%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU321+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 08:53:38 PM UTC 2025
% Result : Theorem 185.06s 152.90s
% Output : CNFRefutation 185.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 111 ( 51 ~; 37 |; 6 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 1 prp; 0-3 aty)
% Number of functors : 440 ( 440 usr; 35 con; 0-8 aty)
% Number of variables : 64 ( 63 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > relation_isomorphism > quasi_total > below > well_orders > subset > proper_subset > ordinal_subset > open_subset > is_well_founded_in > is_transitive_in > is_reflexive_in > is_connected_in > is_antisymmetric_in > in > equipotent > element > disjoint > closed_subset > are_equipotent > well_ordering > well_founded_relation > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > transitive > topological_space > top_str > relation_empty_yielding > relation > reflexive > preboolean > ordinal > one_to_one > one_sorted_str > natural > meet_semilatt_str > meet_commutative > meet_absorbing > latt_str > join_semilatt_str > join_commutative > function > finite > epsilon_transitive > epsilon_connected > empty_carrier > empty > diff_closed > cup_closed > connected > being_limit_ordinal > antisymmetric > apply_binary_as_element > unordered_triple > subset_intersection2 > subset_difference > relation_rng_as_subset > relation_dom_as_subset > meet_commut > meet > join_commut > join > apply_binary > unordered_pair > union_of_subsets > topstr_closure > subset_complement > set_union2 > set_intersection2 > set_difference > relation_rng_restriction > relation_restriction > relation_inverse_image > relation_image > relation_dom_restriction > relation_composition > ordered_pair > meet_of_subsets > fiber > complements_of_subsets > cartesian_product2 > apply > #nlpp > union > the_topology > the_carrier > the_L_meet > the_L_join > succ > singleton > set_meet > relation_rng > relation_inverse > relation_field > relation_dom > powerset > pair_second > pair_first > inclusion_relation > identity_relation > function_inverse > empty_carrier_subset > cast_to_subset > cast_as_carrier_subset > omega > empty_set > #skF_311 > #skF_328 > #skF_13 > #skF_330 > #skF_238 > #skF_172 > #skF_289 > #skF_114 > #skF_227 > #skF_104 > #skF_47 > #skF_210 > #skF_188 > #skF_384 > #skF_354 > #skF_26 > #skF_24 > #skF_337 > #skF_263 > #skF_131 > #skF_374 > #skF_37 > #skF_69 > #skF_62 > #skF_111 > #skF_295 > #skF_315 > #skF_280 > #skF_233 > #skF_130 > #skF_254 > #skF_377 > #skF_258 > #skF_171 > #skF_302 > #skF_375 > #skF_369 > #skF_372 > #skF_75 > #skF_366 > #skF_80 > #skF_296 > #skF_316 > #skF_161 > #skF_382 > #skF_30 > #skF_383 > #skF_17 > #skF_183 > #skF_226 > #skF_345 > #skF_314 > #skF_346 > #skF_57 > #skF_216 > #skF_129 > #skF_124 > #skF_148 > #skF_56 > #skF_220 > #skF_342 > #skF_191 > #skF_285 > #skF_144 > #skF_297 > #skF_157 > #skF_214 > #skF_223 > #skF_125 > #skF_113 > #skF_232 > #skF_380 > #skF_91 > #skF_35 > #skF_173 > #skF_93 > #skF_6 > #skF_141 > #skF_152 > #skF_378 > #skF_44 > #skF_27 > #skF_287 > #skF_195 > #skF_127 > #skF_387 > #skF_276 > #skF_364 > #skF_218 > #skF_153 > #skF_53 > #skF_367 > #skF_18 > #skF_88 > #skF_273 > #skF_196 > #skF_48 > #skF_112 > #skF_115 > #skF_255 > #skF_347 > #skF_63 > #skF_327 > #skF_341 > #skF_72 > #skF_247 > #skF_340 > #skF_352 > #skF_334 > #skF_322 > #skF_103 > #skF_116 > #skF_120 > #skF_356 > #skF_203 > #skF_306 > #skF_22 > #skF_133 > #skF_294 > #skF_166 > #skF_206 > #skF_140 > #skF_118 > #skF_353 > #skF_293 > #skF_64 > #skF_165 > #skF_269 > #skF_305 > #skF_292 > #skF_66 > #skF_357 > #skF_301 > #skF_40 > #skF_82 > #skF_298 > #skF_180 > #skF_52 > #skF_370 > #skF_136 > #skF_92 > #skF_208 > #skF_19 > #skF_200 > #skF_312 > #skF_209 > #skF_281 > #skF_108 > #skF_12 > #skF_3 > #skF_90 > #skF_291 > #skF_138 > #skF_261 > #skF_282 > #skF_359 > #skF_332 > #skF_68 > #skF_224 > #skF_132 > #skF_211 > #skF_225 > #skF_117 > #skF_192 > #skF_219 > #skF_162 > #skF_299 > #skF_212 > #skF_154 > #skF_198 > #skF_102 > #skF_34 > #skF_363 > #skF_324 > #skF_190 > #skF_74 > #skF_32 > #skF_167 > #skF_309 > #skF_123 > #skF_160 > #skF_101 > #skF_25 > #skF_60 > #skF_240 > #skF_23 > #skF_45 > #skF_256 > #skF_275 > #skF_266 > #skF_178 > #skF_252 > #skF_41 > #skF_89 > #skF_156 > #skF_107 > #skF_237 > #skF_175 > #skF_5 > #skF_49 > #skF_313 > #skF_323 > #skF_193 > #skF_38 > #skF_264 > #skF_65 > #skF_319 > #skF_234 > #skF_54 > #skF_149 > #skF_67 > #skF_99 > #skF_76 > #skF_362 > #skF_110 > #skF_245 > #skF_97 > #skF_308 > #skF_239 > #skF_42 > #skF_379 > #skF_242 > #skF_267 > #skF_241 > #skF_265 > #skF_184 > #skF_164 > #skF_300 > #skF_376 > #skF_98 > #skF_128 > #skF_94 > #skF_11 > #skF_217 > #skF_194 > #skF_231 > #skF_321 > #skF_36 > #skF_126 > #skF_29 > #skF_307 > #skF_187 > #skF_351 > #skF_329 > #skF_7 > #skF_257 > #skF_343 > #skF_235 > #skF_286 > #skF_268 > #skF_150 > #skF_39 > #skF_325 > #skF_274 > #skF_290 > #skF_100 > #skF_9 > #skF_20 > #skF_335 > #skF_260 > #skF_51 > #skF_221 > #skF_317 > #skF_33 > #skF_31 > #skF_137 > #skF_71 > #skF_86 > #skF_246 > #skF_386 > #skF_204 > #skF_15 > #skF_182 > #skF_185 > #skF_122 > #skF_205 > #skF_14 > #skF_371 > #skF_50 > #skF_320 > #skF_78 > #skF_95 > #skF_77 > #skF_151 > #skF_147 > #skF_46 > #skF_81 > #skF_284 > #skF_139 > #skF_163 > #skF_244 > #skF_236 > #skF_170 > #skF_59 > #skF_145 > #skF_121 > #skF_230 > #skF_58 > #skF_201 > #skF_181 > #skF_344 > #skF_142 > #skF_177 > #skF_355 > #skF_84 > #skF_279 > #skF_199 > #skF_277 > #skF_222 > #skF_87 > #skF_158 > #skF_169 > #skF_2 > #skF_303 > #skF_365 > #skF_248 > #skF_333 > #skF_349 > #skF_331 > #skF_179 > #skF_251 > #skF_70 > #skF_272 > #skF_385 > #skF_249 > #skF_176 > #skF_105 > #skF_373 > #skF_159 > #skF_83 > #skF_304 > #skF_106 > #skF_135 > #skF_189 > #skF_202 > #skF_215 > #skF_8 > #skF_270 > #skF_228 > #skF_143 > #skF_262 > #skF_381 > #skF_278 > #skF_229 > #skF_326 > #skF_43 > #skF_368 > #skF_338 > #skF_197 > #skF_174 > #skF_186 > #skF_85 > #skF_259 > #skF_253 > #skF_213 > #skF_21 > #skF_310 > #skF_61 > #skF_250 > #skF_360 > #skF_361 > #skF_348 > #skF_96 > #skF_1 > #skF_119 > #skF_336 > #skF_55 > #skF_283 > #skF_358 > #skF_134 > #skF_28 > #skF_146 > #skF_73 > #skF_168 > #skF_4 > #skF_207 > #skF_350 > #skF_16 > #skF_288 > #skF_10 > #skF_79 > #skF_155 > #skF_243 > #skF_271 > #skF_318 > #skF_109 > #skF_339
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff('#skF_311',type,
'#skF_311': ( $i * $i * $i * $i ) > $i ).
