0.00/0.01 % Leo-III: Strategy 1 (for '60') 53.77/22.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 53.77/22.85 % [INFO] Parsing done (238ms). 53.77/22.85 % [INFO] Running in sequential loop mode. 53.77/22.85 % [CONFIG] Using configuration: timeout(60) with strategy 53.77/22.85 % [INFO] eprover registered as external prover. 53.77/22.85 % [INFO] cvc4 registered as external prover. 53.77/22.85 % [INFO] Parsing finished. Scanning for conjecture ... 53.77/22.85 % [INFO] Found a conjecture and 355 axioms. Running axiom selection ... 53.77/22.85 % [INFO] Axiom selection finished. Selected 340 axioms (removed 15 axioms). 53.77/22.85 % [INFO] Problem is higher-order (TPTP THF). 53.77/22.85 % [INFO] Type checking passed. Searching for refutation ... 53.77/22.85 % External prover 'cvc4' found a proof! 53.77/22.85 % [INFO] Killing All external provers ... 53.77/22.85 % Time passed: 18355ms (effective reasoning time: 17768ms) 53.77/22.85 % Solved by strategy 53.77/22.85 % Axioms used in derivation (340): fact_252_ord__le__eq__trans, fact_323_plus__ereal_Osimps_I4_J, fact_134_usc__at__mem, fact_306_ereal2__cases, fact_259_order__trans, fact_318_plus__ereal_Osimps_I3_J, fact_254_ord__le__eq__trans, fact_256_order__class_Oorder_Oantisym, fact_294_ereal__le__real, fact_73_le__minus__iff, fact_351_plus__ereal_Oelims, fact_309_ereal__top, fact_231_order_Otrans, fact_90_Lim__bounded, fact_51_lsc__at__mem, fact_275_ereal__infty__less__eq_I1_J, fact_166_monoI1, fact_282_ereal__less__eq_I2_J, fact_133_usc__at__mem, fact_197_ord__eq__le__subst, fact_74_minus__le__iff, fact_325_ereal__add__le__add__iff2, fact_120_lsc__sequentially, fact_198_ord__eq__le__subst, fact_190_order__subst2, fact_267_linorder__wlog, fact_80_lim__mono, fact_79_lim__mono, fact_296_real__of__ereal_Oinduct, fact_199_ord__eq__le__subst, fact_168_monoI1, fact_218_antisym, fact_91_Lim__bounded, fact_220_linear, fact_3_lsc, fact_137_usc__at__mem, fact_279_ereal__infty__less__eq2_I1_J, fact_4_tendsto__uminus__ereal, fact_116_comp__assoc, fact_40_lsc__sequentially__mem, fact_81_lim__mono, fact_242_antisym__conv, fact_6_tendsto__const, fact_291_uminus__ereal_Osimps_I1_J, fact_216_antisym, fact_302_ereal__all__split, fact_290_PInfty__neq__ereal_I1_J, fact_347_le__antisym, fact_208_ord__le__eq__subst, fact_72_le__minus__iff, fact_10_LIMSEQ__const__iff, fact_195_ord__eq__le__subst, fact_346_nat__le__linear, fact_85_LIMSEQ__le, fact_112_comp__eq__dest__lhs, fact_17_tendsto__minus, fact_221_linear, fact_295_ereal__semiline__unique, fact_98_LIMSEQ__le__const, fact_228_le__cases, fact_99_LIMSEQ__le__const, fact_251_ord__le__eq__trans, fact_316_ereal__plus__eq__MInfty, fact_67_verit__la__disequality, fact_307_ereal__cases, fact_205_ord__le__eq__subst, fact_341_nat__leq__as__int, fact_277_MInfty__neq__PInfty_I1_J, fact_140_usc__at__mem, fact_200_ord__eq__le__subst, fact_86_LIMSEQ__le, fact_303_abs__ereal_Ocases, fact_32_tendsto__cong__limit, fact_174_order__subst1, fact_61_lsc__at__def, fact_175_order__subst1, fact_301_abs__ereal_Oinduct, fact_169_monoI1, fact_114_comp__eq__dest, fact_115_comp__assoc, fact_43_lsc__at__mem, fact_152_lsc__liminf, fact_92_Lim__bounded, fact_19_LIMSEQ__unique, fact_263_dual__order_Orefl, fact_39_lsc__sequentially__mem, fact_13_tendsto__minus__cancel, fact_288_ereal__cong, fact_146_order__refl, fact_326_id__nat__ereal__tendsto__PInf, fact_64_neg__le__iff__le, fact_206_ord__le__eq__subst, fact_77_le__imp__neg__le, fact_38_add_Oinverse__inverse, fact_71_ereal__complete__Sup, fact_352_filterlim__real__sequentially, fact_84_LIMSEQ__le, fact_5_tendsto__const, fact_11_LIMSEQ__const__iff, fact_237_le__cases3, fact_180_order__subst1, fact_48_lsc__at__mem, fact_201_ord__le__eq__subst, fact_104_LIMSEQ__le__const2, fact_241_antisym__conv, fact_315_ereal__MInfty__eq__plus, fact_204_ord__le__eq__subst, fact_317_plus__ereal_Osimps_I2_J, fact_0_x__def_I1_J, fact_194_ord__eq__le__subst, fact_124_usc__at__def, fact_227_le__cases, fact_226_eq__refl, fact_272_dual__order_Otrans, fact_15_tendsto__minus__cancel__left, fact_239_antisym__conv, fact_136_usc__at__mem, fact_34_tendsto__cong__limit, fact_123_usc__at__def, fact_23_ereal__uminus__eq__iff, fact_171_order__subst1, fact_270_linorder__wlog, fact_265_dual__order_Orefl, fact_164_monoI2, fact_148_monoseq__le, fact_262_order__trans, fact_30_tendsto__eq__rhs, fact_248_ord__eq__le__trans, fact_155_LIMSEQ__Uniq, fact_25_verit__minus__simplify_I4_J, fact_320_ereal__add__cancel__left, fact_103_LIMSEQ__le__const2, fact_53_lsc__at__def, fact_144_order__refl, fact_102_LIMSEQ__le__const2, fact_324_ereal__add__le__add__iff, fact_253_ord__le__eq__trans, fact_284_Lim__bounded__MInfty, fact_243_order__class_Oorder_Oeq__iff, fact_287_ereal_Oinject, fact_157_LIMSEQ__Uniq, fact_147_monoseq__le, fact_269_linorder__wlog, fact_182_order__subst2, fact_189_order__subst2, fact_297_real__of__ereal_Ocases, fact_184_order__subst2, fact_188_order__subst2, fact_2__092_060open_062_092_060And_062F_O_A_I_If_A_092_060circ_062_Ax_J_A_092_060longlongrightarrow_062_AA_J_AF_A_092_060Longrightarrow_062_A_I_I_092_060lambda_062xa_O_A_N_A_If_A_092_060circ_062_Ax_J_Axa_J_A_092_060longlongrightarrow_062_A_N_AA_J_AF_092_060close_062, fact_59_lsc__at__def, fact_47_lsc__at__mem, fact_150_monoseq__le, fact_266_dual__order_Orefl, fact_283_Lim__MInfty, fact_22_tendsto__uminus__nhds, fact_117_comp__assoc, fact_54_lsc__at__def, fact_60_lsc__at__def, fact_186_order__subst2, fact_203_ord__le__eq__subst, fact_142_lim__increasing__cl, fact_289_ereal__less__eq_I3_J, fact_126_usc__at__def, fact_273_dual__order_Otrans, fact_274_liminf__PInfty, fact_217_antisym, fact_229_le__cases, fact_113_comp__eq__elim, fact_105_LIMSEQ__le__const2, fact_311_Lim__bounded__PInfty, fact_52_lsc__at__mem, fact_70_ereal__complete__Inf, fact_322_plus__ereal_Osimps_I5_J, fact_55_lsc__at__def, fact_230_le__cases, fact_234_order_Otrans, fact_245_order__class_Oorder_Oeq__iff, fact_240_antisym__conv, fact_196_ord__eq__le__subst, fact_308_MInfty__neq__ereal_I1_J, fact_83_LIMSEQ__le, fact_44_lsc__at__mem, fact_247_ord__eq__le__trans, fact_63_neg__le__iff__le, fact_280_neq__PInf__trans, fact_65_ereal__minus__le__minus, fact_97_Lim__bounded2, fact_125_usc__at__def, fact_33_tendsto__cong__limit, fact_167_monoI1, fact_141_lim__decreasing__cl, fact_281_ereal__infty__less__eq2_I2_J, fact_211_eq__iff, fact_161_monoseq__def, fact_162_monoI2, fact_178_order__subst1, fact_96_Lim__bounded2, fact_37_neg__equal__iff__equal, fact_327_ereal__liminf__add__mono, fact_255_order__class_Oorder_Oantisym, fact_127_usc__at__def, fact_202_ord__le__eq__subst, fact_62_lsc__at__def, fact_278_ereal__less__eq_I1_J, fact_57_lsc__at__def, fact_35_tendsto__cong__limit, fact_28_tendsto__eq__rhs, fact_1_x__def_I2_J, fact_214_eq__iff, fact_153_lsc__imp__liminf, fact_149_monoseq__le, fact_100_LIMSEQ__le__const, fact_321_ereal__add__cancel__right, fact_343_filterlim__uminus__at__bot__at__top, fact_185_order__subst2, fact_163_monoI2, fact_313_ereal__PInfty__eq__plus, fact_314_ereal__plus__eq__PInfty