0.00/0.00 % Leo-III: Strategy 1 (for '60') 38.11/11.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 38.11/11.95 % [INFO] Parsing done (322ms). 38.11/11.95 % [INFO] Running in sequential loop mode. 38.11/11.95 % [CONFIG] Using configuration: timeout(60) with strategy 38.11/11.95 % [INFO] eprover registered as external prover. 38.11/11.95 % [INFO] cvc4 registered as external prover. 38.11/11.95 % [INFO] Parsing finished. Scanning for conjecture ... 38.11/11.95 % [INFO] Found a conjecture and 353 axioms. Running axiom selection ... 38.11/11.95 % [INFO] Axiom selection finished. Selected 263 axioms (removed 90 axioms). 38.11/11.95 % [INFO] Problem is higher-order (TPTP THF). 38.11/11.95 % [INFO] Type checking passed. Searching for refutation ... 38.11/11.95 % External prover 'e' found a proof! 38.11/11.95 % [INFO] Killing All external provers ... 38.11/11.95 % Time passed: 8284ms (effective reasoning time: 7487ms) 38.11/11.95 % Solved by strategy 38.11/11.95 % Axioms used in derivation (263): fact_23_image__vimage__eq, fact_321_range__composition, fact_4_assms_I1_J, fact_179_is__num__normalize_I1_J, fact_127_Diff__Int__distrib2, fact_345_UN__E, fact_180_UNIV__witness, fact_256_range__eqI, fact_85_bex__UN, fact_114_null__sets_OInt__space__eq2, fact_1__092_060open_062_092_060And_062a_O_AT_H_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_35_surj__plus, fact_172_imageI, fact_226_Compr__image__eq, fact_160_ball__imageD, fact_0_emeasure__T_H, fact_22_image__vimage__eq, fact_19_null__setsI, fact_222_Inf_OINF__identity__eq, fact_281_surjE, fact_277_surjI, fact_164_image__cong, fact_234_image__image, fact_285_surjE, fact_195_IntD2, fact_163_image__cong, fact_312_vimage__inter__cong, fact_56_Union__iff, fact_73_image__ident, fact_313_translation__subtract__diff, fact_291_surjD, fact_39_image__eqI, fact_6_T__Int, fact_320_range__composition, fact_130_Diff__Int2, fact_89_UN__ball__bex__simps_I4_J, fact_235_image__image, fact_75_vimage__ident, fact_326_rangeE, fact_15_R__Int, fact_201_IntE, fact_314_range__composition, fact_96_null__sets_OInt, fact_34_surj__plus, fact_198_IntD1, fact_51_IntI, fact_126_top__set__def, fact_117_in__sets__SUP, fact_138_null__sets_Osets__Collect__conj, fact_131_Int__Diff, fact_286_surjE, fact_280_surjE, fact_261_surj__def, fact_324_rangeE, fact_18_null__sets__UN, fact_116_in__sets__SUP, fact_11_f__def, fact_257_range__eqI, fact_33_Sup__eq__top__iff, fact_31_Sup__UNIV, fact_316_range__composition, fact_50_Int__iff, fact_323_rangeE, fact_77_Int__UNIV, fact_191_Int__absorb, fact_140_null__set__Diff, fact_61_UN__ball__bex__simps_I3_J, fact_173_imageI, fact_86_bex__UN, fact_171_image__iff, fact_125_top__set__def, fact_351_UN__extend__simps_I8_J, fact_224_Compr__image__eq, fact_297_SUP__cong, fact_302_Int__UNIV__right, fact_199_IntE, fact_143_vimage__Union, fact_182_UNIV__witness, fact_305_Int__UNIV__left, fact_238_imageE, fact_60_UN__ball__bex__simps_I1_J, fact_67_vimage__eq, fact_350_UN__extend__simps_I8_J, fact_124_space__Sup__eq__UN, fact_72_vimageI, fact_167_bex__imageD, fact_237_imageE, fact_331_SUP__commute, fact_97_vimage__Int, fact_144_UN__extend__simps_I6_J, fact_225_Compr__image__eq, fact_98_SUP__identity__eq, fact_139_translation__diff, fact_99_SUP__identity__eq, fact_340_UN__UN__flatten, fact_46_UNIV__I, fact_307_Int__UNIV__left, fact_346_UN__E, fact_311_null__setsD2, fact_254_less__numeral__extra_I3_J, fact_338_UN__UN__flatten, fact_223_Compr__image__eq, fact_262_surj__def, fact_161_ball__imageD, fact_306_Int__UNIV__left, fact_53_IntI, fact_190_Int__commute, fact_149_Sup_OSUP__cong, fact_91_vimage__UNIV, fact_336_UN__UN__flatten, fact_141_Int__Union2, fact_94_vimage__UNIV, fact_284_surjE, fact_205_vimage__Collect, fact_148_Sup_OSUP__cong, fact_221_Sup_OSUP__identity__eq, fact_220_vimageD, fact_155_rev__image__eqI, fact_317_range__composition, fact_13_of__int__vec__eq__iff, fact_48_Int__iff, fact_271_rangeI, fact_339_UN__UN__flatten, fact_9__092_060open_062_I_092_060lambda_062n_O_Aemeasure_Alebesgue_A_IT_A_If_An_J_J_J_Asums_Aemeasure_Alebesgue_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062, fact_276_surjI, fact_132_vimage__Diff, fact_259_range__eqI, fact_74_vimage__Collect__eq, fact_322_range__composition, fact_268_rangeI, fact_266_surj__def, fact_5_emeasure__T__Int, fact_120_sets__SUP__cong, fact_62_null__sets_ODiff, fact_28__092_060open_062_092_060Union_062_A_Irange_AT_J_A_061_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062, fact_174_imageI, fact_335_UN__UN__flatten, fact_79_ball__UN, fact_8__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_294_less__Sup__iff, fact_231_image__image, fact_283_surjE, fact_189_Int__left__absorb, fact_168_bex__imageD, fact_150_Inf_OINF__cong, fact_337_UN__UN__flatten, fact_267_surj__def, fact_112_image__add__0, fact_119_sets__SUP__cong, fact_292_surjD, fact_36_diff__numeral__special_I9_J, fact_38_image__eqI, fact_107_UN__I, fact_239_imageE, fact_204_UnionE, fact_279_surjI, fact_184_UNIV__eq__I, fact_347_UN__E, fact_20_image__vimage__eq, fact_24_image__vimage__eq, fact_186_UNIV__eq__I, fact_10_T_H__def, fact_187_UNIV__eq__I, fact_109_UN__I, fact_264_surj__def, fact_273_surjI, fact_128_Diff__Int__distrib, fact_196_IntD1, fact_328_SUP__commute, fact_147_Sup_OSUP__cong, fact_78_Int__UNIV, fact_95_vimage__UNIV, fact_92_vimage__UNIV, fact_3_calculation, fact_296_SUP__cong, fact_111_S__decompose, fact_247_Int__Collect, fact_188_Int__left__commute, fact_253_vimage__def, fact_315_range__composition, fact_40_image__eqI, fact_47_UNIV__I, fact_102_UN__iff, fact_108_UN__I, fact_290_surjD, fact_334_image__Union, fact_282_surjE, fact_162_ball__imageD, fact_319_range__composition, fact_113_image__add__0, fact_80_ball__UN, fact_318_range__composition, fact_115_null__sets_OInt__space__eq1, fact_252_Int__def, fact_293_surjD, fact_275_surjI, fact_37_image__eqI, fact_25__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_59_UnionI, fact_152_Inf_OINF__cong, fact_329_SUP__commute, fact_295_SUP__cong, fact_26_surj__diff__right, fact_193_IntD2, fact_154_rev__image__eqI, fact_170_image__iff, fact_12_T_H__altdef, fact_166_bex__imageD, fact_215_vimageE, fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_349_UN__extend__simps_I8_J, fact_101_UN__iff, fact_255_less__numeral__extra_I4_J, fact_210_vimageI2, fact_298_SUP__cong, fact_88_UN__ball__bex__simps_I2_J, fact_250_Int__def, fact_151_Inf_OINF__cong, fact_17_null__sets__UN, fact_289_surjD, fact_129_Diff__Diff__Int, fact_169_image__iff, fact_310_Union__UNIV, fact_81_mem__Collect__eq, fact_83_Collect__mem__eq, fact_145_UN__extend__simps_I6_J, fact_135_null__sets_Osets__Collect__disj, fact_76_Int__UNIV, fact_230_image__image, fact_87_UN__ball__bex__simps_I2_J, fact_27_surj__diff__right, fact_233_image__image, fact_303_Int__UNIV__right, fact_44_UNIV__I, fact_269_rangeI, fact_153_rev__image__eqI, fact_263_surj__def, fact_330_SUP__commute, fact_14_T__def, fact_265_surj__def, fact_304_Int__UNIV__right, fact_287_surjD, fact_146_emeasure__Diff__null__set, fact_240_imageE, fact_249_Int__Collect, fact_236_image__image, fact_16_sums__emeasure_H, fact_232_image__image, fact_288_surjD, fact_175_imageI, fact_142_Int__Union, fact_7_assms_I2_J, fact_246_Collect__conj__eq, fact_21_image__vimage__eq, fact_183_UNIV__witness, fact_278_surjI, fact_274_surjI, fact_165_image__cong, fact_192_Int__assoc, fact_156_rev__image__eqI, fact_90_UN__ball__bex__simps_I4_J, fact_118_in__sets__Sup, fact_93_vimage__UNIV 38.11/11.95 % No. of inferences in proof: 574 38.11/11.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8284 ms resp. 7487 ms w/o parsing 38.11/11.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 38.11/11.95 thf(sigma_1422848389real_n_type, type, sigma_1422848389real_n: $tType). 38.11/11.95 thf(set_Si1125517487real_n_type, type, set_Si1125517487real_n: $tType). 38.11/11.95 thf(set_se820660888real_n_type, type, set_se820660888real_n: $tType). 38.11/11.95 thf(sigma_1466784463real_n_type, type, sigma_1466784463real_n: $tType). 38.11/11.95 thf(set_se2111327970real_n_type, type, set_se2111327970real_n: $tType). 38.11/11.95 thf(set_se944069346_int_n_type, type, set_se944069346_int_n: $tType). 38.11/11.95 thf(set_Fi1058188332real_n_type, type, set_Fi1058188332real_n: $tType). 38.11/11.95 thf(set_Fi160064172_int_n_type, type, set_Fi160064172_int_n: $tType). 38.11/11.95 thf(finite1489363574real_n_type, type, finite1489363574real_n: $tType). 38.11/11.95 thf(finite964658038_int_n_type, type, finite964658038_int_n: $tType). 38.11/11.95 thf(set_Ex113815278nnreal_type, type, set_Ex113815278nnreal: $tType). 38.11/11.95 thf(set_set_nat_type, type, set_set_nat: $tType). 38.11/11.95 thf(extend1728876344nnreal_type, type, extend1728876344nnreal: $tType). 38.11/11.95 thf(sigma_measure_o_type, type, sigma_measure_o: $tType). 38.11/11.95 thf(set_set_o_type, type, set_set_o: $tType). 38.11/11.95 thf(set_nat_type, type, set_nat: $tType). 38.11/11.95 thf(set_o_type, type, set_o: $tType). 38.11/11.95 thf(nat_type, type, nat: $tType). 38.11/11.95 thf(comple1413366923nnreal_type, type, comple1413366923nnreal: (set_Ex113815278nnreal > extend1728876344nnreal)). 38.11/11.95 thf(comple2042271945real_n_type, type, comple2042271945real_n: (set_Fi1058188332real_n > finite1489363574real_n)). 38.11/11.95 thf(comple970917503_int_n_type, type, comple970917503_int_n: (set_se944069346_int_n > set_Fi160064172_int_n)). 38.11/11.95 thf(comple825005695real_n_type, type, comple825005695real_n: (set_se2111327970real_n > set_Fi1058188332real_n)). 38.11/11.95 thf(comple1682161881et_nat_type, type, comple1682161881et_nat: (set_set_nat > set_nat)). 38.11/11.95 thf(comple488165692real_n_type, type, comple488165692real_n: (set_Si1125517487real_n > sigma_1466784463real_n)). 38.11/11.95 thf(comple230862828real_n_type, type, comple230862828real_n: (sigma_1466784463real_n > sigma_1466784463real_n)). 38.11/11.95 thf(counta1142393929_int_n_type, type, counta1142393929_int_n: (set_Fi160064172_int_n > (nat > finite964658038_int_n))). 38.11/11.95 thf(minus_1196255695_int_n_type, type, minus_1196255695_int_n: (finite964658038_int_n > (finite964658038_int_n > finite964658038_int_n))). 38.11/11.95 thf(minus_1037315151real_n_type, type, minus_1037315151real_n: (finite1489363574real_n > (finite1489363574real_n > finite1489363574real_n))). 38.11/11.95 thf(minus_1686442501real_n_type, type, minus_1686442501real_n: (set_Fi1058188332real_n > (set_Fi1058188332real_n > set_Fi1058188332real_n))). 38.11/11.95 thf(one_on705384445nnreal_type, type, one_on705384445nnreal: extend1728876344nnreal). 38.11/11.95 thf(one_on1253059131real_n_type, type, one_on1253059131real_n: finite1489363574real_n). 38.11/11.95 thf(plus_p1763960001nnreal_type, type, plus_p1763960001nnreal: (extend1728876344nnreal > (extend1728876344nnreal > extend1728876344nnreal))). 38.11/11.95 thf(plus_p1654784127_int_n_type, type, plus_p1654784127_int_n: (finite964658038_int_n > (finite964658038_int_n > finite964658038_int_n))). 38.11/11.95 thf(plus_p585657087real_n_type, type, plus_p585657087real_n: (finite1489363574real_n > (finite1489363574real_n > finite1489363574real_n))). 38.11/11.95 thf(zero_z1963244097nnreal_type, type, zero_z1963244097nnreal: extend1728876344nnreal). 38.11/11.95 thf(zero_z200130687real_n_type, type, zero_z200130687real_n: finite1489363574real_n). 38.11/11.95 thf(inf_in1108485182_int_n_type, type, inf_in1108485182_int_n: (set_Fi160064172_int_n > (set_Fi160064172_int_n > set_Fi160064172_int_n))). 38.11/11.95 thf(inf_in1974387902real_n_type, type, inf_in1974387902real_n: (set_Fi1058188332real_n > (set_Fi1058188332real_n > set_Fi1058188332real_n))). 38.11/11.95 thf(inf_inf_set_nat_type, type, inf_inf_set_nat: (set_nat > (set_nat > set_nat))). 38.11/11.95 thf(inf_in632889204real_n_type, type, inf_in632889204real_n: (set_se2111327970real_n > (set_se2111327970real_n > set_se2111327970real_n))). 38.11/11.95 thf(lebesg260170249real_n_type, type, lebesg260170249real_n: sigma_1466784463real_n). 38.11/11.95 thf(measur1402256771real_n_type, type, measur1402256771real_n: (sigma_1466784463real_n > set_se2111327970real_n)). 38.11/11.95 thf(minkow1134813771n_real_type, type, minkow1134813771n_real: (finite964658038_int_n > finite1489363574real_n)). 38.11/11.95 thf(ord_le2133614988nnreal_type, type, ord_le2133614988nnreal: (extend1728876344nnreal > (extend1728876344nnreal > $o))). 38.11/11.95 thf(top_to287930409nt_n_o_type, type, top_to287930409nt_n_o: (finite964658038_int_n > $o)). 38.11/11.95 thf(top_top_nat_o_type, type, top_top_nat_o: (nat > $o)). 38.11/11.95 thf(top_to1845833192nnreal_type, type, top_to1845833192nnreal: extend1728876344nnreal). 38.11/11.95 thf(top_to131672412_int_n_type, type, top_to131672412_int_n: set_Fi160064172_int_n). 38.11/11.95 thf(top_to1292442332real_n_type, type, top_to1292442332real_n: set_Fi1058188332real_n). 38.11/11.95 thf(top_top_set_nat_type, type, top_top_set_nat: set_nat). 38.11/11.95 thf(top_to20708754real_n_type, type, top_to20708754real_n: set_se2111327970real_n). 38.11/11.95 thf(sums_E1192373732nnreal_type, type, sums_E1192373732nnreal: ((nat > extend1728876344nnreal) > (extend1728876344nnreal > $o))). 38.11/11.95 thf(collec1941932235_int_n_type, type, collec1941932235_int_n: ((finite964658038_int_n > $o) > set_Fi160064172_int_n)). 38.11/11.95 thf(collec321817931real_n_type, type, collec321817931real_n: ((finite1489363574real_n > $o) > set_Fi1058188332real_n)). 38.11/11.95 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 38.11/11.95 thf(collec452821761real_n_type, type, collec452821761real_n: ((set_Fi1058188332real_n > $o) > set_se2111327970real_n)). 38.11/11.95 thf(image_1599934780real_n_type, type, image_1599934780real_n: (($o > sigma_1466784463real_n) > (set_o > set_Si1125517487real_n))). 38.11/11.95 thf(image_2066995319nnreal_type, type, image_2066995319nnreal: ((extend1728876344nnreal > extend1728876344nnreal) > (set_Ex113815278nnreal > set_Ex113815278nnreal))). 38.11/11.95 thf(image_1278151539_int_n_type, type, image_1278151539_int_n: ((finite964658038_int_n > finite964658038_int_n) > (set_Fi160064172_int_n > set_Fi160064172_int_n))). 38.11/11.95 thf(image_2058828787real_n_type, type, image_2058828787real_n: ((finite964658038_int_n > finite1489363574real_n) > (set_Fi160064172_int_n > set_Fi1058188332real_n))). 38.11/11.95 thf(image_497739341_n_nat_type, type, image_497739341_n_nat: ((finite964658038_int_n > nat) > (set_Fi160064172_int_n > set_nat))). 38.11/11.95 thf(image_1819506345_int_n_type, type, image_1819506345_int_n: ((finite964658038_int_n > set_Fi160064172_int_n) > (set_Fi160064172_int_n > set_se944069346_int_n))). 38.11/11.95 thf(image_355963305real_n_type, type, image_355963305real_n: ((finite964658038_int_n > set_Fi1058188332real_n) > (set_Fi160064172_int_n > set_se2111327970real_n))). 38.11/11.95 thf(image_1085873667et_nat_type, type, image_1085873667et_nat: ((finite964658038_int_n > set_nat) > (set_Fi160064172_int_n > set_set_nat))). 38.11/11.95 thf(image_439535603real_n_type, type, image_439535603real_n: ((finite1489363574real_n > finite1489363574real_n) > (set_Fi1058188332real_n > set_Fi1058188332real_n))). 38.11/11.95 thf(image_545463721real_n_type, type, image_545463721real_n: ((finite1489363574real_n > set_Fi1058188332real_n) > (set_Fi1058188332real_n > set_se2111327970real_n))). 38.11/11.95 thf(image_1961920973_int_n_type, type, image_1961920973_int_n: ((nat > finite964658038_int_n) > (set_nat > set_Fi160064172_int_n))). 38.11/11.95 thf(image_183184717real_n_type, type, image_183184717real_n: ((nat > finite1489363574real_n) > (set_nat > set_Fi1058188332real_n))). 38.11/11.95 thf(image_nat_nat_type, type, image_nat_nat: ((nat > nat) > (set_nat > set_nat))). 38.11/11.95 thf(image_968789251_int_n_type, type, image_968789251_int_n: ((nat > set_Fi160064172_int_n) > (set_nat > set_se944069346_int_n))). 38.11/11.95 thf(image_1856576259real_n_type, type, image_1856576259real_n: ((nat > set_Fi1058188332real_n) > (set_nat > set_se2111327970real_n))). 38.11/11.95 thf(image_nat_set_nat_type, type, image_nat_set_nat: ((nat > set_nat) > (set_nat > set_set_nat))). 38.11/11.95 thf(image_792439519real_n_type, type, image_792439519real_n: ((set_Fi160064172_int_n > set_Fi1058188332real_n) > (set_se944069346_int_n > set_se2111327970real_n))). 38.11/11.95 thf(image_1661509983real_n_type, type, image_1661509983real_n: ((set_Fi1058188332real_n > set_Fi1058188332real_n) > (set_se2111327970real_n > set_se2111327970real_n))). 38.11/11.95 thf(image_987430492real_n_type, type, image_987430492real_n: ((set_Fi1058188332real_n > sigma_1466784463real_n) > (set_se2111327970real_n > set_Si1125517487real_n))). 38.11/11.95 thf(image_933134521real_n_type, type, image_933134521real_n: ((set_nat > set_Fi1058188332real_n) > (set_set_nat > set_se2111327970real_n))). 38.11/11.95 thf(image_1298280374real_n_type, type, image_1298280374real_n: ((sigma_1466784463real_n > set_Fi1058188332real_n) > (set_Si1125517487real_n > set_se2111327970real_n))). 38.11/11.95 thf(vimage1122713129_int_n_type, type, vimage1122713129_int_n: ((finite964658038_int_n > finite964658038_int_n) > (set_Fi160064172_int_n > set_Fi160064172_int_n))). 38.11/11.95 thf(vimage1276736425real_n_type, type, vimage1276736425real_n: ((finite964658038_int_n > finite1489363574real_n) > (set_Fi1058188332real_n > set_Fi160064172_int_n))). 38.11/11.95 thf(vimage1398021123_n_nat_type, type, vimage1398021123_n_nat: ((finite964658038_int_n > nat) > (set_nat > set_Fi160064172_int_n))). 38.11/11.95 thf(vimage464515423real_n_type, type, vimage464515423real_n: ((finite964658038_int_n > set_Fi1058188332real_n) > (set_se2111327970real_n > set_Fi160064172_int_n))). 38.11/11.95 thf(vimage1233683625real_n_type, type, vimage1233683625real_n: ((finite1489363574real_n > finite1489363574real_n) > (set_Fi1058188332real_n > set_Fi1058188332real_n))). 38.11/11.95 thf(vimage714719107_int_n_type, type, vimage714719107_int_n: ((nat > finite964658038_int_n) > (set_Fi160064172_int_n > set_nat))). 38.11/11.95 thf(vimage1860757507real_n_type, type, vimage1860757507real_n: ((nat > finite1489363574real_n) > (set_Fi1058188332real_n > set_nat))). 38.11/11.95 thf(vimage_nat_nat_type, type, vimage_nat_nat: ((nat > nat) > (set_nat > set_nat))). 38.11/11.95 thf(vimage3210681real_n_type, type, vimage3210681real_n: ((nat > set_Fi1058188332real_n) > (set_se2111327970real_n > set_nat))). 38.11/11.95 thf(sigma_1536574303real_n_type, type, sigma_1536574303real_n: (sigma_1466784463real_n > (set_Fi1058188332real_n > extend1728876344nnreal))). 38.11/11.95 thf(sigma_1235138647real_n_type, type, sigma_1235138647real_n: (sigma_1466784463real_n > set_se2111327970real_n)). 38.11/11.95 thf(sigma_476185326real_n_type, type, sigma_476185326real_n: (sigma_1466784463real_n > set_Fi1058188332real_n)). 38.11/11.95 thf(member_o_type, type, member_o: ($o > (set_o > $o))). 38.11/11.95 thf(member1217042383nnreal_type, type, member1217042383nnreal: (extend1728876344nnreal > (set_Ex113815278nnreal > $o))). 38.11/11.95 thf(member27055245_int_n_type, type, member27055245_int_n: (finite964658038_int_n > (set_Fi160064172_int_n > $o))). 38.11/11.95 thf(member1352538125real_n_type, type, member1352538125real_n: (finite1489363574real_n > (set_Fi1058188332real_n > $o))). 38.11/11.95 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 38.11/11.95 thf(member223413699real_n_type, type, member223413699real_n: (set_Fi1058188332real_n > (set_se2111327970real_n > $o))). 38.11/11.95 thf(member1000184real_n_type, type, member1000184real_n: (sigma_1466784463real_n > (set_Si1125517487real_n > $o))). 38.11/11.95 thf(r_type, type, r: (finite964658038_int_n > set_Fi1058188332real_n)). 38.11/11.95 thf(s_type, type, s: set_Fi1058188332real_n). 38.11/11.95 thf(t_type, type, t: (finite964658038_int_n > set_Fi1058188332real_n)). 38.11/11.95 thf(t2_type, type, t2: (finite964658038_int_n > set_Fi1058188332real_n)). 38.11/11.95 thf(f_type, type, f: (nat > finite964658038_int_n)). 38.11/11.95 thf(sk53_type, type, sk53: (set_Fi1058188332real_n > (set_Si1125517487real_n > sigma_1466784463real_n))). 38.11/11.95 thf(sk71_type, type, sk71: nat). 38.11/11.95 thf(sk72_type, type, sk72: nat). 38.11/11.95 thf(180,axiom,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member223413699real_n @ A @ (image_355963305real_n @ B @ top_to131672412_int_n)) => (~ (! [C:finite964658038_int_n]: (A != (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_rangeE)). 38.11/11.95 thf(892,plain,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member223413699real_n @ A @ (image_355963305real_n @ (B) @ top_to131672412_int_n)) => (~ (! [C:finite964658038_int_n]: ~ (A = (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 38.11/11.95 thf(144,axiom,((! [A:set_se2111327970real_n,B:(set_Fi1058188332real_n > sigma_1466784463real_n),C:(set_Fi1058188332real_n > sigma_1466784463real_n)]: (((sigma_1235138647real_n @ (comple488165692real_n @ (image_987430492real_n @ B @ A))) = (sigma_1235138647real_n @ (comple488165692real_n @ (image_987430492real_n @ C @ A)))) <= (! [D:set_Fi1058188332real_n]: (((sigma_1235138647real_n @ (B @ D)) = (sigma_1235138647real_n @ (C @ D))) <= (member223413699real_n @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_sets__SUP__cong)). 38.11/11.95 thf(760,plain,((! [A:set_se2111327970real_n,B:(set_Fi1058188332real_n > sigma_1466784463real_n),C:(set_Fi1058188332real_n > sigma_1466784463real_n)]: (((sigma_1235138647real_n @ (comple488165692real_n @ (image_987430492real_n @ (B) @ A))) = (sigma_1235138647real_n @ (comple488165692real_n @ (image_987430492real_n @ (C) @ A)))) | ~ (! [D:set_Fi1058188332real_n]: (((sigma_1235138647real_n @ (B @ D)) = (sigma_1235138647real_n @ (C @ D))) | ~ (member223413699real_n @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 38.11/11.95 thf(63,axiom,((! [A:finite1489363574real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_355963305real_n @ B @ C))) = (? [D:finite964658038_int_n]: ((member1352538125real_n @ A @ (B @ D)) & (member27055245_int_n @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_UN__iff)). 38.11/11.95 thf(479,plain,((! [A:finite1489363574real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_355963305real_n @ (B) @ C))) = (? [D:finite964658038_int_n]: ((member1352538125real_n @ A @ (B @ D)) & (member27055245_int_n @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 38.11/11.95 thf(246,axiom,((t = (^ [A:finite964658038_int_n]: (image_439535603real_n @ (^ [B:finite1489363574real_n]: (minus_1037315151real_n @ B @ (minkow1134813771n_real @ A))) @ (t2 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_T_H__def)). 38.11/11.95 thf(1105,plain,(((t) = (^ [A:finite964658038_int_n]: (image_439535603real_n @ (^ [B:finite1489363574real_n]: (minus_1037315151real_n @ B @ (minkow1134813771n_real @ A))) @ (t2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 38.11/11.95 thf(238,axiom,((! [A:(nat > set_Fi1058188332real_n),B:(finite964658038_int_n > nat)]: ((image_355963305real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_1856576259real_n @ A @ (image_497739341_n_nat @ B @ top_to131672412_int_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_range__composition)). 