tff('#skF_328',type,
'#skF_328': $i > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_330',type,
'#skF_330': ( $i * $i ) > $i ).
tff(well_ordering,type,
well_ordering: $i > $o ).
tff(subset_intersection2,type,
subset_intersection2: ( $i * $i * $i ) > $i ).
tff('#skF_238',type,
'#skF_238': ( $i * $i ) > $i ).
tff('#skF_172',type,
'#skF_172': $i ).
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(are_equipotent,type,
are_equipotent: ( $i * $i ) > $o ).
tff('#skF_289',type,
'#skF_289': $i > $i ).
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_114',type,
'#skF_114': ( $i * $i * $i ) > $i ).
tff('#skF_227',type,
'#skF_227': ( $i * $i * $i * $i ) > $i ).
tff('#skF_104',type,
'#skF_104': ( $i * $i ) > $i ).
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff('#skF_47',type,
'#skF_47': ( $i * $i ) > $i ).
tff('#skF_210',type,
'#skF_210': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_188',type,
'#skF_188': $i > $i ).
tff('#skF_384',type,
'#skF_384': ( $i * $i * $i ) > $i ).
tff('#skF_354',type,
'#skF_354': ( $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff('#skF_337',type,
'#skF_337': ( $i * $i ) > $i ).
tff('#skF_263',type,
'#skF_263': ( $i * $i * $i ) > $i ).
tff('#skF_131',type,
'#skF_131': ( $i * $i * $i ) > $i ).
tff('#skF_374',type,
'#skF_374': ( $i * $i ) > $i ).
tff(complements_of_subsets,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i ) > $i ).
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff('#skF_69',type,
'#skF_69': ( $i * $i * $i ) > $i ).
tff('#skF_62',type,
'#skF_62': ( $i * $i ) > $i ).
tff('#skF_111',type,
'#skF_111': ( $i * $i ) > $i ).
tff('#skF_295',type,
'#skF_295': ( $i * $i * $i ) > $i ).
tff('#skF_315',type,
'#skF_315': $i > $i ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_280',type,
'#skF_280': ( $i * $i * $i ) > $i ).
tff('#skF_233',type,
'#skF_233': ( $i * $i ) > $i ).
tff('#skF_130',type,
'#skF_130': ( $i * $i ) > $i ).
tff('#skF_254',type,
'#skF_254': ( $i * $i ) > $i ).
tff('#skF_377',type,
'#skF_377': ( $i * $i ) > $i ).
tff('#skF_258',type,
'#skF_258': ( $i * $i ) > $i ).
tff(cast_to_subset,type,
cast_to_subset: $i > $i ).
tff('#skF_171',type,
'#skF_171': $i > $i ).
tff('#skF_302',type,
'#skF_302': ( $i * $i ) > $i ).
tff(union,type,
union: $i > $i ).
tff('#skF_375',type,
'#skF_375': ( $i * $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_369',type,
'#skF_369': ( $i * $i ) > $i ).
tff('#skF_372',type,
'#skF_372': $i > $i ).
tff('#skF_75',type,
'#skF_75': ( $i * $i * $i * $i ) > $i ).
tff('#skF_366',type,
'#skF_366': ( $i * $i ) > $i ).
tff('#skF_80',type,
'#skF_80': ( $i * $i ) > $i ).
tff('#skF_296',type,
'#skF_296': ( $i * $i * $i ) > $i ).
tff('#skF_316',type,
'#skF_316': ( $i * $i * $i ) > $i ).
tff('#skF_161',type,
'#skF_161': $i ).
tff(unordered_triple,type,
unordered_triple: ( $i * $i * $i ) > $i ).
tff('#skF_382',type,
'#skF_382': $i > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i * $i * $i ) > $i ).
tff('#skF_383',type,
'#skF_383': $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_183',type,
'#skF_183': ( $i * $i ) > $i ).
tff('#skF_226',type,
'#skF_226': ( $i * $i * $i * $i ) > $i ).
tff(cup_closed,type,
cup_closed: $i > $o ).
tff('#skF_345',type,
'#skF_345': $i > $i ).
tff('#skF_314',type,
'#skF_314': ( $i * $i * $i ) > $i ).
tff('#skF_346',type,
'#skF_346': $i ).
tff(topstr_closure,type,
topstr_closure: ( $i * $i ) > $i ).
tff('#skF_57',type,
'#skF_57': ( $i * $i ) > $i ).
tff('#skF_216',type,
'#skF_216': ( $i * $i * $i ) > $i ).
tff('#skF_129',type,
'#skF_129': ( $i * $i ) > $i ).
tff(connected,type,
connected: $i > $o ).
tff('#skF_124',type,
'#skF_124': ( $i * $i * $i ) > $i ).
tff(empty_carrier_subset,type,
empty_carrier_subset: $i > $i ).
tff('#skF_148',type,
'#skF_148': $i ).
tff('#skF_56',type,
'#skF_56': ( $i * $i ) > $i ).
tff('#skF_220',type,
'#skF_220': ( $i * $i * $i ) > $i ).