, fact_238_le__cases3, fact_350_le__refl, fact_285_Lim__PInfty, fact_181_order__subst2, fact_31_tendsto__eq__rhs, fact_236_le__cases3, fact_58_lsc__at__def, fact_128_usc__at__def, fact_233_order_Otrans, fact_310_ereal__bot, fact_222_linear, fact_68_verit__la__disequality, fact_9_ereal__Lim__uminus, fact_183_order__subst2, fact_207_ord__le__eq__subst, fact_286_Lim__bounded__PInfty2, fact_224_eq__refl, fact_191_ord__eq__le__subst, fact_49_lsc__at__mem, fact_193_ord__eq__le__subst, fact_21_LIMSEQ__unique, fact_143_order__refl, fact_106_tendsto__mono, fact_276_ereal__infty__less__eq_I2_J, fact_129_usc__at__def, fact_118_comp__def, fact_170_monoseq__minus, fact_138_usc__at__mem, fact_354_nat__int__comparison_I1_J, fact_258_order__class_Oorder_Oantisym, fact_213_eq__iff, fact_292_ereal__le__le, fact_209_ord__le__eq__subst, fact_260_order__trans, fact_46_lsc__at__mem, fact_257_order__class_Oorder_Oantisym, fact_45_lsc__at__mem, fact_26_verit__negate__coefficient_I3_J, fact_349_le__trans, fact_135_usc__at__mem, fact_130_usc__at__def, fact_7_tendsto__const, fact_93_Lim__bounded, fact_244_order__class_Oorder_Oeq__iff, fact_131_usc__at__mem, fact_14_tendsto__minus__cancel, fact_27_ereal__uminus__eq__reorder, fact_187_order__subst2, fact_29_tendsto__eq__rhs, fact_298_times__ereal_Oinduct, fact_151_lsc__liminf, fact_348_eq__imp__le, fact_82_lim__mono, fact_246_order__class_Oorder_Oeq__iff, fact_223_eq__refl, fact_329_nat__int__comparison_I3_J, fact_69_verit__la__disequality, fact_312_ereal__minus__real__tendsto__MInf, fact_110_equation__minus__iff, fact_16_tendsto__minus__cancel__left, fact_159_monoseq__def, fact_261_order__trans, fact_24_ereal__uminus__uminus, fact_345_Nat_Oex__has__greatest__nat, fact_78_ereal__uminus__le__reorder, fact_210_ord__le__eq__subst, fact_20_LIMSEQ__unique, fact_225_eq__refl, fact_122_usc__at__def, fact_36_comp__apply, fact_215_antisym, fact_139_usc__at__mem, fact_89_Collect__cong, fact_156_LIMSEQ__Uniq, fact_107_tendsto__mono, fact_344_filterlim__uminus__at__top__at__bot, fact_250_ord__eq__le__trans, fact_18_tendsto__minus, fact_145_order__refl, fact_158_monoseq__def, fact_75_minus__le__iff, fact_305_ereal3__cases, fact_342_plus__ereal_Osimps_I1_J, fact_132_usc__at__mem, fact_76_le__imp__neg__le, fact_109_tendsto__mono, fact_160_monoseq__def, fact_56_lsc__at__def, fact_268_linorder__wlog, fact_50_lsc__at__mem, fact_108_tendsto__mono, fact_319_plus__ereal_Osimps_I6_J, fact_172_order__subst1, fact_219_linear, fact_232_order_Otrans, fact_271_dual__order_Otrans, fact_293_le__ereal__le, fact_12_LIMSEQ__const__iff, fact_173_order__subst1, fact_165_monoI2, fact_119_lsc__sequentially, fact_42_lsc__sequentially__gen, fact_8_tendsto__const, fact_41_lsc__sequentially__gen, fact_111_minus__equation__iff, fact_94_Lim__bounded2, fact_95_Lim__bounded2, fact_299_plus__ereal_Oinduct, fact_179_order__subst1, fact_249_ord__eq__le__trans, fact_192_ord__eq__le__subst, fact_212_eq__iff, fact_300_less__ereal_Oinduct, fact_264_dual__order_Orefl, fact_66_verit__la__disequality, fact_235_le__cases3, fact_176_order__subst1, fact_304_ereal__ex__split, fact_154_lsc__imp__liminf, fact_121_usc__at__def, fact_101_LIMSEQ__le__const, fact_177_order__subst1 53.77/22.85 % No. of inferences in proof: 684 53.77/22.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18355 ms resp. 17768 ms w/o parsing 53.77/22.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 53.77/22.85 thf(filter2049122004_ereal_type, type, filter2049122004_ereal: $tType). 