38.11/11.95 thf(1083,plain,((! [A:(nat > set_Fi1058188332real_n),B:(finite964658038_int_n > nat)]: ((image_355963305real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_1856576259real_n @ (A) @ (image_497739341_n_nat @ (B) @ top_to131672412_int_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 38.11/11.95 thf(60,axiom,((! [A:set_o,B:($o > sigma_1466784463real_n),C:($o > sigma_1466784463real_n)]: ((! [D:$o]: (((sigma_1235138647real_n @ (B @ D)) = (sigma_1235138647real_n @ (C @ D))) <= (member_o @ D @ A))) => ((sigma_1235138647real_n @ (comple488165692real_n @ (image_1599934780real_n @ B @ A))) = (sigma_1235138647real_n @ (comple488165692real_n @ (image_1599934780real_n @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_sets__SUP__cong)). 38.11/11.95 thf(468,plain,((! [A:set_o,B:($o > sigma_1466784463real_n),C:($o > sigma_1466784463real_n)]: ((! [D:$o]: (((sigma_1235138647real_n @ (B @ D)) = (sigma_1235138647real_n @ (C @ D))) | ~ (member_o @ D @ A))) => ((sigma_1235138647real_n @ (comple488165692real_n @ (image_1599934780real_n @ (B) @ A))) = (sigma_1235138647real_n @ (comple488165692real_n @ (image_1599934780real_n @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 38.11/11.95 thf(74,axiom,((? [A:nat]: (member_nat @ A @ top_top_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_UNIV__witness)). 38.11/11.95 thf(523,plain,((? [A:nat]: (member_nat @ A @ top_top_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 38.11/11.95 thf(6,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > $o)]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ (collec452821761real_n @ C))) = ((member223413699real_n @ A @ B) & (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Int__Collect)). 38.11/11.95 thf(276,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > $o)]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ (collec452821761real_n @ (C)))) = ((member223413699real_n @ A @ B) & (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 38.11/11.95 thf(212,axiom,((! [A:(finite964658038_int_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((image_2058828787real_n @ A @ (vimage1276736425real_n @ A @ B)) = (inf_in1974387902real_n @ B @ (image_2058828787real_n @ A @ top_to131672412_int_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_image__vimage__eq)). 38.11/11.95 thf(994,plain,((! [A:(finite964658038_int_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((image_2058828787real_n @ (A) @ (vimage1276736425real_n @ (A) @ B)) = (inf_in1974387902real_n @ B @ (image_2058828787real_n @ (A) @ top_to131672412_int_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 38.11/11.95 thf(175,axiom,((! [A:(finite1489363574real_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_545463721real_n @ A @ (comple825005695real_n @ (image_355963305real_n @ B @ C)))) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_545463721real_n @ A @ (B @ D)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_UN__UN__flatten)). 38.11/11.95 thf(873,plain,((! [A:(finite1489363574real_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_545463721real_n @ (A) @ (comple825005695real_n @ (image_355963305real_n @ (B) @ C)))) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_545463721real_n @ A @ (B @ D)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 38.11/11.95 thf(261,axiom,((! [A:finite964658038_int_n,B:finite964658038_int_n]: ((A != B) => (member223413699real_n @ (inf_in1974387902real_n @ (t2 @ A) @ (t2 @ B)) @ (measur1402256771real_n @ (comple230862828real_n @ lebesg260170249real_n)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_T__Int)). 38.11/11.95 thf(1142,plain,((! [A:finite964658038_int_n,B:finite964658038_int_n]: ((~ (A = B)) => (member223413699real_n @ (inf_in1974387902real_n @ (t2 @ A) @ (t2 @ B)) @ (measur1402256771real_n @ (comple230862828real_n @ lebesg260170249real_n)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 38.11/11.95 thf(38,axiom,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((image_1661509983real_n @ A @ (image_355963305real_n @ B @ C)) = (image_355963305real_n @ (^ [D:finite964658038_int_n]: (A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_image__image)). 38.11/11.95 thf(384,plain,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((image_1661509983real_n @ (A) @ (image_355963305real_n @ (B) @ C)) = (image_355963305real_n @ (^ [D:finite964658038_int_n]: (A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 38.11/11.95 thf(258,axiom,((f = (counta1142393929_int_n @ top_to131672412_int_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f__def)). 38.11/11.95 thf(1136,plain,(((f) = (counta1142393929_int_n @ top_to131672412_int_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 38.11/11.95 thf(1137,plain,(((counta1142393929_int_n @ top_to131672412_int_n) = (f))),inference(lifteq,[status(thm)],[1136])). 38.11/11.95 thf(76,axiom,((? [A:set_Fi1058188332real_n]: (member223413699real_n @ A @ top_to20708754real_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_UNIV__witness)). 38.11/11.95 thf(533,plain,((? [A:set_Fi1058188332real_n]: (member223413699real_n @ A @ top_to20708754real_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 38.11/11.95 thf(124,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_se2111327970real_n]: ((image_1856576259real_n @ A @ (vimage3210681real_n @ A @ B)) = (inf_in632889204real_n @ B @ (image_1856576259real_n @ A @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_image__vimage__eq)). 38.11/11.95 thf(698,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_se2111327970real_n]: ((image_1856576259real_n @ (A) @ (vimage3210681real_n @ (A) @ B)) = (inf_in632889204real_n @ B @ (image_1856576259real_n @ (A) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 38.11/11.95 thf(186,axiom,((top_to131672412_int_n = (collec1941932235_int_n @ top_to287930409nt_n_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_top__set__def)). 38.11/11.95 thf(913,plain,((top_to131672412_int_n = (collec1941932235_int_n @ (top_to287930409nt_n_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 38.11/11.95 thf(26,axiom,((! [A:set_nat]: ((top_top_set_nat = A) <= (! [B:nat]: (member_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_UNIV__eq__I)). 38.11/11.95 thf(340,plain,((! [A:set_nat]: ((top_top_set_nat = A) | ~ (! [B:nat]: (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 38.11/11.95 thf(78,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) => (~ ((member1352538125real_n @ A @ B) => (~ (member1352538125real_n @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_IntE)). 38.11/11.95 thf(538,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) => (~ ((member1352538125real_n @ A @ B) => (~ (member1352538125real_n @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 38.11/11.95 thf(1,conjecture,(((^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) = (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t @ (f @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 38.11/11.95 thf(2,negated_conjecture,((~ ((^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) = (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t @ (f @ A))))))),inference(neg_conjecture,[status(cth)],[1])). 38.11/11.95 thf(266,plain,((~ ((^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) = (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t @ (f @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 38.11/11.95 thf(267,plain,(((^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) != (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t @ (f @ A)))))),inference(lifteq,[status(thm)],[266])). 38.11/11.95 thf(1154,plain,(((sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ sk71))) != (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t @ (f @ sk71))))),inference(func_ext,[status(esa)],[267])). 38.11/11.95 thf(1163,plain,(((comple230862828real_n @ lebesg260170249real_n) != (comple230862828real_n @ lebesg260170249real_n)) | ((t2 @ (f @ sk71)) != (t @ (f @ sk71)))),inference(simp,[status(thm)],[1154])). 38.11/11.95 thf(1164,plain,(((t2 @ (f @ sk71)) != (t @ (f @ sk71)))),inference(simp,[status(thm)],[1163])). 38.11/11.95 thf(153,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(nat > finite964658038_int_n),C:set_nat]: ((image_355963305real_n @ A @ (image_1961920973_int_n @ B @ C)) = (image_1856576259real_n @ (^ [D:nat]: (A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_image__image)). 38.11/11.95 thf(797,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(nat > finite964658038_int_n),C:set_nat]: ((image_355963305real_n @ (A) @ (image_1961920973_int_n @ (B) @ C)) = (image_1856576259real_n @ (^ [D:nat]: (A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 38.11/11.95 thf(242,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:finite964658038_int_n]: (member223413699real_n @ (A @ B) @ (image_355963305real_n @ A @ top_to131672412_int_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_rangeI)). 38.11/11.95 thf(1095,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:finite964658038_int_n]: (member223413699real_n @ (A @ B) @ (image_355963305real_n @ (A) @ top_to131672412_int_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 38.11/11.95 thf(214,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite964658038_int_n > finite1489363574real_n)]: ((image_2058828787real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_439535603real_n @ A @ (image_2058828787real_n @ B @ top_to131672412_int_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_range__composition)). 38.11/11.95 thf(1001,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite964658038_int_n > finite1489363574real_n)]: ((image_2058828787real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_439535603real_n @ (A) @ (image_2058828787real_n @ (B) @ top_to131672412_int_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 38.11/11.95 thf(185,axiom,((! [A:set_Si1125517487real_n,B:set_Fi1058188332real_n,C:sigma_1466784463real_n,D:set_Fi1058188332real_n]: ((! [E:sigma_1466784463real_n]: ((member1000184real_n @ E @ A) => ((sigma_476185326real_n @ E) = B))) => (((member223413699real_n @ D @ (sigma_1235138647real_n @ (comple488165692real_n @ A))) <= (member223413699real_n @ D @ (sigma_1235138647real_n @ C))) <= (member1000184real_n @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_in__sets__Sup)). 38.11/11.95 thf(908,plain,((! [A:set_Si1125517487real_n,B:set_Fi1058188332real_n,C:sigma_1466784463real_n,D:set_Fi1058188332real_n]: ((! [E:sigma_1466784463real_n]: ((member1000184real_n @ E @ A) => ((sigma_476185326real_n @ E) = B))) => ((member223413699real_n @ D @ (sigma_1235138647real_n @ (comple488165692real_n @ A))) | ~ (member223413699real_n @ D @ (sigma_1235138647real_n @ C)) | ~ (member1000184real_n @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 38.11/11.95 thf(909,plain,((! [A:set_Si1125517487real_n]: ((? [B:set_Fi1058188332real_n]: ! [C:sigma_1466784463real_n]: ((member1000184real_n @ C @ A) => ((sigma_476185326real_n @ C) = B))) => (! [B:sigma_1466784463real_n]: (! [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ A))) | ~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | ~ (member1000184real_n @ B @ A)))))),inference(miniscope,[status(thm)],[908])). 38.11/11.95 thf(911,plain,(! [D:set_Fi1058188332real_n,C:sigma_1466784463real_n,B:set_Fi1058188332real_n,A:set_Si1125517487real_n] : ((~ ((sigma_476185326real_n @ (sk53 @ B @ A)) = B)) | (member223413699real_n @ D @ (sigma_1235138647real_n @ (comple488165692real_n @ A))) | (~ (member223413699real_n @ D @ (sigma_1235138647real_n @ C))) | (~ (member1000184real_n @ C @ A)))),inference(cnf,[status(esa)],[909])). 38.11/11.95 thf(912,plain,(! [D:set_Fi1058188332real_n,C:sigma_1466784463real_n,B:set_Fi1058188332real_n,A:set_Si1125517487real_n] : (((sigma_476185326real_n @ (sk53 @ B @ A)) != B) | (member223413699real_n @ D @ (sigma_1235138647real_n @ (comple488165692real_n @ A))) | (~ (member223413699real_n @ D @ (sigma_1235138647real_n @ C))) | (~ (member1000184real_n @ C @ A)))),inference(lifteq,[status(thm)],[911])). 38.11/11.95 thf(1211,plain,(! [H:set_Fi1058188332real_n,G:sigma_1466784463real_n,F:set_Fi1058188332real_n,E:set_Si1125517487real_n,D:set_Fi1058188332real_n,C:sigma_1466784463real_n,B:set_Fi1058188332real_n,A:set_Si1125517487real_n] : (((sigma_476185326real_n @ (sk53 @ B @ A)) != B) | (~ (member223413699real_n @ D @ (sigma_1235138647real_n @ C))) | (~ (member1000184real_n @ C @ A)) | ((sigma_476185326real_n @ (sk53 @ F @ E)) != F) | (member223413699real_n @ H @ (sigma_1235138647real_n @ (comple488165692real_n @ E))) | (~ (member1000184real_n @ G @ E)) | ((member223413699real_n @ D @ (sigma_1235138647real_n @ (comple488165692real_n @ A))) != (member223413699real_n @ H @ (sigma_1235138647real_n @ G))))),inference(paramod_ordered,[status(thm)],[912,912])). 38.11/11.95 thf(1212,plain,(! [F:set_Si1125517487real_n,E:set_Fi1058188332real_n,D:set_Si1125517487real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ F)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ F)) | ((sigma_476185326real_n @ (sk53 @ E @ D)) != E) | (member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ D))) | (~ (member1000184real_n @ (comple488165692real_n @ F) @ D)))),inference(pattern_uni,[status(thm)],[1211:[bind(A, $thf(I)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf(E)),bind(F, $thf(F)),bind(G, $thf(comple488165692real_n @ I)),bind(H, $thf(D))]])). 38.11/11.95 thf(1217,plain,(! [F:set_Si1125517487real_n,E:set_Fi1058188332real_n,D:set_Si1125517487real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ F)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ F)) | ((sigma_476185326real_n @ (sk53 @ E @ D)) != E) | (member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ D))) | (~ (member1000184real_n @ (comple488165692real_n @ F) @ D)))),inference(simp,[status(thm)],[1212])). 38.11/11.95 thf(1223,plain,(! [L:set_Si1125517487real_n,K:set_Fi1058188332real_n,J:set_Si1125517487real_n,I:set_Fi1058188332real_n,H:sigma_1466784463real_n,G:set_Fi1058188332real_n,F:set_Si1125517487real_n,E:set_Fi1058188332real_n,D:set_Si1125517487real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ F)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ F)) | ((sigma_476185326real_n @ (sk53 @ E @ D)) != E) | (~ (member1000184real_n @ (comple488165692real_n @ F) @ D)) | ((sigma_476185326real_n @ (sk53 @ G @ L)) != G) | (~ (member1000184real_n @ H @ L)) | ((sigma_476185326real_n @ (sk53 @ K @ J)) != K) | (member223413699real_n @ I @ (sigma_1235138647real_n @ (comple488165692real_n @ J))) | (~ (member1000184real_n @ (comple488165692real_n @ L) @ J)) | ((member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ D))) != (member223413699real_n @ I @ (sigma_1235138647real_n @ H))))),inference(paramod_ordered,[status(thm)],[1217,1217])). 38.11/11.95 thf(1224,plain,(! [J:set_Si1125517487real_n,I:set_Si1125517487real_n,H:set_Fi1058188332real_n,G:set_Si1125517487real_n,F:set_Fi1058188332real_n,E:set_Si1125517487real_n,D:set_Fi1058188332real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ E)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ E)) | ((sigma_476185326real_n @ (sk53 @ D @ J)) != D) | (~ (member1000184real_n @ (comple488165692real_n @ E) @ J)) | ((sigma_476185326real_n @ (sk53 @ F @ I)) != F) | (~ (member1000184real_n @ (comple488165692real_n @ J) @ I)) | ((sigma_476185326real_n @ (sk53 @ H @ G)) != H) | (member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ G))) | (~ (member1000184real_n @ (comple488165692real_n @ I) @ G)))),inference(pattern_uni,[status(thm)],[1223:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(M)),bind(E, $thf(E)),bind(F, $thf(F)),bind(G, $thf(G)),bind(H, $thf(comple488165692real_n @ M)),bind(I, $thf(C))]])). 38.11/11.95 thf(1243,plain,(! [J:set_Si1125517487real_n,I:set_Si1125517487real_n,H:set_Fi1058188332real_n,G:set_Si1125517487real_n,F:set_Fi1058188332real_n,E:set_Si1125517487real_n,D:set_Fi1058188332real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ E)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ E)) | ((sigma_476185326real_n @ (sk53 @ D @ J)) != D) | (~ (member1000184real_n @ (comple488165692real_n @ E) @ J)) | ((sigma_476185326real_n @ (sk53 @ F @ I)) != F) | (~ (member1000184real_n @ (comple488165692real_n @ J) @ I)) | ((sigma_476185326real_n @ (sk53 @ H @ G)) != H) | (member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ G))) | (~ (member1000184real_n @ (comple488165692real_n @ I) @ G)))),inference(simp,[status(thm)],[1224])). 38.11/11.95 thf(47,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((C @ (A @ D)) & (member1352538125real_n @ D @ B))) <= (? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (image_439535603real_n @ A @ B)) & (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_bex__imageD)). 38.11/11.95 thf(417,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: (? [D:finite1489363574real_n]: ((C @ (A @ D)) & (member1352538125real_n @ D @ B)) | ~ (? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (image_439535603real_n @ (A) @ B)) & (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 38.11/11.95 thf(10,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((C @ D) <= (member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ A @ B))))) = (! [D:nat]: ((! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) => (C @ E))) <= (member_nat @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ball__UN)). 38.11/11.95 thf(288,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((C @ D) | ~ (member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ (A) @ B))))) = (! [D:nat]: (! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) => (C @ E)) | ~ (member_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 38.11/11.95 thf(20,axiom,((! [A:(finite1489363574real_n > $o),B:(finite1489363574real_n > finite1489363574real_n),C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((A @ (B @ D)) = (C @ D))) => ((vimage1233683625real_n @ B @ (collec321817931real_n @ A)) = (collec321817931real_n @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_vimage__Collect)). 38.11/11.95 thf(320,plain,((! [A:(finite1489363574real_n > $o),B:(finite1489363574real_n > finite1489363574real_n),C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((A @ (B @ D)) = (C @ D))) => ((vimage1233683625real_n @ (B) @ (collec321817931real_n @ (A))) = (collec321817931real_n @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 38.11/11.95 thf(178,axiom,((! [A:finite964658038_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member223413699real_n @ (C @ A) @ (image_355963305real_n @ C @ B)) <= (member27055245_int_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_imageI)). 38.11/11.95 thf(885,plain,((! [A:finite964658038_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member223413699real_n @ (C @ A) @ (image_355963305real_n @ (C) @ B)) | ~ (member27055245_int_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 38.11/11.95 thf(229,axiom,((! [A:set_se2111327970real_n,B:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ (comple825005695real_n @ A) @ B) = (comple825005695real_n @ (image_1661509983real_n @ (^ [C:set_Fi1058188332real_n]: (inf_in1974387902real_n @ C @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Int__Union2)). 38.11/11.95 thf(1046,plain,((! [A:set_se2111327970real_n,B:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ (comple825005695real_n @ A) @ B) = (comple825005695real_n @ (image_1661509983real_n @ (^ [C:set_Fi1058188332real_n]: (inf_in1974387902real_n @ C @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 38.11/11.95 thf(40,axiom,((! [A:set_Fi1058188332real_n]: (member223413699real_n @ A @ top_to20708754real_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_UNIV__I)). 38.11/11.95 thf(389,plain,((! [A:set_Fi1058188332real_n]: (member223413699real_n @ A @ top_to20708754real_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 38.11/11.95 thf(101,axiom,((! [A:finite964658038_int_n]: (member27055245_int_n @ A @ top_to131672412_int_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_UNIV__I)). 38.11/11.95 thf(619,plain,((! [A:finite964658038_int_n]: (member27055245_int_n @ A @ top_to131672412_int_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 38.11/11.95 thf(193,axiom,((~ (ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_less__numeral__extra_I4_J)). 38.11/11.95 thf(934,plain,((~ (ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 38.11/11.95 thf(257,axiom,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: ((((sigma_1536574303real_n @ B @ (minus_1686442501real_n @ C @ A)) = (sigma_1536574303real_n @ B @ C)) <= (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) <= (member223413699real_n @ A @ (measur1402256771real_n @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_emeasure__Diff__null__set)). 38.11/11.95 thf(1132,plain,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: (((sigma_1536574303real_n @ B @ (minus_1686442501real_n @ C @ A)) = (sigma_1536574303real_n @ B @ C)) | ~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B)) | ~ (member223413699real_n @ A @ (measur1402256771real_n @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 38.11/11.95 thf(183,axiom,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n]: (((inf_in1974387902real_n @ A @ (sigma_476185326real_n @ B)) = A) <= (member223413699real_n @ A @ (measur1402256771real_n @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_null__sets_OInt__space__eq2)). 38.11/11.95 thf(902,plain,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n]: (((inf_in1974387902real_n @ A @ (sigma_476185326real_n @ B)) = A) | ~ (member223413699real_n @ A @ (measur1402256771real_n @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 38.11/11.95 thf(171,axiom,((! [A:set_se2111327970real_n,B:(finite1489363574real_n > $o)]: ((? [C:finite1489363574real_n]: ((member1352538125real_n @ C @ (comple825005695real_n @ A)) & (B @ C))) = (? [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ A) & ? [D:finite1489363574real_n]: ((B @ D) & (member1352538125real_n @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_UN__ball__bex__simps_I3_J)). 38.11/11.95 thf(853,plain,((! [A:set_se2111327970real_n,B:(finite1489363574real_n > $o)]: ((? [C:finite1489363574real_n]: ((member1352538125real_n @ C @ (comple825005695real_n @ A)) & (B @ C))) = (? [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ A) & ? [D:finite1489363574real_n]: ((B @ D) & (member1352538125real_n @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 38.11/11.95 thf(264,axiom,((ord_le2133614988nnreal @ one_on705384445nnreal @ (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ s))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_assms_I2_J)). 38.11/11.95 thf(1147,plain,((ord_le2133614988nnreal @ one_on705384445nnreal @ (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ s))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 38.11/11.95 thf(174,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_se944069346_int_n]: ((comple825005695real_n @ (image_792439519real_n @ (^ [C:set_Fi160064172_int_n]: (comple825005695real_n @ (image_355963305real_n @ A @ C))) @ B)) = (comple825005695real_n @ (image_355963305real_n @ A @ (comple970917503_int_n @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_UN__extend__simps_I8_J)). 