tff('#skF_342',type,
'#skF_342': $i > $i ).
tff('#skF_191',type,
'#skF_191': $i > $i ).
tff(relation_inverse,type,
relation_inverse: $i > $i ).
tff('#skF_285',type,
'#skF_285': ( $i * $i * $i ) > $i ).
tff('#skF_144',type,
'#skF_144': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_297',type,
'#skF_297': ( $i * $i * $i ) > $i ).
tff('#skF_157',type,
'#skF_157': $i ).
tff('#skF_214',type,
'#skF_214': ( $i * $i * $i ) > $i ).
tff('#skF_223',type,
'#skF_223': ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_125',type,
'#skF_125': ( $i * $i * $i ) > $i ).
tff('#skF_113',type,
'#skF_113': ( $i * $i ) > $i ).
tff('#skF_232',type,
'#skF_232': ( $i * $i ) > $i ).
tff('#skF_380',type,
'#skF_380': ( $i * $i ) > $i ).
tff('#skF_91',type,
'#skF_91': ( $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': $i > $i ).
tff('#skF_173',type,
'#skF_173': $i ).
tff('#skF_93',type,
'#skF_93': ( $i * $i ) > $i ).
tff(is_reflexive_in,type,
is_reflexive_in: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_141',type,
'#skF_141': $i > $i ).
tff('#skF_152',type,
'#skF_152': ( $i * $i ) > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_378',type,
'#skF_378': ( $i * $i ) > $i ).
tff(meet_commut,type,
meet_commut: ( $i * $i * $i ) > $i ).
tff('#skF_44',type,
'#skF_44': ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i ) > $i ).
tff(quasi_total,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff('#skF_287',type,
'#skF_287': ( $i * $i * $i * $i ) > $i ).
tff('#skF_195',type,
'#skF_195': $i > $i ).
tff('#skF_127',type,
'#skF_127': ( $i * $i * $i ) > $i ).
tff('#skF_387',type,
'#skF_387': ( $i * $i ) > $i ).
tff('#skF_276',type,
'#skF_276': ( $i * $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_364',type,
'#skF_364': $i > $i ).
tff('#skF_218',type,
'#skF_218': ( $i * $i * $i ) > $i ).
tff('#skF_153',type,
'#skF_153': $i ).
tff('#skF_53',type,
'#skF_53': ( $i * $i ) > $i ).
tff('#skF_367',type,
'#skF_367': ( $i * $i ) > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff('#skF_88',type,
'#skF_88': ( $i * $i ) > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(v1_int_1,type,
v1_int_1: $i > $o ).
tff('#skF_273',type,
'#skF_273': ( $i * $i ) > $i ).
tff(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff('#skF_196',type,
'#skF_196': $i ).
tff('#skF_48',type,
'#skF_48': ( $i * $i ) > $i ).
tff('#skF_112',type,
'#skF_112': ( $i * $i ) > $i ).
tff('#skF_115',type,
'#skF_115': ( $i * $i * $i ) > $i ).
tff('#skF_255',type,
'#skF_255': ( $i * $i ) > $i ).
tff('#skF_347',type,
'#skF_347': ( $i * $i ) > $i ).
tff('#skF_63',type,
'#skF_63': ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff('#skF_327',type,
'#skF_327': ( $i * $i * $i * $i ) > $i ).
tff('#skF_341',type,
'#skF_341': $i > $i ).
tff('#skF_72',type,
'#skF_72': ( $i * $i * $i ) > $i ).
tff('#skF_247',type,
'#skF_247': $i > $i ).
tff('#skF_340',type,
'#skF_340': ( $i * $i * $i ) > $i ).
tff('#skF_352',type,
'#skF_352': ( $i * $i ) > $i ).
tff('#skF_334',type,
'#skF_334': ( $i * $i ) > $i ).
tff('#skF_322',type,
'#skF_322': ( $i * $i ) > $i ).
tff('#skF_103',type,
'#skF_103': $i > $i ).
tff('#skF_116',type,
'#skF_116': ( $i * $i * $i ) > $i ).
tff('#skF_120',type,
'#skF_120': $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_356',type,
'#skF_356': ( $i * $i * $i ) > $i ).
tff('#skF_203',type,
'#skF_203': ( $i * $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_306',type,
'#skF_306': ( $i * $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i ) > $i ).
tff('#skF_133',type,
'#skF_133': $i ).
tff('#skF_294',type,
'#skF_294': ( $i * $i * $i ) > $i ).
tff('#skF_166',type,
'#skF_166': $i ).
tff(join,type,
join: ( $i * $i * $i ) > $i ).
tff('#skF_206',type,
'#skF_206': ( $i * $i ) > $i ).
tff('#skF_140',type,
'#skF_140': $i > $i ).
tff('#skF_118',type,
'#skF_118': $i > $i ).
tff('#skF_353',type,
'#skF_353': ( $i * $i * $i ) > $i ).
tff(pair_second,type,
pair_second: $i > $i ).
tff('#skF_293',type,
'#skF_293': ( $i * $i ) > $i ).
tff('#skF_64',type,
'#skF_64': ( $i * $i ) > $i ).
tff(relation_rng_restriction,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff('#skF_165',type,
'#skF_165': $i ).
tff(inclusion_relation,type,
inclusion_relation: $i > $i ).
tff('#skF_269',type,
'#skF_269': ( $i * $i * $i ) > $i ).
tff('#skF_305',type,
'#skF_305': ( $i * $i * $i ) > $i ).
tff('#skF_292',type,
'#skF_292': $i > $i ).
tff('#skF_66',type,
'#skF_66': ( $i * $i * $i ) > $i ).
tff('#skF_357',type,
'#skF_357': ( $i * $i * $i ) > $i ).
tff('#skF_301',type,
'#skF_301': ( $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': $i > $i ).
tff('#skF_82',type,
'#skF_82': ( $i * $i ) > $i ).
tff('#skF_298',type,
'#skF_298': ( $i * $i * $i * $i ) > $i ).
tff('#skF_180',type,
'#skF_180': ( $i * $i ) > $i ).
tff(relation_inverse_image,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff('#skF_52',type,
'#skF_52': ( $i * $i * $i ) > $i ).
tff('#skF_370',type,
'#skF_370': ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_136',type,
'#skF_136': $i ).
tff('#skF_92',type,
'#skF_92': ( $i * $i ) > $i ).
tff('#skF_208',type,
'#skF_208': ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i * $i ) > $i ).
tff('#skF_200',type,
'#skF_200': $i ).
tff('#skF_312',type,
'#skF_312': ( $i * $i ) > $i ).
tff('#skF_209',type,
'#skF_209': ( $i * $i ) > $i ).
tff('#skF_281',type,
'#skF_281': ( $i * $i * $i ) > $i ).
tff(meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
tff('#skF_108',type,
'#skF_108': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i * $i ) > $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_90',type,
'#skF_90': ( $i * $i ) > $i ).
