_bound ?35 ?36)
2699 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
2700 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
2702 multiply ?38 (greatest_lower_bound ?39 ?40)
2704 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
2705 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
2707 multiply (least_upper_bound ?42 ?43) ?44
2709 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
2710 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
2712 multiply (greatest_lower_bound ?46 ?47) ?48
2714 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
2715 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
2717 greatest_lower_bound (least_upper_bound a (inverse a))
2718 (least_upper_bound b (inverse b))
2723 Id : 2, {_}: multiply a b =>= multiply b a [] by prove_p33
2725 FAILURE in 534 iterations
2726 % SZS status Timeout for GRP187-1.p
2735 left_division_multiply is 88
2740 multiply_left_division is 89
2741 multiply_right_division is 86
2742 prove_moufang2 is 94
2743 right_division is 87
2744 right_division_multiply is 85
2745 right_identity is 91
2748 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2749 Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
2751 multiply ?6 (left_division ?6 ?7) =>= ?7
2752 [7, 6] by multiply_left_division ?6 ?7
2754 left_division ?9 (multiply ?9 ?10) =>= ?10
2755 [10, 9] by left_division_multiply ?9 ?10
2757 multiply (right_division ?12 ?13) ?13 =>= ?12
2758 [13, 12] by multiply_right_division ?12 ?13
2760 right_division (multiply ?15 ?16) ?16 =>= ?15
2761 [16, 15] by right_division_multiply ?15 ?16
2763 multiply ?18 (right_inverse ?18) =>= identity
2764 [18] by right_inverse ?18
2766 multiply (left_inverse ?20) ?20 =>= identity
2767 [20] by left_inverse ?20
2769 multiply (multiply ?22 (multiply ?23 ?24)) ?22
2771 multiply (multiply ?22 ?23) (multiply ?24 ?22)
2772 [24, 23, 22] by moufang1 ?22 ?23 ?24
2775 multiply (multiply (multiply a b) c) b
2777 multiply a (multiply b (multiply c b))
2778 [] by prove_moufang2
2780 FAILURE in 276 iterations
2781 % SZS status Timeout for GRP200-1.p
2790 left_division_multiply is 88
2795 multiply_left_division is 89
2796 multiply_right_division is 86
2797 prove_moufang1 is 94
2798 right_division is 87
2799 right_division_multiply is 85
2800 right_identity is 91
2803 Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
2804 Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
2806 multiply ?6 (left_division ?6 ?7) =>= ?7
2807 [7, 6] by multiply_left_division ?6 ?7
2809 left_division ?9 (multiply ?9 ?10) =>= ?10
2810 [10, 9] by left_division_multiply ?9 ?10
2812 multiply (right_division ?12 ?13) ?13 =>= ?12
2813 [13, 12] by multiply_right_division ?12 ?13
2815 right_division (multiply ?15 ?16) ?16 =>= ?15
2816 [16, 15] by right_division_multiply ?15 ?16
2818 multiply ?18 (right_inverse ?18) =>= identity
2819 [18] by right_inverse ?18
2821 multiply (left_inverse ?20) ?20 =>= identity
2822 [20] by left_inverse ?20
2824 multiply (multiply (multiply ?22 ?23) ?22) ?24
2826 multiply ?22 (multiply ?23 (multiply ?22 ?24))
2827 [24, 23, 22] by moufang3 ?22 ?23 ?24
2830 multiply (multiply a (multiply b c)) a
2832 multiply (multiply a b) (multiply c a)
2833 [] by prove_moufang1
2835 FAILURE in 260 iterations
2836 % SZS status Timeout for GRP202-1.p
2844 prove_these_axioms_2 is 94
2850 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
2851 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
2854 [4, 3, 2] by single_axiom ?2 ?3 ?4
2857 multiply (multiply (inverse b2) b2) a2 =>= a2
2858 [] by prove_these_axioms_2
2860 FAILURE in 62 iterations
2861 % SZS status Timeout for GRP404-1.p
2870 prove_these_axioms_3 is 94
2876 (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
2877 (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
2880 [4, 3, 2] by single_axiom ?2 ?3 ?4
2883 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
2884 [] by prove_these_axioms_3
2886 FAILURE in 62 iterations
2887 % SZS status Timeout for GRP405-1.p
2895 prove_these_axioms_2 is 94
2904 (multiply (inverse ?3)
2905 (multiply (inverse ?4)
2906 (inverse (multiply (inverse ?4) ?4)))))))
2910 [4, 3, 2] by single_axiom ?2 ?3 ?4
2913 multiply (multiply (inverse b2) b2) a2 =>= a2
2914 [] by prove_these_axioms_2
2916 FAILURE in 52 iterations
2917 % SZS status Timeout for GRP422-1.p
2926 prove_these_axioms_3 is 94
2935 (multiply (inverse ?3)
2936 (multiply (inverse ?4)
2937 (inverse (multiply (inverse ?4) ?4)))))))
2941 [4, 3, 2] by single_axiom ?2 ?3 ?4
2944 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
2945 [] by prove_these_axioms_3
2947 FAILURE in 52 iterations
2948 % SZS status Timeout for GRP423-1.p
2957 prove_these_axioms_3 is 94
2964 (multiply (multiply ?4 (inverse ?4))
2965 (inverse (multiply ?5 (multiply ?2 ?3))))))
2968 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
2971 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
2972 [] by prove_these_axioms_3
2974 FAILURE in 72 iterations
2975 % SZS status Timeout for GRP444-1.p
2984 prove_these_axioms_2 is 94
2989 (divide (divide ?2 ?2)
2990 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
2994 [4, 3, 2] by single_axiom ?2 ?3 ?4
2996 multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
2997 [8, 7, 6] by multiply ?6 ?7 ?8
2999 inverse ?10 =<= divide (divide ?11 ?11) ?10
3000 [11, 10] by inverse ?10 ?11
3003 multiply (multiply (inverse b2) b2) a2 =>= a2
3004 [] by prove_these_axioms_2
3005 Found proof, 0.089757s
3006 % SZS status Unsatisfiable for GRP452-1.p
3007 % SZS output start CNFRefutation for GRP452-1.p
3008 Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
3009 Id : 4, {_}: 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
3010 Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
3011 Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
3012 Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
3013 Id : 45, {_}: multiply (divide ?108 ?108) ?109 =>= inverse (inverse ?109) [109, 108] by Super 33 with 8 at 3
3014 Id : 47, {_}: multiply (multiply (inverse ?114) ?114) ?115 =>= inverse (inverse ?115) [115, 114] by Super 45 with 33 at 1,2
3015 Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
3016 Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
3017 Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
3018 Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
3019 Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
3020 Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
3021 Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
3022 Id : 265, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
3023 Id : 270, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 265 with 40 at 2,1,1,3
3024 Id : 286, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 270 with 8 at 1,1,2
3025 Id : 306, {_}: divide (divide (inverse (inverse ?778)) ?779) (inverse ?779) =>= ?778 [779, 778] by Super 63 with 286 at 1,2
3026 Id : 319, {_}: multiply (divide (inverse (inverse ?778)) ?779) ?779 =>= ?778 [779, 778] by Demod 306 with 33 at 2
3027 Id : 682, {_}: ?1380 =<= inverse (inverse (inverse (inverse ?1380))) [1380] by Super 36 with 319 at 2
3028 Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
3029 Id : 269, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 265 with 33 at 2,1,1,3
3030 Id : 285, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 269 with 33 at 2
3031 Id : 743, {_}: ?1513 =<= inverse (inverse (inverse (inverse ?1513))) [1513] by Super 36 with 319 at 2
3032 Id : 138, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
3033 Id : 1731, {_}: multiply ?3407 (divide (inverse ?3408) ?3409) =<= inverse (inverse (divide (inverse (divide ?3408 ?3407)) ?3409)) [3409, 3408, 3407] by Super 743 with 138 at 1,1,3
3034 Id : 1810, {_}: multiply ?3532 (divide (inverse ?3532) ?3533) =>= inverse (inverse (inverse ?3533)) [3533, 3532] by Super 1731 with 40 at 1,1,3
3035 Id : 735, {_}: multiply ?1490 (inverse (inverse (inverse ?1489))) =>= divide ?1490 ?1489 [1489, 1490] by Super 33 with 682 at 2,3
3036 Id : 742, {_}: multiply (divide ?1510 ?1511) ?1511 =>= inverse (inverse ?1510) [1511, 1510] by Super 319 with 682 at 1,1,2
3037 Id : 867, {_}: inverse (inverse ?1672) =<= divide (divide ?1672 (inverse (inverse (inverse ?1673)))) ?1673 [1673, 1672] by Super 735 with 742 at 2
3038 Id : 1192, {_}: inverse (inverse ?2233) =<= divide (multiply ?2233 (inverse (inverse ?2234))) ?2234 [2234, 2233] by Demod 867 with 33 at 1,3
3039 Id : 55, {_}: multiply (inverse (inverse (divide ?138 ?138))) ?139 =>= inverse (inverse ?139) [139, 138] by Super 36 with 40 at 1,2
3040 Id : 1206, {_}: inverse (inverse (inverse (inverse (divide ?2285 ?2285)))) =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Super 1192 with 55 at 1,3
3041 Id : 1239, {_}: divide ?2285 ?2285 =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Demod 1206 with 682 at 2
3042 Id : 1240, {_}: divide ?2285 ?2285 =?= divide ?2286 ?2286 [2286, 2285] by Demod 1239 with 682 at 1,3
3043 Id : 1820, {_}: multiply ?3573 (divide ?3572 ?3572) =?= inverse (inverse (inverse (inverse ?3573))) [3572, 3573] by Super 1810 with 1240 at 2,2
3044 Id : 1859, {_}: multiply ?3573 (divide ?3572 ?3572) =>= ?3573 [3572, 3573] by Demod 1820 with 682 at 3
3045 Id : 1899, {_}: multiply (inverse (divide ?3678 ?3679)) (divide ?3677 ?3677) =>= inverse (inverse (multiply ?3679 (inverse ?3678))) [3677, 3679, 3678] by Super 285 with 1859 at 2,1,1,3
3046 Id : 1926, {_}: inverse (divide ?3678 ?3679) =<= inverse (inverse (multiply ?3679 (inverse ?3678))) [3679, 3678] by Demod 1899 with 1859 at 2
3047 Id : 1927, {_}: inverse (divide ?3678 ?3679) =<= divide (inverse (inverse ?3679)) ?3678 [3679, 3678] by Demod 1926 with 286 at 3
3048 Id : 1948, {_}: inverse ?121 =<= inverse (divide ?121 (divide ?120 ?120)) [120, 121] by Demod 50 with 1927 at 3
3049 Id : 1882, {_}: divide ?3627 (divide ?3626 ?3626) =>= inverse (inverse ?3627) [3626, 3627] by Super 742 with 1859 at 2
3050 Id : 2237, {_}: inverse ?121 =<= inverse (inverse (inverse ?121)) [121] by Demod 1948 with 1882 at 1,3
3051 Id : 2241, {_}: ?1380 =<= inverse (inverse ?1380) [1380] by Demod 682 with 2237 at 3
3052 Id : 2403, {_}: a2 === a2 [] by Demod 85 with 2241 at 2
3053 Id : 85, {_}: inverse (inverse a2) =>= a2 [] by Demod 2 with 47 at 2
3054 Id : 2, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
3055 % SZS output end CNFRefutation for GRP452-1.p
3065 prove_these_axioms_3 is 94
3070 (divide (divide ?2 ?2)
3071 (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
3075 [4, 3, 2] by single_axiom ?2 ?3 ?4
3077 multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
3078 [8, 7, 6] by multiply ?6 ?7 ?8
3080 inverse ?10 =<= divide (divide ?11 ?11) ?10
3081 [11, 10] by inverse ?10 ?11
3084 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
3085 [] by prove_these_axioms_3
3086 Found proof, 0.810429s
3087 % SZS status Unsatisfiable for GRP453-1.p
3088 % SZS output start CNFRefutation for GRP453-1.p
3089 Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
3090 Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
3091 Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
3092 Id : 4, {_}: 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
3093 Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
3094 Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
3095 Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
3096 Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
3097 Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
3098 Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
3099 Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
3100 Id : 264, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
3101 Id : 269, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 264 with 40 at 2,1,1,3
3102 Id : 285, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 269 with 8 at 1,1,2