53.77/22.85 thf(set_Extended_ereal_type, type, set_Extended_ereal: $tType). 53.77/22.85 thf(filter_real_type, type, filter_real: $tType). 53.77/22.85 thf(filter_nat_type, type, filter_nat: $tType). 53.77/22.85 thf(filter_int_type, type, filter_int: $tType). 53.77/22.85 thf(set_real_type, type, set_real: $tType). 53.77/22.85 thf(filter_a_type, type, filter_a: $tType). 53.77/22.85 thf(extended_ereal_type, type, extended_ereal: $tType). 53.77/22.85 thf(real_type, type, real: $tType). 53.77/22.85 thf(nat_type, type, nat: $tType). 53.77/22.85 thf(int_type, type, int: $tType). 53.77/22.85 thf(a_type, type, a: $tType). 53.77/22.85 thf(extend1289208545_ereal_type, type, extend1289208545_ereal: extended_ereal). 53.77/22.85 thf(extended_ereal2_type, type, extended_ereal2: (real > extended_ereal)). 53.77/22.85 thf(at_bot_real_type, type, at_bot_real: filter_real). 53.77/22.85 thf(at_top_nat_type, type, at_top_nat: filter_nat). 53.77/22.85 thf(at_top_real_type, type, at_top_real: filter_real). 53.77/22.85 thf(filter1531173832_ereal_type, type, filter1531173832_ereal: ((nat > extended_ereal) > (filter2049122004_ereal > (filter_nat > $o)))). 53.77/22.85 thf(filterlim_nat_int_type, type, filterlim_nat_int: ((nat > int) > (filter_int > (filter_nat > $o)))). 53.77/22.85 thf(filterlim_nat_nat_type, type, filterlim_nat_nat: ((nat > nat) > (filter_nat > (filter_nat > $o)))). 53.77/22.85 thf(filterlim_nat_real_type, type, filterlim_nat_real: ((nat > real) > (filter_real > (filter_nat > $o)))). 53.77/22.85 thf(filterlim_nat_a_type, type, filterlim_nat_a: ((nat > a) > (filter_a > (filter_nat > $o)))). 53.77/22.85 thf(filterlim_real_real_type, type, filterlim_real_real: ((real > real) > (filter_real > (filter_real > $o)))). 53.77/22.85 thf(comp_E1308517939al_nat_type, type, comp_E1308517939al_nat: ((extended_ereal > extended_ereal) > ((nat > extended_ereal) > (nat > extended_ereal)))). 53.77/22.85 thf(comp_E489644891real_a_type, type, comp_E489644891real_a: ((extended_ereal > extended_ereal) > ((a > extended_ereal) > (a > extended_ereal)))). 53.77/22.85 thf(comp_E1436437929nt_nat_type, type, comp_E1436437929nt_nat: ((extended_ereal > int) > ((nat > extended_ereal) > (nat > int)))). 53.77/22.85 thf(comp_E1523169101at_nat_type, type, comp_E1523169101at_nat: ((extended_ereal > nat) > ((nat > extended_ereal) > (nat > nat)))). 53.77/22.85 thf(comp_E1477338153al_nat_type, type, comp_E1477338153al_nat: ((extended_ereal > real) > ((nat > extended_ereal) > (nat > real)))). 53.77/22.85 thf(comp_n1096781355al_nat_type, type, comp_n1096781355al_nat: ((nat > extended_ereal) > ((nat > nat) > (nat > extended_ereal)))). 53.77/22.85 thf(comp_nat_a_nat_type, type, comp_nat_a_nat: ((nat > a) > ((nat > nat) > (nat > a)))). 53.77/22.85 thf(comp_r1410008527al_nat_type, type, comp_r1410008527al_nat: ((real > extended_ereal) > ((nat > real) > (nat > extended_ereal)))). 53.77/22.85 thf(comp_real_int_nat_type, type, comp_real_int_nat: ((real > int) > ((nat > real) > (nat > int)))). 53.77/22.85 thf(comp_real_nat_nat_type, type, comp_real_nat_nat: ((real > nat) > ((nat > real) > (nat > nat)))). 53.77/22.85 thf(comp_a1112243075al_nat_type, type, comp_a1112243075al_nat: ((a > extended_ereal) > ((nat > a) > (nat > extended_ereal)))). 53.77/22.85 thf(comp_a780206603real_a_type, type, comp_a780206603real_a: ((a > extended_ereal) > ((a > a) > (a > extended_ereal)))). 53.77/22.85 thf(comp_a_int_nat_type, type, comp_a_int_nat: ((a > int) > ((nat > a) > (nat > int)))). 