tff('#skF_291',type,
'#skF_291': $i > $i ).
tff(apply_binary,type,
apply_binary: ( $i * $i * $i ) > $i ).
tff('#skF_138',type,
'#skF_138': $i > $i ).
tff('#skF_261',type,
'#skF_261': ( $i * $i ) > $i ).
tff('#skF_282',type,
'#skF_282': ( $i * $i * $i ) > $i ).
tff('#skF_359',type,
'#skF_359': ( $i * $i * $i ) > $i ).
tff('#skF_332',type,
'#skF_332': ( $i * $i ) > $i ).
tff('#skF_68',type,
'#skF_68': $i > $i ).
tff(the_L_join,type,
the_L_join: $i > $i ).
tff('#skF_224',type,
'#skF_224': ( $i * $i * $i * $i ) > $i ).
tff(join_commut,type,
join_commut: ( $i * $i * $i ) > $i ).
tff('#skF_132',type,
'#skF_132': $i ).
tff('#skF_211',type,
'#skF_211': ( $i * $i * $i ) > $i ).
tff(open_subset,type,
open_subset: ( $i * $i ) > $o ).
tff('#skF_225',type,
'#skF_225': ( $i * $i * $i * $i ) > $i ).
tff('#skF_117',type,
'#skF_117': ( $i * $i * $i ) > $i ).
tff('#skF_192',type,
'#skF_192': $i ).
tff('#skF_219',type,
'#skF_219': ( $i * $i * $i ) > $i ).
tff('#skF_162',type,
'#skF_162': $i > $i ).
tff('#skF_299',type,
'#skF_299': ( $i * $i ) > $i ).
tff('#skF_212',type,
'#skF_212': ( $i * $i * $i ) > $i ).
tff('#skF_154',type,
'#skF_154': $i ).
tff('#skF_198',type,
'#skF_198': $i ).
tff('#skF_102',type,
'#skF_102': ( $i * $i * $i ) > $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff('#skF_34',type,
'#skF_34': $i > $i ).
tff('#skF_363',type,
'#skF_363': $i > $i ).
tff('#skF_324',type,
'#skF_324': ( $i * $i * $i ) > $i ).
tff('#skF_190',type,
'#skF_190': $i > $i ).
tff(well_founded_relation,type,
well_founded_relation: $i > $o ).
tff('#skF_74',type,
'#skF_74': ( $i * $i * $i ) > $i ).
tff(latt_str,type,
latt_str: $i > $o ).
tff('#skF_32',type,
'#skF_32': $i > $i ).
tff('#skF_167',type,
'#skF_167': ( $i * $i ) > $i ).
tff('#skF_309',type,
'#skF_309': ( $i * $i * $i * $i ) > $i ).
tff('#skF_123',type,
'#skF_123': ( $i * $i * $i ) > $i ).
tff('#skF_160',type,
'#skF_160': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff('#skF_101',type,
'#skF_101': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i * $i ) > $i ).
tff('#skF_60',type,
'#skF_60': $i > $i ).
tff('#skF_240',type,
'#skF_240': ( $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i * $i ) > $i ).
tff('#skF_256',type,
'#skF_256': ( $i * $i * $i ) > $i ).
tff('#skF_275',type,
'#skF_275': ( $i * $i ) > $i ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff('#skF_266',type,
'#skF_266': ( $i * $i ) > $i ).
tff('#skF_178',type,
'#skF_178': $i > $i ).
tff('#skF_252',type,
'#skF_252': ( $i * $i * $i * $i ) > $i ).
tff('#skF_41',type,
'#skF_41': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(preboolean,type,
preboolean: $i > $o ).
tff(is_well_founded_in,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff('#skF_89',type,
'#skF_89': ( $i * $i * $i ) > $i ).
tff(identity_relation,type,
identity_relation: $i > $i ).
tff('#skF_156',type,
'#skF_156': ( $i * $i ) > $i ).
tff(function_inverse,type,
function_inverse: $i > $i ).
tff('#skF_107',type,
'#skF_107': ( $i * $i * $i ) > $i ).
tff('#skF_237',type,
'#skF_237': ( $i * $i ) > $i ).
tff('#skF_175',type,
'#skF_175': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $i ) > $i ).
tff('#skF_313',type,
'#skF_313': ( $i * $i * $i ) > $i ).
tff('#skF_323',type,
'#skF_323': ( $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff(diff_closed,type,
diff_closed: $i > $o ).
tff('#skF_193',type,
'#skF_193': $i > $i ).
tff('#skF_38',type,
'#skF_38': $i > $i ).
tff('#skF_264',type,
'#skF_264': ( $i * $i * $i ) > $i ).
tff('#skF_65',type,
'#skF_65': ( $i * $i * $i ) > $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff('#skF_319',type,
'#skF_319': ( $i * $i * $i ) > $i ).
tff('#skF_234',type,
'#skF_234': ( $i * $i ) > $i ).
tff('#skF_54',type,
'#skF_54': ( $i * $i ) > $i ).
tff('#skF_149',type,
'#skF_149': $i ).
tff('#skF_67',type,
'#skF_67': ( $i * $i ) > $i ).
tff('#skF_99',type,
'#skF_99': ( $i * $i ) > $i ).
tff(relation_image,type,
relation_image: ( $i * $i ) > $i ).
tff('#skF_76',type,
'#skF_76': ( $i * $i * $i * $i ) > $i ).
tff(relation_dom_as_subset,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff('#skF_362',type,
'#skF_362': ( $i * $i * $i * $i ) > $i ).
tff('#skF_110',type,
'#skF_110': ( $i * $i ) > $i ).
tff('#skF_245',type,
'#skF_245': $i > $i ).
tff('#skF_97',type,
'#skF_97': ( $i * $i * $i ) > $i ).
tff('#skF_308',type,
'#skF_308': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
tff('#skF_239',type,
'#skF_239': ( $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i ) > $i ).
tff('#skF_379',type,
'#skF_379': ( $i * $i ) > $i ).
tff('#skF_242',type,
'#skF_242': ( $i * $i * $i ) > $i ).
tff('#skF_267',type,
'#skF_267': ( $i * $i ) > $i ).
tff('#skF_241',type,
'#skF_241': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_265',type,
'#skF_265': ( $i * $i ) > $i ).
tff('#skF_184',type,
'#skF_184': ( $i * $i ) > $i ).
tff(closed_subset,type,
closed_subset: ( $i * $i ) > $o ).
tff('#skF_164',type,
'#skF_164': $i > $i ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_300',type,
'#skF_300': ( $i * $i ) > $i ).
tff('#skF_376',type,
'#skF_376': ( $i * $i ) > $i ).
tff('#skF_98',type,
'#skF_98': ( $i * $i * $i ) > $i ).
tff('#skF_128',type,
'#skF_128': ( $i * $i ) > $i ).
tff(v1_xreal_0,type,
v1_xreal_0: $i > $o ).