38.11/11.95 thf(870,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_se944069346_int_n]: ((comple825005695real_n @ (image_792439519real_n @ (^ [C:set_Fi160064172_int_n]: (comple825005695real_n @ (image_355963305real_n @ A @ C))) @ B)) = (comple825005695real_n @ (image_355963305real_n @ (A) @ (comple970917503_int_n @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 38.11/11.95 thf(147,axiom,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:finite964658038_int_n]: ((member223413699real_n @ A @ (image_355963305real_n @ B @ top_to131672412_int_n)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_range__eqI)). 38.11/11.95 thf(770,plain,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:finite964658038_int_n]: ((member223413699real_n @ A @ (image_355963305real_n @ (B) @ top_to131672412_int_n)) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 38.11/11.95 thf(54,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: ((collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (image_439535603real_n @ A @ B)) & (C @ D)))) = (image_439535603real_n @ A @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ B) & (C @ (A @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Compr__image__eq)). 38.11/11.95 thf(448,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: ((collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (image_439535603real_n @ A @ B)) & (C @ D)))) = (image_439535603real_n @ (A) @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ B) & (C @ (A @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 38.11/11.95 thf(190,axiom,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: ((member223413699real_n @ A @ (image_1856576259real_n @ B @ C)) = (? [D:nat]: ((A = (B @ D)) & (member_nat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_image__iff)). 38.11/11.95 thf(924,plain,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: ((member223413699real_n @ A @ (image_1856576259real_n @ (B) @ C)) = (? [D:nat]: ((A = (B @ D)) & (member_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 38.11/11.95 thf(66,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) => (member1352538125real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_IntD1)). 38.11/11.95 thf(492,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) => (member1352538125real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 38.11/11.95 thf(142,axiom,((inf_in1974387902real_n = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (inf_in1974387902real_n @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Int__commute)). 38.11/11.95 thf(755,plain,(((inf_in1974387902real_n) = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (inf_in1974387902real_n @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 38.11/11.95 thf(756,plain,(((inf_in1974387902real_n) = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (inf_in1974387902real_n @ B @ A)))),inference(lifteq,[status(thm)],[755])). 38.11/11.95 thf(94,axiom,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n)]: ((A = B) => ((! [E:nat]: (((C @ E) = (D @ E)) <= (member_nat @ E @ B))) => ((image_1856576259real_n @ C @ A) = (image_1856576259real_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_image__cong)). 38.11/11.95 thf(591,plain,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n)]: ((A = B) => ((! [E:nat]: (((C @ E) = (D @ E)) | ~ (member_nat @ E @ B))) => ((image_1856576259real_n @ (C) @ A) = (image_1856576259real_n @ (D) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 38.11/11.95 thf(156,axiom,((! [A:(nat > finite964658038_int_n),B:finite964658038_int_n]: (((image_1961920973_int_n @ A @ top_top_set_nat) = top_to131672412_int_n) => (? [C:nat]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_surjD)). 38.11/11.95 thf(806,plain,((! [A:(nat > finite964658038_int_n),B:finite964658038_int_n]: (((image_1961920973_int_n @ (A) @ top_top_set_nat) = top_to131672412_int_n) => (? [C:nat]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 38.11/11.95 thf(184,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((image_439535603real_n @ A @ (image_439535603real_n @ B @ C)) = (image_439535603real_n @ (^ [D:finite1489363574real_n]: (A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_image__image)). 38.11/11.95 thf(905,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((image_439535603real_n @ (A) @ (image_439535603real_n @ (B) @ C)) = (image_439535603real_n @ (^ [D:finite1489363574real_n]: (A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 38.11/11.95 thf(227,axiom,((! [A:finite964658038_int_n]: ((image_1278151539_int_n @ (^ [B:finite964658038_int_n]: (minus_1196255695_int_n @ B @ A)) @ top_to131672412_int_n) = top_to131672412_int_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_surj__diff__right)). 38.11/11.95 thf(1040,plain,((! [A:finite964658038_int_n]: ((image_1278151539_int_n @ (^ [B:finite964658038_int_n]: (minus_1196255695_int_n @ B @ A)) @ top_to131672412_int_n) = top_to131672412_int_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 38.11/11.95 thf(248,axiom,((! [A:finite964658038_int_n]: ((sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t @ A)) = (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_emeasure__T_H)). 38.11/11.95 thf(1109,plain,((! [A:finite964658038_int_n]: ((sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t @ A)) = (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 38.11/11.95 thf(88,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > $o)]: ((vimage1233683625real_n @ A @ (collec321817931real_n @ B)) = (collec321817931real_n @ (^ [C:finite1489363574real_n]: (B @ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_vimage__Collect__eq)). 38.11/11.95 thf(574,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > $o)]: ((vimage1233683625real_n @ (A) @ (collec321817931real_n @ (B))) = (collec321817931real_n @ (^ [C:finite1489363574real_n]: (B @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 38.11/11.95 thf(220,axiom,((! [A:(nat > (finite964658038_int_n > set_Fi1058188332real_n)),B:set_Fi160064172_int_n,C:set_nat]: ((comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_355963305real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_1856576259real_n @ (^ [E:nat]: (A @ E @ D)) @ C))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_SUP__commute)). 38.11/11.95 thf(1020,plain,((! [A:(nat > (finite964658038_int_n > set_Fi1058188332real_n)),B:set_Fi160064172_int_n,C:set_nat]: ((comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_355963305real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_1856576259real_n @ (^ [E:nat]: (A @ E @ D)) @ C))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 38.11/11.95 thf(28,axiom,((! [A:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ top_to1292442332real_n) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_Int__UNIV__right)). 38.11/11.95 thf(348,plain,((! [A:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ top_to1292442332real_n) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 38.11/11.95 thf(121,axiom,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:nat,D:set_nat]: ((A = (B @ C)) => ((member_nat @ C @ D) => (member223413699real_n @ A @ (image_1856576259real_n @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_image__eqI)). 38.11/11.95 thf(687,plain,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:nat,D:set_nat]: ((A = (B @ C)) => ((member_nat @ C @ D) => (member223413699real_n @ A @ (image_1856576259real_n @ (B) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 38.11/11.95 thf(122,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ top_top_set_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_Int__UNIV__left)). 38.11/11.95 thf(692,plain,((! [A:set_nat]: ((inf_inf_set_nat @ top_top_set_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 38.11/11.95 thf(135,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ (inf_in1974387902real_n @ A @ B) @ C) = (inf_in1974387902real_n @ A @ (inf_in1974387902real_n @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Int__assoc)). 38.11/11.95 thf(734,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ (inf_in1974387902real_n @ A @ B) @ C) = (inf_in1974387902real_n @ A @ (inf_in1974387902real_n @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 38.11/11.95 thf(252,axiom,((! [A:finite964658038_int_n]: (member223413699real_n @ (t2 @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062)). 38.11/11.95 thf(1119,plain,((! [A:finite964658038_int_n]: (member223413699real_n @ (t2 @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 38.11/11.95 thf(210,axiom,((! [A:nat,B:set_nat,C:(nat > set_Fi1058188332real_n)]: ((member_nat @ A @ B) => (member223413699real_n @ (C @ A) @ (image_1856576259real_n @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_imageI)). 38.11/11.95 thf(988,plain,((! [A:nat,B:set_nat,C:(nat > set_Fi1058188332real_n)]: ((member_nat @ A @ B) => (member223413699real_n @ (C @ A) @ (image_1856576259real_n @ (C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 38.11/11.95 thf(50,axiom,((inf_in1974387902real_n = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: ((member1352538125real_n @ C @ A) & (member1352538125real_n @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Int__def)). 38.11/11.95 thf(427,plain,(((inf_in1974387902real_n) = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: ((member1352538125real_n @ C @ A) & (member1352538125real_n @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 38.11/11.95 thf(428,plain,(((inf_in1974387902real_n) = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: ((member1352538125real_n @ C @ A) & (member1352538125real_n @ C @ B))))))),inference(lifteq,[status(thm)],[427])). 38.11/11.95 thf(17,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) => (~ ((member223413699real_n @ A @ B) => (~ (member223413699real_n @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_IntE)). 38.11/11.95 thf(312,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) => (~ ((member223413699real_n @ A @ B) => (~ (member223413699real_n @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 38.11/11.95 thf(118,axiom,((! [A:set_Ex113815278nnreal]: ((image_2066995319nnreal @ (plus_p1763960001nnreal @ zero_z1963244097nnreal) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_image__add__0)). 38.11/11.95 thf(678,plain,((! [A:set_Ex113815278nnreal]: ((image_2066995319nnreal @ (plus_p1763960001nnreal @ zero_z1963244097nnreal) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 38.11/11.95 thf(3,axiom,((! [A:set_se2111327970real_n]: ((collec452821761real_n @ (^ [B:set_Fi1058188332real_n]: (member223413699real_n @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Collect__mem__eq)). 38.11/11.95 thf(268,plain,((! [A:set_se2111327970real_n]: ((collec452821761real_n @ (^ [B:set_Fi1058188332real_n]: (member223413699real_n @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 38.11/11.95 thf(269,plain,(! [A:set_se2111327970real_n] : (((collec452821761real_n @ (^ [B:set_Fi1058188332real_n]: (member223413699real_n @ B @ A))) = A))),inference(cnf,[status(esa)],[268])). 38.11/11.95 thf(270,plain,(! [A:set_se2111327970real_n] : (((collec452821761real_n @ (^ [B:set_Fi1058188332real_n]: (member223413699real_n @ B @ A))) = A))),inference(lifteq,[status(thm)],[269])). 38.11/11.95 thf(157,axiom,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = top_top_set_nat) = ((A = top_top_set_nat) & (B = top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Int__UNIV)). 38.11/11.95 thf(810,plain,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = top_top_set_nat) = ((A = top_top_set_nat) & (B = top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 38.11/11.95 thf(37,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ (collec321817931real_n @ C))) = ((member1352538125real_n @ A @ B) & (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Int__Collect)). 38.11/11.95 thf(381,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ (collec321817931real_n @ (C)))) = ((member1352538125real_n @ A @ B) & (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 38.11/11.95 thf(235,axiom,((! [A:set_se2111327970real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > set_Fi1058188332real_n),D:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: ((A = B) => ((! [E:set_Fi1058188332real_n]: ((member223413699real_n @ E @ B) => ((C @ E) = (D @ E)))) => ((comple825005695real_n @ (image_1661509983real_n @ C @ A)) = (comple825005695real_n @ (image_1661509983real_n @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_SUP__cong)). 38.11/11.95 thf(1067,plain,((! [A:set_se2111327970real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > set_Fi1058188332real_n),D:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: ((A = B) => ((! [E:set_Fi1058188332real_n]: ((member223413699real_n @ E @ B) => ((C @ E) = (D @ E)))) => ((comple825005695real_n @ (image_1661509983real_n @ (C) @ A)) = (comple825005695real_n @ (image_1661509983real_n @ (D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 38.11/11.95 thf(129,axiom,((! [A:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Int__absorb)). 38.11/11.95 thf(714,plain,((! [A:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 38.11/11.95 thf(232,axiom,((! [A:(finite964658038_int_n > nat)]: ((vimage1398021123_n_nat @ A @ top_top_set_nat) = top_to131672412_int_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_vimage__UNIV)). 38.11/11.95 thf(1057,plain,((! [A:(finite964658038_int_n > nat)]: ((vimage1398021123_n_nat @ (A) @ top_top_set_nat) = top_to131672412_int_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 38.11/11.95 thf(24,axiom,((! [A:finite1489363574real_n,B:(set_Fi1058188332real_n > set_Fi1058188332real_n),C:set_se2111327970real_n]: ((~ (! [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ C) => (~ (member1352538125real_n @ A @ (B @ D)))))) <= (member1352538125real_n @ A @ (comple825005695real_n @ (image_1661509983real_n @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_UN__E)). 38.11/11.95 thf(334,plain,((! [A:finite1489363574real_n,B:(set_Fi1058188332real_n > set_Fi1058188332real_n),C:set_se2111327970real_n]: (~ (! [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ C) => (~ (member1352538125real_n @ A @ (B @ D))))) | ~ (member1352538125real_n @ A @ (comple825005695real_n @ (image_1661509983real_n @ (B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 38.11/11.95 thf(139,axiom,((! [A:(nat > (nat > set_Fi1058188332real_n)),B:set_nat,C:set_nat]: ((comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_1856576259real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_1856576259real_n @ (^ [E:nat]: (A @ E @ D)) @ C))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_SUP__commute)). 38.11/11.95 thf(746,plain,((! [A:(nat > (nat > set_Fi1058188332real_n)),B:set_nat,C:set_nat]: ((comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_1856576259real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_1856576259real_n @ (^ [E:nat]: (A @ E @ D)) @ C))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 38.11/11.95 thf(162,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: ((minus_1686442501real_n @ A @ (minus_1686442501real_n @ A @ B)) = (inf_in1974387902real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Diff__Diff__Int)). 38.11/11.95 thf(825,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: ((minus_1686442501real_n @ A @ (minus_1686442501real_n @ A @ B)) = (inf_in1974387902real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 38.11/11.95 thf(199,axiom,((! [A:(set_Fi1058188332real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((A @ (image_439535603real_n @ (^ [C:finite1489363574real_n]: (C)) @ B)) = (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Inf_OINF__identity__eq)). 38.11/11.95 thf(952,plain,((! [A:(set_Fi1058188332real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((A @ (image_439535603real_n @ (^ [C:finite1489363574real_n]: (C)) @ B)) = (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 38.11/11.95 thf(15,axiom,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((A = B) => ((! [E:finite964658038_int_n]: ((member27055245_int_n @ E @ B) => ((C @ E) = (D @ E)))) => ((image_355963305real_n @ C @ A) = (image_355963305real_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_image__cong)). 38.11/11.95 thf(302,plain,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((A = B) => ((! [E:finite964658038_int_n]: ((member27055245_int_n @ E @ B) => ((C @ E) = (D @ E)))) => ((image_355963305real_n @ (C) @ A) = (image_355963305real_n @ (D) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 38.11/11.95 thf(254,axiom,((! [A:finite964658038_int_n]: (member223413699real_n @ (t @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062a_O_AT_H_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062)). 38.11/11.95 thf(1123,plain,((! [A:finite964658038_int_n]: (member223413699real_n @ (t @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 38.11/11.95 thf(13,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((C @ D) & (member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ A @ B))))) = (? [D:finite964658038_int_n]: (? [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) & (C @ E)) & (member27055245_int_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_UN__ball__bex__simps_I4_J)). 38.11/11.95 thf(297,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((C @ D) & (member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ (A) @ B))))) = (? [D:finite964658038_int_n]: (? [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) & (C @ E)) & (member27055245_int_n @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 38.11/11.95 thf(51,axiom,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: ((((E @ (image_355963305real_n @ C @ A)) = (E @ (image_355963305real_n @ D @ B))) <= (! [F:finite964658038_int_n]: (((C @ F) = (D @ F)) <= (member27055245_int_n @ F @ B)))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Inf_OINF__cong)). 38.11/11.95 thf(429,plain,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: (((E @ (image_355963305real_n @ (C) @ A)) = (E @ (image_355963305real_n @ (D) @ B))) | ~ (! [F:finite964658038_int_n]: (((C @ F) = (D @ F)) | ~ (member27055245_int_n @ F @ B))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 38.11/11.95 thf(5,axiom,((inf_in632889204real_n = (^ [A:set_se2111327970real_n,B:set_se2111327970real_n]: (collec452821761real_n @ (^ [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ A) & (member223413699real_n @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Int__def)). 38.11/11.95 thf(274,plain,(((inf_in632889204real_n) = (^ [A:set_se2111327970real_n,B:set_se2111327970real_n]: (collec452821761real_n @ (^ [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ A) & (member223413699real_n @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 38.11/11.95 thf(275,plain,(((inf_in632889204real_n) = (^ [A:set_se2111327970real_n,B:set_se2111327970real_n]: (collec452821761real_n @ (^ [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ A) & (member223413699real_n @ C @ B))))))),inference(lifteq,[status(thm)],[274])). 38.11/11.95 thf(44,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ C) <= (member223413699real_n @ A @ (inf_in632889204real_n @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_IntD2)). 38.11/11.95 thf(407,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ C) | ~ (member223413699real_n @ A @ (inf_in632889204real_n @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 38.11/11.95 thf(104,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ A @ B))) => (C @ D))) = (! [D:finite964658038_int_n]: ((! [E:finite1489363574real_n]: ((C @ E) <= (member1352538125real_n @ E @ (A @ D)))) <= (member27055245_int_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_UN__ball__bex__simps_I2_J)). 38.11/11.95 thf(630,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ (A) @ B))) => (C @ D))) = (! [D:finite964658038_int_n]: (! [E:finite1489363574real_n]: ((C @ E) | ~ (member1352538125real_n @ E @ (A @ D))) | ~ (member27055245_int_n @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 38.11/11.95 thf(169,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi160064172_int_n),C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_355963305real_n @ A @ (comple970917503_int_n @ (image_1819506345_int_n @ B @ C)))) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_355963305real_n @ A @ (B @ D)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_UN__UN__flatten)). 38.11/11.95 thf(847,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi160064172_int_n),C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_355963305real_n @ (A) @ (comple970917503_int_n @ (image_1819506345_int_n @ (B) @ C)))) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_355963305real_n @ A @ (B @ D)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 38.11/11.95 thf(224,axiom,((! [A:set_Fi160064172_int_n]: ((inf_in1108485182_int_n @ A @ top_to131672412_int_n) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_Int__UNIV__right)). 38.11/11.95 thf(1032,plain,((! [A:set_Fi160064172_int_n]: ((inf_in1108485182_int_n @ A @ top_to131672412_int_n) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 38.11/11.95 thf(177,axiom,((! [A:set_Fi1058188332real_n,B:(finite1489363574real_n > finite1489363574real_n),C:(finite1489363574real_n > finite1489363574real_n),D:set_Fi1058188332real_n]: ((! [E:finite1489363574real_n]: (((B @ E) = (C @ E)) <= (member1352538125real_n @ E @ A))) => ((inf_in1974387902real_n @ (vimage1233683625real_n @ B @ D) @ A) = (inf_in1974387902real_n @ (vimage1233683625real_n @ C @ D) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_vimage__inter__cong)). 38.11/11.95 thf(879,plain,((! [A:set_Fi1058188332real_n,B:(finite1489363574real_n > finite1489363574real_n),C:(finite1489363574real_n > finite1489363574real_n),D:set_Fi1058188332real_n]: ((! [E:finite1489363574real_n]: (((B @ E) = (C @ E)) | ~ (member1352538125real_n @ E @ A))) => ((inf_in1974387902real_n @ (vimage1233683625real_n @ (B) @ D) @ A) = (inf_in1974387902real_n @ (vimage1233683625real_n @ (C) @ D) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 38.11/11.95 thf(23,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:finite1489363574real_n]: ((A = (B @ C)) => (member1352538125real_n @ A @ (image_439535603real_n @ B @ top_to1292442332real_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_range__eqI)). 38.11/11.95 thf(329,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:finite1489363574real_n]: ((A = (B @ C)) => (member1352538125real_n @ A @ (image_439535603real_n @ (B) @ top_to1292442332real_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 38.11/11.95 thf(91,axiom,((! [A:finite1489363574real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_355963305real_n @ B @ C))) => (~ (! [D:finite964658038_int_n]: ((~ (member1352538125real_n @ A @ (B @ D))) <= (member27055245_int_n @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_UN__E)). 