53.77/22.85 thf(comp_a_nat_nat_type, type, comp_a_nat_nat: ((a > nat) > ((nat > a) > (nat > nat)))). 53.77/22.85 thf(comp_a_real_nat_type, type, comp_a_real_nat: ((a > real) > ((nat > a) > (nat > real)))). 53.77/22.85 thf(comp_a_a_nat_type, type, comp_a_a_nat: ((a > a) > ((nat > a) > (nat > a)))). 53.77/22.85 thf(plus_p2118002693_ereal_type, type, plus_p2118002693_ereal: (extended_ereal > (extended_ereal > extended_ereal))). 53.77/22.85 thf(plus_plus_real_type, type, plus_plus_real: (real > (real > real))). 53.77/22.85 thf(uminus1208298309_ereal_type, type, uminus1208298309_ereal: (extended_ereal > extended_ereal)). 53.77/22.85 thf(uminus_uminus_int_type, type, uminus_uminus_int: (int > int)). 53.77/22.85 thf(uminus_uminus_real_type, type, uminus_uminus_real: (real > real)). 53.77/22.85 thf(uniq_Extended_ereal_type, type, uniq_Extended_ereal: ((extended_ereal > $o) > $o)). 53.77/22.85 thf(uniq_real_type, type, uniq_real: ((real > $o) > $o)). 53.77/22.85 thf(uniq_a_type, type, uniq_a: ((a > $o) > $o)). 53.77/22.85 thf(liminf1045857232_ereal_type, type, liminf1045857232_ereal: (filter_nat > ((nat > extended_ereal) > extended_ereal))). 53.77/22.85 thf(lower_1087098792_ereal_type, type, lower_1087098792_ereal: (extended_ereal > ((extended_ereal > extended_ereal) > $o))). 53.77/22.85 thf(lower_48196818al_int_type, type, lower_48196818al_int: (extended_ereal > ((extended_ereal > int) > $o))). 53.77/22.85 thf(lower_1558406774al_nat_type, type, lower_1558406774al_nat: (extended_ereal > ((extended_ereal > nat) > $o))). 53.77/22.85 thf(lower_1165973074l_real_type, type, lower_1165973074l_real: (extended_ereal > ((extended_ereal > real) > $o))). 53.77/22.85 thf(lower_551915512_ereal_type, type, lower_551915512_ereal: (real > ((real > extended_ereal) > $o))). 53.77/22.85 thf(lower_153911426al_int_type, type, lower_153911426al_int: (real > ((real > int) > $o))). 53.77/22.85 thf(lower_1664121382al_nat_type, type, lower_1664121382al_nat: (real > ((real > nat) > $o))). 53.77/22.85 thf(lower_191460856_ereal_type, type, lower_191460856_ereal: (a > ((a > extended_ereal) > $o))). 53.77/22.85 thf(lower_956963458_a_int_type, type, lower_956963458_a_int: (a > ((a > int) > $o))). 53.77/22.85 thf(lower_319689766_a_nat_type, type, lower_319689766_a_nat: (a > ((a > nat) > $o))). 53.77/22.85 thf(lower_231615490a_real_type, type, lower_231615490a_real: (a > ((a > real) > $o))). 53.77/22.85 thf(lower_1071158961_ereal_type, type, lower_1071158961_ereal: (extended_ereal > ((extended_ereal > extended_ereal) > $o))). 53.77/22.85 thf(lower_637387785al_int_type, type, lower_637387785al_int: (extended_ereal > ((extended_ereal > int) > $o))). 53.77/22.85 thf(lower_114093al_nat_type, type, lower_114093al_nat: (extended_ereal > ((extended_ereal > nat) > $o))). 53.77/22.85 thf(lower_737640969l_real_type, type, lower_737640969l_real: (extended_ereal > ((extended_ereal > real) > $o))). 53.77/22.86 thf(lower_1075504779al_int_type, type, lower_1075504779al_int: (real > ((real > int) > $o))). 53.77/22.86 thf(lower_438231087al_nat_type, type, lower_438231087al_nat: (real > ((real > nat) > $o))). 53.77/22.86 thf(lower_534855297_ereal_type, type, lower_534855297_ereal: (a > ((a > extended_ereal) > $o))). 53.77/22.86 thf(lower_1672990777_a_int_type, type, lower_1672990777_a_int: (a > ((a > int) > $o))). 53.77/22.86 thf(lower_1035717085_a_nat_type, type, lower_1035717085_a_nat: (a > ((a > nat) > $o))). 53.77/22.86 thf(lower_755922489a_real_type, type, lower_755922489a_real: (a > ((a > real) > $o))). 