3103 Id : 307, {_}: divide (inverse (inverse ?786)) ?787 =<= inverse (inverse (multiply ?786 (inverse ?787))) [787, 786] by Demod 269 with 8 at 1,1,2
3104 Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
3105 Id : 310, {_}: divide (inverse (inverse (divide ?798 ?798))) ?799 =>= inverse (inverse (inverse (inverse (inverse ?799)))) [799, 798] by Super 307 with 36 at 1,1,3
3106 Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
3107 Id : 325, {_}: inverse ?799 =<= inverse (inverse (inverse (inverse (inverse ?799)))) [799] by Demod 310 with 50 at 2
3108 Id : 332, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= divide ?837 (inverse ?836) [836, 837] by Super 33 with 325 at 2,3
3109 Id : 354, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= multiply ?837 ?836 [836, 837] by Demod 332 with 33 at 3
3110 Id : 364, {_}: divide (inverse (inverse ?880)) (inverse (inverse (inverse ?881))) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Super 285 with 354 at 1,1,3
3111 Id : 423, {_}: multiply (inverse (inverse ?880)) (inverse (inverse ?881)) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Demod 364 with 33 at 2
3112 Id : 448, {_}: divide (inverse (inverse (inverse (inverse ?1012)))) (inverse ?1013) =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Super 285 with 423 at 1,1,3
3113 Id : 470, {_}: multiply (inverse (inverse (inverse (inverse ?1012)))) ?1013 =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Demod 448 with 33 at 2
3114 Id : 499, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?1108 ?1109))))))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Super 63 with 470 at 1,1,1,2
3115 Id : 519, {_}: divide (inverse (inverse (multiply ?1108 ?1109))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Demod 499 with 325 at 1,2
3116 Id : 520, {_}: ?1108 =<= inverse (inverse (inverse (inverse ?1108))) [1108] by Demod 519 with 63 at 2
3117 Id : 268, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 264 with 33 at 2,1,1,3
3118 Id : 284, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 268 with 33 at 2
3119 Id : 1304, {_}: multiply ?2415 (multiply (inverse ?2414) ?2416) =<= inverse (inverse (multiply (inverse (divide ?2414 ?2415)) ?2416)) [2416, 2414, 2415] by Super 520 with 284 at 1,1,3
3120 Id : 565, {_}: multiply ?1187 (inverse (inverse (inverse ?1186))) =>= divide ?1187 ?1186 [1186, 1187] by Super 33 with 520 at 2,3
3121 Id : 590, {_}: divide (inverse (inverse ?1228)) (inverse (inverse ?1229)) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Super 285 with 565 at 1,1,3
3122 Id : 687, {_}: multiply (inverse (inverse ?1369)) (inverse ?1370) =>= inverse (inverse (divide ?1369 ?1370)) [1370, 1369] by Demod 590 with 33 at 2
3123 Id : 781, {_}: multiply ?1560 (inverse ?1561) =<= inverse (inverse (divide (inverse (inverse ?1560)) ?1561)) [1561, 1560] by Super 687 with 520 at 1,2
3124 Id : 791, {_}: multiply ?1599 (inverse (inverse ?1598)) =<= inverse (inverse (multiply (inverse (inverse ?1599)) ?1598)) [1598, 1599] by Super 781 with 33 at 1,1,3
3125 Id : 2425, {_}: multiply ?4605 (multiply (inverse ?4606) ?4607) =<= inverse (inverse (multiply (inverse (divide ?4606 ?4605)) ?4607)) [4607, 4606, 4605] by Super 520 with 284 at 1,1,3
3126 Id : 652, {_}: multiply (inverse (inverse ?1228)) (inverse ?1229) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Demod 590 with 33 at 2
3127 Id : 676, {_}: divide (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) (inverse ?1337) =>= inverse (inverse ?1336) [1337, 1336] by Super 63 with 652 at 1,1,1,2
3128 Id : 716, {_}: multiply (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 676 with 33 at 2
3129 Id : 734, {_}: multiply (divide ?1438 ?1439) ?1439 =>= inverse (inverse ?1438) [1439, 1438] by Demod 716 with 520 at 1,2
3130 Id : 741, {_}: multiply (inverse ?1461) ?1461 =?= inverse (inverse (inverse (inverse (divide ?1460 ?1460)))) [1460, 1461] by Super 734 with 50 at 1,2
3131 Id : 756, {_}: multiply (inverse ?1461) ?1461 =?= divide ?1460 ?1460 [1460, 1461] by Demod 741 with 520 at 3
3132 Id : 2438, {_}: multiply ?4659 (multiply (inverse ?4659) ?4660) =?= inverse (inverse (multiply (inverse (multiply (inverse ?4658) ?4658)) ?4660)) [4658, 4660, 4659] by Super 2425 with 756 at 1,1,1,1,3
3133 Id : 41, {_}: inverse ?100 =<= divide (multiply (inverse ?99) ?99) ?100 [99, 100] by Super 39 with 33 at 1,3
3134 Id : 65, {_}: multiply (inverse (multiply (inverse ?159) ?159)) ?160 =>= inverse (inverse ?160) [160, 159] by Super 36 with 41 at 1,2
3135 Id : 2490, {_}: multiply ?4659 (multiply (inverse ?4659) ?4660) =>= inverse (inverse (inverse (inverse ?4660))) [4660, 4659] by Demod 2438 with 65 at 1,1,3
3136 Id : 2491, {_}: multiply ?4659 (multiply (inverse ?4659) ?4660) =>= ?4660 [4660, 4659] by Demod 2490 with 520 at 3
3137 Id : 738, {_}: multiply (multiply ?1452 ?1451) (inverse ?1451) =>= inverse (inverse ?1452) [1451, 1452] by Super 734 with 33 at 1,2
3138 Id : 2508, {_}: multiply ?4731 (inverse (multiply (inverse ?4730) ?4731)) =>= inverse (inverse ?4730) [4730, 4731] by Super 738 with 2491 at 1,2
3139 Id : 2677, {_}: multiply ?4949 (inverse (inverse ?4948)) =<= inverse (multiply (inverse ?4948) (inverse ?4949)) [4948, 4949] by Super 2491 with 2508 at 2,2
3140 Id : 2810, {_}: multiply ?5205 (inverse (inverse (inverse ?5204))) =<= inverse (multiply ?5204 (inverse (inverse (inverse ?5205)))) [5204, 5205] by Super 791 with 2677 at 1,3
3141 Id : 2855, {_}: divide ?5205 ?5204 =<= inverse (multiply ?5204 (inverse (inverse (inverse ?5205)))) [5204, 5205] by Demod 2810 with 565 at 2
3142 Id : 2856, {_}: divide ?5205 ?5204 =<= inverse (divide ?5204 ?5205) [5204, 5205] by Demod 2855 with 565 at 1,3
3143 Id : 2935, {_}: multiply ?2415 (multiply (inverse ?2414) ?2416) =<= inverse (inverse (multiply (divide ?2415 ?2414) ?2416)) [2416, 2414, 2415] by Demod 1304 with 2856 at 1,1,1,3
3144 Id : 70, {_}: inverse ?177 =<= divide (inverse (inverse (multiply (inverse ?176) ?176))) ?177 [176, 177] by Super 40 with 41 at 1,1,3
3145 Id : 696, {_}: multiply ?1405 (inverse ?1406) =<= inverse (inverse (divide (inverse (inverse ?1405)) ?1406)) [1406, 1405] by Super 687 with 520 at 1,2
3146 Id : 2929, {_}: multiply ?1405 (inverse ?1406) =<= inverse (divide ?1406 (inverse (inverse ?1405))) [1406, 1405] by Demod 696 with 2856 at 1,3
3147 Id : 2930, {_}: multiply ?1405 (inverse ?1406) =<= divide (inverse (inverse ?1405)) ?1406 [1406, 1405] by Demod 2929 with 2856 at 3
3148 Id : 2938, {_}: inverse ?177 =<= multiply (multiply (inverse ?176) ?176) (inverse ?177) [176, 177] by Demod 70 with 2930 at 3
3149 Id : 45, {_}: multiply (divide ?108 ?108) ?109 =>= inverse (inverse ?109) [109, 108] by Super 33 with 8 at 3
3150 Id : 47, {_}: multiply (multiply (inverse ?114) ?114) ?115 =>= inverse (inverse ?115) [115, 114] by Super 45 with 33 at 1,2
3151 Id : 2941, {_}: inverse ?177 =<= inverse (inverse (inverse ?177)) [177] by Demod 2938 with 47 at 3
3152 Id : 2943, {_}: ?1108 =<= inverse (inverse ?1108) [1108] by Demod 520 with 2941 at 3
3153 Id : 2962, {_}: multiply ?2415 (multiply (inverse ?2414) ?2416) =>= multiply (divide ?2415 ?2414) ?2416 [2416, 2414, 2415] by Demod 2935 with 2943 at 3
3154 Id : 717, {_}: multiply (divide ?1336 ?1337) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 716 with 520 at 1,2
3155 Id : 2957, {_}: multiply (divide ?1336 ?1337) ?1337 =>= ?1336 [1337, 1336] by Demod 717 with 2943 at 3
3156 Id : 2946, {_}: multiply ?4731 (inverse (multiply (inverse ?4730) ?4731)) =>= ?4730 [4730, 4731] by Demod 2508 with 2943 at 3
3157 Id : 2963, {_}: multiply ?1405 (inverse ?1406) =>= divide ?1405 ?1406 [1406, 1405] by Demod 2930 with 2943 at 1,3
3158 Id : 2983, {_}: divide ?4731 (multiply (inverse ?4730) ?4731) =>= ?4730 [4730, 4731] by Demod 2946 with 2963 at 2
3159 Id : 3087, {_}: divide ?5518 (multiply (divide ?5519 ?5520) ?5518) =>= divide ?5520 ?5519 [5520, 5519, 5518] by Super 2983 with 2856 at 1,2,2
3160 Id : 3092, {_}: divide ?5541 (multiply ?5540 ?5541) =?= divide (multiply (inverse ?5540) ?5542) ?5542 [5542, 5540, 5541] by Super 3087 with 2983 at 1,2,2
3161 Id : 2958, {_}: multiply (multiply ?1452 ?1451) (inverse ?1451) =>= ?1452 [1451, 1452] by Demod 738 with 2943 at 3
3162 Id : 2979, {_}: divide (multiply ?1452 ?1451) ?1451 =>= ?1452 [1451, 1452] by Demod 2958 with 2963 at 2
3163 Id : 3136, {_}: divide ?5541 (multiply ?5540 ?5541) =>= inverse ?5540 [5540, 5541] by Demod 3092 with 2979 at 3
3164 Id : 3184, {_}: multiply (inverse ?5645) (multiply ?5645 ?5644) =>= ?5644 [5644, 5645] by Super 2957 with 3136 at 1,2
3165 Id : 4178, {_}: multiply ?6966 ?6967 =<= multiply (divide ?6966 ?6968) (multiply ?6968 ?6967) [6968, 6967, 6966] by Super 2962 with 3184 at 2,2
3166 Id : 309, {_}: divide (inverse (inverse ?796)) (inverse (multiply ?794 (inverse ?795))) =>= inverse (inverse (multiply ?796 (divide (inverse (inverse ?794)) ?795))) [795, 794, 796] by Super 307 with 285 at 2,1,1,3
3167 Id : 323, {_}: multiply (inverse (inverse ?796)) (multiply ?794 (inverse ?795)) =<= inverse (inverse (multiply ?796 (divide (inverse (inverse ?794)) ?795))) [795, 794, 796] by Demod 309 with 33 at 2
3168 Id : 137, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
3169 Id : 324, {_}: multiply (inverse (inverse ?796)) (multiply ?794 (inverse ?795)) =>= divide (inverse (divide (inverse ?794) ?796)) ?795 [795, 794, 796] by Demod 323 with 137 at 3
3170 Id : 2912, {_}: multiply (inverse (inverse ?796)) (multiply ?794 (inverse ?795)) =>= divide (divide ?796 (inverse ?794)) ?795 [795, 794, 796] by Demod 324 with 2856 at 1,3
3171 Id : 3003, {_}: multiply ?796 (multiply ?794 (inverse ?795)) =>= divide (divide ?796 (inverse ?794)) ?795 [795, 794, 796] by Demod 2912 with 2943 at 1,2
3172 Id : 3004, {_}: multiply ?796 (divide ?794 ?795) =<= divide (divide ?796 (inverse ?794)) ?795 [795, 794, 796] by Demod 3003 with 2963 at 2,2
3173 Id : 606, {_}: multiply ?1276 (inverse (inverse (inverse ?1277))) =>= divide ?1276 ?1277 [1277, 1276] by Super 33 with 520 at 2,3
3174 Id : 611, {_}: multiply ?1298 (inverse (divide (inverse (inverse ?1296)) ?1297)) =>= divide ?1298 (multiply ?1296 (inverse ?1297)) [1297, 1296, 1298] by Super 606 with 285 at 1,2,2
3175 Id : 2932, {_}: multiply ?1298 (divide ?1297 (inverse (inverse ?1296))) =>= divide ?1298 (multiply ?1296 (inverse ?1297)) [1296, 1297, 1298] by Demod 611 with 2856 at 2,2
3176 Id : 2936, {_}: multiply ?1298 (multiply ?1297 (inverse ?1296)) =>= divide ?1298 (multiply ?1296 (inverse ?1297)) [1296, 1297, 1298] by Demod 2932 with 33 at 2,2
3177 Id : 2965, {_}: multiply ?1298 (divide ?1297 ?1296) =<= divide ?1298 (multiply ?1296 (inverse ?1297)) [1296, 1297, 1298] by Demod 2936 with 2963 at 2,2
3178 Id : 2966, {_}: multiply ?1298 (divide ?1297 ?1296) =>= divide ?1298 (divide ?1296 ?1297) [1296, 1297, 1298] by Demod 2965 with 2963 at 2,3
3179 Id : 3005, {_}: divide ?796 (divide ?795 ?794) =<= divide (divide ?796 (inverse ?794)) ?795 [794, 795, 796] by Demod 3004 with 2966 at 2
3180 Id : 3006, {_}: divide ?796 (divide ?795 ?794) =?= divide (multiply ?796 ?794) ?795 [794, 795, 796] by Demod 3005 with 33 at 1,3
3181 Id : 4201, {_}: multiply (multiply ?7065 ?7066) ?7067 =<= multiply (divide ?7065 (divide ?7068 ?7066)) (multiply ?7068 ?7067) [7068, 7067, 7066, 7065] by Super 4178 with 3006 at 1,3
3182 Id : 3248, {_}: multiply ?5734 ?5733 =<= multiply (divide ?5734 ?5732) (multiply ?5732 ?5733) [5732, 5733, 5734] by Super 2962 with 3184 at 2,2
3183 Id : 4188, {_}: multiply ?7012 (multiply ?7011 ?7010) =<= multiply (divide ?7012 (divide ?7009 ?7011)) (multiply ?7009 ?7010) [7009, 7010, 7011, 7012] by Super 4178 with 3248 at 2,3
3184 Id : 12339, {_}: multiply (multiply ?7065 ?7066) ?7067 =?= multiply ?7065 (multiply ?7066 ?7067) [7067, 7066, 7065] by Demod 4201 with 4188 at 3
3185 Id : 12708, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 12339 at 2