38.11/11.95 thf(583,plain,((! [A:finite1489363574real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_355963305real_n @ (B) @ C))) => (~ (! [D:finite964658038_int_n]: (~ (member1352538125real_n @ A @ (B @ D)) | ~ (member27055245_int_n @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 38.11/11.95 thf(237,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(set_Fi1058188332real_n > finite964658038_int_n)]: ((! [C:set_Fi1058188332real_n]: ((A @ (B @ C)) = C)) => ((image_355963305real_n @ A @ top_to131672412_int_n) = top_to20708754real_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_surjI)). 38.11/11.95 thf(1079,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(set_Fi1058188332real_n > finite964658038_int_n)]: ((! [C:set_Fi1058188332real_n]: ((A @ (B @ C)) = C)) => ((image_355963305real_n @ (A) @ top_to131672412_int_n) = top_to20708754real_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 38.11/11.95 thf(143,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((vimage1233683625real_n @ A @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (vimage1233683625real_n @ A @ B) @ (vimage1233683625real_n @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_vimage__Diff)). 38.11/11.95 thf(757,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((vimage1233683625real_n @ (A) @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (vimage1233683625real_n @ (A) @ B) @ (vimage1233683625real_n @ (A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 38.11/11.95 thf(167,axiom,((top_top_set_nat = (collect_nat @ top_top_nat_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_top__set__def)). 38.11/11.95 thf(842,plain,((top_top_set_nat = (collect_nat @ (top_top_nat_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 38.11/11.95 thf(9,axiom,((! [A:nat,B:set_nat,C:finite1489363574real_n,D:(nat > set_Fi1058188332real_n)]: ((member_nat @ A @ B) => ((member1352538125real_n @ C @ (D @ A)) => (member1352538125real_n @ C @ (comple825005695real_n @ (image_1856576259real_n @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_UN__I)). 38.11/11.95 thf(285,plain,((! [A:nat,B:set_nat,C:finite1489363574real_n,D:(nat > set_Fi1058188332real_n)]: ((member_nat @ A @ B) => ((member1352538125real_n @ C @ (D @ A)) => (member1352538125real_n @ C @ (comple825005695real_n @ (image_1856576259real_n @ (D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 38.11/11.95 thf(1106,plain,(((^ [A:finite964658038_int_n]: (image_439535603real_n @ (^ [B:finite1489363574real_n]: (minus_1037315151real_n @ B @ (minkow1134813771n_real @ A))) @ (t2 @ A))) = (t))),inference(lifteq,[status(thm)],[1105])). 38.11/11.95 thf(240,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_se2111327970real_n]: ((image_439535603real_n @ A @ (comple825005695real_n @ B)) = (comple825005695real_n @ (image_1661509983real_n @ (image_439535603real_n @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_image__Union)). 38.11/11.95 thf(1089,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_se2111327970real_n]: ((image_439535603real_n @ (A) @ (comple825005695real_n @ B)) = (comple825005695real_n @ (image_1661509983real_n @ (image_439535603real_n @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 38.11/11.95 thf(219,axiom,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member223413699real_n @ A @ (image_355963305real_n @ B @ C)) = (? [D:finite964658038_int_n]: ((member27055245_int_n @ D @ C) & (A = (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_image__iff)). 38.11/11.95 thf(1017,plain,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member223413699real_n @ A @ (image_355963305real_n @ (B) @ C)) = (? [D:finite964658038_int_n]: ((member27055245_int_n @ D @ C) & (A = (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 38.11/11.95 thf(100,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (image_439535603real_n @ B @ C)) => (~ (! [D:finite1489363574real_n]: ((A = (B @ D)) => (~ (member1352538125real_n @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_imageE)). 38.11/11.95 thf(615,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (image_439535603real_n @ (B) @ C)) => (~ (! [D:finite1489363574real_n]: ((A = (B @ D)) => (~ (member1352538125real_n @ D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 38.11/11.95 thf(253,axiom,(((comple825005695real_n @ (image_355963305real_n @ t2 @ top_to131672412_int_n)) = (comple825005695real_n @ (image_1856576259real_n @ (^ [A:nat]: (t2 @ (f @ A))) @ top_top_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28__092_060open_062_092_060Union_062_A_Irange_AT_J_A_061_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062)). 38.11/11.95 thf(1121,plain,(((comple825005695real_n @ (image_355963305real_n @ (t2) @ top_to131672412_int_n)) = (comple825005695real_n @ (image_1856576259real_n @ (^ [A:nat]: (t2 @ (f @ A))) @ top_top_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 38.11/11.95 thf(234,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ (inf_in1974387902real_n @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Diff__Int__distrib)). 38.11/11.95 thf(1064,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ (inf_in1974387902real_n @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 38.11/11.95 thf(132,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(set_Fi1058188332real_n > $o)]: ((? [D:set_Fi1058188332real_n]: ((C @ D) & (member223413699real_n @ D @ (image_355963305real_n @ A @ B)))) => (? [D:finite964658038_int_n]: ((C @ (A @ D)) & (member27055245_int_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_bex__imageD)). 38.11/11.95 thf(725,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(set_Fi1058188332real_n > $o)]: ((? [D:set_Fi1058188332real_n]: ((C @ D) & (member223413699real_n @ D @ (image_355963305real_n @ (A) @ B)))) => (? [D:finite964658038_int_n]: ((C @ (A @ D)) & (member27055245_int_n @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 38.11/11.95 thf(259,axiom,((! [A:finite964658038_int_n,B:finite964658038_int_n]: ((A != B) => ((sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (inf_in1974387902real_n @ (t2 @ A) @ (t2 @ B))) = zero_z1963244097nnreal)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_emeasure__T__Int)). 38.11/11.95 thf(1138,plain,((! [A:finite964658038_int_n,B:finite964658038_int_n]: ((~ (A = B)) => ((sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (inf_in1974387902real_n @ (t2 @ A) @ (t2 @ B))) = zero_z1963244097nnreal)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 38.11/11.95 thf(111,axiom,((! [A:(finite964658038_int_n > (finite964658038_int_n > set_Fi1058188332real_n)),B:set_Fi160064172_int_n,C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_355963305real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_355963305real_n @ (^ [E:finite964658038_int_n]: (A @ E @ D)) @ C))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_SUP__commute)). 38.11/11.95 thf(650,plain,((! [A:(finite964658038_int_n > (finite964658038_int_n > set_Fi1058188332real_n)),B:set_Fi160064172_int_n,C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_355963305real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_355963305real_n @ (^ [E:finite964658038_int_n]: (A @ E @ D)) @ C))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 38.11/11.95 thf(198,axiom,((! [A:(finite964658038_int_n > nat),B:nat]: ((~ (! [C:finite964658038_int_n]: (B != (A @ C)))) <= ((image_497739341_n_nat @ A @ top_to131672412_int_n) = top_top_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_surjE)). 38.11/11.95 thf(948,plain,((! [A:(finite964658038_int_n > nat),B:nat]: (~ (! [C:finite964658038_int_n]: ~ (B = (A @ C))) | ~ ((image_497739341_n_nat @ (A) @ top_to131672412_int_n) = top_top_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 38.11/11.95 thf(150,axiom,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi1058188332real_n)]: ((image_355963305real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_1661509983real_n @ A @ (image_355963305real_n @ B @ top_to131672412_int_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_range__composition)). 38.11/11.95 thf(783,plain,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(finite964658038_int_n > set_Fi1058188332real_n)]: ((image_355963305real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_1661509983real_n @ (A) @ (image_355963305real_n @ (B) @ top_to131672412_int_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 38.11/11.95 thf(48,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) = ((member223413699real_n @ A @ B) & (member223413699real_n @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Int__iff)). 38.11/11.95 thf(420,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) = ((member223413699real_n @ A @ B) & (member223413699real_n @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 38.11/11.95 thf(251,axiom,((t2 = (^ [A:finite964658038_int_n]: (inf_in1974387902real_n @ s @ (r @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_T__def)). 38.11/11.95 thf(1117,plain,(((t2) = (^ [A:finite964658038_int_n]: (inf_in1974387902real_n @ s @ (r @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 38.11/11.95 thf(1118,plain,(((^ [A:finite964658038_int_n]: (inf_in1974387902real_n @ s @ (r @ A))) = (t2))),inference(lifteq,[status(thm)],[1117])). 38.11/11.95 thf(223,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: ((? [C:nat]: (B = (A @ C))) <= ((image_1856576259real_n @ A @ top_top_set_nat) = top_to20708754real_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_surjD)). 38.11/11.95 thf(1028,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: (? [C:nat]: (B = (A @ C)) | ~ ((image_1856576259real_n @ (A) @ top_top_set_nat) = top_to20708754real_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 38.11/11.95 thf(83,axiom,((! [A:(finite1489363574real_n > $o),B:(finite1489363574real_n > $o)]: ((collec321817931real_n @ (^ [C:finite1489363574real_n]: ((A @ C) & (B @ C)))) = (inf_in1974387902real_n @ (collec321817931real_n @ A) @ (collec321817931real_n @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Collect__conj__eq)). 38.11/11.95 thf(554,plain,((! [A:(finite1489363574real_n > $o),B:(finite1489363574real_n > $o)]: ((collec321817931real_n @ (^ [C:finite1489363574real_n]: ((A @ C) & (B @ C)))) = (inf_in1974387902real_n @ (collec321817931real_n @ (A)) @ (collec321817931real_n @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 38.11/11.95 thf(236,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: ((~ (! [C:nat]: (B != (A @ C)))) <= ((image_1856576259real_n @ A @ top_top_set_nat) = top_to20708754real_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_surjE)). 38.11/11.95 thf(1075,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: (~ (! [C:nat]: ~ (B = (A @ C))) | ~ ((image_1856576259real_n @ (A) @ top_top_set_nat) = top_to20708754real_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 38.11/11.95 thf(108,axiom,(((minus_1037315151real_n @ one_on1253059131real_n @ one_on1253059131real_n) = zero_z200130687real_n)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_diff__numeral__special_I9_J)). 38.11/11.95 thf(642,plain,(((minus_1037315151real_n @ one_on1253059131real_n @ one_on1253059131real_n) = zero_z200130687real_n)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 38.11/11.95 thf(93,axiom,((vimage1233683625real_n = (^ [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: (member1352538125real_n @ (A @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_vimage__def)). 38.11/11.95 thf(589,plain,(((vimage1233683625real_n) = (^ [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: (member1352538125real_n @ (A @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 38.11/11.95 thf(590,plain,(((vimage1233683625real_n) = (^ [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: (member1352538125real_n @ (A @ C) @ B)))))),inference(lifteq,[status(thm)],[589])). 38.11/11.95 thf(1153,plain,(((^ [A:nat]: (comple230862828real_n @ lebesg260170249real_n)) != (^ [A:nat]: (comple230862828real_n @ lebesg260170249real_n))) | ((^ [A:nat]: (t2 @ (f @ A))) != (^ [A:nat]: (t @ (f @ A))))),inference(simp,[status(thm)],[267])). 38.11/11.95 thf(1155,plain,(((^ [A:nat]: (t2 @ (f @ A))) != (^ [A:nat]: (t @ (f @ A))))),inference(simp,[status(thm)],[1153])). 38.11/11.95 thf(81,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (vimage1233683625real_n @ B @ C)) => (member1352538125real_n @ (B @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_vimageD)). 38.11/11.95 thf(547,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (vimage1233683625real_n @ (B) @ C)) => (member1352538125real_n @ (B @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 38.11/11.95 thf(250,axiom,((! [A:sigma_1466784463real_n,B:set_Fi1058188332real_n]: (((sigma_1536574303real_n @ A @ B) = zero_z1963244097nnreal) => ((member223413699real_n @ B @ (sigma_1235138647real_n @ A)) => (member223413699real_n @ B @ (measur1402256771real_n @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_null__setsI)). 38.11/11.95 thf(1114,plain,((! [A:sigma_1466784463real_n,B:set_Fi1058188332real_n]: (((sigma_1536574303real_n @ A @ B) = zero_z1963244097nnreal) => ((member223413699real_n @ B @ (sigma_1235138647real_n @ A)) => (member223413699real_n @ B @ (measur1402256771real_n @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 38.11/11.95 thf(125,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((image_439535603real_n @ (^ [D:finite1489363574real_n]: (minus_1037315151real_n @ D @ A)) @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (image_439535603real_n @ (^ [D:finite1489363574real_n]: (minus_1037315151real_n @ D @ A)) @ B) @ (image_439535603real_n @ (^ [D:finite1489363574real_n]: (minus_1037315151real_n @ D @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_translation__subtract__diff)). 38.11/11.95 thf(701,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((image_439535603real_n @ (^ [D:finite1489363574real_n]: (minus_1037315151real_n @ D @ A)) @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (image_439535603real_n @ (^ [D:finite1489363574real_n]: (minus_1037315151real_n @ D @ A)) @ B) @ (image_439535603real_n @ (^ [D:finite1489363574real_n]: (minus_1037315151real_n @ D @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 38.11/11.95 thf(233,axiom,((! [A:(nat > finite964658038_int_n),B:finite964658038_int_n]: (((image_1961920973_int_n @ A @ top_top_set_nat) = top_to131672412_int_n) => (~ (! [C:nat]: (B != (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_surjE)). 38.11/11.95 thf(1060,plain,((! [A:(nat > finite964658038_int_n),B:finite964658038_int_n]: (((image_1961920973_int_n @ (A) @ top_top_set_nat) = top_to131672412_int_n) => (~ (! [C:nat]: ~ (B = (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 38.11/11.95 thf(149,axiom,((! [A:(nat > set_Fi1058188332real_n),B:(set_Fi1058188332real_n > nat)]: (((image_1856576259real_n @ A @ top_top_set_nat) = top_to20708754real_n) <= (! [C:set_Fi1058188332real_n]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_surjI)). 38.11/11.95 thf(779,plain,((! [A:(nat > set_Fi1058188332real_n),B:(set_Fi1058188332real_n > nat)]: (((image_1856576259real_n @ (A) @ top_top_set_nat) = top_to20708754real_n) | ~ (! [C:set_Fi1058188332real_n]: ((A @ (B @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 38.11/11.95 thf(68,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((member1352538125real_n @ D @ B) => (C @ (A @ D)))) <= (! [D:finite1489363574real_n]: ((C @ D) <= (member1352538125real_n @ D @ (image_439535603real_n @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_ball__imageD)). 38.11/11.95 thf(503,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:(finite1489363574real_n > $o)]: (! [D:finite1489363574real_n]: ((member1352538125real_n @ D @ B) => (C @ (A @ D))) | ~ (! [D:finite1489363574real_n]: ((C @ D) | ~ (member1352538125real_n @ D @ (image_439535603real_n @ (A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 38.11/11.95 thf(110,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ A @ top_top_set_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_Int__UNIV__right)). 38.11/11.95 thf(647,plain,((! [A:set_nat]: ((inf_inf_set_nat @ A @ top_top_set_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 38.11/11.95 thf(213,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: (((image_355963305real_n @ A @ top_to131672412_int_n) = top_to20708754real_n) => (~ (! [C:finite964658038_int_n]: (B != (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_surjE)). 38.11/11.95 thf(997,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: (((image_355963305real_n @ (A) @ top_to131672412_int_n) = top_to20708754real_n) => (~ (! [C:finite964658038_int_n]: ~ (B = (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 38.11/11.95 thf(244,axiom,((! [A:set_Ex113815278nnreal]: (((comple1413366923nnreal @ A) = top_to1845833192nnreal) = (! [B:extend1728876344nnreal]: ((ord_le2133614988nnreal @ B @ top_to1845833192nnreal) => (? [C:extend1728876344nnreal]: ((member1217042383nnreal @ C @ A) & (ord_le2133614988nnreal @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Sup__eq__top__iff)). 38.11/11.95 thf(1099,plain,((! [A:set_Ex113815278nnreal]: (((comple1413366923nnreal @ A) = top_to1845833192nnreal) = (! [B:extend1728876344nnreal]: ((ord_le2133614988nnreal @ B @ top_to1845833192nnreal) => (? [C:extend1728876344nnreal]: ((member1217042383nnreal @ C @ A) & (ord_le2133614988nnreal @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 38.11/11.95 thf(209,axiom,((! [A:set_Fi1058188332real_n]: ((vimage1233683625real_n @ (^ [B:finite1489363574real_n]: (B)) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_vimage__ident)). 38.11/11.95 thf(985,plain,((! [A:set_Fi1058188332real_n]: ((vimage1233683625real_n @ (^ [B:finite1489363574real_n]: (B)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 38.11/11.95 thf(27,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n,C:finite1489363574real_n,D:set_Fi1058188332real_n]: (((member1352538125real_n @ C @ D) => (member1352538125real_n @ B @ (vimage1233683625real_n @ A @ D))) <= ((A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_vimageI)). 38.11/11.95 thf(343,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n,C:finite1489363574real_n,D:set_Fi1058188332real_n]: (((member1352538125real_n @ C @ D) => (member1352538125real_n @ B @ (vimage1233683625real_n @ (A) @ D))) | ~ ((A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 38.11/11.95 thf(239,axiom,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: ((member223413699real_n @ A @ (measur1402256771real_n @ B)) => ((member223413699real_n @ (minus_1686442501real_n @ A @ C) @ (measur1402256771real_n @ B)) <= (member223413699real_n @ C @ (sigma_1235138647real_n @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_null__set__Diff)). 38.11/11.95 thf(1086,plain,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: ((member223413699real_n @ A @ (measur1402256771real_n @ B)) => ((member223413699real_n @ (minus_1686442501real_n @ A @ C) @ (measur1402256771real_n @ B)) | ~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 38.11/11.95 thf(105,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ A @ B))) & (C @ D))) = (? [D:nat]: (? [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) & (C @ E)) & (member_nat @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_UN__ball__bex__simps_I4_J)). 38.11/11.95 thf(633,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ (A) @ B))) & (C @ D))) = (? [D:nat]: (? [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) & (C @ E)) & (member_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 38.11/11.95 thf(189,axiom,((! [A:(nat > set_Fi1058188332real_n),B:(finite964658038_int_n > nat),C:set_Fi160064172_int_n]: ((image_1856576259real_n @ A @ (image_497739341_n_nat @ B @ C)) = (image_355963305real_n @ (^ [D:finite964658038_int_n]: (A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_image__image)). 38.11/11.95 thf(921,plain,((! [A:(nat > set_Fi1058188332real_n),B:(finite964658038_int_n > nat),C:set_Fi160064172_int_n]: ((image_1856576259real_n @ (A) @ (image_497739341_n_nat @ (B) @ C)) = (image_355963305real_n @ (^ [D:finite964658038_int_n]: (A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 38.11/11.95 thf(79,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(set_Fi1058188332real_n > $o)]: ((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_355963305real_n @ A @ B)) & (C @ D)))) = (image_355963305real_n @ A @ (collec1941932235_int_n @ (^ [D:finite964658038_int_n]: ((member27055245_int_n @ D @ B) & (C @ (A @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Compr__image__eq)). 38.11/11.95 thf(541,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(set_Fi1058188332real_n > $o)]: ((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_355963305real_n @ A @ B)) & (C @ D)))) = (image_355963305real_n @ (A) @ (collec1941932235_int_n @ (^ [D:finite964658038_int_n]: ((member27055245_int_n @ D @ B) & (C @ (A @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 38.11/11.95 thf(225,axiom,((! [A:(nat > set_Fi1058188332real_n),B:sigma_1466784463real_n]: ((member223413699real_n @ (comple825005695real_n @ (image_1856576259real_n @ A @ top_top_set_nat)) @ (measur1402256771real_n @ B)) <= (! [C:nat]: (member223413699real_n @ (A @ C) @ (measur1402256771real_n @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_null__sets__UN)). 38.11/11.95 thf(1035,plain,((! [A:(nat > set_Fi1058188332real_n),B:sigma_1466784463real_n]: ((member223413699real_n @ (comple825005695real_n @ (image_1856576259real_n @ (A) @ top_top_set_nat)) @ (measur1402256771real_n @ B)) | ~ (! [C:nat]: (member223413699real_n @ (A @ C) @ (measur1402256771real_n @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 38.11/11.95 thf(145,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_se2111327970real_n]: ((vimage1233683625real_n @ A @ (comple825005695real_n @ B)) = (comple825005695real_n @ (image_1661509983real_n @ (vimage1233683625real_n @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_vimage__Union)). 38.11/11.95 thf(765,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_se2111327970real_n]: ((vimage1233683625real_n @ (A) @ (comple825005695real_n @ B)) = (comple825005695real_n @ (image_1661509983real_n @ (vimage1233683625real_n @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 38.11/11.95 thf(231,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(set_Fi1058188332real_n > $o)]: ((! [D:finite964658038_int_n]: ((C @ (A @ D)) <= (member27055245_int_n @ D @ B))) <= (! [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_355963305real_n @ A @ B)) => (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_ball__imageD)). 38.11/11.95 thf(1054,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(set_Fi1058188332real_n > $o)]: (! [D:finite964658038_int_n]: ((C @ (A @ D)) | ~ (member27055245_int_n @ D @ B)) | ~ (! [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_355963305real_n @ (A) @ B)) => (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 38.11/11.95 thf(152,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n]: ((inf_in1974387902real_n @ A @ (comple825005695real_n @ B)) = (comple825005695real_n @ (image_1661509983real_n @ (inf_in1974387902real_n @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Int__Union)). 