tff(relation_dom_restriction,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff('#skF_94',type,
'#skF_94': ( $i * $i ) > $i ).
tff(the_topology,type,
the_topology: $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_217',type,
'#skF_217': ( $i * $i * $i ) > $i ).
tff('#skF_194',type,
'#skF_194': $i ).
tff('#skF_231',type,
'#skF_231': $i > $i ).
tff('#skF_321',type,
'#skF_321': ( $i * $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff(v5_membered,type,
v5_membered: $i > $o ).
tff('#skF_126',type,
'#skF_126': ( $i * $i * $i ) > $i ).
tff(meet,type,
meet: ( $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i * $i ) > $i ).
tff('#skF_307',type,
'#skF_307': ( $i * $i * $i ) > $i ).
tff('#skF_187',type,
'#skF_187': $i > $i ).
tff('#skF_351',type,
'#skF_351': $i > $i ).
tff('#skF_329',type,
'#skF_329': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff('#skF_257',type,
'#skF_257': ( $i * $i ) > $i ).
tff('#skF_343',type,
'#skF_343': $i > $i ).
tff('#skF_235',type,
'#skF_235': ( $i * $i ) > $i ).
tff(well_orders,type,
well_orders: ( $i * $i ) > $o ).
tff('#skF_286',type,
'#skF_286': ( $i * $i * $i * $i ) > $i ).
tff('#skF_268',type,
'#skF_268': ( $i * $i ) > $i ).
tff('#skF_150',type,
'#skF_150': $i > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(equipotent,type,
equipotent: ( $i * $i ) > $o ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_39',type,
'#skF_39': $i > $i ).
tff('#skF_325',type,
'#skF_325': ( $i * $i * $i ) > $i ).
tff('#skF_274',type,
'#skF_274': ( $i * $i ) > $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(v2_membered,type,
v2_membered: $i > $o ).
tff('#skF_290',type,
'#skF_290': $i > $i ).
tff('#skF_100',type,
'#skF_100': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff('#skF_335',type,
'#skF_335': ( $i * $i ) > $i ).
tff('#skF_260',type,
'#skF_260': ( $i * $i ) > $i ).
tff(v1_membered,type,
v1_membered: $i > $o ).
tff('#skF_51',type,
'#skF_51': ( $i * $i * $i ) > $i ).
tff('#skF_221',type,
'#skF_221': ( $i * $i * $i ) > $i ).
tff('#skF_317',type,
'#skF_317': ( $i * $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i > $i ).
tff(set_meet,type,
set_meet: $i > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i * $i ) > $i ).
tff(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_137',type,
'#skF_137': ( $i * $i ) > $i ).
tff('#skF_71',type,
'#skF_71': ( $i * $i * $i ) > $i ).
tff('#skF_86',type,
'#skF_86': ( $i * $i ) > $i ).
tff('#skF_246',type,
'#skF_246': $i > $i ).
tff('#skF_386',type,
'#skF_386': $i > $i ).
tff(relation_isomorphism,type,
relation_isomorphism: ( $i * $i * $i ) > $o ).
tff('#skF_204',type,
'#skF_204': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_182',type,
'#skF_182': ( $i * $i ) > $i ).
tff(being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
tff('#skF_185',type,
'#skF_185': ( $i * $i * $i * $i * $i ) > $i ).
tff(relation_rng_as_subset,type,
relation_rng_as_subset: ( $i * $i * $i ) > $i ).
tff('#skF_122',type,
'#skF_122': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_205',type,
'#skF_205': ( $i * $i ) > $i ).
tff(the_L_meet,type,
the_L_meet: $i > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_371',type,
'#skF_371': ( $i * $i ) > $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i ) > $i ).
tff('#skF_320',type,
'#skF_320': ( $i * $i ) > $i ).
tff('#skF_78',type,
'#skF_78': $i > $i ).
tff('#skF_95',type,
'#skF_95': ( $i * $i * $i ) > $i ).
tff('#skF_77',type,
'#skF_77': $i > $i ).
tff('#skF_151',type,
'#skF_151': $i > $i ).
tff('#skF_147',type,
'#skF_147': $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i ) > $i ).
tff('#skF_81',type,
'#skF_81': ( $i * $i ) > $i ).
tff(join_semilatt_str,type,
join_semilatt_str: $i > $o ).
tff('#skF_284',type,
'#skF_284': ( $i * $i * $i ) > $i ).
tff('#skF_139',type,
'#skF_139': ( $i * $i ) > $i ).
tff('#skF_163',type,
'#skF_163': $i ).
tff('#skF_244',type,
'#skF_244': $i > $i ).
tff('#skF_236',type,
'#skF_236': ( $i * $i ) > $i ).
tff('#skF_170',type,
'#skF_170': $i ).
tff('#skF_59',type,
'#skF_59': ( $i * $i ) > $i ).
tff('#skF_145',type,
'#skF_145': $i > $i ).
tff('#skF_121',type,
'#skF_121': $i > $i ).
tff('#skF_230',type,
'#skF_230': $i > $i ).
tff('#skF_58',type,
'#skF_58': ( $i * $i ) > $i ).
tff('#skF_201',type,
'#skF_201': $i > $i ).
tff('#skF_181',type,
'#skF_181': ( $i * $i ) > $i ).
tff(relation_restriction,type,
relation_restriction: ( $i * $i ) > $i ).
tff('#skF_344',type,
'#skF_344': $i > $i ).
tff('#skF_142',type,
'#skF_142': $i > $i ).
tff('#skF_177',type,
'#skF_177': $i > $i ).
tff('#skF_355',type,
'#skF_355': $i > $i ).
tff('#skF_84',type,
'#skF_84': ( $i * $i * $i ) > $i ).
tff('#skF_279',type,
'#skF_279': ( $i * $i * $i ) > $i ).
tff('#skF_199',type,
'#skF_199': ( $i * $i ) > $i ).
tff('#skF_277',type,
'#skF_277': ( $i * $i * $i ) > $i ).
tff('#skF_222',type,
'#skF_222': ( $i * $i * $i ) > $i ).
tff('#skF_87',type,
'#skF_87': ( $i * $i ) > $i ).
tff('#skF_158',type,
'#skF_158': $i ).
tff('#skF_169',type,
'#skF_169': $i > $i ).
tff(below,type,
below: ( $i * $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(transitive,type,
transitive: $i > $o ).
tff('#skF_303',type,
'#skF_303': ( $i * $i ) > $i ).
tff('#skF_365',type,
'#skF_365': $i > $i ).
tff('#skF_248',type,
'#skF_248': ( $i * $i ) > $i ).
tff('#skF_333',type,
'#skF_333': ( $i * $i ) > $i ).
tff('#skF_349',type,
'#skF_349': $i > $i ).
tff('#skF_331',type,
'#skF_331': ( $i * $i * $i ) > $i ).