53.77/22.86 thf(semiri2019852685at_int_type, type, semiri2019852685at_int: (nat > int)). 53.77/22.86 thf(semiri2110766477t_real_type, type, semiri2110766477t_real: (nat > real)). 53.77/22.86 thf(ord_le824540014_ereal_type, type, ord_le824540014_ereal: (extended_ereal > (extended_ereal > $o))). 53.77/22.86 thf(ord_le1745708096er_nat_type, type, ord_le1745708096er_nat: (filter_nat > (filter_nat > $o))). 53.77/22.86 thf(ord_le132810396r_real_type, type, ord_le132810396r_real: (filter_real > (filter_real > $o))). 53.77/22.86 thf(ord_less_eq_int_type, type, ord_less_eq_int: (int > (int > $o))). 53.77/22.86 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 53.77/22.86 thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))). 53.77/22.86 thf(collect_real_type, type, collect_real: ((real > $o) > set_real)). 53.77/22.86 thf(topolo1069469409_ereal_type, type, topolo1069469409_ereal: ((nat > extended_ereal) > $o)). 53.77/22.86 thf(topolo411883481eq_int_type, type, topolo411883481eq_int: ((nat > int) > $o)). 53.77/22.86 thf(topolo1922093437eq_nat_type, type, topolo1922093437eq_nat: ((nat > nat) > $o)). 53.77/22.86 thf(topolo144289241q_real_type, type, topolo144289241q_real: ((nat > real) > $o)). 53.77/22.86 thf(topolo2140997059_ereal_type, type, topolo2140997059_ereal: (extended_ereal > filter2049122004_ereal)). 53.77/22.86 thf(topolo54776183ds_int_type, type, topolo54776183ds_int: (int > filter_int)). 53.77/22.86 thf(topolo1564986139ds_nat_type, type, topolo1564986139ds_nat: (nat > filter_nat)). 53.77/22.86 thf(topolo1664202871s_real_type, type, topolo1664202871s_real: (real > filter_real)). 53.77/22.86 thf(topolo705128563nhds_a_type, type, topolo705128563nhds_a: (a > filter_a)). 53.77/22.86 thf(member1900190071_ereal_type, type, member1900190071_ereal: (extended_ereal > (set_Extended_ereal > $o))). 53.77/22.86 thf(a2_type, type, a2: extended_ereal). 53.77/22.86 thf(f_type, type, f: (a > extended_ereal)). 53.77/22.86 thf(x0_type, type, x0: a). 53.77/22.86 thf(x_type, type, x: (nat > a)). 53.77/22.86 thf(226,axiom,((! [A:(nat > extended_ereal),B:extended_ereal]: ((topolo1069469409_ereal @ A) => ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((! [C:nat,D:nat]: ((ord_le824540014_ereal @ (A @ C) @ (A @ D)) <= (ord_less_eq_nat @ C @ D)) & ! [C:nat]: (ord_le824540014_ereal @ (A @ C) @ B)) | (! [C:nat]: (ord_le824540014_ereal @ B @ (A @ C)) & ! [C:nat,D:nat]: ((ord_le824540014_ereal @ (A @ D) @ (A @ C)) <= (ord_less_eq_nat @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_monoseq__le)). 53.77/22.86 thf(1190,plain,((! [A:(nat > extended_ereal),B:extended_ereal]: ((topolo1069469409_ereal @ (A)) => ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((! [C:nat,D:nat]: ((ord_le824540014_ereal @ (A @ C) @ (A @ D)) | ~ (ord_less_eq_nat @ C @ D)) & ! [C:nat]: (ord_le824540014_ereal @ (A @ C) @ B)) | (! [C:nat]: (ord_le824540014_ereal @ B @ (A @ C)) & ! [C:nat,D:nat]: ((ord_le824540014_ereal @ (A @ D) @ (A @ C)) | ~ (ord_less_eq_nat @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 53.77/22.86 thf(140,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_le__imp__neg__le)). 53.77/22.86 thf(893,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 53.77/22.86 thf(222,axiom,((('?' @ extended_ereal) = (^ [A:(extended_ereal > $o)]: ((A @ extend1289208545_ereal) | (A @ (uminus1208298309_ereal @ extend1289208545_ereal)) | ? [B:real]: (A @ (extended_ereal2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_ereal__ex__split)). 