38.11/11.95 thf(794,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n]: ((inf_in1974387902real_n @ A @ (comple825005695real_n @ B)) = (comple825005695real_n @ (image_1661509983real_n @ (inf_in1974387902real_n @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 38.11/11.95 thf(92,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ A @ B))) & (C @ D))) = (? [D:nat]: ((member_nat @ D @ B) & ? [E:finite1489363574real_n]: ((C @ E) & (member1352538125real_n @ E @ (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_bex__UN)). 38.11/11.95 thf(586,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ (A) @ B))) & (C @ D))) = (? [D:nat]: ((member_nat @ D @ B) & ? [E:finite1489363574real_n]: ((C @ E) & (member1352538125real_n @ E @ (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 38.11/11.95 thf(115,axiom,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:nat]: ((A = (B @ C)) => (member223413699real_n @ A @ (image_1856576259real_n @ B @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_range__eqI)). 38.11/11.95 thf(662,plain,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:nat]: ((A = (B @ C)) => (member223413699real_n @ A @ (image_1856576259real_n @ (B) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 38.11/11.95 thf(179,axiom,((! [A:(nat > finite964658038_int_n),B:(finite964658038_int_n > nat)]: ((! [C:finite964658038_int_n]: ((A @ (B @ C)) = C)) => ((image_1961920973_int_n @ A @ top_top_set_nat) = top_to131672412_int_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_surjI)). 38.11/11.95 thf(888,plain,((! [A:(nat > finite964658038_int_n),B:(finite964658038_int_n > nat)]: ((! [C:finite964658038_int_n]: ((A @ (B @ C)) = C)) => ((image_1961920973_int_n @ (A) @ top_top_set_nat) = top_to131672412_int_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 38.11/11.95 thf(172,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(finite964658038_int_n > finite964658038_int_n)]: ((image_355963305real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_355963305real_n @ A @ (image_1278151539_int_n @ B @ top_to131672412_int_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_range__composition)). 38.11/11.95 thf(856,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(finite964658038_int_n > finite964658038_int_n)]: ((image_355963305real_n @ (^ [C:finite964658038_int_n]: (A @ (B @ C))) @ top_to131672412_int_n) = (image_355963305real_n @ (A) @ (image_1278151539_int_n @ (B) @ top_to131672412_int_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 38.11/11.95 thf(7,axiom,((! [A:set_Fi1058188332real_n,B:(set_Fi1058188332real_n > $o)]: ((member223413699real_n @ A @ (collec452821761real_n @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_mem__Collect__eq)). 38.11/11.95 thf(279,plain,((! [A:set_Fi1058188332real_n,B:(set_Fi1058188332real_n > $o)]: ((member223413699real_n @ A @ (collec452821761real_n @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 38.11/11.95 thf(96,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((C @ D) <= (member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ A @ B))))) = (! [D:nat]: ((! [E:finite1489363574real_n]: ((C @ E) <= (member1352538125real_n @ E @ (A @ D)))) <= (member_nat @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_UN__ball__bex__simps_I2_J)). 38.11/11.95 thf(601,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((C @ D) | ~ (member1352538125real_n @ D @ (comple825005695real_n @ (image_1856576259real_n @ (A) @ B))))) = (! [D:nat]: (! [E:finite1489363574real_n]: ((C @ E) | ~ (member1352538125real_n @ E @ (A @ D))) | ~ (member_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 38.11/11.95 thf(71,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (image_439535603real_n @ B @ C)) = (? [D:finite1489363574real_n]: ((A = (B @ D)) & (member1352538125real_n @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_image__iff)). 38.11/11.95 thf(513,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (image_439535603real_n @ (B) @ C)) = (? [D:finite1489363574real_n]: ((A = (B @ D)) & (member1352538125real_n @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 38.11/11.95 thf(263,axiom,((member223413699real_n @ s @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms_I1_J)). 38.11/11.95 thf(1146,plain,((member223413699real_n @ s @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 38.11/11.95 thf(160,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_set_nat]: ((comple825005695real_n @ (image_933134521real_n @ (^ [C:set_nat]: (comple825005695real_n @ (image_1856576259real_n @ A @ C))) @ B)) = (comple825005695real_n @ (image_1856576259real_n @ A @ (comple1682161881et_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_UN__extend__simps_I8_J)). 38.11/11.95 thf(819,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_set_nat]: ((comple825005695real_n @ (image_933134521real_n @ (^ [C:set_nat]: (comple825005695real_n @ (image_1856576259real_n @ A @ C))) @ B)) = (comple825005695real_n @ (image_1856576259real_n @ (A) @ (comple1682161881et_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 38.11/11.95 thf(206,axiom,((! [A:(nat > nat)]: ((vimage_nat_nat @ A @ top_top_set_nat) = top_top_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_vimage__UNIV)). 38.11/11.95 thf(975,plain,((! [A:(nat > nat)]: ((vimage_nat_nat @ (A) @ top_top_set_nat) = top_top_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 38.11/11.95 thf(49,axiom,((! [A:(finite964658038_int_n > finite964658038_int_n),B:(finite964658038_int_n > finite964658038_int_n)]: (((image_1278151539_int_n @ A @ top_to131672412_int_n) = top_to131672412_int_n) <= (! [C:finite964658038_int_n]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_surjI)). 38.11/11.95 thf(423,plain,((! [A:(finite964658038_int_n > finite964658038_int_n),B:(finite964658038_int_n > finite964658038_int_n)]: (((image_1278151539_int_n @ (A) @ top_to131672412_int_n) = top_to131672412_int_n) | ~ (! [C:finite964658038_int_n]: ((A @ (B @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 38.11/11.95 thf(216,axiom,((! [A:(nat > finite964658038_int_n)]: (((image_1961920973_int_n @ A @ top_top_set_nat) = top_to131672412_int_n) = (! [B:finite964658038_int_n]: ? [C:nat]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_surj__def)). 38.11/11.95 thf(1007,plain,((! [A:(nat > finite964658038_int_n)]: (((image_1961920973_int_n @ (A) @ top_top_set_nat) = top_to131672412_int_n) = (! [B:finite964658038_int_n]: ? [C:nat]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 38.11/11.95 thf(138,axiom,((! [A:set_Fi1058188332real_n]: ((image_439535603real_n @ (^ [B:finite1489363574real_n]: (B)) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_image__ident)). 38.11/11.95 thf(743,plain,((! [A:set_Fi1058188332real_n]: ((image_439535603real_n @ (^ [B:finite1489363574real_n]: (B)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 38.11/11.95 thf(11,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: (((member1352538125real_n @ A @ C) => (member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C))) <= (member1352538125real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_IntI)). 38.11/11.95 thf(291,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: (((member1352538125real_n @ A @ C) => (member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C))) | ~ (member1352538125real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 38.11/11.95 thf(201,axiom,((! [A:set_se2111327970real_n,B:(finite1489363574real_n > $o)]: ((! [C:finite1489363574real_n]: ((member1352538125real_n @ C @ (comple825005695real_n @ A)) => (B @ C))) = (! [C:set_Fi1058188332real_n]: ((! [D:finite1489363574real_n]: ((member1352538125real_n @ D @ C) => (B @ D))) <= (member223413699real_n @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_UN__ball__bex__simps_I1_J)). 38.11/11.95 thf(958,plain,((! [A:set_se2111327970real_n,B:(finite1489363574real_n > $o)]: ((! [C:finite1489363574real_n]: ((member1352538125real_n @ C @ (comple825005695real_n @ A)) => (B @ C))) = (! [C:set_Fi1058188332real_n]: (! [D:finite1489363574real_n]: ((member1352538125real_n @ D @ C) => (B @ D)) | ~ (member223413699real_n @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 38.11/11.95 thf(46,axiom,((! [A:(nat > nat),B:nat]: ((? [C:nat]: (B = (A @ C))) <= ((image_nat_nat @ A @ top_top_set_nat) = top_top_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_surjD)). 38.11/11.95 thf(413,plain,((! [A:(nat > nat),B:nat]: (? [C:nat]: (B = (A @ C)) | ~ ((image_nat_nat @ (A) @ top_top_set_nat) = top_top_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 38.11/11.95 thf(843,plain,(((collect_nat @ (top_top_nat_o)) = top_top_set_nat)),inference(lifteq,[status(thm)],[842])). 38.11/11.95 thf(255,axiom,((! [A:(nat > set_Fi1058188332real_n),B:sigma_1466784463real_n]: ((! [C:nat]: (member223413699real_n @ (A @ C) @ (sigma_1235138647real_n @ B))) => ((! [C:nat,D:nat]: ((C != D) => ((sigma_1536574303real_n @ B @ (inf_in1974387902real_n @ (A @ C) @ (A @ D))) = zero_z1963244097nnreal))) => (sums_E1192373732nnreal @ (^ [C:nat]: (sigma_1536574303real_n @ B @ (A @ C))) @ (sigma_1536574303real_n @ B @ (comple825005695real_n @ (image_1856576259real_n @ A @ top_top_set_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_sums__emeasure_H)). 38.11/11.95 thf(1125,plain,((! [A:(nat > set_Fi1058188332real_n),B:sigma_1466784463real_n]: ((! [C:nat]: (member223413699real_n @ (A @ C) @ (sigma_1235138647real_n @ B))) => ((! [C:nat,D:nat]: ((~ (C = D)) => ((sigma_1536574303real_n @ B @ (inf_in1974387902real_n @ (A @ C) @ (A @ D))) = zero_z1963244097nnreal))) => (sums_E1192373732nnreal @ (^ [C:nat]: (sigma_1536574303real_n @ B @ (A @ C))) @ (sigma_1536574303real_n @ B @ (comple825005695real_n @ (image_1856576259real_n @ (A) @ top_top_set_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 38.11/11.95 thf(89,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((C @ D) <= (member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ A @ B))))) = (! [D:finite964658038_int_n]: ((! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) => (C @ E))) <= (member27055245_int_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ball__UN)). 38.11/11.95 thf(577,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((! [D:finite1489363574real_n]: ((C @ D) | ~ (member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ (A) @ B))))) = (! [D:finite964658038_int_n]: (! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) => (C @ E)) | ~ (member27055245_int_n @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 38.11/11.95 thf(128,axiom,((! [A:(nat > set_Fi1058188332real_n),B:(nat > set_nat),C:set_nat]: ((comple825005695real_n @ (image_1856576259real_n @ A @ (comple1682161881et_nat @ (image_nat_set_nat @ B @ C)))) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_1856576259real_n @ A @ (B @ D)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_UN__UN__flatten)). 38.11/11.95 thf(711,plain,((! [A:(nat > set_Fi1058188332real_n),B:(nat > set_nat),C:set_nat]: ((comple825005695real_n @ (image_1856576259real_n @ (A) @ (comple1682161881et_nat @ (image_nat_set_nat @ (B) @ C)))) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_1856576259real_n @ A @ (B @ D)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 38.11/11.95 thf(41,axiom,((! [A:(finite1489363574real_n > set_Fi1058188332real_n),B:set_se2111327970real_n]: ((comple825005695real_n @ (image_1661509983real_n @ (^ [C:set_Fi1058188332real_n]: (comple825005695real_n @ (image_545463721real_n @ A @ C))) @ B)) = (comple825005695real_n @ (image_545463721real_n @ A @ (comple825005695real_n @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_UN__extend__simps_I8_J)). 38.11/11.95 thf(391,plain,((! [A:(finite1489363574real_n > set_Fi1058188332real_n),B:set_se2111327970real_n]: ((comple825005695real_n @ (image_1661509983real_n @ (^ [C:set_Fi1058188332real_n]: (comple825005695real_n @ (image_545463721real_n @ A @ C))) @ B)) = (comple825005695real_n @ (image_545463721real_n @ (A) @ (comple825005695real_n @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 38.11/11.95 thf(247,axiom,((s = (comple825005695real_n @ (image_355963305real_n @ t2 @ top_to131672412_int_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_S__decompose)). 38.11/11.95 thf(1107,plain,((s = (comple825005695real_n @ (image_355963305real_n @ (t2) @ top_to131672412_int_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 38.11/11.95 thf(241,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(nat > finite964658038_int_n)]: ((image_1856576259real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_355963305real_n @ A @ (image_1961920973_int_n @ B @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_range__composition)). 38.11/11.95 thf(1092,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(nat > finite964658038_int_n)]: ((image_1856576259real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_355963305real_n @ (A) @ (image_1961920973_int_n @ (B) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 38.11/11.95 thf(126,axiom,((! [A:(finite964658038_int_n > nat),B:(nat > finite964658038_int_n)]: ((! [C:nat]: ((A @ (B @ C)) = C)) => ((image_497739341_n_nat @ A @ top_to131672412_int_n) = top_top_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_surjI)). 38.11/11.95 thf(704,plain,((! [A:(finite964658038_int_n > nat),B:(nat > finite964658038_int_n)]: ((! [C:nat]: ((A @ (B @ C)) = C)) => ((image_497739341_n_nat @ (A) @ top_to131672412_int_n) = top_top_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 38.11/11.95 thf(53,axiom,((! [A:(nat > set_Fi1058188332real_n),B:(nat > nat),C:set_nat]: ((image_1856576259real_n @ A @ (image_nat_nat @ B @ C)) = (image_1856576259real_n @ (^ [D:nat]: (A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_image__image)). 38.11/11.95 thf(445,plain,((! [A:(nat > set_Fi1058188332real_n),B:(nat > nat),C:set_nat]: ((image_1856576259real_n @ (A) @ (image_nat_nat @ (B) @ C)) = (image_1856576259real_n @ (^ [D:nat]: (A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 38.11/11.95 thf(194,axiom,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n]: (((inf_in1108485182_int_n @ A @ B) = top_to131672412_int_n) = ((A = top_to131672412_int_n) & (B = top_to131672412_int_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Int__UNIV)). 38.11/11.95 thf(936,plain,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n]: (((inf_in1108485182_int_n @ A @ B) = top_to131672412_int_n) = ((A = top_to131672412_int_n) & (B = top_to131672412_int_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 38.11/11.95 thf(97,axiom,((! [A:(finite964658038_int_n > finite964658038_int_n),B:finite964658038_int_n]: ((? [C:finite964658038_int_n]: (B = (A @ C))) <= ((image_1278151539_int_n @ A @ top_to131672412_int_n) = top_to131672412_int_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_surjD)). 38.11/11.95 thf(604,plain,((! [A:(finite964658038_int_n > finite964658038_int_n),B:finite964658038_int_n]: (? [C:finite964658038_int_n]: (B = (A @ C)) | ~ ((image_1278151539_int_n @ (A) @ top_to131672412_int_n) = top_to131672412_int_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 38.11/11.95 thf(164,axiom,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:finite964658038_int_n,D:set_Fi160064172_int_n]: (((member27055245_int_n @ C @ D) => (member223413699real_n @ A @ (image_355963305real_n @ B @ D))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_image__eqI)). 38.11/11.95 thf(831,plain,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:finite964658038_int_n,D:set_Fi160064172_int_n]: (((member27055245_int_n @ C @ D) => (member223413699real_n @ A @ (image_355963305real_n @ (B) @ D))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 38.11/11.95 thf(119,axiom,((! [A:finite1489363574real_n]: ((image_439535603real_n @ (^ [B:finite1489363574real_n]: (minus_1037315151real_n @ B @ A)) @ top_to1292442332real_n) = top_to1292442332real_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_surj__diff__right)). 38.11/11.95 thf(681,plain,((! [A:finite1489363574real_n]: ((image_439535603real_n @ (^ [B:finite1489363574real_n]: (minus_1037315151real_n @ B @ A)) @ top_to1292442332real_n) = top_to1292442332real_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 38.11/11.95 thf(228,axiom,((! [A:(finite1489363574real_n > set_Fi1058188332real_n),B:(nat > set_Fi1058188332real_n),C:set_nat]: ((comple825005695real_n @ (image_545463721real_n @ A @ (comple825005695real_n @ (image_1856576259real_n @ B @ C)))) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_545463721real_n @ A @ (B @ D)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_UN__UN__flatten)). 38.11/11.95 thf(1043,plain,((! [A:(finite1489363574real_n > set_Fi1058188332real_n),B:(nat > set_Fi1058188332real_n),C:set_nat]: ((comple825005695real_n @ (image_545463721real_n @ (A) @ (comple825005695real_n @ (image_1856576259real_n @ (B) @ C)))) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_545463721real_n @ A @ (B @ D)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 38.11/11.95 thf(4,axiom,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:set_se2111327970real_n,C:(set_Fi1058188332real_n > $o)]: ((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_1661509983real_n @ A @ B)) & (C @ D)))) = (image_1661509983real_n @ A @ (collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((C @ (A @ D)) & (member223413699real_n @ D @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Compr__image__eq)). 38.11/11.95 thf(271,plain,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:set_se2111327970real_n,C:(set_Fi1058188332real_n > $o)]: ((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_1661509983real_n @ A @ B)) & (C @ D)))) = (image_1661509983real_n @ (A) @ (collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((C @ (A @ D)) & (member223413699real_n @ D @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 38.11/11.95 thf(95,axiom,(((comple825005695real_n @ top_to20708754real_n) = top_to1292442332real_n)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_Union__UNIV)). 38.11/11.95 thf(599,plain,(((comple825005695real_n @ top_to20708754real_n) = top_to1292442332real_n)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 38.11/11.95 thf(32,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ (B @ A) @ C) <= (member1352538125real_n @ A @ (vimage1233683625real_n @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_vimageE)). 38.11/11.95 thf(362,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ (B @ A) @ C) | ~ (member1352538125real_n @ A @ (vimage1233683625real_n @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 38.11/11.95 thf(55,axiom,((! [A:(finite964658038_int_n > finite964658038_int_n)]: (((image_1278151539_int_n @ A @ top_to131672412_int_n) = top_to131672412_int_n) = (! [B:finite964658038_int_n]: ? [C:finite964658038_int_n]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_surj__def)). 38.11/11.95 thf(451,plain,((! [A:(finite964658038_int_n > finite964658038_int_n)]: (((image_1278151539_int_n @ (A) @ top_to131672412_int_n) = top_to131672412_int_n) = (! [B:finite964658038_int_n]: ? [C:finite964658038_int_n]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 38.11/11.95 thf(136,axiom,((! [A:(nat > finite964658038_int_n)]: ((vimage714719107_int_n @ A @ top_to131672412_int_n) = top_top_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_vimage__UNIV)). 38.11/11.95 thf(737,plain,((! [A:(nat > finite964658038_int_n)]: ((vimage714719107_int_n @ (A) @ top_to131672412_int_n) = top_top_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 38.11/11.95 thf(19,axiom,((? [A:finite964658038_int_n]: (member27055245_int_n @ A @ top_to131672412_int_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_UNIV__witness)). 38.11/11.95 thf(318,plain,((? [A:finite964658038_int_n]: (member27055245_int_n @ A @ top_to131672412_int_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 38.11/11.95 thf(62,axiom,((! [A:nat]: (member_nat @ A @ top_top_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_UNIV__I)). 38.11/11.95 thf(477,plain,((! [A:nat]: (member_nat @ A @ top_top_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 38.11/11.95 thf(39,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ B @ (vimage1233683625real_n @ A @ C)) <= (member1352538125real_n @ (A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_vimageI2)). 38.11/11.95 thf(387,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ B @ (vimage1233683625real_n @ (A) @ C)) | ~ (member1352538125real_n @ (A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 38.11/11.95 thf(34,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n)]: (((image_439535603real_n @ A @ top_to1292442332real_n) = top_to1292442332real_n) = (! [B:finite1489363574real_n]: ? [C:finite1489363574real_n]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_surj__def)). 38.11/11.95 thf(367,plain,((! [A:(finite1489363574real_n > finite1489363574real_n)]: (((image_439535603real_n @ (A) @ top_to1292442332real_n) = top_to1292442332real_n) = (! [B:finite1489363574real_n]: ? [C:finite1489363574real_n]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 38.11/11.95 thf(77,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n)]: ((vimage1233683625real_n @ A @ top_to1292442332real_n) = top_to1292442332real_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_vimage__UNIV)). 38.11/11.95 thf(535,plain,((! [A:(finite1489363574real_n > finite1489363574real_n)]: ((vimage1233683625real_n @ (A) @ top_to1292442332real_n) = top_to1292442332real_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 38.11/11.95 thf(159,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ (inf_in1974387902real_n @ B @ C)) = (inf_in1974387902real_n @ B @ (inf_in1974387902real_n @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Int__left__commute)). 38.11/11.95 thf(816,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ (inf_in1974387902real_n @ B @ C)) = (inf_in1974387902real_n @ B @ (inf_in1974387902real_n @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 38.11/11.95 thf(21,axiom,((! [A:(nat > nat)]: (((image_nat_nat @ A @ top_top_set_nat) = top_top_set_nat) = (! [B:nat]: ? [C:nat]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_surj__def)). 38.11/11.95 thf(323,plain,((! [A:(nat > nat)]: (((image_nat_nat @ (A) @ top_top_set_nat) = top_top_set_nat) = (! [B:nat]: ? [C:nat]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 38.11/11.95 thf(102,axiom,((! [A:set_Fi1058188332real_n,B:(set_Fi1058188332real_n > set_Fi1058188332real_n),C:set_Fi1058188332real_n,D:set_se2111327970real_n]: ((A = (B @ C)) => ((member223413699real_n @ C @ D) => (member223413699real_n @ A @ (image_1661509983real_n @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_image__eqI)). 38.11/11.95 thf(621,plain,((! [A:set_Fi1058188332real_n,B:(set_Fi1058188332real_n > set_Fi1058188332real_n),C:set_Fi1058188332real_n,D:set_se2111327970real_n]: ((A = (B @ C)) => ((member223413699real_n @ C @ D) => (member223413699real_n @ A @ (image_1661509983real_n @ (B) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 38.11/11.95 thf(73,axiom,((! [A:finite1489363574real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_1856576259real_n @ B @ C))) = (? [D:nat]: ((member1352538125real_n @ A @ (B @ D)) & (member_nat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_UN__iff)). 