3186 Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
3187 % SZS output end CNFRefutation for GRP453-1.p
3197 prove_these_axioms_3 is 94
3201 divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
3202 (divide (divide ?5 ?4) ?2)
3205 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
3207 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
3208 [8, 7] by multiply ?7 ?8
3211 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
3212 [] by prove_these_axioms_3
3214 FAILURE in 180 iterations
3215 % SZS status Timeout for GRP471-1.p
3225 prove_these_axioms_3 is 94
3229 divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
3233 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
3235 multiply ?7 ?8 =<= divide ?7 (inverse ?8)
3236 [8, 7] by multiply ?7 ?8
3239 multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
3240 [] by prove_these_axioms_3
3241 Found proof, 9.696012s
3242 % SZS status Unsatisfiable for GRP477-1.p
3243 % SZS output start CNFRefutation for GRP477-1.p
3244 Id : 6, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
3245 Id : 7, {_}: 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
3246 Id : 4, {_}: 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
3247 Id : 9, {_}: divide (inverse (divide (divide (divide ?26 ?27) (divide ?23 ?22)) ?25)) (divide ?27 ?26) =?= inverse (divide (divide (divide ?22 ?23) ?24) (divide ?25 ?24)) [24, 25, 22, 23, 27, 26] by Super 7 with 4 at 2,1,1,2
3248 Id : 8947, {_}: inverse (divide (divide (divide ?66899 ?66900) ?66901) (divide (divide ?66902 (divide ?66900 ?66899)) ?66901)) =>= ?66902 [66902, 66901, 66900, 66899] by Super 4 with 9 at 2
3249 Id : 9487, {_}: inverse (divide (divide (divide (inverse ?70062) ?70063) ?70064) (divide (divide ?70065 (multiply ?70063 ?70062)) ?70064)) =>= ?70065 [70065, 70064, 70063, 70062] by Super 8947 with 6 at 2,1,2,1,2
3250 Id : 13, {_}: divide (inverse (divide (divide (divide ?48 ?49) (inverse ?47)) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Super 4 with 6 at 2,1,1,2
3251 Id : 23, {_}: divide (inverse (divide (multiply (divide ?88 ?89) ?90) (multiply ?91 ?90))) (divide ?89 ?88) =>= ?91 [91, 90, 89, 88] by Demod 13 with 6 at 1,1,1,2
3252 Id : 27, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (divide (divide ?113 ?112) (inverse (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114)))) =>= ?117 [114, 112, 113, 117, 116, 115] by Super 23 with 4 at 1,1,1,1,2
3253 Id : 35, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (multiply (divide ?113 ?112) (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114))) =>= ?117 [114, 112, 113, 117, 116, 115] by Demod 27 with 6 at 2,2
3254 Id : 9506, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?70226 ?70225) ?70227) (divide ?70222 ?70227))) (divide ?70225 ?70226)) ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222, 70227, 70225, 70226] by Super 9487 with 35 at 1,2,1,2
3255 Id : 9604, {_}: inverse (divide (divide ?70222 ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222] by Demod 9506 with 4 at 1,1,1,2
3256 Id : 27713, {_}: divide (divide (inverse (divide (divide (divide ?169617 ?169618) (divide ?169619 ?169620)) ?169621)) (divide ?169618 ?169617)) (divide ?169619 ?169620) =>= ?169621 [169621, 169620, 169619, 169618, 169617] by Super 4 with 9 at 1,2
3257 Id : 27714, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) (divide (inverse (divide (divide (divide ?169623 ?169624) ?169625) (divide ?169626 ?169625))) (divide ?169624 ?169623))) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169625, 169624, 169623, 169628, 169627] by Super 27713 with 4 at 2,2
3258 Id : 28344, {_}: divide (divide (inverse (divide (divide (divide ?173215 ?173216) ?173217) ?173218)) (divide ?173216 ?173215)) ?173217 =>= ?173218 [173218, 173217, 173216, 173215] by Demod 27714 with 4 at 2,1,1,1,1,2
3259 Id : 28449, {_}: divide (divide (inverse (multiply (divide (divide ?174106 ?174107) ?174108) ?174105)) (divide ?174107 ?174106)) ?174108 =>= inverse ?174105 [174105, 174108, 174107, 174106] by Super 28344 with 6 at 1,1,1,2
3260 Id : 28803, {_}: multiply (divide (inverse (multiply (divide (divide ?175142 ?175143) (inverse ?175145)) ?175144)) (divide ?175143 ?175142)) ?175145 =>= inverse ?175144 [175144, 175145, 175143, 175142] by Super 6 with 28449 at 3
3261 Id : 29850, {_}: multiply (divide (inverse (multiply (multiply (divide ?180549 ?180550) ?180551) ?180552)) (divide ?180550 ?180549)) ?180551 =>= inverse ?180552 [180552, 180551, 180550, 180549] by Demod 28803 with 6 at 1,1,1,1,2
3262 Id : 33200, {_}: multiply (divide (inverse (multiply (multiply (divide (inverse ?199058) ?199059) ?199060) ?199061)) (multiply ?199059 ?199058)) ?199060 =>= inverse ?199061 [199061, 199060, 199059, 199058] by Super 29850 with 6 at 2,1,2
3263 Id : 33302, {_}: multiply (divide (inverse (multiply (multiply (multiply (inverse ?199942) ?199941) ?199943) ?199944)) (multiply (inverse ?199941) ?199942)) ?199943 =>= inverse ?199944 [199944, 199943, 199941, 199942] by Super 33200 with 6 at 1,1,1,1,1,2
3264 Id : 43, {_}: divide (inverse (divide (divide (divide (inverse ?171) ?172) ?173) (divide ?174 ?173))) (multiply ?172 ?171) =>= ?174 [174, 173, 172, 171] by Super 4 with 6 at 2,2
3265 Id : 48, {_}: divide (inverse (divide (divide ?205 ?206) (divide ?207 ?206))) (multiply (divide ?203 ?202) (divide (divide (divide ?202 ?203) ?204) (divide ?205 ?204))) =>= ?207 [204, 202, 203, 207, 206, 205] by Super 43 with 4 at 1,1,1,1,2
3266 Id : 8271, {_}: inverse (divide (divide (divide ?62998 ?62997) ?62999) (divide (divide ?63000 (divide ?62997 ?62998)) ?62999)) =>= ?63000 [63000, 62999, 62997, 62998] by Super 4 with 9 at 2
3267 Id : 8914, {_}: divide ?66588 (multiply (divide ?66589 ?66590) (divide (divide (divide ?66590 ?66589) ?66591) (divide (divide ?66585 ?66586) ?66591))) =>= divide ?66588 (divide ?66586 ?66585) [66586, 66585, 66591, 66590, 66589, 66588] by Super 48 with 8271 at 1,2
3268 Id : 28446, {_}: divide (divide (inverse (divide (divide (divide ?174083 ?174084) ?174085) (divide ?174082 ?174081))) (divide ?174084 ?174083)) ?174085 =?= multiply (divide ?174078 ?174079) (divide (divide (divide ?174079 ?174078) ?174080) (divide (divide ?174081 ?174082) ?174080)) [174080, 174079, 174078, 174081, 174082, 174085, 174084, 174083] by Super 28344 with 8914 at 1,1,1,2
3269 Id : 27948, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) ?169626) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169628, 169627] by Demod 27714 with 4 at 2,1,1,1,1,2
3270 Id : 28598, {_}: divide ?174082 ?174081 =<= multiply (divide ?174078 ?174079) (divide (divide (divide ?174079 ?174078) ?174080) (divide (divide ?174081 ?174082) ?174080)) [174080, 174079, 174078, 174081, 174082] by Demod 28446 with 27948 at 2
3271 Id : 18, {_}: divide (inverse (divide (multiply (divide ?48 ?49) ?47) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Demod 13 with 6 at 1,1,1,2
3272 Id : 22, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (divide (divide ?82 ?81) (inverse (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83)))) =>= ?86 [83, 81, 82, 86, 85, 84] by Super 4 with 18 at 1,1,1,1,2
3273 Id : 32, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (multiply (divide ?82 ?81) (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83))) =>= ?86 [83, 81, 82, 86, 85, 84] by Demod 22 with 6 at 2,2
3274 Id : 8902, {_}: divide ?66500 (multiply (divide ?66501 ?66502) (divide (multiply (divide ?66502 ?66501) ?66503) (multiply (divide ?66497 ?66498) ?66503))) =>= divide ?66500 (divide ?66498 ?66497) [66498, 66497, 66503, 66502, 66501, 66500] by Super 32 with 8271 at 1,2
3275 Id : 28445, {_}: divide (divide (inverse (divide (divide (divide ?174074 ?174075) ?174076) (divide ?174073 ?174072))) (divide ?174075 ?174074)) ?174076 =?= multiply (divide ?174069 ?174070) (divide (multiply (divide ?174070 ?174069) ?174071) (multiply (divide ?174072 ?174073) ?174071)) [174071, 174070, 174069, 174072, 174073, 174076, 174075, 174074] by Super 28344 with 8902 at 1,1,1,2
3276 Id : 28597, {_}: divide ?174073 ?174072 =<= multiply (divide ?174069 ?174070) (divide (multiply (divide ?174070 ?174069) ?174071) (multiply (divide ?174072 ?174073) ?174071)) [174071, 174070, 174069, 174072, 174073] by Demod 28445 with 27948 at 2
3277 Id : 34240, {_}: divide (divide (inverse (divide ?204167 ?204168)) (divide ?204171 ?204170)) ?204172 =<= inverse (divide (multiply (divide ?204172 (divide ?204170 ?204171)) ?204169) (multiply (divide ?204168 ?204167) ?204169)) [204169, 204172, 204170, 204171, 204168, 204167] by Super 28449 with 28597 at 1,1,1,2
3278 Id : 34776, {_}: divide (divide (divide (inverse (divide ?206532 ?206533)) (divide ?206534 ?206535)) ?206536) (divide (divide ?206535 ?206534) ?206536) =>= divide ?206533 ?206532 [206536, 206535, 206534, 206533, 206532] by Super 18 with 34240 at 1,2
3279 Id : 52856, {_}: divide ?292676 ?292677 =<= multiply (divide (divide ?292676 ?292677) (inverse (divide ?292674 ?292675))) (divide ?292675 ?292674) [292675, 292674, 292677, 292676] by Super 28598 with 34776 at 2,3
3280 Id : 53526, {_}: divide ?296370 ?296371 =<= multiply (multiply (divide ?296370 ?296371) (divide ?296372 ?296373)) (divide ?296373 ?296372) [296373, 296372, 296371, 296370] by Demod 52856 with 6 at 1,3
3281 Id : 53629, {_}: divide (inverse (divide (divide (divide ?297219 ?297220) ?297221) (divide ?297222 ?297221))) (divide ?297220 ?297219) =?= multiply (multiply ?297222 (divide ?297223 ?297224)) (divide ?297224 ?297223) [297224, 297223, 297222, 297221, 297220, 297219] by Super 53526 with 4 at 1,1,3
3282 Id : 53865, {_}: ?297222 =<= multiply (multiply ?297222 (divide ?297223 ?297224)) (divide ?297224 ?297223) [297224, 297223, 297222] by Demod 53629 with 4 at 2
3283 Id : 28234, {_}: multiply (divide (inverse (divide (divide (divide ?172298 ?172299) (inverse ?172301)) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Super 6 with 27948 at 3
3284 Id : 28487, {_}: multiply (divide (inverse (divide (multiply (divide ?172298 ?172299) ?172301) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Demod 28234 with 6 at 1,1,1,1,2
3285 Id : 9011, {_}: inverse (divide (divide (divide ?67439 ?67440) (inverse ?67438)) (multiply (divide ?67441 (divide ?67440 ?67439)) ?67438)) =>= ?67441 [67441, 67438, 67440, 67439] by Super 8947 with 6 at 2,1,2
3286 Id : 9220, {_}: inverse (divide (multiply (divide ?68482 ?68483) ?68484) (multiply (divide ?68485 (divide ?68483 ?68482)) ?68484)) =>= ?68485 [68485, 68484, 68483, 68482] by Demod 9011 with 6 at 1,1,2
3287 Id : 9262, {_}: inverse (divide (multiply (divide (inverse ?68840) ?68841) ?68842) (multiply (divide ?68843 (multiply ?68841 ?68840)) ?68842)) =>= ?68843 [68843, 68842, 68841, 68840] by Super 9220 with 6 at 2,1,2,1,2
3288 Id : 34816, {_}: inverse (divide (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) (divide (divide ?206979 ?206978) ?206984)) =>= divide (divide (inverse (divide ?206978 ?206979)) (divide ?206980 ?206981)) ?206982 [206978, 206979, 206984, 206980, 206981, 206982] by Super 9604 with 34240 at 3
3289 Id : 52845, {_}: inverse (divide ?292579 ?292578) =<= divide (divide (inverse (divide ?292580 ?292581)) (divide ?292581 ?292580)) (inverse (divide ?292578 ?292579)) [292581, 292580, 292578, 292579] by Super 34816 with 34776 at 1,2
3290 Id : 53105, {_}: inverse (divide ?292579 ?292578) =<= multiply (divide (inverse (divide ?292580 ?292581)) (divide ?292581 ?292580)) (divide ?292578 ?292579) [292581, 292580, 292578, 292579] by Demod 52845 with 6 at 3
3291 Id : 57037, {_}: inverse (divide (inverse (divide ?313195 ?313196)) (multiply (divide ?313199 (multiply (divide ?313198 ?313197) (divide ?313197 ?313198))) (divide ?313196 ?313195))) =>= ?313199 [313197, 313198, 313199, 313196, 313195] by Super 9262 with 53105 at 1,1,2