tff('#skF_179',type,
'#skF_179': ( $i * $i ) > $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff('#skF_251',type,
'#skF_251': $i > $i ).
tff('#skF_70',type,
'#skF_70': ( $i * $i * $i ) > $i ).
tff('#skF_272',type,
'#skF_272': ( $i * $i ) > $i ).
tff('#skF_385',type,
'#skF_385': ( $i * $i ) > $i ).
tff(is_connected_in,type,
is_connected_in: ( $i * $i ) > $o ).
tff('#skF_249',type,
'#skF_249': $i > $i ).
tff('#skF_176',type,
'#skF_176': $i ).
tff('#skF_105',type,
'#skF_105': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_373',type,
'#skF_373': $i > $i ).
tff(v1_rat_1,type,
v1_rat_1: $i > $o ).
tff('#skF_159',type,
'#skF_159': $i ).
tff(meet_absorbing,type,
meet_absorbing: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(reflexive,type,
reflexive: $i > $o ).
tff('#skF_83',type,
'#skF_83': ( $i * $i * $i ) > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_304',type,
'#skF_304': ( $i * $i ) > $i ).
tff('#skF_106',type,
'#skF_106': ( $i * $i ) > $i ).
tff('#skF_135',type,
'#skF_135': $i ).
tff(is_transitive_in,type,
is_transitive_in: ( $i * $i ) > $o ).
tff('#skF_189',type,
'#skF_189': $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff(ordinal_subset,type,
ordinal_subset: ( $i * $i ) > $o ).
tff('#skF_202',type,
'#skF_202': ( $i * $i ) > $i ).
tff('#skF_215',type,
'#skF_215': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_270',type,
'#skF_270': ( $i * $i ) > $i ).
tff('#skF_228',type,
'#skF_228': $i > $i ).
tff('#skF_143',type,
'#skF_143': $i > $i ).
tff('#skF_262',type,
'#skF_262': ( $i * $i ) > $i ).
tff(meet_commutative,type,
meet_commutative: $i > $o ).
tff('#skF_381',type,
'#skF_381': ( $i * $i ) > $i ).
tff(is_antisymmetric_in,type,
is_antisymmetric_in: ( $i * $i ) > $o ).
tff('#skF_278',type,
'#skF_278': ( $i * $i * $i ) > $i ).
tff('#skF_229',type,
'#skF_229': $i > $i ).
tff('#skF_326',type,
'#skF_326': ( $i * $i * $i * $i ) > $i ).
tff('#skF_43',type,
'#skF_43': ( $i * $i ) > $i ).
tff('#skF_368',type,
'#skF_368': $i > $i ).
tff('#skF_338',type,
'#skF_338': ( $i * $i * $i * $i ) > $i ).
tff('#skF_197',type,
'#skF_197': $i > $i ).
tff('#skF_174',type,
'#skF_174': $i ).
tff('#skF_186',type,
'#skF_186': ( $i * $i * $i * $i ) > $i ).
tff('#skF_85',type,
'#skF_85': ( $i * $i * $i ) > $i ).
tff('#skF_259',type,
'#skF_259': ( $i * $i ) > $i ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_253',type,
'#skF_253': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_213',type,
'#skF_213': ( $i * $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff('#skF_310',type,
'#skF_310': ( $i * $i * $i * $i ) > $i ).
tff('#skF_61',type,
'#skF_61': ( $i * $i ) > $i ).
tff('#skF_250',type,
'#skF_250': ( $i * $i ) > $i ).
tff('#skF_360',type,
'#skF_360': ( $i * $i * $i * $i ) > $i ).
tff('#skF_361',type,
'#skF_361': ( $i * $i * $i ) > $i ).
tff('#skF_348',type,
'#skF_348': $i ).
tff('#skF_96',type,
'#skF_96': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(succ,type,
succ: $i > $i ).
tff('#skF_119',type,
'#skF_119': $i > $i ).
tff('#skF_336',type,
'#skF_336': ( $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': $i > $i ).
tff('#skF_283',type,
'#skF_283': ( $i * $i * $i ) > $i ).
tff('#skF_358',type,
'#skF_358': ( $i * $i ) > $i ).
tff(apply_binary_as_element,type,
apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(relation_of2_as_subset,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff('#skF_134',type,
'#skF_134': $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i ) > $i ).
tff('#skF_146',type,
'#skF_146': $i > $i ).
tff(join_commutative,type,
join_commutative: $i > $o ).
tff('#skF_73',type,
'#skF_73': ( $i * $i * $i ) > $i ).
tff('#skF_168',type,
'#skF_168': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_207',type,
'#skF_207': ( $i * $i ) > $i ).
tff('#skF_350',type,
'#skF_350': ( $i * $i ) > $i ).
tff(fiber,type,
fiber: ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(pair_first,type,
pair_first: $i > $i ).
tff('#skF_288',type,
'#skF_288': ( $i * $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff('#skF_79',type,
'#skF_79': ( $i * $i ) > $i ).
tff('#skF_155',type,
'#skF_155': $i ).
tff(topological_space,type,
topological_space: $i > $o ).
tff('#skF_243',type,
'#skF_243': ( $i * $i * $i ) > $i ).
tff('#skF_271',type,
'#skF_271': ( $i * $i ) > $i ).
tff('#skF_318',type,
'#skF_318': ( $i * $i ) > $i ).
tff(top_str,type,
top_str: $i > $o ).
tff('#skF_109',type,
'#skF_109': ( $i * $i ) > $i ).
tff('#skF_339',type,
'#skF_339': ( $i * $i ) > $i ).
tff(f_1969,negated_conjecture,
~ ! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,subset_complement(the_carrier(A),B))
<=> ~ in(C,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
tff(f_2100,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_4711,lemma,
! [A] :
( ( relation_dom(identity_relation(A)) = A )
& ( relation_rng(identity_relation(A)) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
tff(f_1574,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
tff(f_4679,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_4644,lemma,
! [A] :
( relation(A)
=> ( ( ( relation_dom(A) = empty_set )
| ( relation_rng(A) = empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
tff(f_1827,axiom,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
tff(f_3537,lemma,
! [A] :
( one_sorted_str(A)
=> ( cast_as_carrier_subset(A) = the_carrier(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
tff(f_4204,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_4185,lemma,
! [A,B] : ( set_union2(A,set_difference(B,A)) = set_union2(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
tff(f_4323,lemma,
! [A,B] :
( subset(A,B)
=> ( B = set_union2(A,set_difference(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
tff(f_1604,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
tff(f_4047,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
tff(f_949,axiom,
! [A,B,C] :
( ( C = set_difference(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
tff(f_1005,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,B) = set_difference(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
tff(f_1534,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
tff(c_1504,plain,
( in('#skF_149','#skF_148')
| ~ in('#skF_149',subset_complement(the_carrier('#skF_147'),'#skF_148')) ),
inference(cnfTransformation,[status(thm)],[f_1969]) ).