38.11/11.95 thf(520,plain,((! [A:finite1489363574real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_1856576259real_n @ (B) @ C))) = (? [D:nat]: ((member1352538125real_n @ A @ (B @ D)) & (member_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 38.11/11.95 thf(203,axiom,((! [A:(finite964658038_int_n > nat)]: (((image_497739341_n_nat @ A @ top_to131672412_int_n) = top_top_set_nat) = (! [B:nat]: ? [C:finite964658038_int_n]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_surj__def)). 38.11/11.95 thf(964,plain,((! [A:(finite964658038_int_n > nat)]: (((image_497739341_n_nat @ (A) @ top_to131672412_int_n) = top_top_set_nat) = (! [B:nat]: ? [C:finite964658038_int_n]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 38.11/11.95 thf(196,axiom,((! [A:finite1489363574real_n,B:set_se2111327970real_n]: ((member1352538125real_n @ A @ (comple825005695real_n @ B)) = (? [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ B) & (member1352538125real_n @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Union__iff)). 38.11/11.95 thf(943,plain,((! [A:finite1489363574real_n,B:set_se2111327970real_n]: ((member1352538125real_n @ A @ (comple825005695real_n @ B)) = (? [C:set_Fi1058188332real_n]: ((member223413699real_n @ C @ B) & (member1352538125real_n @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 38.11/11.95 thf(58,axiom,((! [A:set_se2111327970real_n]: ((! [B:set_Fi1058188332real_n]: (member223413699real_n @ B @ A)) => (top_to20708754real_n = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_UNIV__eq__I)). 38.11/11.95 thf(462,plain,((! [A:set_se2111327970real_n]: ((! [B:set_Fi1058188332real_n]: (member223413699real_n @ B @ A)) => (top_to20708754real_n = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 38.11/11.95 thf(249,axiom,((! [A:finite964658038_int_n]: ((member223413699real_n @ (t2 @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) => (member223413699real_n @ (inf_in1974387902real_n @ (vimage1233683625real_n @ (^ [B:finite1489363574real_n]: (plus_p585657087real_n @ B @ (minkow1134813771n_real @ A))) @ (t2 @ A)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062)). 38.11/11.95 thf(1112,plain,((! [A:finite964658038_int_n]: ((member223413699real_n @ (t2 @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) => (member223413699real_n @ (inf_in1974387902real_n @ (vimage1233683625real_n @ (^ [B:finite1489363574real_n]: (plus_p585657087real_n @ B @ (minkow1134813771n_real @ A))) @ (t2 @ A)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 38.11/11.95 thf(103,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n)]: ((member1352538125real_n @ A @ (image_439535603real_n @ B @ top_to1292442332real_n)) => (~ (! [C:finite1489363574real_n]: (A != (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_rangeE)). 38.11/11.95 thf(626,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n)]: ((member1352538125real_n @ A @ (image_439535603real_n @ (B) @ top_to1292442332real_n)) => (~ (! [C:finite1489363574real_n]: ~ (A = (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 38.11/11.95 thf(187,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_se2111327970real_n]: ((image_355963305real_n @ A @ (vimage464515423real_n @ A @ B)) = (inf_in632889204real_n @ B @ (image_355963305real_n @ A @ top_to131672412_int_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_image__vimage__eq)). 38.11/11.95 thf(915,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_se2111327970real_n]: ((image_355963305real_n @ (A) @ (vimage464515423real_n @ (A) @ B)) = (inf_in632889204real_n @ B @ (image_355963305real_n @ (A) @ top_to131672412_int_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 38.11/11.95 thf(1197,plain,(((^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: ((member1352538125real_n @ C @ A) & (member1352538125real_n @ C @ B))))) = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (inf_in1974387902real_n @ B @ A))) | ((inf_in1974387902real_n) != (inf_in1974387902real_n))),inference(paramod_ordered,[status(thm)],[428,756])). 38.11/11.95 thf(1198,plain,(((^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (collec321817931real_n @ (^ [C:finite1489363574real_n]: ((member1352538125real_n @ C @ A) & (member1352538125real_n @ C @ B))))) = (^ [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (inf_in1974387902real_n @ B @ A)))),inference(pattern_uni,[status(thm)],[1197:[]])). 38.11/11.95 thf(43,axiom,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: (((! [F:finite964658038_int_n]: ((member27055245_int_n @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_355963305real_n @ C @ A)) = (E @ (image_355963305real_n @ D @ B)))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Sup_OSUP__cong)). 38.11/11.95 thf(399,plain,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: (((! [F:finite964658038_int_n]: ((member27055245_int_n @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_355963305real_n @ (C) @ A)) = (E @ (image_355963305real_n @ (D) @ B)))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 38.11/11.95 thf(146,axiom,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n]: ((member223413699real_n @ A @ (measur1402256771real_n @ B)) => (member223413699real_n @ A @ (sigma_1235138647real_n @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_null__setsD2)). 38.11/11.95 thf(768,plain,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n]: ((member223413699real_n @ A @ (measur1402256771real_n @ B)) => (member223413699real_n @ A @ (sigma_1235138647real_n @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 38.11/11.95 thf(277,plain,(! [C:(set_Fi1058188332real_n > $o),B:set_se2111327970real_n,A:set_Fi1058188332real_n] : (((member223413699real_n @ A @ (inf_in632889204real_n @ B @ (collec452821761real_n @ (C)))) = ((member223413699real_n @ A @ B) & (C @ A))))),inference(cnf,[status(esa)],[276])). 38.11/11.95 thf(278,plain,(! [C:(set_Fi1058188332real_n > $o),B:set_se2111327970real_n,A:set_Fi1058188332real_n] : (((member223413699real_n @ A @ (inf_in632889204real_n @ B @ (collec452821761real_n @ (C)))) = ((member223413699real_n @ A @ B) & (C @ A))))),inference(lifteq,[status(thm)],[277])). 38.11/11.95 thf(98,axiom,((! [A:set_Fi1058188332real_n,B:(set_Fi1058188332real_n > set_Fi1058188332real_n),C:set_se2111327970real_n]: ((member223413699real_n @ A @ (image_1661509983real_n @ B @ C)) => (~ (! [D:set_Fi1058188332real_n]: ((A = (B @ D)) => (~ (member223413699real_n @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_imageE)). 38.11/11.95 thf(608,plain,((! [A:set_Fi1058188332real_n,B:(set_Fi1058188332real_n > set_Fi1058188332real_n),C:set_se2111327970real_n]: ((member223413699real_n @ A @ (image_1661509983real_n @ (B) @ C)) => (~ (! [D:set_Fi1058188332real_n]: ((A = (B @ D)) => (~ (member223413699real_n @ D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 38.11/11.95 thf(42,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:finite1489363574real_n,D:set_Fi1058188332real_n]: (((member1352538125real_n @ C @ D) => (member1352538125real_n @ A @ (image_439535603real_n @ B @ D))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_image__eqI)). 38.11/11.95 thf(394,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:finite1489363574real_n,D:set_Fi1058188332real_n]: (((member1352538125real_n @ C @ D) => (member1352538125real_n @ A @ (image_439535603real_n @ (B) @ D))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 38.11/11.95 thf(112,axiom,((! [A:set_Fi160064172_int_n]: ((inf_in1108485182_int_n @ top_to131672412_int_n @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_Int__UNIV__left)). 38.11/11.95 thf(653,plain,((! [A:set_Fi160064172_int_n]: ((inf_in1108485182_int_n @ top_to131672412_int_n @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 38.11/11.95 thf(106,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:finite1489363574real_n,D:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: (((member1352538125real_n @ C @ (D @ A)) => (member1352538125real_n @ C @ (comple825005695real_n @ (image_1661509983real_n @ D @ B)))) <= (member223413699real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_UN__I)). 38.11/11.95 thf(636,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:finite1489363574real_n,D:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: (((member1352538125real_n @ C @ (D @ A)) => (member1352538125real_n @ C @ (comple825005695real_n @ (image_1661509983real_n @ (D) @ B)))) | ~ (member223413699real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 38.11/11.95 thf(123,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((image_439535603real_n @ A @ (vimage1233683625real_n @ A @ B)) = (inf_in1974387902real_n @ B @ (image_439535603real_n @ A @ top_to1292442332real_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_image__vimage__eq)). 38.11/11.95 thf(695,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((image_439535603real_n @ (A) @ (vimage1233683625real_n @ (A) @ B)) = (inf_in1974387902real_n @ B @ (image_439535603real_n @ (A) @ top_to1292442332real_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 38.11/11.95 thf(245,axiom,((! [A:finite964658038_int_n]: ((t @ A) = (vimage1233683625real_n @ (^ [B:finite1489363574real_n]: (plus_p585657087real_n @ B @ (minkow1134813771n_real @ A))) @ (t2 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_T_H__altdef)). 38.11/11.95 thf(1102,plain,((! [A:finite964658038_int_n]: ((t @ A) = (vimage1233683625real_n @ (^ [B:finite1489363574real_n]: (plus_p585657087real_n @ B @ (minkow1134813771n_real @ A))) @ (t2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 38.11/11.95 thf(61,axiom,((! [A:(finite964658038_int_n > finite964658038_int_n),B:finite964658038_int_n]: ((~ (! [C:finite964658038_int_n]: (B != (A @ C)))) <= ((image_1278151539_int_n @ A @ top_to131672412_int_n) = top_to131672412_int_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_surjE)). 38.11/11.95 thf(473,plain,((! [A:(finite964658038_int_n > finite964658038_int_n),B:finite964658038_int_n]: (~ (! [C:finite964658038_int_n]: ~ (B = (A @ C))) | ~ ((image_1278151539_int_n @ (A) @ top_to131672412_int_n) = top_to131672412_int_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 38.11/11.95 thf(191,axiom,((! [A:(finite964658038_int_n > nat),B:nat]: (((image_497739341_n_nat @ A @ top_to131672412_int_n) = top_top_set_nat) => (? [C:finite964658038_int_n]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_surjD)). 38.11/11.95 thf(927,plain,((! [A:(finite964658038_int_n > nat),B:nat]: (((image_497739341_n_nat @ (A) @ top_to131672412_int_n) = top_top_set_nat) => (? [C:finite964658038_int_n]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 38.11/11.95 thf(140,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ (minus_1686442501real_n @ A @ B) @ C) = (minus_1686442501real_n @ (inf_in1974387902real_n @ A @ C) @ (inf_in1974387902real_n @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Diff__Int__distrib2)). 38.11/11.95 thf(749,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ (minus_1686442501real_n @ A @ B) @ C) = (minus_1686442501real_n @ (inf_in1974387902real_n @ A @ C) @ (inf_in1974387902real_n @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 38.11/11.95 thf(72,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n]: ((~ (! [C:finite1489363574real_n]: (B != (A @ C)))) <= ((image_439535603real_n @ A @ top_to1292442332real_n) = top_to1292442332real_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_surjE)). 38.11/11.95 thf(516,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n]: (~ (! [C:finite1489363574real_n]: ~ (B = (A @ C))) | ~ ((image_439535603real_n @ (A) @ top_to1292442332real_n) = top_to1292442332real_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 38.11/11.95 thf(195,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: ((? [C:finite964658038_int_n]: (B = (A @ C))) <= ((image_355963305real_n @ A @ top_to131672412_int_n) = top_to20708754real_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_surjD)). 38.11/11.95 thf(939,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi1058188332real_n]: (? [C:finite964658038_int_n]: (B = (A @ C)) | ~ ((image_355963305real_n @ (A) @ top_to131672412_int_n) = top_to20708754real_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 38.11/11.95 thf(262,axiom,((sums_E1192373732nnreal @ (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) @ (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ s))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_calculation)). 38.11/11.95 thf(1145,plain,((sums_E1192373732nnreal @ (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) @ (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ s))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 38.11/11.95 thf(30,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > finite1489363574real_n)]: (((image_439535603real_n @ A @ top_to1292442332real_n) = top_to1292442332real_n) <= (! [C:finite1489363574real_n]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_surjI)). 38.11/11.95 thf(355,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > finite1489363574real_n)]: (((image_439535603real_n @ (A) @ top_to1292442332real_n) = top_to1292442332real_n) | ~ (! [C:finite1489363574real_n]: ((A @ (B @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 38.11/11.95 thf(165,axiom,((! [A:sigma_1466784463real_n,B:(finite1489363574real_n > $o),C:(finite1489363574real_n > $o)]: (((member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (C @ D)))) @ (measur1402256771real_n @ A)) => (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (B @ D) & (C @ D)))) @ (measur1402256771real_n @ A))) <= (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (B @ D)))) @ (measur1402256771real_n @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_null__sets_Osets__Collect__conj)). 38.11/11.95 thf(836,plain,((! [A:sigma_1466784463real_n,B:(finite1489363574real_n > $o),C:(finite1489363574real_n > $o)]: (((member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (C @ D)))) @ (measur1402256771real_n @ A)) => (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (B @ D) & (C @ D)))) @ (measur1402256771real_n @ A))) | ~ (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (B @ D)))) @ (measur1402256771real_n @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 38.11/11.95 thf(230,axiom,((! [A:nat,B:set_nat,C:set_Fi1058188332real_n,D:(nat > set_Fi1058188332real_n)]: (((C = (D @ A)) => (member223413699real_n @ C @ (image_1856576259real_n @ D @ B))) <= (member_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_rev__image__eqI)). 38.11/11.95 thf(1049,plain,((! [A:nat,B:set_nat,C:set_Fi1058188332real_n,D:(nat > set_Fi1058188332real_n)]: (((C = (D @ A)) => (member223413699real_n @ C @ (image_1856576259real_n @ (D) @ B))) | ~ (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 38.11/11.95 thf(65,axiom,(((comple825005695real_n @ top_to20708754real_n) = top_to1292442332real_n)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Sup__UNIV)). 38.11/11.95 thf(490,plain,(((comple825005695real_n @ top_to20708754real_n) = top_to1292442332real_n)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 38.11/11.95 thf(117,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((image_439535603real_n @ (plus_p585657087real_n @ A) @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (image_439535603real_n @ (plus_p585657087real_n @ A) @ B) @ (image_439535603real_n @ (plus_p585657087real_n @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_translation__diff)). 38.11/11.95 thf(675,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((image_439535603real_n @ (plus_p585657087real_n @ A) @ (minus_1686442501real_n @ B @ C)) = (minus_1686442501real_n @ (image_439535603real_n @ (plus_p585657087real_n @ A) @ B) @ (image_439535603real_n @ (plus_p585657087real_n @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 38.11/11.95 thf(75,axiom,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: ((A = B) => ((! [F:nat]: ((member_nat @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_1856576259real_n @ C @ A)) = (E @ (image_1856576259real_n @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Inf_OINF__cong)). 38.11/11.95 thf(525,plain,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: ((A = B) => ((! [F:nat]: ((member_nat @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_1856576259real_n @ (C) @ A)) = (E @ (image_1856576259real_n @ (D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 38.11/11.95 thf(84,axiom,((! [A:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ top_to1292442332real_n @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_Int__UNIV__left)). 38.11/11.95 thf(557,plain,((! [A:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ top_to1292442332real_n @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 38.11/11.95 thf(90,axiom,((! [A:set_se2111327970real_n]: ((comple825005695real_n @ (image_1661509983real_n @ (^ [B:set_Fi1058188332real_n]: (B)) @ A)) = (comple825005695real_n @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_SUP__identity__eq)). 38.11/11.95 thf(580,plain,((! [A:set_se2111327970real_n]: ((comple825005695real_n @ (image_1661509983real_n @ (^ [B:set_Fi1058188332real_n]: (B)) @ A)) = (comple825005695real_n @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 38.11/11.95 thf(222,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:finite1489363574real_n]: (((member1352538125real_n @ C @ A) => (member1352538125real_n @ C @ (comple825005695real_n @ B))) <= (member223413699real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_UnionI)). 38.11/11.95 thf(1025,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:finite1489363574real_n]: (((member1352538125real_n @ C @ A) => (member1352538125real_n @ C @ (comple825005695real_n @ B))) | ~ (member223413699real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 38.11/11.95 thf(45,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n]: (((image_439535603real_n @ A @ top_to1292442332real_n) = top_to1292442332real_n) => (? [C:finite1489363574real_n]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_surjD)). 38.11/11.95 thf(409,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n]: (((image_439535603real_n @ (A) @ top_to1292442332real_n) = top_to1292442332real_n) => (? [C:finite1489363574real_n]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 38.11/11.95 thf(8,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(set_Fi1058188332real_n > $o)]: ((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((C @ D) & (member223413699real_n @ D @ (image_1856576259real_n @ A @ B))))) = (image_1856576259real_n @ A @ (collect_nat @ (^ [D:nat]: ((C @ (A @ D)) & (member_nat @ D @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Compr__image__eq)). 38.11/11.95 thf(282,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(set_Fi1058188332real_n > $o)]: ((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((C @ D) & (member223413699real_n @ D @ (image_1856576259real_n @ A @ B))))) = (image_1856576259real_n @ (A) @ (collect_nat @ (^ [D:nat]: ((C @ (A @ D)) & (member_nat @ D @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 38.11/11.95 thf(1156,plain,(((t2 @ (f @ sk72)) != (t @ (f @ sk72)))),inference(func_ext,[status(esa)],[1155])). 38.11/11.95 thf(243,axiom,((~ (ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_less__numeral__extra_I3_J)). 38.11/11.95 thf(1097,plain,((~ (ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 38.11/11.95 thf(1098,plain,((~ (ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal))),inference(polarity_switch,[status(thm)],[1097])). 38.11/11.95 thf(16,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n]: (member1352538125real_n @ (A @ B) @ (image_439535603real_n @ A @ top_to1292442332real_n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_rangeI)). 38.11/11.95 thf(310,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:finite1489363574real_n]: (member1352538125real_n @ (A @ B) @ (image_439535603real_n @ (A) @ top_to1292442332real_n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 38.11/11.95 thf(35,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(finite964658038_int_n > finite964658038_int_n),C:set_Fi160064172_int_n]: ((image_355963305real_n @ A @ (image_1278151539_int_n @ B @ C)) = (image_355963305real_n @ (^ [D:finite964658038_int_n]: (A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_image__image)). 38.11/11.95 thf(370,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(finite964658038_int_n > finite964658038_int_n),C:set_Fi160064172_int_n]: ((image_355963305real_n @ (A) @ (image_1278151539_int_n @ (B) @ C)) = (image_355963305real_n @ (^ [D:finite964658038_int_n]: (A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 38.11/11.95 thf(130,axiom,((! [A:(nat > set_Fi1058188332real_n)]: (((image_1856576259real_n @ A @ top_top_set_nat) = top_to20708754real_n) = (! [B:set_Fi1058188332real_n]: ? [C:nat]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_surj__def)). 38.11/11.95 thf(717,plain,((! [A:(nat > set_Fi1058188332real_n)]: (((image_1856576259real_n @ (A) @ top_top_set_nat) = top_to20708754real_n) = (! [B:set_Fi1058188332real_n]: ? [C:nat]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 38.11/11.95 thf(31,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > finite1489363574real_n)]: ((image_439535603real_n @ (^ [C:finite1489363574real_n]: (A @ (B @ C))) @ top_to1292442332real_n) = (image_439535603real_n @ A @ (image_439535603real_n @ B @ top_to1292442332real_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_range__composition)). 38.11/11.95 thf(359,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(finite1489363574real_n > finite1489363574real_n)]: ((image_439535603real_n @ (^ [C:finite1489363574real_n]: (A @ (B @ C))) @ top_to1292442332real_n) = (image_439535603real_n @ (A) @ (image_439535603real_n @ (B) @ top_to1292442332real_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 38.11/11.95 thf(256,axiom,((! [A:finite964658038_int_n]: (member223413699real_n @ (r @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062)). 38.11/11.95 thf(1130,plain,((! [A:finite964658038_int_n]: (member223413699real_n @ (r @ A) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 38.11/11.95 thf(643,plain,(((minus_1037315151real_n @ one_on1253059131real_n @ one_on1253059131real_n) = zero_z200130687real_n)),inference(lifteq,[status(thm)],[642])). 38.11/11.95 thf(80,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: ((member223413699real_n @ A @ B) => (member223413699real_n @ (C @ A) @ (image_1661509983real_n @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_imageI)). 38.11/11.95 thf(544,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: ((member223413699real_n @ A @ B) => (member223413699real_n @ (C @ A) @ (image_1661509983real_n @ (C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 38.11/11.95 thf(260,axiom,((sums_E1192373732nnreal @ (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) @ (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (comple825005695real_n @ (image_1856576259real_n @ (^ [A:nat]: (t2 @ (f @ A))) @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__092_060open_062_I_092_060lambda_062n_O_Aemeasure_Alebesgue_A_IT_A_If_An_J_J_J_Asums_Aemeasure_Alebesgue_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062)). 