3292 Id : 12, {_}: divide (inverse (divide (divide (divide (inverse ?42) ?41) ?43) (divide ?44 ?43))) (multiply ?41 ?42) =>= ?44 [44, 43, 41, 42] by Super 4 with 6 at 2,2
3293 Id : 52731, {_}: divide (inverse (divide ?291529 ?291528)) (multiply (divide ?291530 ?291531) (divide ?291528 ?291529)) =>= divide ?291531 ?291530 [291531, 291530, 291528, 291529] by Super 12 with 34776 at 1,1,2
3294 Id : 57379, {_}: inverse (divide (multiply (divide ?313198 ?313197) (divide ?313197 ?313198)) ?313199) =>= ?313199 [313199, 313197, 313198] by Demod 57037 with 52731 at 1,2
3295 Id : 57732, {_}: multiply (divide ?315540 (divide ?315539 ?315538)) (divide ?315539 ?315538) =>= ?315540 [315538, 315539, 315540] by Super 28487 with 57379 at 1,1,2
3296 Id : 58290, {_}: divide ?318875 (divide ?318876 ?318877) =<= multiply ?318875 (divide ?318877 ?318876) [318877, 318876, 318875] by Super 53865 with 57732 at 1,3
3297 Id : 58885, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?321635) ?321636) ?321637) (divide ?321633 ?321634))) (multiply (inverse ?321636) ?321635)) ?321637 =>= inverse (divide ?321634 ?321633) [321634, 321633, 321637, 321636, 321635] by Super 33302 with 58290 at 1,1,1,2
3298 Id : 29397, {_}: multiply (divide (inverse (divide (multiply (divide ?178179 ?178180) ?178181) ?178182)) (divide ?178180 ?178179)) ?178181 =>= ?178182 [178182, 178181, 178180, 178179] by Demod 28234 with 6 at 1,1,1,1,2
3299 Id : 32339, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?194066) ?194067) ?194068) ?194069)) (multiply ?194067 ?194066)) ?194068 =>= ?194069 [194069, 194068, 194067, 194066] by Super 29397 with 6 at 2,1,2
3300 Id : 32439, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?194936) ?194935) ?194937) ?194938)) (multiply (inverse ?194935) ?194936)) ?194937 =>= ?194938 [194938, 194937, 194935, 194936] by Super 32339 with 6 at 1,1,1,1,1,2
3301 Id : 59201, {_}: divide ?321633 ?321634 =<= inverse (divide ?321634 ?321633) [321634, 321633] by Demod 58885 with 32439 at 2
3302 Id : 59708, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70222, 70228, 70224] by Demod 9604 with 59201 at 2
3303 Id : 59709, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= divide (multiply ?70224 ?70223) (multiply ?70222 ?70223) [70223, 70222, 70228, 70224] by Demod 59708 with 59201 at 3
3304 Id : 29064, {_}: multiply (divide (inverse (multiply (multiply (divide ?175142 ?175143) ?175145) ?175144)) (divide ?175143 ?175142)) ?175145 =>= inverse ?175144 [175144, 175145, 175143, 175142] by Demod 28803 with 6 at 1,1,1,1,2
3305 Id : 59905, {_}: divide ?323677 ?323678 =<= inverse (divide ?323678 ?323677) [323678, 323677] by Demod 58885 with 32439 at 2
3306 Id : 59980, {_}: divide (inverse ?324139) ?324140 =>= inverse (multiply ?324140 ?324139) [324140, 324139] by Super 59905 with 6 at 1,3
3307 Id : 60322, {_}: multiply (inverse (multiply (divide ?175143 ?175142) (multiply (multiply (divide ?175142 ?175143) ?175145) ?175144))) ?175145 =>= inverse ?175144 [175144, 175145, 175142, 175143] by Demod 29064 with 59980 at 1,2
3308 Id : 58656, {_}: inverse (divide (divide (divide ?313198 ?313197) (divide ?313198 ?313197)) ?313199) =>= ?313199 [313199, 313197, 313198] by Demod 57379 with 58290 at 1,1,2
3309 Id : 59766, {_}: divide ?313199 (divide (divide ?313198 ?313197) (divide ?313198 ?313197)) =>= ?313199 [313197, 313198, 313199] by Demod 58656 with 59201 at 2
3310 Id : 64277, {_}: divide (divide (divide ?332921 ?332922) (divide ?332921 ?332922)) ?332923 =>= inverse ?332923 [332923, 332922, 332921] by Super 59905 with 59766 at 1,3
3311 Id : 29, {_}: divide (inverse (divide (multiply (multiply ?127 ?126) ?128) (multiply ?129 ?128))) (divide (inverse ?126) ?127) =>= ?129 [129, 128, 126, 127] by Super 23 with 6 at 1,1,1,1,2
3312 Id : 95, {_}: divide (inverse (divide (multiply (divide (inverse ?431) ?432) ?433) (multiply ?434 ?433))) (multiply ?432 ?431) =>= ?434 [434, 433, 432, 431] by Super 23 with 6 at 2,2
3313 Id : 101, {_}: divide (inverse (divide (multiply (multiply (inverse ?472) ?471) ?473) (multiply ?474 ?473))) (multiply (inverse ?471) ?472) =>= ?474 [474, 473, 471, 472] by Super 95 with 6 at 1,1,1,1,2
3314 Id : 163, {_}: divide (inverse (divide (multiply (multiply (multiply (inverse ?755) ?754) (divide (multiply (multiply (inverse ?754) ?755) ?756) (multiply ?757 ?756))) ?758) (multiply ?759 ?758))) ?757 =>= ?759 [759, 758, 757, 756, 754, 755] by Super 29 with 101 at 2,2
3315 Id : 58602, {_}: divide (inverse (divide (multiply (divide (multiply (inverse ?755) ?754) (divide (multiply ?757 ?756) (multiply (multiply (inverse ?754) ?755) ?756))) ?758) (multiply ?759 ?758))) ?757 =>= ?759 [759, 758, 756, 757, 754, 755] by Demod 163 with 58290 at 1,1,1,1,2
3316 Id : 59646, {_}: divide (divide (multiply ?759 ?758) (multiply (divide (multiply (inverse ?755) ?754) (divide (multiply ?757 ?756) (multiply (multiply (inverse ?754) ?755) ?756))) ?758)) ?757 =>= ?759 [756, 757, 754, 755, 758, 759] by Demod 58602 with 59201 at 1,2
3317 Id : 64278, {_}: divide (divide (divide (divide (multiply ?332925 ?332926) (multiply (divide (multiply (inverse ?332927) ?332928) (divide (multiply ?332930 ?332929) (multiply (multiply (inverse ?332928) ?332927) ?332929))) ?332926)) ?332930) ?332925) ?332931 =>= inverse ?332931 [332931, 332929, 332930, 332928, 332927, 332926, 332925] by Super 64277 with 59646 at 2,1,2
3318 Id : 65204, {_}: divide (divide ?332925 ?332925) ?332931 =>= inverse ?332931 [332931, 332925] by Demod 64278 with 59646 at 1,1,2
3319 Id : 66466, {_}: multiply (divide ?338522 ?338522) ?338523 =>= inverse (inverse ?338523) [338523, 338522] by Super 6 with 65204 at 3
3320 Id : 60452, {_}: divide ?324438 (inverse ?324437) =<= inverse (inverse (multiply ?324438 ?324437)) [324437, 324438] by Super 59201 with 59980 at 1,3
3321 Id : 61190, {_}: multiply ?326165 ?326166 =<= inverse (inverse (multiply ?326165 ?326166)) [326166, 326165] by Demod 60452 with 6 at 2
3322 Id : 20, {_}: divide (inverse (divide (divide (divide (divide ?68 ?67) (inverse (divide (multiply (divide ?67 ?68) ?69) (multiply ?70 ?69)))) ?71) (divide ?72 ?71))) ?70 =>= ?72 [72, 71, 70, 69, 67, 68] by Super 4 with 18 at 2,2
3323 Id : 31, {_}: divide (inverse (divide (divide (multiply (divide ?68 ?67) (divide (multiply (divide ?67 ?68) ?69) (multiply ?70 ?69))) ?71) (divide ?72 ?71))) ?70 =>= ?72 [72, 71, 70, 69, 67, 68] by Demod 20 with 6 at 1,1,1,1,2
3324 Id : 188, {_}: multiply (inverse (divide (divide (multiply (divide ?884 ?885) (divide (multiply (divide ?885 ?884) ?886) (multiply (inverse ?889) ?886))) ?887) (divide ?888 ?887))) ?889 =>= ?888 [888, 887, 889, 886, 885, 884] by Super 6 with 31 at 3
3325 Id : 58606, {_}: multiply (inverse (divide (divide (divide (divide ?884 ?885) (divide (multiply (inverse ?889) ?886) (multiply (divide ?885 ?884) ?886))) ?887) (divide ?888 ?887))) ?889 =>= ?888 [888, 887, 886, 889, 885, 884] by Demod 188 with 58290 at 1,1,1,1,2
3326 Id : 59648, {_}: multiply (divide (divide ?888 ?887) (divide (divide (divide ?884 ?885) (divide (multiply (inverse ?889) ?886) (multiply (divide ?885 ?884) ?886))) ?887)) ?889 =>= ?888 [886, 889, 885, 884, 887, 888] by Demod 58606 with 59201 at 1,2
3327 Id : 61191, {_}: multiply (divide (divide ?326168 ?326169) (divide (divide (divide ?326170 ?326171) (divide (multiply (inverse ?326173) ?326172) (multiply (divide ?326171 ?326170) ?326172))) ?326169)) ?326173 =>= inverse (inverse ?326168) [326172, 326173, 326171, 326170, 326169, 326168] by Super 61190 with 59648 at 1,1,3
3328 Id : 61231, {_}: ?326168 =<= inverse (inverse ?326168) [326168] by Demod 61191 with 59648 at 2
3329 Id : 67123, {_}: multiply (divide ?338522 ?338522) ?338523 =>= ?338523 [338523, 338522] by Demod 66466 with 61231 at 3
3330 Id : 69503, {_}: multiply (inverse (multiply (divide ?344249 ?344249) (multiply ?344250 ?344251))) ?344250 =>= inverse ?344251 [344251, 344250, 344249] by Super 60322 with 67123 at 1,2,1,1,2
3331 Id : 70168, {_}: multiply (inverse (multiply ?344250 ?344251)) ?344250 =>= inverse ?344251 [344251, 344250] by Demod 69503 with 67123 at 1,1,2
3332 Id : 71425, {_}: divide (divide ?348688 ?348689) (divide (inverse (multiply ?348686 ?348687)) ?348689) =>= divide (multiply ?348688 ?348686) (inverse ?348687) [348687, 348686, 348689, 348688] by Super 59709 with 70168 at 2,3
3333 Id : 71942, {_}: divide (divide ?348688 ?348689) (inverse (multiply ?348689 (multiply ?348686 ?348687))) =>= divide (multiply ?348688 ?348686) (inverse ?348687) [348687, 348686, 348689, 348688] by Demod 71425 with 59980 at 2,2
3334 Id : 71943, {_}: multiply (divide ?348688 ?348689) (multiply ?348689 (multiply ?348686 ?348687)) =>= divide (multiply ?348688 ?348686) (inverse ?348687) [348687, 348686, 348689, 348688] by Demod 71942 with 6 at 2
3335 Id : 71944, {_}: multiply (divide ?348688 ?348689) (multiply ?348689 (multiply ?348686 ?348687)) =>= multiply (multiply ?348688 ?348686) ?348687 [348687, 348686, 348689, 348688] by Demod 71943 with 6 at 3
3336 Id : 26, {_}: divide (inverse (divide (multiply (divide (inverse ?107) ?108) ?109) (multiply ?110 ?109))) (multiply ?108 ?107) =>= ?110 [110, 109, 108, 107] by Super 23 with 6 at 2,2
3337 Id : 91, {_}: divide (inverse (divide (multiply (divide (multiply ?404 ?403) (inverse (divide (multiply (divide (inverse ?403) ?404) ?405) (multiply ?406 ?405)))) ?407) (multiply ?408 ?407))) ?406 =>= ?408 [408, 407, 406, 405, 403, 404] by Super 18 with 26 at 2,2
3338 Id : 103, {_}: divide (inverse (divide (multiply (multiply (multiply ?404 ?403) (divide (multiply (divide (inverse ?403) ?404) ?405) (multiply ?406 ?405))) ?407) (multiply ?408 ?407))) ?406 =>= ?408 [408, 407, 406, 405, 403, 404] by Demod 91 with 6 at 1,1,1,1,2
3339 Id : 58628, {_}: divide (inverse (divide (multiply (divide (multiply ?404 ?403) (divide (multiply ?406 ?405) (multiply (divide (inverse ?403) ?404) ?405))) ?407) (multiply ?408 ?407))) ?406 =>= ?408 [408, 407, 405, 406, 403, 404] by Demod 103 with 58290 at 1,1,1,1,2
3340 Id : 59659, {_}: divide (divide (multiply ?408 ?407) (multiply (divide (multiply ?404 ?403) (divide (multiply ?406 ?405) (multiply (divide (inverse ?403) ?404) ?405))) ?407)) ?406 =>= ?408 [405, 406, 403, 404, 407, 408] by Demod 58628 with 59201 at 1,2
3341 Id : 60280, {_}: divide (divide (multiply ?408 ?407) (multiply (divide (multiply ?404 ?403) (divide (multiply ?406 ?405) (multiply (inverse (multiply ?404 ?403)) ?405))) ?407)) ?406 =>= ?408 [405, 406, 403, 404, 407, 408] by Demod 59659 with 59980 at 1,2,2,1,2,1,2
3342 Id : 69677, {_}: multiply (divide ?345297 ?345297) ?345298 =>= ?345298 [345298, 345297] by Demod 66466 with 61231 at 3
3343 Id : 69694, {_}: multiply (multiply (inverse ?345392) ?345392) ?345393 =>= ?345393 [345393, 345392] by Super 69677 with 6 at 1,2
3344 Id : 70939, {_}: divide (divide (multiply ?347989 ?347990) (multiply (divide (multiply ?347991 ?347992) (divide ?347988 (multiply (inverse (multiply ?347991 ?347992)) ?347988))) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347988, 347992, 347991, 347990, 347989] by Super 60280 with 69694 at 1,2,1,2,1,2
3345 Id : 59713, {_}: divide (divide (divide ?63000 (divide ?62997 ?62998)) ?62999) (divide (divide ?62998 ?62997) ?62999) =>= ?63000 [62999, 62998, 62997, 63000] by Demod 8271 with 59201 at 2
3346 Id : 59961, {_}: divide (divide (divide ?324009 ?324010) (divide ?324009 ?324010)) ?324011 =>= inverse ?324011 [324011, 324010, 324009] by Super 59905 with 59766 at 1,3
3347 Id : 64211, {_}: divide (divide (divide ?332479 (inverse ?332478)) ?332480) (divide (divide ?332478 (divide (divide ?332476 ?332477) (divide ?332476 ?332477))) ?332480) =>= ?332479 [332477, 332476, 332480, 332478, 332479] by Super 59713 with 59961 at 2,1,1,2
3348 Id : 59760, {_}: divide (divide (divide ?206979 ?206978) ?206984) (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) =>= divide (divide (inverse (divide ?206978 ?206979)) (divide ?206980 ?206981)) ?206982 [206980, 206981, 206982, 206984, 206978, 206979] by Demod 34816 with 59201 at 2