tff(c_6972,plain,
~ in('#skF_149',subset_complement(the_carrier('#skF_147'),'#skF_148')),
inference(splitLeft,[status(thm)],[c_1504]) ).
tff(c_1502,plain,
~ empty_carrier('#skF_147'),
inference(cnfTransformation,[status(thm)],[f_1969]) ).
tff(c_1500,plain,
one_sorted_str('#skF_147'),
inference(cnfTransformation,[status(thm)],[f_1969]) ).
tff(c_1616,plain,
empty('#skF_163'),
inference(cnfTransformation,[status(thm)],[f_2100]) ).
tff(c_6650,plain,
! [A_4907] : ( relation_rng(identity_relation(A_4907)) = A_4907 ),
inference(cnfTransformation,[status(thm)],[f_4711]) ).
tff(c_1256,plain,
! [A_1208] : relation(identity_relation(A_1208)),
inference(cnfTransformation,[status(thm)],[f_1574]) ).
tff(c_7249,plain,
! [A_5081] :
( ( empty_set = A_5081 )
| ~ empty(A_5081) ),
inference(cnfTransformation,[status(thm)],[f_4679]) ).
tff(c_7276,plain,
empty_set = '#skF_163',
inference(resolution,[status(thm)],[c_1616,c_7249]) ).
tff(c_6616,plain,
! [A_4880] :
( ( relation_rng(A_4880) != empty_set )
| ( empty_set = A_4880 )
| ~ relation(A_4880) ),
inference(cnfTransformation,[status(thm)],[f_4644]) ).
tff(c_230187,plain,
! [A_3932061] :
( ( relation_rng(A_3932061) != '#skF_163' )
| ( A_3932061 = '#skF_163' )
| ~ relation(A_3932061) ),
inference(demodulation,[status(thm),theory(equality)],[c_7276,c_7276,c_6616]) ).
tff(c_230235,plain,
! [A_1208] :
( ( relation_rng(identity_relation(A_1208)) != '#skF_163' )
| ( identity_relation(A_1208) = '#skF_163' ) ),
inference(resolution,[status(thm)],[c_1256,c_230187]) ).
tff(c_231776,plain,
! [A_3932157] :
( ( A_3932157 != '#skF_163' )
| ( identity_relation(A_3932157) = '#skF_163' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6650,c_230235]) ).
tff(c_8120,plain,
! [A_5158] :
( empty(relation_rng(A_5158))
| ~ empty(A_5158) ),
inference(cnfTransformation,[status(thm)],[f_1827]) ).
tff(c_8129,plain,
! [A_4907] :
( empty(A_4907)
| ~ empty(identity_relation(A_4907)) ),
inference(superposition,[status(thm),theory(equality)],[c_6650,c_8120]) ).
tff(c_231788,plain,
! [A_3932157] :
( empty(A_3932157)
| ~ empty('#skF_163')
| ( A_3932157 != '#skF_163' ) ),
inference(superposition,[status(thm),theory(equality)],[c_231776,c_8129]) ).
tff(c_231839,plain,
empty('#skF_163'),
inference(demodulation,[status(thm),theory(equality)],[c_1616,c_231788]) ).
tff(c_8139,plain,
! [A_5161] :
( ( the_carrier(A_5161) = cast_as_carrier_subset(A_5161) )
| ~ one_sorted_str(A_5161) ),
inference(cnfTransformation,[status(thm)],[f_3537]) ).
tff(c_8162,plain,
the_carrier('#skF_147') = cast_as_carrier_subset('#skF_147'),
inference(resolution,[status(thm)],[c_1500,c_8139]) ).
tff(c_1498,plain,
element('#skF_148',powerset(the_carrier('#skF_147'))),
inference(cnfTransformation,[status(thm)],[f_1969]) ).
tff(c_8169,plain,
element('#skF_148',powerset(cast_as_carrier_subset('#skF_147'))),
inference(demodulation,[status(thm),theory(equality)],[c_8162,c_1498]) ).
tff(c_11006,plain,
! [A_5446,B_5447] :
( subset(A_5446,B_5447)
| ~ element(A_5446,powerset(B_5447)) ),
inference(cnfTransformation,[status(thm)],[f_4204]) ).
tff(c_11047,plain,
subset('#skF_148',cast_as_carrier_subset('#skF_147')),
inference(resolution,[status(thm)],[c_8169,c_11006]) ).
tff(c_6428,plain,
! [A_4696,B_4697] : ( set_union2(A_4696,set_difference(B_4697,A_4696)) = set_union2(A_4696,B_4697) ),
inference(cnfTransformation,[status(thm)],[f_4185]) ).
tff(c_6494,plain,
! [A_4761,B_4762] :
( ( set_union2(A_4761,set_difference(B_4762,A_4761)) = B_4762 )
| ~ subset(A_4761,B_4762) ),
inference(cnfTransformation,[status(thm)],[f_4323]) ).
tff(c_6735,plain,
! [A_4761,B_4762] :
( ( set_union2(A_4761,B_4762) = B_4762 )
| ~ subset(A_4761,B_4762) ),
inference(demodulation,[status(thm),theory(equality)],[c_6428,c_6494]) ).
tff(c_11059,plain,
set_union2('#skF_148',cast_as_carrier_subset('#skF_147')) = cast_as_carrier_subset('#skF_147'),
inference(resolution,[status(thm)],[c_11047,c_6735]) ).
tff(c_1280,plain,
! [A_1212,B_1213] :
( ~ empty(set_union2(A_1212,B_1213))
| empty(A_1212) ),
inference(cnfTransformation,[status(thm)],[f_1604]) ).
tff(c_11081,plain,
( ~ empty(cast_as_carrier_subset('#skF_147'))
| empty('#skF_148') ),
inference(superposition,[status(thm),theory(equality)],[c_11059,c_1280]) ).
tff(c_11115,plain,
~ empty(cast_as_carrier_subset('#skF_147')),
inference(splitLeft,[status(thm)],[c_11081]) ).
tff(c_1496,plain,
element('#skF_149',the_carrier('#skF_147')),
inference(cnfTransformation,[status(thm)],[f_1969]) ).
tff(c_8170,plain,
element('#skF_149',cast_as_carrier_subset('#skF_147')),
inference(demodulation,[status(thm),theory(equality)],[c_8162,c_1496]) ).
tff(c_6350,plain,
! [A_4641,B_4642] :
( in(A_4641,B_4642)
| empty(B_4642)
| ~ element(A_4641,B_4642) ),
inference(cnfTransformation,[status(thm)],[f_4047]) ).
tff(c_1510,plain,
( in('#skF_149',subset_complement(the_carrier('#skF_147'),'#skF_148'))
| ~ in('#skF_149','#skF_148') ),
inference(cnfTransformation,[status(thm)],[f_1969]) ).
tff(c_6973,plain,
~ in('#skF_149','#skF_148'),
inference(splitLeft,[status(thm)],[c_1510]) ).