38.11/11.95 thf(1141,plain,((sums_E1192373732nnreal @ (^ [A:nat]: (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (t2 @ (f @ A)))) @ (sigma_1536574303real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (comple825005695real_n @ (image_1856576259real_n @ (^ [A:nat]: (t2 @ (f @ A))) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 38.11/11.95 thf(1391,plain,(! [T:set_Si1125517487real_n,S:set_Si1125517487real_n,R:set_Fi1058188332real_n,Q:set_Si1125517487real_n,P:set_Fi1058188332real_n,O:set_Si1125517487real_n,N:set_Fi1058188332real_n,M:set_Fi1058188332real_n,L:sigma_1466784463real_n,K:set_Fi1058188332real_n,J:set_Si1125517487real_n,I:set_Si1125517487real_n,H:set_Fi1058188332real_n,G:set_Si1125517487real_n,F:set_Fi1058188332real_n,E:set_Si1125517487real_n,D:set_Fi1058188332real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ E)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ E)) | ((sigma_476185326real_n @ (sk53 @ D @ J)) != D) | (~ (member1000184real_n @ (comple488165692real_n @ E) @ J)) | ((sigma_476185326real_n @ (sk53 @ F @ I)) != F) | (~ (member1000184real_n @ (comple488165692real_n @ J) @ I)) | ((sigma_476185326real_n @ (sk53 @ H @ G)) != H) | (~ (member1000184real_n @ (comple488165692real_n @ I) @ G)) | ((sigma_476185326real_n @ (sk53 @ K @ O)) != K) | (~ (member1000184real_n @ L @ O)) | ((sigma_476185326real_n @ (sk53 @ N @ T)) != N) | (~ (member1000184real_n @ (comple488165692real_n @ O) @ T)) | ((sigma_476185326real_n @ (sk53 @ P @ S)) != P) | (~ (member1000184real_n @ (comple488165692real_n @ T) @ S)) | ((sigma_476185326real_n @ (sk53 @ R @ Q)) != R) | (member223413699real_n @ M @ (sigma_1235138647real_n @ (comple488165692real_n @ Q))) | (~ (member1000184real_n @ (comple488165692real_n @ S) @ Q)) | ((member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ G))) != (member223413699real_n @ M @ (sigma_1235138647real_n @ L))))),inference(paramod_ordered,[status(thm)],[1243,1243])). 38.11/11.95 thf(1392,plain,(! [R:set_Si1125517487real_n,Q:set_Si1125517487real_n,P:set_Si1125517487real_n,O:set_Fi1058188332real_n,N:set_Si1125517487real_n,M:set_Fi1058188332real_n,L:set_Si1125517487real_n,K:set_Fi1058188332real_n,J:set_Fi1058188332real_n,I:set_Si1125517487real_n,H:set_Si1125517487real_n,G:set_Fi1058188332real_n,F:set_Fi1058188332real_n,E:set_Si1125517487real_n,D:set_Fi1058188332real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ E)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ E)) | ((sigma_476185326real_n @ (sk53 @ D @ I)) != D) | (~ (member1000184real_n @ (comple488165692real_n @ E) @ I)) | ((sigma_476185326real_n @ (sk53 @ F @ H)) != F) | (~ (member1000184real_n @ (comple488165692real_n @ I) @ H)) | ((sigma_476185326real_n @ (sk53 @ G @ R)) != G) | (~ (member1000184real_n @ (comple488165692real_n @ H) @ R)) | ((sigma_476185326real_n @ (sk53 @ J @ L)) != J) | (~ (member1000184real_n @ (comple488165692real_n @ R) @ L)) | ((sigma_476185326real_n @ (sk53 @ K @ Q)) != K) | (~ (member1000184real_n @ (comple488165692real_n @ L) @ Q)) | ((sigma_476185326real_n @ (sk53 @ M @ P)) != M) | (~ (member1000184real_n @ (comple488165692real_n @ Q) @ P)) | ((sigma_476185326real_n @ (sk53 @ O @ N)) != O) | (member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ N))) | (~ (member1000184real_n @ (comple488165692real_n @ P) @ N)))),inference(pattern_uni,[status(thm)],[1391:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf(E)),bind(F, $thf(F)),bind(G, $thf(U)),bind(H, $thf(H)),bind(I, $thf(I)),bind(J, $thf(J)),bind(K, $thf(K)),bind(L, $thf(comple488165692real_n @ U)),bind(M, $thf(C))]])). 38.11/11.95 thf(1485,plain,(! [R:set_Si1125517487real_n,Q:set_Si1125517487real_n,P:set_Si1125517487real_n,O:set_Fi1058188332real_n,N:set_Si1125517487real_n,M:set_Fi1058188332real_n,L:set_Si1125517487real_n,K:set_Fi1058188332real_n,J:set_Fi1058188332real_n,I:set_Si1125517487real_n,H:set_Si1125517487real_n,G:set_Fi1058188332real_n,F:set_Fi1058188332real_n,E:set_Si1125517487real_n,D:set_Fi1058188332real_n,C:set_Fi1058188332real_n,B:sigma_1466784463real_n,A:set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sk53 @ A @ E)) != A) | (~ (member223413699real_n @ C @ (sigma_1235138647real_n @ B))) | (~ (member1000184real_n @ B @ E)) | ((sigma_476185326real_n @ (sk53 @ D @ I)) != D) | (~ (member1000184real_n @ (comple488165692real_n @ E) @ I)) | ((sigma_476185326real_n @ (sk53 @ F @ H)) != F) | (~ (member1000184real_n @ (comple488165692real_n @ I) @ H)) | ((sigma_476185326real_n @ (sk53 @ G @ R)) != G) | (~ (member1000184real_n @ (comple488165692real_n @ H) @ R)) | ((sigma_476185326real_n @ (sk53 @ J @ L)) != J) | (~ (member1000184real_n @ (comple488165692real_n @ R) @ L)) | ((sigma_476185326real_n @ (sk53 @ K @ Q)) != K) | (~ (member1000184real_n @ (comple488165692real_n @ L) @ Q)) | ((sigma_476185326real_n @ (sk53 @ M @ P)) != M) | (~ (member1000184real_n @ (comple488165692real_n @ Q) @ P)) | ((sigma_476185326real_n @ (sk53 @ O @ N)) != O) | (member223413699real_n @ C @ (sigma_1235138647real_n @ (comple488165692real_n @ N))) | (~ (member1000184real_n @ (comple488165692real_n @ P) @ N)))),inference(simp,[status(thm)],[1392])). 38.11/11.95 thf(207,axiom,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: ((~ (! [D:nat]: ((A = (B @ D)) => (~ (member_nat @ D @ C))))) <= (member223413699real_n @ A @ (image_1856576259real_n @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_imageE)). 38.11/11.95 thf(978,plain,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: (~ (! [D:nat]: ((A = (B @ D)) => (~ (member_nat @ D @ C)))) | ~ (member223413699real_n @ A @ (image_1856576259real_n @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 38.11/11.95 thf(87,axiom,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (vimage1233683625real_n @ B @ C)) = (member1352538125real_n @ (B @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_vimage__eq)). 38.11/11.95 thf(571,plain,((! [A:finite1489363574real_n,B:(finite1489363574real_n > finite1489363574real_n),C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (vimage1233683625real_n @ (B) @ C)) = (member1352538125real_n @ (B @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 38.11/11.95 thf(99,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) = ((member1352538125real_n @ A @ C) & (member1352538125real_n @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Int__iff)). 38.11/11.95 thf(612,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) = ((member1352538125real_n @ A @ C) & (member1352538125real_n @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 38.11/11.95 thf(176,axiom,((! [A:finite1489363574real_n,B:finite1489363574real_n,C:finite1489363574real_n]: ((plus_p585657087real_n @ (plus_p585657087real_n @ A @ B) @ C) = (plus_p585657087real_n @ A @ (plus_p585657087real_n @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_is__num__normalize_I1_J)). 38.11/11.95 thf(876,plain,((! [A:finite1489363574real_n,B:finite1489363574real_n,C:finite1489363574real_n]: ((plus_p585657087real_n @ (plus_p585657087real_n @ A @ B) @ C) = (plus_p585657087real_n @ A @ (plus_p585657087real_n @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 38.11/11.95 thf(173,axiom,((! [A:$o,B:set_o,C:($o > sigma_1466784463real_n),D:set_Fi1058188332real_n,E:set_Fi1058188332real_n]: (((! [F:$o]: ((member_o @ F @ B) => ((sigma_476185326real_n @ (C @ F)) = D))) => ((member223413699real_n @ E @ (sigma_1235138647real_n @ (C @ A))) => (member223413699real_n @ E @ (sigma_1235138647real_n @ (comple488165692real_n @ (image_1599934780real_n @ C @ B)))))) <= (member_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_in__sets__SUP)). 38.11/11.95 thf(859,plain,((! [A:$o,B:set_o,C:($o > sigma_1466784463real_n),D:set_Fi1058188332real_n,E:set_Fi1058188332real_n]: (((! [F:$o]: ((member_o @ F @ B) => ((sigma_476185326real_n @ (C @ F)) = D))) => ((member223413699real_n @ E @ (sigma_1235138647real_n @ (C @ A))) => (member223413699real_n @ E @ (sigma_1235138647real_n @ (comple488165692real_n @ (image_1599934780real_n @ (C) @ B)))))) | ~ (member_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 38.11/11.95 thf(211,axiom,((! [A:sigma_1466784463real_n,B:(finite1489363574real_n > $o),C:(finite1489363574real_n > $o)]: (((member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (C @ D)))) @ (measur1402256771real_n @ A)) => (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & ((B @ D) | (C @ D))))) @ (measur1402256771real_n @ A))) <= (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((B @ D) & (member1352538125real_n @ D @ (sigma_476185326real_n @ A))))) @ (measur1402256771real_n @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_null__sets_Osets__Collect__disj)). 38.11/11.95 thf(991,plain,((! [A:sigma_1466784463real_n,B:(finite1489363574real_n > $o),C:(finite1489363574real_n > $o)]: (((member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & (C @ D)))) @ (measur1402256771real_n @ A)) => (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (sigma_476185326real_n @ A)) & ((B @ D) | (C @ D))))) @ (measur1402256771real_n @ A))) | ~ (member223413699real_n @ (collec321817931real_n @ (^ [D:finite1489363574real_n]: ((B @ D) & (member1352538125real_n @ D @ (sigma_476185326real_n @ A))))) @ (measur1402256771real_n @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 38.11/11.95 thf(113,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(set_Fi1058188332real_n > $o)]: ((? [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_1856576259real_n @ A @ B)) & (C @ D))) => (? [D:nat]: ((member_nat @ D @ B) & (C @ (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_bex__imageD)). 38.11/11.95 thf(656,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(set_Fi1058188332real_n > $o)]: ((? [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_1856576259real_n @ (A) @ B)) & (C @ D))) => (? [D:nat]: ((member_nat @ D @ B) & (C @ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 38.11/11.95 thf(221,axiom,((! [A:(nat > set_Fi1058188332real_n),B:nat]: (member223413699real_n @ (A @ B) @ (image_1856576259real_n @ A @ top_top_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_rangeI)). 38.11/11.95 thf(1023,plain,((! [A:(nat > set_Fi1058188332real_n),B:nat]: (member223413699real_n @ (A @ B) @ (image_1856576259real_n @ (A) @ top_top_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 38.11/11.95 thf(59,axiom,((! [A:set_Fi160064172_int_n]: ((! [B:finite964658038_int_n]: (member27055245_int_n @ B @ A)) => (top_to131672412_int_n = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_UNIV__eq__I)). 38.11/11.95 thf(465,plain,((! [A:set_Fi160064172_int_n]: ((! [B:finite964658038_int_n]: (member27055245_int_n @ B @ A)) => (top_to131672412_int_n = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 38.11/11.95 thf(192,axiom,((! [A:set_Fi1058188332real_n]: ((comple2042271945real_n @ (image_439535603real_n @ (^ [B:finite1489363574real_n]: (B)) @ A)) = (comple2042271945real_n @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_SUP__identity__eq)). 38.11/11.95 thf(931,plain,((! [A:set_Fi1058188332real_n]: ((comple2042271945real_n @ (image_439535603real_n @ (^ [B:finite1489363574real_n]: (B)) @ A)) = (comple2042271945real_n @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 38.11/11.95 thf(64,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n),E:(set_Fi1058188332real_n > finite1489363574real_n)]: ((((E @ (image_439535603real_n @ C @ A)) = (E @ (image_439535603real_n @ D @ B))) <= (! [F:finite1489363574real_n]: ((member1352538125real_n @ F @ B) => ((C @ F) = (D @ F))))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Sup_OSUP__cong)). 38.11/11.95 thf(482,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n),E:(set_Fi1058188332real_n > finite1489363574real_n)]: (((E @ (image_439535603real_n @ (C) @ A)) = (E @ (image_439535603real_n @ (D) @ B))) | ~ (! [F:finite1489363574real_n]: ((member1352538125real_n @ F @ B) => ((C @ F) = (D @ F)))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 38.11/11.95 thf(67,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n)]: ((A = B) => ((! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ B) => ((C @ E) = (D @ E)))) => ((image_439535603real_n @ C @ A) = (image_439535603real_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_image__cong)). 38.11/11.95 thf(495,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n)]: ((A = B) => ((! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ B) => ((C @ E) = (D @ E)))) => ((image_439535603real_n @ (C) @ A) = (image_439535603real_n @ (D) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 38.11/11.95 thf(217,axiom,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member223413699real_n @ A @ (image_355963305real_n @ B @ C)) => (~ (! [D:finite964658038_int_n]: ((~ (member27055245_int_n @ D @ C)) <= (A = (B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_imageE)). 38.11/11.95 thf(1010,plain,((! [A:set_Fi1058188332real_n,B:(finite964658038_int_n > set_Fi1058188332real_n),C:set_Fi160064172_int_n]: ((member223413699real_n @ A @ (image_355963305real_n @ (B) @ C)) => (~ (! [D:finite964658038_int_n]: (~ (member27055245_int_n @ D @ C) | ~ (A = (B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 38.11/11.95 thf(168,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ C) = (inf_in1974387902real_n @ A @ (minus_1686442501real_n @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Int__Diff)). 38.11/11.95 thf(844,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ C) = (inf_in1974387902real_n @ A @ (minus_1686442501real_n @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 38.11/11.95 thf(1108,plain,(((comple825005695real_n @ (image_355963305real_n @ (t2) @ top_to131672412_int_n)) = s)),inference(lifteq,[status(thm)],[1107])). 38.11/11.95 thf(181,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(set_Fi1058188332real_n > $o)]: ((! [D:nat]: ((member_nat @ D @ B) => (C @ (A @ D)))) <= (! [D:set_Fi1058188332real_n]: ((C @ D) <= (member223413699real_n @ D @ (image_1856576259real_n @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_ball__imageD)). 38.11/11.95 thf(896,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:(set_Fi1058188332real_n > $o)]: (! [D:nat]: ((member_nat @ D @ B) => (C @ (A @ D))) | ~ (! [D:set_Fi1058188332real_n]: ((C @ D) | ~ (member223413699real_n @ D @ (image_1856576259real_n @ (A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 38.11/11.95 thf(197,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:sigma_1466784463real_n]: ((member223413699real_n @ (comple825005695real_n @ (image_355963305real_n @ A @ top_to131672412_int_n)) @ (measur1402256771real_n @ B)) <= (! [C:finite964658038_int_n]: (member223413699real_n @ (A @ C) @ (measur1402256771real_n @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_null__sets__UN)). 38.11/11.95 thf(946,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:sigma_1466784463real_n]: ((member223413699real_n @ (comple825005695real_n @ (image_355963305real_n @ (A) @ top_to131672412_int_n)) @ (measur1402256771real_n @ B)) | ~ (! [C:finite964658038_int_n]: (member223413699real_n @ (A @ C) @ (measur1402256771real_n @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 38.11/11.95 thf(29,axiom,((! [A:(nat > nat),B:nat]: (((image_nat_nat @ A @ top_top_set_nat) = top_top_set_nat) => (~ (! [C:nat]: (B != (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_surjE)). 38.11/11.95 thf(351,plain,((! [A:(nat > nat),B:nat]: (((image_nat_nat @ (A) @ top_top_set_nat) = top_top_set_nat) => (~ (! [C:nat]: ~ (B = (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 38.11/11.95 thf(390,plain,(! [A:set_Fi1058188332real_n] : ((member223413699real_n @ A @ top_to20708754real_n))),inference(cnf,[status(esa)],[389])). 38.11/11.95 thf(202,axiom,((! [A:(nat > finite1489363574real_n),B:set_Fi1058188332real_n]: ((image_183184717real_n @ A @ (vimage1860757507real_n @ A @ B)) = (inf_in1974387902real_n @ B @ (image_183184717real_n @ A @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_image__vimage__eq)). 38.11/11.95 thf(961,plain,((! [A:(nat > finite1489363574real_n),B:set_Fi1058188332real_n]: ((image_183184717real_n @ (A) @ (vimage1860757507real_n @ (A) @ B)) = (inf_in1974387902real_n @ B @ (image_183184717real_n @ (A) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 38.11/11.95 thf(158,axiom,((! [A:finite1489363574real_n]: ((image_439535603real_n @ (plus_p585657087real_n @ A) @ top_to1292442332real_n) = top_to1292442332real_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_surj__plus)). 38.11/11.95 thf(813,plain,((! [A:finite1489363574real_n]: ((image_439535603real_n @ (plus_p585657087real_n @ A) @ top_to1292442332real_n) = top_to1292442332real_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 38.11/11.95 thf(134,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (comple825005695real_n @ (image_355963305real_n @ A @ B)) @ C) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (minus_1686442501real_n @ (A @ D) @ C)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_UN__extend__simps_I6_J)). 38.11/11.95 thf(731,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (comple825005695real_n @ (image_355963305real_n @ (A) @ B)) @ C) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (minus_1686442501real_n @ (A @ D) @ C)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 38.11/11.95 thf(151,axiom,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n)]: ((A = B) => (((comple825005695real_n @ (image_1856576259real_n @ C @ A)) = (comple825005695real_n @ (image_1856576259real_n @ D @ B))) <= (! [E:nat]: ((member_nat @ E @ B) => ((C @ E) = (D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_SUP__cong)). 38.11/11.95 thf(786,plain,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n)]: ((A = B) => (((comple825005695real_n @ (image_1856576259real_n @ (C) @ A)) = (comple825005695real_n @ (image_1856576259real_n @ (D) @ B))) | ~ (! [E:nat]: ((member_nat @ E @ B) => ((C @ E) = (D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 38.11/11.95 thf(86,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) => (member223413699real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_IntD1)). 38.11/11.95 thf(568,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) => (member223413699real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 38.11/11.95 thf(914,plain,(((collec1941932235_int_n @ (top_to287930409nt_n_o)) = top_to131672412_int_n)),inference(lifteq,[status(thm)],[913])). 38.11/11.95 thf(70,axiom,((! [A:finite1489363574real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_1856576259real_n @ B @ C))) => (~ (! [D:nat]: ((~ (member1352538125real_n @ A @ (B @ D))) <= (member_nat @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_UN__E)). 38.11/11.95 thf(510,plain,((! [A:finite1489363574real_n,B:(nat > set_Fi1058188332real_n),C:set_nat]: ((member1352538125real_n @ A @ (comple825005695real_n @ (image_1856576259real_n @ (B) @ C))) => (~ (! [D:nat]: (~ (member1352538125real_n @ A @ (B @ D)) | ~ (member_nat @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 38.11/11.95 thf(116,axiom,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((A = B) => (((comple825005695real_n @ (image_355963305real_n @ C @ A)) = (comple825005695real_n @ (image_355963305real_n @ D @ B))) <= (! [E:finite964658038_int_n]: ((member27055245_int_n @ E @ B) => ((C @ E) = (D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_SUP__cong)). 38.11/11.95 thf(667,plain,((! [A:set_Fi160064172_int_n,B:set_Fi160064172_int_n,C:(finite964658038_int_n > set_Fi1058188332real_n),D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((A = B) => (((comple825005695real_n @ (image_355963305real_n @ (C) @ A)) = (comple825005695real_n @ (image_355963305real_n @ (D) @ B))) | ~ (! [E:finite964658038_int_n]: ((member27055245_int_n @ E @ B) => ((C @ E) = (D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 38.11/11.95 thf(478,plain,(! [A:nat] : ((member_nat @ A @ top_top_set_nat))),inference(cnf,[status(esa)],[477])). 38.11/11.95 thf(182,axiom,((! [A:set_Fi1058188332real_n]: ((image_439535603real_n @ (plus_p585657087real_n @ zero_z200130687real_n) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_image__add__0)). 38.11/11.95 thf(899,plain,((! [A:set_Fi1058188332real_n]: ((image_439535603real_n @ (plus_p585657087real_n @ zero_z200130687real_n) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 38.11/11.95 thf(120,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n)]: (((image_355963305real_n @ A @ top_to131672412_int_n) = top_to20708754real_n) = (! [B:set_Fi1058188332real_n]: ? [C:finite964658038_int_n]: (B = (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_surj__def)). 38.11/11.95 thf(684,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n)]: (((image_355963305real_n @ (A) @ top_to131672412_int_n) = top_to20708754real_n) = (! [B:set_Fi1058188332real_n]: ? [C:finite964658038_int_n]: (B = (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 38.11/11.95 thf(82,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:finite1489363574real_n,D:(finite1489363574real_n > finite1489363574real_n)]: (((member1352538125real_n @ C @ (image_439535603real_n @ D @ B)) <= (C = (D @ A))) <= (member1352538125real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_rev__image__eqI)). 38.11/11.95 thf(549,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:finite1489363574real_n,D:(finite1489363574real_n > finite1489363574real_n)]: ((member1352538125real_n @ C @ (image_439535603real_n @ (D) @ B)) | ~ (C = (D @ A)) | ~ (member1352538125real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 38.11/11.95 thf(154,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ (inf_in1974387902real_n @ C @ B)) = (minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Diff__Int2)). 38.11/11.95 thf(800,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ (inf_in1974387902real_n @ C @ B)) = (minus_1686442501real_n @ (inf_in1974387902real_n @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 38.11/11.95 thf(14,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) => (member1352538125real_n @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_IntD2)). 38.11/11.95 thf(300,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((member1352538125real_n @ A @ (inf_in1974387902real_n @ B @ C)) => (member1352538125real_n @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 38.11/11.95 thf(620,plain,(! [A:finite964658038_int_n] : ((member27055245_int_n @ A @ top_to131672412_int_n))),inference(cnf,[status(esa)],[619])). 38.11/11.95 thf(141,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((vimage1233683625real_n @ A @ (inf_in1974387902real_n @ B @ C)) = (inf_in1974387902real_n @ (vimage1233683625real_n @ A @ B) @ (vimage1233683625real_n @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_vimage__Int)). 38.11/11.95 thf(752,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:set_Fi1058188332real_n,C:set_Fi1058188332real_n]: ((vimage1233683625real_n @ (A) @ (inf_in1974387902real_n @ B @ C)) = (inf_in1974387902real_n @ (vimage1233683625real_n @ (A) @ B) @ (vimage1233683625real_n @ (A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 38.11/11.95 thf(18,axiom,((! [A:finite964658038_int_n,B:set_Fi160064172_int_n,C:finite1489363574real_n,D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member27055245_int_n @ A @ B) => ((member1352538125real_n @ C @ (comple825005695real_n @ (image_355963305real_n @ D @ B))) <= (member1352538125real_n @ C @ (D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_UN__I)). 