3349 Id : 59761, {_}: divide (divide (divide ?206979 ?206978) ?206984) (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) =>= divide (divide (divide ?206979 ?206978) (divide ?206980 ?206981)) ?206982 [206980, 206981, 206982, 206984, 206978, 206979] by Demod 59760 with 59201 at 1,1,3
3350 Id : 64644, {_}: divide (divide (divide ?332479 (inverse ?332478)) (divide (divide ?332476 ?332477) (divide ?332476 ?332477))) ?332478 =>= ?332479 [332477, 332476, 332478, 332479] by Demod 64211 with 59761 at 2
3351 Id : 64645, {_}: divide (divide ?332479 (inverse ?332478)) ?332478 =>= ?332479 [332478, 332479] by Demod 64644 with 59766 at 1,2
3352 Id : 64646, {_}: divide (multiply ?332479 ?332478) ?332478 =>= ?332479 [332478, 332479] by Demod 64645 with 6 at 1,2
3353 Id : 66156, {_}: divide ?337261 (multiply ?337260 ?337261) =>= inverse ?337260 [337260, 337261] by Super 59201 with 64646 at 1,3
3354 Id : 71006, {_}: divide (divide (multiply ?347989 ?347990) (multiply (divide (multiply ?347991 ?347992) (inverse (inverse (multiply ?347991 ?347992)))) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347992, 347991, 347990, 347989] by Demod 70939 with 66156 at 2,1,2,1,2
3355 Id : 71007, {_}: divide (divide (multiply ?347989 ?347990) (multiply (multiply (multiply ?347991 ?347992) (inverse (multiply ?347991 ?347992))) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347992, 347991, 347990, 347989] by Demod 71006 with 6 at 1,2,1,2
3356 Id : 61286, {_}: multiply ?326469 (inverse ?326468) =>= divide ?326469 ?326468 [326468, 326469] by Super 6 with 61231 at 2,3
3357 Id : 71008, {_}: divide (divide (multiply ?347989 ?347990) (multiply (divide (multiply ?347991 ?347992) (multiply ?347991 ?347992)) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347992, 347991, 347990, 347989] by Demod 71007 with 61286 at 1,2,1,2
3358 Id : 71009, {_}: divide (divide (multiply ?347989 ?347990) ?347990) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347990, 347989] by Demod 71008 with 67123 at 2,1,2
3359 Id : 71010, {_}: divide ?347989 (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347989] by Demod 71009 with 64646 at 1,2
3360 Id : 73616, {_}: divide (divide ?351709 ?351710) (divide (inverse ?351708) ?351710) =>= multiply ?351709 ?351708 [351708, 351710, 351709] by Super 59709 with 71010 at 3
3361 Id : 74280, {_}: divide (divide ?351709 ?351710) (inverse (multiply ?351710 ?351708)) =>= multiply ?351709 ?351708 [351708, 351710, 351709] by Demod 73616 with 59980 at 2,2
3362 Id : 74281, {_}: multiply (divide ?351709 ?351710) (multiply ?351710 ?351708) =>= multiply ?351709 ?351708 [351708, 351710, 351709] by Demod 74280 with 6 at 2
3363 Id : 89373, {_}: multiply ?348688 (multiply ?348686 ?348687) =?= multiply (multiply ?348688 ?348686) ?348687 [348687, 348686, 348688] by Demod 71944 with 74281 at 2
3364 Id : 89656, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 89373 at 2
3365 Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
3366 % SZS output end CNFRefutation for GRP477-1.p
3374 prove_these_axioms_2 is 94
3382 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
3383 (multiply (inverse (multiply ?4 ?5))
3386 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
3390 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
3393 multiply (multiply (inverse b2) b2) a2 =>= a2
3394 [] by prove_these_axioms_2
3396 FAILURE in 41 iterations
3397 % SZS status Timeout for GRP506-1.p
3405 prove_these_axioms_4 is 95
3413 (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
3414 (multiply (inverse (multiply ?4 ?5))
3417 (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
3421 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
3423 Id : 2, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
3425 FAILURE in 41 iterations
3426 % SZS status Timeout for GRP508-1.p
3433 prove_normal_axioms_1 is 96
3437 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
3439 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
3443 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
3446 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
3447 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
3448 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
3451 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
3453 Id : 2, {_}: meet a a =>= a [] by prove_normal_axioms_1
3455 FAILURE in 12 iterations
3456 % SZS status Timeout for LAT080-1.p
3464 prove_normal_axioms_8 is 94
3468 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
3470 (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
3474 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
3477 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
3478 (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
3479 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
3482 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
3484 Id : 2, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
3486 FAILURE in 12 iterations
3487 % SZS status Timeout for LAT087-1.p
3495 prove_wal_axioms_2 is 95
3499 join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
3501 (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
3503 (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
3505 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
3506 (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
3507 (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
3510 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
3512 Id : 2, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
3514 FAILURE in 14 iterations
3515 % SZS status Timeout for LAT093-1.p
3522 associativity_of_join is 85
3523 associativity_of_meet is 86
3526 commutativity_of_join is 87
3527 commutativity_of_meet is 88
3529 idempotence_of_join is 91
3530 idempotence_of_meet is 92
3535 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3536 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3537 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3538 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3540 meet ?12 ?13 =?= meet ?13 ?12
3541 [13, 12] by commutativity_of_meet ?12 ?13
3543 join ?15 ?16 =?= join ?16 ?15
3544 [16, 15] by commutativity_of_join ?15 ?16
3546 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3547 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3549 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3550 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3552 meet ?26 (join ?27 (meet ?26 ?28))
3556 (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
3557 [28, 27, 26] by equation_H7 ?26 ?27 ?28
3560 meet a (join b (meet a c))
3562 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
3565 FAILURE in 141 iterations
3566 % SZS status Timeout for LAT138-1.p
3573 associativity_of_join is 85
3574 associativity_of_meet is 86
3577 commutativity_of_join is 87
3578 commutativity_of_meet is 88
3580 idempotence_of_join is 91
3581 idempotence_of_meet is 92
3586 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3587 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3588 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3589 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3591 meet ?12 ?13 =?= meet ?13 ?12
3592 [13, 12] by commutativity_of_meet ?12 ?13
3594 join ?15 ?16 =?= join ?16 ?15
3595 [16, 15] by commutativity_of_join ?15 ?16
3597 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3598 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3600 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3601 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3603 join (meet ?26 ?27) (meet ?26 ?28)
3606 (join (meet ?27 (join ?26 (meet ?27 ?28)))
3607 (meet ?28 (join ?26 ?27)))
3608 [28, 27, 26] by equation_H21 ?26 ?27 ?28
3611 meet a (join b (meet a c))
3613 meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
3616 FAILURE in 142 iterations
3617 % SZS status Timeout for LAT140-1.p
3624 associativity_of_join is 84
3625 associativity_of_meet is 85
3628 commutativity_of_join is 86
3629 commutativity_of_meet is 87
3632 idempotence_of_join is 90
3633 idempotence_of_meet is 91
3638 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3639 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3640 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3641 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3643 meet ?12 ?13 =?= meet ?13 ?12
3644 [13, 12] by commutativity_of_meet ?12 ?13
3646 join ?15 ?16 =?= join ?16 ?15
3647 [16, 15] by commutativity_of_join ?15 ?16
3649 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3650 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3652 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3653 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3655 meet ?26 (join ?27 (meet ?28 ?29))
3657 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
3658 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
3661 meet a (join b (meet a (meet c d)))
3663 meet a (join b (meet c (meet d (join a (meet b d)))))
3666 FAILURE in 143 iterations
3667 % SZS status Timeout for LAT146-1.p
3674 associativity_of_join is 85
3675 associativity_of_meet is 86
3678 commutativity_of_join is 87
3679 commutativity_of_meet is 88
3681 idempotence_of_join is 91
3682 idempotence_of_meet is 92
3687 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3688 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3689 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3690 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3692 meet ?12 ?13 =?= meet ?13 ?12
3693 [13, 12] by commutativity_of_meet ?12 ?13
3695 join ?15 ?16 =?= join ?16 ?15
3696 [16, 15] by commutativity_of_join ?15 ?16
3698 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3699 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3701 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3702 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3704 meet ?26 (join ?27 (meet ?28 ?29))
3706 meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
3707 [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
3710 meet a (join b (meet a c))
3712 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
3715 FAILURE in 141 iterations
3716 % SZS status Timeout for LAT148-1.p
3723 associativity_of_join is 85
3724 associativity_of_meet is 86
3727 commutativity_of_join is 87
3728 commutativity_of_meet is 88
3730 idempotence_of_join is 91
3731 idempotence_of_meet is 92
3736 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3737 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3738 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3739 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3741 meet ?12 ?13 =?= meet ?13 ?12
3742 [13, 12] by commutativity_of_meet ?12 ?13
3744 join ?15 ?16 =?= join ?16 ?15
3745 [16, 15] by commutativity_of_join ?15 ?16
3747 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3748 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3750 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3751 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3753 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
3755 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
3756 [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
3759 meet a (join b (meet a c))
3761 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
3764 FAILURE in 142 iterations
3765 % SZS status Timeout for LAT152-1.p
3772 associativity_of_join is 85
3773 associativity_of_meet is 86
3776 commutativity_of_join is 87
3777 commutativity_of_meet is 88
3779 idempotence_of_join is 91
3780 idempotence_of_meet is 92
3785 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3786 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3787 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3788 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3790 meet ?12 ?13 =?= meet ?13 ?12