53.77/22.86 thf(1179,plain,((('?' @ extended_ereal) = (^ [A:(extended_ereal > $o)]: ((A @ extend1289208545_ereal) | (A @ (uminus1208298309_ereal @ extend1289208545_ereal)) | ? [B:real]: (A @ (extended_ereal2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 53.77/22.86 thf(183,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (B = C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_ord__le__eq__trans)). 53.77/22.86 thf(1036,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 53.77/22.86 thf(294,axiom,((lower_1071158961_ereal = (^ [A:extended_ereal,B:(extended_ereal > extended_ereal)]: ! [C:(nat > extended_ereal),D:extended_ereal]: ((ord_le824540014_ereal @ D @ (B @ A)) <= ((filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) & (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_usc__at__def)). 53.77/22.86 thf(2822,plain,(((lower_1071158961_ereal) = (^ [A:extended_ereal,B:(extended_ereal > extended_ereal)]: ! [C:(nat > extended_ereal),D:extended_ereal]: ((ord_le824540014_ereal @ D @ (B @ A)) | ~ ((filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) & (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 53.77/22.86 thf(312,axiom,((! [A:extended_ereal,B:extended_ereal]: (((((? [C:real]: (A = (extended_ereal2 @ C))) => (B != (uminus1208298309_ereal @ extend1289208545_ereal))) => (((! [C:real]: (B != (extended_ereal2 @ C))) <= (A = extend1289208545_ereal)) => ((((A = extend1289208545_ereal) => (B != (uminus1208298309_ereal @ extend1289208545_ereal))) => (((~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => (B != (uminus1208298309_ereal @ extend1289208545_ereal)))) <= ((B != extend1289208545_ereal) <= (A = (uminus1208298309_ereal @ extend1289208545_ereal)))) <= ((! [C:real]: (B != (extended_ereal2 @ C))) <= (A = (uminus1208298309_ereal @ extend1289208545_ereal))))) <= ((B != extend1289208545_ereal) <= (A = extend1289208545_ereal))))) <= ((? [C:real]: (A = (extended_ereal2 @ C))) => (B != extend1289208545_ereal))) <= ((! [C:real]: (B != (extended_ereal2 @ C))) <= (? [C:real]: (A = (extended_ereal2 @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_ereal2__cases)). 53.77/22.86 thf(2876,plain,((! [A:extended_ereal,B:extended_ereal]: ((((? [C:real]: (A = (extended_ereal2 @ C))) => (~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)))) => ((! [C:real]: ~ (B = (extended_ereal2 @ C)) | ~ (A = extend1289208545_ereal)) => ((((A = extend1289208545_ereal) => (~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)))) => (~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => (~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)))) | ~ (~ (B = extend1289208545_ereal) | ~ (A = (uminus1208298309_ereal @ extend1289208545_ereal))) | ~ (! [C:real]: ~ (B = (extended_ereal2 @ C)) | ~ (A = (uminus1208298309_ereal @ extend1289208545_ereal))))) | ~ (~ (B = extend1289208545_ereal) | ~ (A = extend1289208545_ereal))))) | ~ ((? [C:real]: (A = (extended_ereal2 @ C))) => (~ (B = extend1289208545_ereal))) | ~ (! [C:real]: ~ (B = (extended_ereal2 @ C)) | ~ (? [C:real]: (A = (extended_ereal2 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 53.77/22.86 thf(236,axiom,((filterlim_nat_a @ x @ (topolo705128563nhds_a @ x0) @ at_top_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_x__def_I1_J)). 53.77/22.86 thf(1237,plain,((filterlim_nat_a @ (x) @ (topolo705128563nhds_a @ x0) @ at_top_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 53.77/22.86 thf(146,axiom,((! [A:real,B:real]: (~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ A @ B) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_verit__la__disequality)). 