38.11/11.95 thf(315,plain,((! [A:finite964658038_int_n,B:set_Fi160064172_int_n,C:finite1489363574real_n,D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member27055245_int_n @ A @ B) => ((member1352538125real_n @ C @ (comple825005695real_n @ (image_355963305real_n @ (D) @ B))) | ~ (member1352538125real_n @ C @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 38.11/11.95 thf(204,axiom,((! [A:finite964658038_int_n,B:set_Fi160064172_int_n,C:set_Fi1058188332real_n,D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member27055245_int_n @ A @ B) => ((C = (D @ A)) => (member223413699real_n @ C @ (image_355963305real_n @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_rev__image__eqI)). 38.11/11.95 thf(967,plain,((! [A:finite964658038_int_n,B:set_Fi160064172_int_n,C:set_Fi1058188332real_n,D:(finite964658038_int_n > set_Fi1058188332real_n)]: ((member27055245_int_n @ A @ B) => ((C = (D @ A)) => (member223413699real_n @ C @ (image_355963305real_n @ (D) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 38.11/11.95 thf(265,axiom,((! [A:finite964658038_int_n,B:finite964658038_int_n]: ((member223413699real_n @ (inf_in1974387902real_n @ (r @ A) @ (r @ B)) @ (measur1402256771real_n @ (comple230862828real_n @ lebesg260170249real_n))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_R__Int)). 38.11/11.95 thf(1148,plain,((! [A:finite964658038_int_n,B:finite964658038_int_n]: ((member223413699real_n @ (inf_in1974387902real_n @ (r @ A) @ (r @ B)) @ (measur1402256771real_n @ (comple230862828real_n @ lebesg260170249real_n))) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 38.11/11.95 thf(272,plain,(! [C:(set_Fi1058188332real_n > $o),B:set_se2111327970real_n,A:(set_Fi1058188332real_n > set_Fi1058188332real_n)] : (((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_1661509983real_n @ A @ B)) & (C @ D)))) = (image_1661509983real_n @ (A) @ (collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((C @ (A @ D)) & (member223413699real_n @ D @ B)))))))),inference(cnf,[status(esa)],[271])). 38.11/11.95 thf(273,plain,(! [C:(set_Fi1058188332real_n > $o),B:set_se2111327970real_n,A:(set_Fi1058188332real_n > set_Fi1058188332real_n)] : (((collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((member223413699real_n @ D @ (image_1661509983real_n @ A @ B)) & (C @ D)))) = (image_1661509983real_n @ (A) @ (collec452821761real_n @ (^ [D:set_Fi1058188332real_n]: ((C @ (A @ D)) & (member223413699real_n @ D @ B)))))))),inference(lifteq,[status(thm)],[272])). 38.11/11.95 thf(36,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n)]: ((A = B) => (((comple2042271945real_n @ (image_439535603real_n @ C @ A)) = (comple2042271945real_n @ (image_439535603real_n @ D @ B))) <= (! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ B) => ((C @ E) = (D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_SUP__cong)). 38.11/11.95 thf(373,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n)]: ((A = B) => (((comple2042271945real_n @ (image_439535603real_n @ (C) @ A)) = (comple2042271945real_n @ (image_439535603real_n @ (D) @ B))) | ~ (! [E:finite1489363574real_n]: ((member1352538125real_n @ E @ B) => ((C @ E) = (D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 38.11/11.95 thf(22,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (((inf_in1974387902real_n @ A @ B) = top_to1292442332real_n) = ((A = top_to1292442332real_n) & (B = top_to1292442332real_n))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Int__UNIV)). 38.11/11.95 thf(326,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: (((inf_in1974387902real_n @ A @ B) = top_to1292442332real_n) = ((A = top_to1292442332real_n) & (B = top_to1292442332real_n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 38.11/11.95 thf(52,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n),E:(set_Fi1058188332real_n > finite1489363574real_n)]: ((A = B) => ((! [F:finite1489363574real_n]: ((member1352538125real_n @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_439535603real_n @ C @ A)) = (E @ (image_439535603real_n @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Inf_OINF__cong)). 38.11/11.95 thf(437,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n),D:(finite1489363574real_n > finite1489363574real_n),E:(set_Fi1058188332real_n > finite1489363574real_n)]: ((A = B) => ((! [F:finite1489363574real_n]: ((member1352538125real_n @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_439535603real_n @ (C) @ A)) = (E @ (image_439535603real_n @ (D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 38.11/11.95 thf(163,axiom,((! [A:(finite964658038_int_n > (nat > set_Fi1058188332real_n)),B:set_nat,C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_1856576259real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_355963305real_n @ (^ [E:finite964658038_int_n]: (A @ E @ D)) @ C))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_SUP__commute)). 38.11/11.95 thf(828,plain,((! [A:(finite964658038_int_n > (nat > set_Fi1058188332real_n)),B:set_nat,C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_1856576259real_n @ (A @ D) @ B))) @ C)) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_355963305real_n @ (^ [E:finite964658038_int_n]: (A @ E @ D)) @ C))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 38.11/11.95 thf(131,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > sigma_1466784463real_n),D:set_Fi1058188332real_n,E:set_Fi1058188332real_n]: ((((member223413699real_n @ E @ (sigma_1235138647real_n @ (C @ A))) => (member223413699real_n @ E @ (sigma_1235138647real_n @ (comple488165692real_n @ (image_987430492real_n @ C @ B))))) <= (! [F:set_Fi1058188332real_n]: ((member223413699real_n @ F @ B) => ((sigma_476185326real_n @ (C @ F)) = D)))) <= (member223413699real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_in__sets__SUP)). 38.11/11.95 thf(720,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:(set_Fi1058188332real_n > sigma_1466784463real_n),D:set_Fi1058188332real_n,E:set_Fi1058188332real_n]: (((member223413699real_n @ E @ (sigma_1235138647real_n @ (C @ A))) => (member223413699real_n @ E @ (sigma_1235138647real_n @ (comple488165692real_n @ (image_987430492real_n @ (C) @ B))))) | ~ (! [F:set_Fi1058188332real_n]: ((member223413699real_n @ F @ B) => ((sigma_476185326real_n @ (C @ F)) = D))) | ~ (member223413699real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 38.11/11.95 thf(200,axiom,((! [A:finite964658038_int_n]: ((image_1278151539_int_n @ (plus_p1654784127_int_n @ A) @ top_to131672412_int_n) = top_to131672412_int_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_surj__plus)). 38.11/11.95 thf(955,plain,((! [A:finite964658038_int_n]: ((image_1278151539_int_n @ (plus_p1654784127_int_n @ A) @ top_to131672412_int_n) = top_to131672412_int_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 38.11/11.95 thf(12,axiom,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(nat > set_Fi1058188332real_n),C:set_nat]: ((image_1661509983real_n @ A @ (image_1856576259real_n @ B @ C)) = (image_1856576259real_n @ (^ [D:nat]: (A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_image__image)). 38.11/11.95 thf(294,plain,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(nat > set_Fi1058188332real_n),C:set_nat]: ((image_1661509983real_n @ (A) @ (image_1856576259real_n @ (B) @ C)) = (image_1856576259real_n @ (^ [D:nat]: (A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 38.11/11.95 thf(188,axiom,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: (((member223413699real_n @ C @ (measur1402256771real_n @ B)) => (member223413699real_n @ (inf_in1974387902real_n @ A @ C) @ (measur1402256771real_n @ B))) <= (member223413699real_n @ A @ (measur1402256771real_n @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_null__sets_OInt)). 38.11/11.95 thf(918,plain,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: (((member223413699real_n @ C @ (measur1402256771real_n @ B)) => (member223413699real_n @ (inf_in1974387902real_n @ A @ C) @ (measur1402256771real_n @ B))) | ~ (member223413699real_n @ A @ (measur1402256771real_n @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 38.11/11.95 thf(69,axiom,((! [A:(nat > nat),B:(nat > nat)]: (((image_nat_nat @ A @ top_top_set_nat) = top_top_set_nat) <= (! [C:nat]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_surjI)). 38.11/11.95 thf(506,plain,((! [A:(nat > nat),B:(nat > nat)]: (((image_nat_nat @ (A) @ top_top_set_nat) = top_top_set_nat) | ~ (! [C:nat]: ((A @ (B @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 38.11/11.95 thf(166,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(nat > set_Fi160064172_int_n),C:set_nat]: ((comple825005695real_n @ (image_355963305real_n @ A @ (comple970917503_int_n @ (image_968789251_int_n @ B @ C)))) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_355963305real_n @ A @ (B @ D)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_UN__UN__flatten)). 38.11/11.95 thf(839,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:(nat > set_Fi160064172_int_n),C:set_nat]: ((comple825005695real_n @ (image_355963305real_n @ (A) @ (comple970917503_int_n @ (image_968789251_int_n @ (B) @ C)))) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (comple825005695real_n @ (image_355963305real_n @ A @ (B @ D)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 38.11/11.95 thf(109,axiom,((! [A:finite964658038_int_n,B:finite964658038_int_n]: (((minkow1134813771n_real @ A) = (minkow1134813771n_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_of__int__vec__eq__iff)). 38.11/11.95 thf(644,plain,((! [A:finite964658038_int_n,B:finite964658038_int_n]: (((minkow1134813771n_real @ A) = (minkow1134813771n_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 38.11/11.95 thf(57,axiom,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n)]: ((member1352538125real_n @ (C @ A) @ (image_439535603real_n @ C @ B)) <= (member1352538125real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_imageI)). 38.11/11.95 thf(459,plain,((! [A:finite1489363574real_n,B:set_Fi1058188332real_n,C:(finite1489363574real_n > finite1489363574real_n)]: ((member1352538125real_n @ (C @ A) @ (image_439535603real_n @ (C) @ B)) | ~ (member1352538125real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 38.11/11.95 thf(161,axiom,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(nat > set_Fi1058188332real_n)]: ((image_1856576259real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_1661509983real_n @ A @ (image_1856576259real_n @ B @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_range__composition)). 38.11/11.95 thf(822,plain,((! [A:(set_Fi1058188332real_n > set_Fi1058188332real_n),B:(nat > set_Fi1058188332real_n)]: ((image_1856576259real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_1661509983real_n @ (A) @ (image_1856576259real_n @ (B) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 38.11/11.95 thf(170,axiom,((! [A:finite1489363574real_n,B:set_se2111327970real_n]: ((~ (! [C:set_Fi1058188332real_n]: ((~ (member223413699real_n @ C @ B)) <= (member1352538125real_n @ A @ C)))) <= (member1352538125real_n @ A @ (comple825005695real_n @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_UnionE)). 38.11/11.95 thf(850,plain,((! [A:finite1489363574real_n,B:set_se2111327970real_n]: (~ (! [C:set_Fi1058188332real_n]: (~ (member223413699real_n @ C @ B) | ~ (member1352538125real_n @ A @ C))) | ~ (member1352538125real_n @ A @ (comple825005695real_n @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 38.11/11.95 thf(133,axiom,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ (inf_in1974387902real_n @ A @ B)) = (inf_in1974387902real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Int__left__absorb)). 38.11/11.95 thf(728,plain,((! [A:set_Fi1058188332real_n,B:set_Fi1058188332real_n]: ((inf_in1974387902real_n @ A @ (inf_in1974387902real_n @ A @ B)) = (inf_in1974387902real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 38.11/11.95 thf(137,axiom,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(nat > finite1489363574real_n)]: ((image_183184717real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_439535603real_n @ A @ (image_183184717real_n @ B @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_range__composition)). 38.11/11.95 thf(740,plain,((! [A:(finite1489363574real_n > finite1489363574real_n),B:(nat > finite1489363574real_n)]: ((image_183184717real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_439535603real_n @ (A) @ (image_183184717real_n @ (B) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 38.11/11.95 thf(208,axiom,((! [A:extend1728876344nnreal,B:set_Ex113815278nnreal]: ((ord_le2133614988nnreal @ A @ (comple1413366923nnreal @ B)) = (? [C:extend1728876344nnreal]: ((ord_le2133614988nnreal @ A @ C) & (member1217042383nnreal @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_less__Sup__iff)). 38.11/11.95 thf(982,plain,((! [A:extend1728876344nnreal,B:set_Ex113815278nnreal]: ((ord_le2133614988nnreal @ A @ (comple1413366923nnreal @ B)) = (? [C:extend1728876344nnreal]: ((ord_le2133614988nnreal @ A @ C) & (member1217042383nnreal @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 38.11/11.95 thf(215,axiom,((! [A:(nat > set_Fi1058188332real_n),B:(nat > nat)]: ((image_1856576259real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_1856576259real_n @ A @ (image_nat_nat @ B @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_range__composition)). 38.11/11.95 thf(1004,plain,((! [A:(nat > set_Fi1058188332real_n),B:(nat > nat)]: ((image_1856576259real_n @ (^ [C:nat]: (A @ (B @ C))) @ top_top_set_nat) = (image_1856576259real_n @ (A) @ (image_nat_nat @ (B) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 38.11/11.95 thf(155,axiom,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n]: (((inf_in1974387902real_n @ (sigma_476185326real_n @ B) @ A) = A) <= (member223413699real_n @ A @ (measur1402256771real_n @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_null__sets_OInt__space__eq1)). 38.11/11.95 thf(803,plain,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n]: (((inf_in1974387902real_n @ (sigma_476185326real_n @ B) @ A) = A) | ~ (member223413699real_n @ A @ (measur1402256771real_n @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 38.11/11.95 thf(25,axiom,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ A @ B))) & (C @ D))) = (? [D:finite964658038_int_n]: ((member27055245_int_n @ D @ B) & ? [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) & (C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_bex__UN)). 38.11/11.95 thf(337,plain,((! [A:(finite964658038_int_n > set_Fi1058188332real_n),B:set_Fi160064172_int_n,C:(finite1489363574real_n > $o)]: ((? [D:finite1489363574real_n]: ((member1352538125real_n @ D @ (comple825005695real_n @ (image_355963305real_n @ (A) @ B))) & (C @ D))) = (? [D:finite964658038_int_n]: ((member27055245_int_n @ D @ B) & ? [E:finite1489363574real_n]: ((member1352538125real_n @ E @ (A @ D)) & (C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 38.11/11.95 thf(935,plain,((~ (ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal))),inference(polarity_switch,[status(thm)],[934])). 38.11/11.95 thf(114,axiom,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: ((member223413699real_n @ A @ (measur1402256771real_n @ B)) => ((member223413699real_n @ (minus_1686442501real_n @ A @ C) @ (measur1402256771real_n @ B)) <= (member223413699real_n @ C @ (measur1402256771real_n @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_null__sets_ODiff)). 38.11/11.95 thf(659,plain,((! [A:set_Fi1058188332real_n,B:sigma_1466784463real_n,C:set_Fi1058188332real_n]: ((member223413699real_n @ A @ (measur1402256771real_n @ B)) => ((member223413699real_n @ (minus_1686442501real_n @ A @ C) @ (measur1402256771real_n @ B)) | ~ (member223413699real_n @ C @ (measur1402256771real_n @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 38.11/11.95 thf(107,axiom,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (comple825005695real_n @ (image_1856576259real_n @ A @ B)) @ C) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (minus_1686442501real_n @ (A @ D) @ C)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_UN__extend__simps_I6_J)). 38.11/11.95 thf(639,plain,((! [A:(nat > set_Fi1058188332real_n),B:set_nat,C:set_Fi1058188332real_n]: ((minus_1686442501real_n @ (comple825005695real_n @ (image_1856576259real_n @ (A) @ B)) @ C) = (comple825005695real_n @ (image_1856576259real_n @ (^ [D:nat]: (minus_1686442501real_n @ (A @ D) @ C)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 38.11/11.95 thf(491,plain,(((comple825005695real_n @ top_to20708754real_n) = top_to1292442332real_n)),inference(lifteq,[status(thm)],[490])). 38.11/11.95 thf(56,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_Fi1058188332real_n,D:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: (((C = (D @ A)) => (member223413699real_n @ C @ (image_1661509983real_n @ D @ B))) <= (member223413699real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rev__image__eqI)). 38.11/11.95 thf(454,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_Fi1058188332real_n,D:(set_Fi1058188332real_n > set_Fi1058188332real_n)]: (((C = (D @ A)) => (member223413699real_n @ C @ (image_1661509983real_n @ (D) @ B))) | ~ (member223413699real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 38.11/11.95 thf(33,axiom,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: (((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) <= (member223413699real_n @ A @ C)) <= (member223413699real_n @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_IntI)). 38.11/11.95 thf(364,plain,((! [A:set_Fi1058188332real_n,B:set_se2111327970real_n,C:set_se2111327970real_n]: ((member223413699real_n @ A @ (inf_in632889204real_n @ B @ C)) | ~ (member223413699real_n @ A @ C) | ~ (member223413699real_n @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 38.11/11.95 thf(127,axiom,((! [A:set_Si1125517487real_n]: ((sigma_476185326real_n @ (comple488165692real_n @ A)) = (comple825005695real_n @ (image_1298280374real_n @ sigma_476185326real_n @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_space__Sup__eq__UN)). 38.11/11.95 thf(708,plain,((! [A:set_Si1125517487real_n]: ((sigma_476185326real_n @ (comple488165692real_n @ A)) = (comple825005695real_n @ (image_1298280374real_n @ (sigma_476185326real_n) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 38.11/11.95 thf(226,axiom,((! [A:(finite964658038_int_n > finite964658038_int_n)]: ((vimage1122713129_int_n @ A @ top_to131672412_int_n) = top_to131672412_int_n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_vimage__UNIV)). 38.11/11.95 thf(1037,plain,((! [A:(finite964658038_int_n > finite964658038_int_n)]: ((vimage1122713129_int_n @ (A) @ top_to131672412_int_n) = top_to131672412_int_n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 38.11/11.95 thf(148,axiom,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n)]: ((~ (! [C:nat]: (A != (B @ C)))) <= (member223413699real_n @ A @ (image_1856576259real_n @ B @ top_top_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_rangeE)). 38.11/11.95 thf(775,plain,((! [A:set_Fi1058188332real_n,B:(nat > set_Fi1058188332real_n)]: (~ (! [C:nat]: ~ (A = (B @ C))) | ~ (member223413699real_n @ A @ (image_1856576259real_n @ (B) @ top_top_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 38.11/11.95 thf(85,axiom,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: ((A = B) => ((! [F:nat]: ((member_nat @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_1856576259real_n @ C @ A)) = (E @ (image_1856576259real_n @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Sup_OSUP__cong)). 38.11/11.95 thf(560,plain,((! [A:set_nat,B:set_nat,C:(nat > set_Fi1058188332real_n),D:(nat > set_Fi1058188332real_n),E:(set_se2111327970real_n > set_Fi1058188332real_n)]: ((A = B) => ((! [F:nat]: ((member_nat @ F @ B) => ((C @ F) = (D @ F)))) => ((E @ (image_1856576259real_n @ (C) @ A)) = (E @ (image_1856576259real_n @ (D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 38.11/11.95 thf(218,axiom,((! [A:(set_Fi1058188332real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((A @ (image_439535603real_n @ (^ [C:finite1489363574real_n]: (C)) @ B)) = (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Sup_OSUP__identity__eq)). 38.11/11.95 thf(1014,plain,((! [A:(set_Fi1058188332real_n > finite1489363574real_n),B:set_Fi1058188332real_n]: ((A @ (image_439535603real_n @ (^ [C:finite1489363574real_n]: (C)) @ B)) = (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 38.11/11.95 thf(205,axiom,((! [A:(nat > set_Fi1058188332real_n),B:(finite964658038_int_n > set_nat),C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_1856576259real_n @ A @ (comple1682161881et_nat @ (image_1085873667et_nat @ B @ C)))) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_1856576259real_n @ A @ (B @ D)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_UN__UN__flatten)). 38.11/11.95 thf(972,plain,((! [A:(nat > set_Fi1058188332real_n),B:(finite964658038_int_n > set_nat),C:set_Fi160064172_int_n]: ((comple825005695real_n @ (image_1856576259real_n @ (A) @ (comple1682161881et_nat @ (image_1085873667et_nat @ (B) @ C)))) = (comple825005695real_n @ (image_355963305real_n @ (^ [D:finite964658038_int_n]: (comple825005695real_n @ (image_1856576259real_n @ A @ (B @ D)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 38.11/11.95 thf(1809,plain,($false),inference(e,[status(thm)],[892,760,479,1105,1083,468,523,276,994,873,1142,384,1137,533,698,913,340,538,1164,797,1095,1001,1243,417,288,320,885,1046,389,619,934,1132,902,853,1147,870,770,448,924,492,756,591,1136,806,905,1040,1109,574,1020,348,687,692,734,1119,988,428,312,678,270,810,381,1067,714,1057,334,746,825,952,302,1123,1217,297,429,275,407,630,847,1032,879,329,583,1079,757,842,285,1106,1089,1017,615,1121,1064,725,1138,650,948,783,420,1118,1028,554,1075,642,590,1155,547,1114,701,1060,779,503,647,997,1099,985,343,1086,266,633,921,541,1035,765,1054,794,586,662,888,856,279,601,513,1146,1154,819,975,423,1007,743,291,958,413,843,1125,577,711,391,1107,1092,704,445,936,604,831,681,274,1117,1043,271,599,362,451,737,318,477,387,367,535,816,323,621,520,964,943,462,1112,626,915,912,1198,399,768,278,608,394,653,636,695,267,1102,473,589,927,749,516,939,1145,355,836,1049,490,675,525,557,580,1025,409,282,1156,1098,310,370,717,359,1130,643,544,1141,1485,978,571,612,876,859,991,656,1023,465,931,482,495,1010,844,1108,896,946,351,390,961,813,731,786,568,914,510,667,478,899,684,549,800,300,620,752,315,967,1097,1148,273,373,326,437,828,720,955,294,918,506,268,839,427,644,459,908,822,850,728,740,982,1004,803,337,935,659,639,755,491,454,364,708,1037,775,560,1014,972])). 38.11/11.95 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 38.11/11.95 % [INFO] Killing All external provers ... 38.11/11.95 FINAL WATCH: 31.9 CPU 8.7 WC 38.11/11.95 Killed 2 orphans 38.11/11.95 Killed 1 orphans 38.11/11.95 EOF