3791 [13, 12] by commutativity_of_meet ?12 ?13
3793 join ?15 ?16 =?= join ?16 ?15
3794 [16, 15] by commutativity_of_join ?15 ?16
3796 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3797 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3799 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3800 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3802 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
3804 meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
3805 [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
3808 meet a (join b (meet a c))
3810 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
3813 FAILURE in 142 iterations
3814 % SZS status Timeout for LAT156-1.p
3821 associativity_of_join is 85
3822 associativity_of_meet is 86
3825 commutativity_of_join is 87
3826 commutativity_of_meet is 88
3828 idempotence_of_join is 91
3829 idempotence_of_meet is 92
3834 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3835 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3836 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3837 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3839 meet ?12 ?13 =?= meet ?13 ?12
3840 [13, 12] by commutativity_of_meet ?12 ?13
3842 join ?15 ?16 =?= join ?16 ?15
3843 [16, 15] by commutativity_of_join ?15 ?16
3845 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3846 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3848 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3849 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3851 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
3853 meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
3854 [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
3857 meet a (join b (meet a c))
3859 meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
3862 FAILURE in 143 iterations
3863 % SZS status Timeout for LAT159-1.p
3870 associativity_of_join is 85
3871 associativity_of_meet is 86
3874 commutativity_of_join is 87
3875 commutativity_of_meet is 88
3877 idempotence_of_join is 91
3878 idempotence_of_meet is 92
3883 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3884 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3885 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3886 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3888 meet ?12 ?13 =?= meet ?13 ?12
3889 [13, 12] by commutativity_of_meet ?12 ?13
3891 join ?15 ?16 =?= join ?16 ?15
3892 [16, 15] by commutativity_of_join ?15 ?16
3894 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3895 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3897 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3898 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3900 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
3902 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
3903 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
3906 meet a (join b (meet a c))
3908 meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
3911 FAILURE in 142 iterations
3912 % SZS status Timeout for LAT164-1.p
3919 associativity_of_join is 84
3920 associativity_of_meet is 85
3923 commutativity_of_join is 86
3924 commutativity_of_meet is 87
3927 idempotence_of_join is 90
3928 idempotence_of_meet is 91
3933 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3934 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3935 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3936 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3938 meet ?12 ?13 =?= meet ?13 ?12
3939 [13, 12] by commutativity_of_meet ?12 ?13
3941 join ?15 ?16 =?= join ?16 ?15
3942 [16, 15] by commutativity_of_join ?15 ?16
3944 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3945 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3947 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3948 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
3950 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
3952 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
3953 [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
3956 meet a (join b (meet c (join b d)))
3958 meet a (join b (meet c (join d (meet a (meet b c)))))
3961 FAILURE in 142 iterations
3962 % SZS status Timeout for LAT165-1.p
3969 associativity_of_join is 84
3970 associativity_of_meet is 85
3973 commutativity_of_join is 86
3974 commutativity_of_meet is 87
3977 idempotence_of_join is 90
3978 idempotence_of_meet is 91
3983 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
3984 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
3985 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
3986 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
3988 meet ?12 ?13 =?= meet ?13 ?12
3989 [13, 12] by commutativity_of_meet ?12 ?13
3991 join ?15 ?16 =?= join ?16 ?15
3992 [16, 15] by commutativity_of_join ?15 ?16
3994 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
3995 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
3997 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
3998 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
4000 meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
4002 meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
4003 [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
4006 meet a (join b (meet c (join b d)))
4008 meet a (join b (meet c (join d (meet b (join a d)))))
4011 FAILURE in 142 iterations
4012 % SZS status Timeout for LAT166-1.p
4019 associativity_of_join is 85
4020 associativity_of_meet is 86
4023 commutativity_of_join is 87
4024 commutativity_of_meet is 88
4025 equation_H21_dual is 84
4026 idempotence_of_join is 91
4027 idempotence_of_meet is 92
4032 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
4033 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
4034 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
4035 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
4037 meet ?12 ?13 =?= meet ?13 ?12
4038 [13, 12] by commutativity_of_meet ?12 ?13
4040 join ?15 ?16 =?= join ?16 ?15
4041 [16, 15] by commutativity_of_join ?15 ?16
4043 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
4044 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
4046 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
4047 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
4049 meet (join ?26 ?27) (join ?26 ?28)
4052 (meet (join ?27 (meet ?26 (join ?27 ?28)))
4053 (join ?28 (meet ?26 ?27)))
4054 [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
4059 meet a (join b (meet (join a b) (join c (meet a b))))
4062 FAILURE in 142 iterations
4063 % SZS status Timeout for LAT169-1.p
4070 associativity_of_join is 85
4071 associativity_of_meet is 86
4074 commutativity_of_join is 87
4075 commutativity_of_meet is 88
4076 equation_H49_dual is 84
4077 idempotence_of_join is 91
4078 idempotence_of_meet is 92
4083 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
4084 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
4085 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
4086 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
4088 meet ?12 ?13 =?= meet ?13 ?12
4089 [13, 12] by commutativity_of_meet ?12 ?13
4091 join ?15 ?16 =?= join ?16 ?15
4092 [16, 15] by commutativity_of_join ?15 ?16
4094 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
4095 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
4097 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
4098 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
4100 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
4102 join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
4103 [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
4108 meet a (join b (meet (join a b) (join c (meet a b))))
4111 FAILURE in 143 iterations
4112 % SZS status Timeout for LAT170-1.p
4119 associativity_of_join is 84
4120 associativity_of_meet is 85
4123 commutativity_of_join is 86
4124 commutativity_of_meet is 87
4126 equation_H76_dual is 83
4127 idempotence_of_join is 90
4128 idempotence_of_meet is 91
4133 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
4134 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
4135 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
4136 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
4138 meet ?12 ?13 =?= meet ?13 ?12
4139 [13, 12] by commutativity_of_meet ?12 ?13
4141 join ?15 ?16 =?= join ?16 ?15
4142 [16, 15] by commutativity_of_join ?15 ?16
4144 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
4145 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
4147 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
4148 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
4150 join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
4152 join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
4153 [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
4156 meet a (join b (meet c (join a d)))
4158 meet a (join b (meet c (join d (meet c (join a b)))))
4161 FAILURE in 142 iterations
4162 % SZS status Timeout for LAT173-1.p
4169 associativity_of_join is 84
4170 associativity_of_meet is 85
4173 commutativity_of_join is 86
4174 commutativity_of_meet is 87
4176 equation_H79_dual is 83
4177 idempotence_of_join is 90
4178 idempotence_of_meet is 91
4183 Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
4184 Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
4185 Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
4186 Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
4188 meet ?12 ?13 =?= meet ?13 ?12
4189 [13, 12] by commutativity_of_meet ?12 ?13
4191 join ?15 ?16 =?= join ?16 ?15
4192 [16, 15] by commutativity_of_join ?15 ?16
4194 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
4195 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
4197 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
4198 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
4200 join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
4202 join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
4203 [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
4206 meet a (join b (meet a (meet c d)))
4208 meet a (join b (meet c (join (meet a d) (meet b d))))
4211 FAILURE in 142 iterations
4212 % SZS status Timeout for LAT175-1.p
4217 a_times_b_is_c is 80
4219 additive_identity is 93
4220 additive_inverse is 89
4221 associativity_for_addition is 86
4222 associativity_for_multiplication is 84
4225 commutativity_for_addition is 85
4228 left_additive_identity is 91
4229 left_additive_inverse is 88
4231 prove_commutativity is 94
4232 right_additive_identity is 90
4233 right_additive_inverse is 87
4236 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4238 add ?4 additive_identity =>= ?4
4239 [4] by right_additive_identity ?4
4241 add (additive_inverse ?6) ?6 =>= additive_identity
4242 [6] by left_additive_inverse ?6
4244 add ?8 (additive_inverse ?8) =>= additive_identity
4245 [8] by right_additive_inverse ?8
4247 add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
4248 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
4250 add ?14 ?15 =?= add ?15 ?14
4251 [15, 14] by commutativity_for_addition ?14 ?15
4253 multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
4254 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
4256 multiply ?21 (add ?22 ?23)
4258 add (multiply ?21 ?22) (multiply ?21 ?23)
4259 [23, 22, 21] by distribute1 ?21 ?22 ?23
4261 multiply (add ?25 ?26) ?27
4263 add (multiply ?25 ?27) (multiply ?26 ?27)
4264 [27, 26, 25] by distribute2 ?25 ?26 ?27
4265 Id : 22, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
4266 Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
4268 Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
4270 FAILURE in 832 iterations
4271 % SZS status Timeout for RNG009-7.p
4276 additive_identity is 91
4277 additive_inverse is 85
4278 additive_inverse_additive_inverse is 82