tff(c_228430,plain,
! [D_3930168,A_3930169,B_3930170] :
( in(D_3930168,set_difference(A_3930169,B_3930170))
| in(D_3930168,B_3930170)
| ~ in(D_3930168,A_3930169) ),
inference(cnfTransformation,[status(thm)],[f_949]) ).
tff(c_157575,plain,
! [A_2008809,B_2008810] :
( ( subset_complement(A_2008809,B_2008810) = set_difference(A_2008809,B_2008810) )
| ~ element(B_2008810,powerset(A_2008809)) ),
inference(cnfTransformation,[status(thm)],[f_1005]) ).
tff(c_157677,plain,
subset_complement(cast_as_carrier_subset('#skF_147'),'#skF_148') = set_difference(cast_as_carrier_subset('#skF_147'),'#skF_148'),
inference(resolution,[status(thm)],[c_8169,c_157575]) ).
tff(c_8168,plain,
~ in('#skF_149',subset_complement(cast_as_carrier_subset('#skF_147'),'#skF_148')),
inference(demodulation,[status(thm),theory(equality)],[c_8162,c_6972]) ).
tff(c_157717,plain,
~ in('#skF_149',set_difference(cast_as_carrier_subset('#skF_147'),'#skF_148')),
inference(demodulation,[status(thm),theory(equality)],[c_157677,c_8168]) ).
tff(c_228457,plain,
( in('#skF_149','#skF_148')
| ~ in('#skF_149',cast_as_carrier_subset('#skF_147')) ),
inference(resolution,[status(thm)],[c_228430,c_157717]) ).
tff(c_228720,plain,
~ in('#skF_149',cast_as_carrier_subset('#skF_147')),
inference(negUnitSimplification,[status(thm)],[c_6973,c_228457]) ).
tff(c_228798,plain,
( empty(cast_as_carrier_subset('#skF_147'))
| ~ element('#skF_149',cast_as_carrier_subset('#skF_147')) ),
inference(resolution,[status(thm)],[c_6350,c_228720]) ).
tff(c_228803,plain,
empty(cast_as_carrier_subset('#skF_147')),
inference(demodulation,[status(thm),theory(equality)],[c_8170,c_228798]) ).
tff(c_228805,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11115,c_228803]) ).
tff(c_228807,plain,
empty(cast_as_carrier_subset('#skF_147')),
inference(splitRight,[status(thm)],[c_11081]) ).
tff(c_6638,plain,
! [A_4896] :
( ( empty_set = A_4896 )
| ~ empty(A_4896) ),
inference(cnfTransformation,[status(thm)],[f_4679]) ).
tff(c_7283,plain,
! [A_4896] :
( ( A_4896 = '#skF_163' )
| ~ empty(A_4896) ),
inference(demodulation,[status(thm),theory(equality)],[c_7276,c_6638]) ).
tff(c_228860,plain,
cast_as_carrier_subset('#skF_147') = '#skF_163',
inference(resolution,[status(thm)],[c_228807,c_7283]) ).
tff(c_228867,plain,
the_carrier('#skF_147') = '#skF_163',
inference(demodulation,[status(thm),theory(equality)],[c_228860,c_8162]) ).
tff(c_231973,plain,
! [A_3932162] :
( ~ empty(the_carrier(A_3932162))
| ~ one_sorted_str(A_3932162)
| empty_carrier(A_3932162) ),
inference(cnfTransformation,[status(thm)],[f_1534]) ).
tff(c_231979,plain,
( ~ empty('#skF_163')
| ~ one_sorted_str('#skF_147')
| empty_carrier('#skF_147') ),
inference(superposition,[status(thm),theory(equality)],[c_228867,c_231973]) ).
tff(c_231991,plain,
empty_carrier('#skF_147'),
inference(demodulation,[status(thm),theory(equality)],[c_1500,c_231839,c_231979]) ).
tff(c_231993,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1502,c_231991]) ).
tff(c_231994,plain,
in('#skF_149',subset_complement(the_carrier('#skF_147'),'#skF_148')),
inference(splitRight,[status(thm)],[c_1510]) ).
tff(c_231996,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6972,c_231994]) ).
tff(c_231997,plain,
in('#skF_149','#skF_148'),
inference(splitRight,[status(thm)],[c_1504]) ).
tff(c_231999,plain,
~ in('#skF_149','#skF_148'),
inference(splitLeft,[status(thm)],[c_1510]) ).
tff(c_232001,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_231997,c_231999]) ).
tff(c_232003,plain,
in('#skF_149','#skF_148'),
inference(splitRight,[status(thm)],[c_1510]) ).
tff(c_233329,plain,
! [A_3932341] :
( ( the_carrier(A_3932341) = cast_as_carrier_subset(A_3932341) )
| ~ one_sorted_str(A_3932341) ),
inference(cnfTransformation,[status(thm)],[f_3537]) ).
tff(c_233352,plain,
the_carrier('#skF_147') = cast_as_carrier_subset('#skF_147'),
inference(resolution,[status(thm)],[c_1500,c_233329]) ).
tff(c_233360,plain,
element('#skF_148',powerset(cast_as_carrier_subset('#skF_147'))),
inference(demodulation,[status(thm),theory(equality)],[c_233352,c_1498]) ).
tff(c_422294,plain,
! [A_6152243,B_6152244] :
( ( subset_complement(A_6152243,B_6152244) = set_difference(A_6152243,B_6152244) )
| ~ element(B_6152244,powerset(A_6152243)) ),
inference(cnfTransformation,[status(thm)],[f_1005]) ).
tff(c_422399,plain,
subset_complement(cast_as_carrier_subset('#skF_147'),'#skF_148') = set_difference(cast_as_carrier_subset('#skF_147'),'#skF_148'),
inference(resolution,[status(thm)],[c_233360,c_422294]) ).
tff(c_231998,plain,
in('#skF_149',subset_complement(the_carrier('#skF_147'),'#skF_148')),
inference(splitRight,[status(thm)],[c_1504]) ).
tff(c_233359,plain,
in('#skF_149',subset_complement(cast_as_carrier_subset('#skF_147'),'#skF_148')),
inference(demodulation,[status(thm),theory(equality)],[c_233352,c_231998]) ).
tff(c_422464,plain,
in('#skF_149',set_difference(cast_as_carrier_subset('#skF_147'),'#skF_148')),
inference(demodulation,[status(thm),theory(equality)],[c_422399,c_233359]) ).
tff(c_786,plain,
! [D_771,B_767,A_766] :
( ~ in(D_771,B_767)
| ~ in(D_771,set_difference(A_766,B_767)) ),
inference(cnfTransformation,[status(thm)],[f_949]) ).
tff(c_423008,plain,
~ in('#skF_149','#skF_148'),
inference(resolution,[status(thm)],[c_422464,c_786]) ).
tff(c_423046,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_232003,c_423008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU321+2 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:48:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 185.06/152.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 185.15/152.92
% 185.15/152.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------