4279 associativity_for_addition is 78
4281 commutativity_for_addition is 79
4285 left_additive_identity is 90
4286 left_additive_inverse is 84
4287 left_alternative is 76
4288 left_multiplicative_zero is 87
4290 prove_linearised_form1 is 92
4291 right_additive_identity is 89
4292 right_additive_inverse is 83
4293 right_alternative is 77
4294 right_multiplicative_zero is 86
4300 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4302 add ?4 additive_identity =>= ?4
4303 [4] by right_additive_identity ?4
4305 multiply additive_identity ?6 =>= additive_identity
4306 [6] by left_multiplicative_zero ?6
4308 multiply ?8 additive_identity =>= additive_identity
4309 [8] by right_multiplicative_zero ?8
4311 add (additive_inverse ?10) ?10 =>= additive_identity
4312 [10] by left_additive_inverse ?10
4314 add ?12 (additive_inverse ?12) =>= additive_identity
4315 [12] by right_additive_inverse ?12
4317 additive_inverse (additive_inverse ?14) =>= ?14
4318 [14] by additive_inverse_additive_inverse ?14
4320 multiply ?16 (add ?17 ?18)
4322 add (multiply ?16 ?17) (multiply ?16 ?18)
4323 [18, 17, 16] by distribute1 ?16 ?17 ?18
4325 multiply (add ?20 ?21) ?22
4327 add (multiply ?20 ?22) (multiply ?21 ?22)
4328 [22, 21, 20] by distribute2 ?20 ?21 ?22
4330 add ?24 ?25 =?= add ?25 ?24
4331 [25, 24] by commutativity_for_addition ?24 ?25
4333 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
4334 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
4336 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
4337 [32, 31] by right_alternative ?31 ?32
4339 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
4340 [35, 34] by left_alternative ?34 ?35
4342 associator ?37 ?38 ?39
4344 add (multiply (multiply ?37 ?38) ?39)
4345 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
4346 [39, 38, 37] by associator ?37 ?38 ?39
4350 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
4351 [42, 41] by commutator ?41 ?42
4354 associator x y (add u v)
4356 add (associator x y u) (associator x y v)
4357 [] by prove_linearised_form1
4359 FAILURE in 109 iterations
4360 % SZS status Timeout for RNG019-6.p
4365 additive_identity is 91
4366 additive_inverse is 85
4367 additive_inverse_additive_inverse is 82
4368 associativity_for_addition is 78
4370 commutativity_for_addition is 79
4374 distributivity_of_difference1 is 71
4375 distributivity_of_difference2 is 70
4376 distributivity_of_difference3 is 69
4377 distributivity_of_difference4 is 68
4378 inverse_product1 is 73
4379 inverse_product2 is 72
4380 left_additive_identity is 90
4381 left_additive_inverse is 84
4382 left_alternative is 76
4383 left_multiplicative_zero is 87
4385 product_of_inverses is 74
4386 prove_linearised_form1 is 92
4387 right_additive_identity is 89
4388 right_additive_inverse is 83
4389 right_alternative is 77
4390 right_multiplicative_zero is 86
4396 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4398 add ?4 additive_identity =>= ?4
4399 [4] by right_additive_identity ?4
4401 multiply additive_identity ?6 =>= additive_identity
4402 [6] by left_multiplicative_zero ?6
4404 multiply ?8 additive_identity =>= additive_identity
4405 [8] by right_multiplicative_zero ?8
4407 add (additive_inverse ?10) ?10 =>= additive_identity
4408 [10] by left_additive_inverse ?10
4410 add ?12 (additive_inverse ?12) =>= additive_identity
4411 [12] by right_additive_inverse ?12
4413 additive_inverse (additive_inverse ?14) =>= ?14
4414 [14] by additive_inverse_additive_inverse ?14
4416 multiply ?16 (add ?17 ?18)
4418 add (multiply ?16 ?17) (multiply ?16 ?18)
4419 [18, 17, 16] by distribute1 ?16 ?17 ?18
4421 multiply (add ?20 ?21) ?22
4423 add (multiply ?20 ?22) (multiply ?21 ?22)
4424 [22, 21, 20] by distribute2 ?20 ?21 ?22
4426 add ?24 ?25 =?= add ?25 ?24
4427 [25, 24] by commutativity_for_addition ?24 ?25
4429 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
4430 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
4432 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
4433 [32, 31] by right_alternative ?31 ?32
4435 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
4436 [35, 34] by left_alternative ?34 ?35
4438 associator ?37 ?38 ?39
4440 add (multiply (multiply ?37 ?38) ?39)
4441 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
4442 [39, 38, 37] by associator ?37 ?38 ?39
4446 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
4447 [42, 41] by commutator ?41 ?42
4449 multiply (additive_inverse ?44) (additive_inverse ?45)
4452 [45, 44] by product_of_inverses ?44 ?45
4454 multiply (additive_inverse ?47) ?48
4456 additive_inverse (multiply ?47 ?48)
4457 [48, 47] by inverse_product1 ?47 ?48
4459 multiply ?50 (additive_inverse ?51)
4461 additive_inverse (multiply ?50 ?51)
4462 [51, 50] by inverse_product2 ?50 ?51
4464 multiply ?53 (add ?54 (additive_inverse ?55))
4466 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
4467 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
4469 multiply (add ?57 (additive_inverse ?58)) ?59
4471 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
4472 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
4474 multiply (additive_inverse ?61) (add ?62 ?63)
4476 add (additive_inverse (multiply ?61 ?62))
4477 (additive_inverse (multiply ?61 ?63))
4478 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
4480 multiply (add ?65 ?66) (additive_inverse ?67)
4482 add (additive_inverse (multiply ?65 ?67))
4483 (additive_inverse (multiply ?66 ?67))
4484 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
4487 associator x y (add u v)
4489 add (associator x y u) (associator x y v)
4490 [] by prove_linearised_form1
4492 FAILURE in 149 iterations
4493 % SZS status Timeout for RNG019-7.p
4498 additive_identity is 91
4499 additive_inverse is 85
4500 additive_inverse_additive_inverse is 82
4501 associativity_for_addition is 78
4503 commutativity_for_addition is 79
4507 left_additive_identity is 90
4508 left_additive_inverse is 84
4509 left_alternative is 76
4510 left_multiplicative_zero is 87
4512 prove_linearised_form2 is 92
4513 right_additive_identity is 89
4514 right_additive_inverse is 83
4515 right_alternative is 77
4516 right_multiplicative_zero is 86
4522 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4524 add ?4 additive_identity =>= ?4
4525 [4] by right_additive_identity ?4
4527 multiply additive_identity ?6 =>= additive_identity
4528 [6] by left_multiplicative_zero ?6
4530 multiply ?8 additive_identity =>= additive_identity
4531 [8] by right_multiplicative_zero ?8
4533 add (additive_inverse ?10) ?10 =>= additive_identity
4534 [10] by left_additive_inverse ?10
4536 add ?12 (additive_inverse ?12) =>= additive_identity
4537 [12] by right_additive_inverse ?12
4539 additive_inverse (additive_inverse ?14) =>= ?14
4540 [14] by additive_inverse_additive_inverse ?14
4542 multiply ?16 (add ?17 ?18)
4544 add (multiply ?16 ?17) (multiply ?16 ?18)
4545 [18, 17, 16] by distribute1 ?16 ?17 ?18
4547 multiply (add ?20 ?21) ?22
4549 add (multiply ?20 ?22) (multiply ?21 ?22)
4550 [22, 21, 20] by distribute2 ?20 ?21 ?22
4552 add ?24 ?25 =?= add ?25 ?24
4553 [25, 24] by commutativity_for_addition ?24 ?25
4555 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
4556 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
4558 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
4559 [32, 31] by right_alternative ?31 ?32
4561 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
4562 [35, 34] by left_alternative ?34 ?35
4564 associator ?37 ?38 ?39
4566 add (multiply (multiply ?37 ?38) ?39)
4567 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
4568 [39, 38, 37] by associator ?37 ?38 ?39
4572 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
4573 [42, 41] by commutator ?41 ?42
4576 associator x (add u v) y
4578 add (associator x u y) (associator x v y)
4579 [] by prove_linearised_form2
4581 FAILURE in 109 iterations
4582 % SZS status Timeout for RNG020-6.p
4588 additive_identity is 90
4589 additive_inverse is 91
4590 additive_inverse_additive_inverse is 82
4591 associativity_for_addition is 78
4595 commutativity_for_addition is 79
4600 left_additive_identity is 88
4601 left_additive_inverse is 84
4602 left_alternative is 76
4603 left_multiplicative_zero is 86
4605 prove_teichmuller_identity is 89
4606 right_additive_identity is 87
4607 right_additive_inverse is 83
4608 right_alternative is 77
4609 right_multiplicative_zero is 85
4611 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4613 add ?4 additive_identity =>= ?4
4614 [4] by right_additive_identity ?4
4616 multiply additive_identity ?6 =>= additive_identity
4617 [6] by left_multiplicative_zero ?6
4619 multiply ?8 additive_identity =>= additive_identity
4620 [8] by right_multiplicative_zero ?8
4622 add (additive_inverse ?10) ?10 =>= additive_identity
4623 [10] by left_additive_inverse ?10
4625 add ?12 (additive_inverse ?12) =>= additive_identity
4626 [12] by right_additive_inverse ?12
4628 additive_inverse (additive_inverse ?14) =>= ?14
4629 [14] by additive_inverse_additive_inverse ?14
4631 multiply ?16 (add ?17 ?18)
4633 add (multiply ?16 ?17) (multiply ?16 ?18)
4634 [18, 17, 16] by distribute1 ?16 ?17 ?18
4636 multiply (add ?20 ?21) ?22
4638 add (multiply ?20 ?22) (multiply ?21 ?22)
4639 [22, 21, 20] by distribute2 ?20 ?21 ?22
4641 add ?24 ?25 =?= add ?25 ?24
4642 [25, 24] by commutativity_for_addition ?24 ?25
4644 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
4645 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
4647 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
4648 [32, 31] by right_alternative ?31 ?32
4650 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
4651 [35, 34] by left_alternative ?34 ?35
4653 associator ?37 ?38 ?39
4655 add (multiply (multiply ?37 ?38) ?39)
4656 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
4657 [39, 38, 37] by associator ?37 ?38 ?39
4661 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
4662 [42, 41] by commutator ?41 ?42
4666 (add (associator (multiply a b) c d)
4667 (associator a b (multiply c d)))
4670 (add (associator a (multiply b c) d)
4671 (multiply a (associator b c d)))
4672 (multiply (associator a b c) d)))
4675 [] by prove_teichmuller_identity
4677 FAILURE in 109 iterations
4678 % SZS status Timeout for RNG026-6.p
4683 additive_identity is 93
4684 additive_inverse is 87
4685 additive_inverse_additive_inverse is 84
4686 associativity_for_addition is 80
4688 commutativity_for_addition is 81
4695 distributivity_of_difference1 is 72
4696 distributivity_of_difference2 is 71
4697 distributivity_of_difference3 is 70
4698 distributivity_of_difference4 is 69
4699 inverse_product1 is 74
4700 inverse_product2 is 73
4701 left_additive_identity is 91
4702 left_additive_inverse is 86
4703 left_alternative is 78
4704 left_multiplicative_zero is 89
4706 product_of_inverses is 75
4707 prove_right_moufang is 94
4708 right_additive_identity is 90
4709 right_additive_inverse is 85
4710 right_alternative is 79
4711 right_multiplicative_zero is 88
4713 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4715 add ?4 additive_identity =>= ?4
4716 [4] by right_additive_identity ?4
4718 multiply additive_identity ?6 =>= additive_identity
4719 [6] by left_multiplicative_zero ?6
4721 multiply ?8 additive_identity =>= additive_identity
4722 [8] by right_multiplicative_zero ?8
4724 add (additive_inverse ?10) ?10 =>= additive_identity
4725 [10] by left_additive_inverse ?10
4727 add ?12 (additive_inverse ?12) =>= additive_identity
4728 [12] by right_additive_inverse ?12
4730 additive_inverse (additive_inverse ?14) =>= ?14
4731 [14] by additive_inverse_additive_inverse ?14
4733 multiply ?16 (add ?17 ?18)
4735 add (multiply ?16 ?17) (multiply ?16 ?18)
4736 [18, 17, 16] by distribute1 ?16 ?17 ?18
4738 multiply (add ?20 ?21) ?22
4740 add (multiply ?20 ?22) (multiply ?21 ?22)
4741 [22, 21, 20] by distribute2 ?20 ?21 ?22
4743 add ?24 ?25 =?= add ?25 ?24
4744 [25, 24] by commutativity_for_addition ?24 ?25
4746 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
4747 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
4749 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
4750 [32, 31] by right_alternative ?31 ?32
4752 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
4753 [35, 34] by left_alternative ?34 ?35
4755 associator ?37 ?38 ?39
4757 add (multiply (multiply ?37 ?38) ?39)
4758 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
4759 [39, 38, 37] by associator ?37 ?38 ?39
4763 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
4764 [42, 41] by commutator ?41 ?42
4766 multiply (additive_inverse ?44) (additive_inverse ?45)
4769 [45, 44] by product_of_inverses ?44 ?45
4771 multiply (additive_inverse ?47) ?48
4773 additive_inverse (multiply ?47 ?48)
4774 [48, 47] by inverse_product1 ?47 ?48
4776 multiply ?50 (additive_inverse ?51)
4778 additive_inverse (multiply ?50 ?51)
4779 [51, 50] by inverse_product2 ?50 ?51
4781 multiply ?53 (add ?54 (additive_inverse ?55))
4783 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
4784 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
4786 multiply (add ?57 (additive_inverse ?58)) ?59
4788 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
4789 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
4791 multiply (additive_inverse ?61) (add ?62 ?63)
4793 add (additive_inverse (multiply ?61 ?62))
4794 (additive_inverse (multiply ?61 ?63))
4795 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
4797 multiply (add ?65 ?66) (additive_inverse ?67)
4799 add (additive_inverse (multiply ?65 ?67))
4800 (additive_inverse (multiply ?66 ?67))
4801 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
4804 multiply cz (multiply cx (multiply cy cx))
4806 multiply (multiply (multiply cz cx) cy) cx
4807 [] by prove_right_moufang
4809 FAILURE in 149 iterations
4810 % SZS status Timeout for RNG027-7.p
4815 additive_identity is 92
4816 additive_inverse is 86
4817 additive_inverse_additive_inverse is 83
4818 associativity_for_addition is 79
4820 commutativity_for_addition is 80
4824 distributivity_of_difference1 is 72
4825 distributivity_of_difference2 is 71
4826 distributivity_of_difference3 is 70
4827 distributivity_of_difference4 is 69
4828 inverse_product1 is 74
4829 inverse_product2 is 73
4830 left_additive_identity is 90
4831 left_additive_inverse is 85
4832 left_alternative is 77
4833 left_multiplicative_zero is 88
4835 product_of_inverses is 75
4836 prove_left_moufang is 93
4837 right_additive_identity is 89
4838 right_additive_inverse is 84
4839 right_alternative is 78
4840 right_multiplicative_zero is 87
4845 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4847 add ?4 additive_identity =>= ?4
4848 [4] by right_additive_identity ?4
4850 multiply additive_identity ?6 =>= additive_identity
4851 [6] by left_multiplicative_zero ?6
4853 multiply ?8 additive_identity =>= additive_identity
4854 [8] by right_multiplicative_zero ?8
4856 add (additive_inverse ?10) ?10 =>= additive_identity
4857 [10] by left_additive_inverse ?10
4859 add ?12 (additive_inverse ?12) =>= additive_identity
4860 [12] by right_additive_inverse ?12
4862 additive_inverse (additive_inverse ?14) =>= ?14
4863 [14] by additive_inverse_additive_inverse ?14
4865 multiply ?16 (add ?17 ?18)
4867 add (multiply ?16 ?17) (multiply ?16 ?18)
4868 [18, 17, 16] by distribute1 ?16 ?17 ?18
4870 multiply (add ?20 ?21) ?22
4872 add (multiply ?20 ?22) (multiply ?21 ?22)
4873 [22, 21, 20] by distribute2 ?20 ?21 ?22
4875 add ?24 ?25 =?= add ?25 ?24
4876 [25, 24] by commutativity_for_addition ?24 ?25
4878 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
4879 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
4881 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
4882 [32, 31] by right_alternative ?31 ?32
4884 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
4885 [35, 34] by left_alternative ?34 ?35
4887 associator ?37 ?38 ?39
4889 add (multiply (multiply ?37 ?38) ?39)
4890 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
4891 [39, 38, 37] by associator ?37 ?38 ?39
4895 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
4896 [42, 41] by commutator ?41 ?42
4898 multiply (additive_inverse ?44) (additive_inverse ?45)
4901 [45, 44] by product_of_inverses ?44 ?45
4903 multiply (additive_inverse ?47) ?48
4905 additive_inverse (multiply ?47 ?48)
4906 [48, 47] by inverse_product1 ?47 ?48
4908 multiply ?50 (additive_inverse ?51)
4910 additive_inverse (multiply ?50 ?51)
4911 [51, 50] by inverse_product2 ?50 ?51
4913 multiply ?53 (add ?54 (additive_inverse ?55))
4915 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
4916 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
4918 multiply (add ?57 (additive_inverse ?58)) ?59
4920 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
4921 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
4923 multiply (additive_inverse ?61) (add ?62 ?63)
4925 add (additive_inverse (multiply ?61 ?62))
4926 (additive_inverse (multiply ?61 ?63))
4927 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
4929 multiply (add ?65 ?66) (additive_inverse ?67)
4931 add (additive_inverse (multiply ?65 ?67))
4932 (additive_inverse (multiply ?66 ?67))
4933 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
4936 associator x (multiply y x) z =<= multiply x (associator x y z)
4937 [] by prove_left_moufang
4939 FAILURE in 149 iterations
4940 % SZS status Timeout for RNG028-9.p
4945 additive_identity is 93
4946 additive_inverse is 87
4947 additive_inverse_additive_inverse is 84
4948 associativity_for_addition is 80
4950 commutativity_for_addition is 81
4954 distributivity_of_difference1 is 72
4955 distributivity_of_difference2 is 71
4956 distributivity_of_difference3 is 70
4957 distributivity_of_difference4 is 69
4958 inverse_product1 is 74
4959 inverse_product2 is 73
4960 left_additive_identity is 91
4961 left_additive_inverse is 86
4962 left_alternative is 78
4963 left_multiplicative_zero is 89
4965 product_of_inverses is 75
4966 prove_middle_moufang is 94
4967 right_additive_identity is 90
4968 right_additive_inverse is 85
4969 right_alternative is 79
4970 right_multiplicative_zero is 88
4975 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
4977 add ?4 additive_identity =>= ?4
4978 [4] by right_additive_identity ?4
4980 multiply additive_identity ?6 =>= additive_identity
4981 [6] by left_multiplicative_zero ?6
4983 multiply ?8 additive_identity =>= additive_identity
4984 [8] by right_multiplicative_zero ?8
4986 add (additive_inverse ?10) ?10 =>= additive_identity
4987 [10] by left_additive_inverse ?10
4989 add ?12 (additive_inverse ?12) =>= additive_identity
4990 [12] by right_additive_inverse ?12
4992 additive_inverse (additive_inverse ?14) =>= ?14
4993 [14] by additive_inverse_additive_inverse ?14
4995 multiply ?16 (add ?17 ?18)
4997 add (multiply ?16 ?17) (multiply ?16 ?18)
4998 [18, 17, 16] by distribute1 ?16 ?17 ?18
5000 multiply (add ?20 ?21) ?22
5002 add (multiply ?20 ?22) (multiply ?21 ?22)
5003 [22, 21, 20] by distribute2 ?20 ?21 ?22
5005 add ?24 ?25 =?= add ?25 ?24
5006 [25, 24] by commutativity_for_addition ?24 ?25
5008 add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
5009 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
5011 multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
5012 [32, 31] by right_alternative ?31 ?32
5014 multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
5015 [35, 34] by left_alternative ?34 ?35
5017 associator ?37 ?38 ?39
5019 add (multiply (multiply ?37 ?38) ?39)
5020 (additive_inverse (multiply ?37 (multiply ?38 ?39)))
5021 [39, 38, 37] by associator ?37 ?38 ?39
5025 add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
5026 [42, 41] by commutator ?41 ?42
5028 multiply (additive_inverse ?44) (additive_inverse ?45)
5031 [45, 44] by product_of_inverses ?44 ?45
5033 multiply (additive_inverse ?47) ?48
5035 additive_inverse (multiply ?47 ?48)
5036 [48, 47] by inverse_product1 ?47 ?48
5038 multiply ?50 (additive_inverse ?51)
5040 additive_inverse (multiply ?50 ?51)
5041 [51, 50] by inverse_product2 ?50 ?51
5043 multiply ?53 (add ?54 (additive_inverse ?55))
5045 add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
5046 [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
5048 multiply (add ?57 (additive_inverse ?58)) ?59
5050 add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
5051 [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
5053 multiply (additive_inverse ?61) (add ?62 ?63)
5055 add (additive_inverse (multiply ?61 ?62))
5056 (additive_inverse (multiply ?61 ?63))
5057 [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
5059 multiply (add ?65 ?66) (additive_inverse ?67)
5061 add (additive_inverse (multiply ?65 ?67))
5062 (additive_inverse (multiply ?66 ?67))
5063 [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
5066 multiply (multiply x y) (multiply z x)
5068 multiply (multiply x (multiply y z)) x
5069 [] by prove_middle_moufang
5071 FAILURE in 150 iterations
5072 % SZS status Timeout for RNG029-7.p
5077 a_times_b_is_c is 80
5079 additive_identity is 93
5080 additive_inverse is 89
5081 associativity_for_addition is 86
5082 associativity_for_multiplication is 84
5085 commutativity_for_addition is 85
5088 left_additive_identity is 91
5089 left_additive_inverse is 88
5091 prove_commutativity is 94
5092 right_additive_identity is 90
5093 right_additive_inverse is 87
5094 x_fourthed_is_x is 81
5096 Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
5098 add ?4 additive_identity =>= ?4
5099 [4] by right_additive_identity ?4
5101 add (additive_inverse ?6) ?6 =>= additive_identity
5102 [6] by left_additive_inverse ?6
5104 add ?8 (additive_inverse ?8) =>= additive_identity
5105 [8] by right_additive_inverse ?8
5107 add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
5108 [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
5110 add ?14 ?15 =?= add ?15 ?14
5111 [15, 14] by commutativity_for_addition ?14 ?15
5113 multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
5114 [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
5116 multiply ?21 (add ?22 ?23)
5118 add (multiply ?21 ?22) (multiply ?21 ?23)
5119 [23, 22, 21] by distribute1 ?21 ?22 ?23
5121 multiply (add ?25 ?26) ?27
5123 add (multiply ?25 ?27) (multiply ?26 ?27)
5124 [27, 26, 25] by distribute2 ?25 ?26 ?27
5126 multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
5127 [29] by x_fourthed_is_x ?29
5128 Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
5130 Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
5132 FAILURE in 743 iterations
5133 % SZS status Timeout for RNG035-7.p
5140 associativity_of_add is 92
5143 commutativity_of_add is 93
5146 prove_huntingtons_axiom is 94
5149 Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
5151 add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
5152 [7, 6, 5] by associativity_of_add ?5 ?6 ?7
5154 negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
5157 [10, 9] by robbins_axiom ?9 ?10
5158 Id : 10, {_}: add c d =>= d [] by absorbtion
5161 add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
5164 [] by prove_huntingtons_axiom
5166 FAILURE in 61 iterations
5167 % SZS status Timeout for ROB006-1.p
5173 associativity_of_add is 95
5175 commutativity_of_add is 96
5178 prove_idempotence is 97
5181 Id : 4, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
5183 add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
5184 [8, 7, 6] by associativity_of_add ?6 ?7 ?8
5186 negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
5189 [11, 10] by robbins_axiom ?10 ?11
5190 Id : 10, {_}: add c d =>= d [] by absorbtion
5192 Id : 2, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
5194 FAILURE in 30 iterations
5195 % SZS status Timeout for ROB006-2.p