53.77/22.86 thf(909,plain,((! [A:real,B:real]: (~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 53.77/22.86 thf(83,axiom,((! [A:real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add_Oinverse__inverse)). 53.77/22.86 thf(628,plain,((! [A:real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 53.77/22.86 thf(259,axiom,((filterlim_nat_real @ semiri2110766477t_real @ at_top_real @ at_top_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_filterlim__real__sequentially)). 53.77/22.86 thf(1315,plain,((filterlim_nat_real @ (semiri2110766477t_real) @ at_top_real @ at_top_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 53.77/22.86 thf(50,axiom,((! [A:extended_ereal]: ((plus_p2118002693_ereal @ A @ extend1289208545_ereal) = extend1289208545_ereal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_plus__ereal_Osimps_I3_J)). 53.77/22.86 thf(518,plain,((! [A:extended_ereal]: ((plus_p2118002693_ereal @ A @ extend1289208545_ereal) = extend1289208545_ereal))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 53.77/22.86 thf(91,axiom,((! [A:nat,B:nat,C:(nat > extended_ereal),D:extended_ereal]: ((ord_less_eq_nat @ A @ B) => (((ord_le824540014_ereal @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_le824540014_ereal @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_order__subst2)). 53.77/22.86 thf(666,plain,((! [A:nat,B:nat,C:(nat > extended_ereal),D:extended_ereal]: ((ord_less_eq_nat @ A @ B) => ((ord_le824540014_ereal @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_le824540014_ereal @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 53.77/22.86 thf(253,axiom,((! [A:filter_nat,B:filter_nat,C:(nat > extended_ereal),D:extended_ereal]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ D) @ A) <= (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ D) @ B)) <= (ord_le1745708096er_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_tendsto__mono)). 53.77/22.86 thf(1295,plain,((! [A:filter_nat,B:filter_nat,C:(nat > extended_ereal),D:extended_ereal]: ((filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ D) @ A) | ~ (filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ D) @ B) | ~ (ord_le1745708096er_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 53.77/22.86 thf(227,axiom,((filter1531173832_ereal @ (^ [A:nat]: (extended_ereal2 @ (uminus_uminus_real @ (semiri2110766477t_real @ A)))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal)) @ at_top_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_ereal__minus__real__tendsto__MInf)). 53.77/22.86 thf(1200,plain,((filter1531173832_ereal @ (^ [A:nat]: (extended_ereal2 @ (uminus_uminus_real @ (semiri2110766477t_real @ A)))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal)) @ at_top_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 53.77/22.86 thf(192,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E)))) <= (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_linorder__wlog)). 53.77/22.86 thf(1068,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) | ~ (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 53.77/22.86 thf(291,axiom,((! [A:real,B:(real > int),C:(nat > real),D:int]: ((lower_153911426al_int @ A @ B) => ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) => ((ord_less_eq_int @ (B @ A) @ D) <= (filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_lsc__at__mem)). 53.77/22.86 thf(2808,plain,((! [A:real,B:(real > int),C:(nat > real),D:int]: ((lower_153911426al_int @ A @ (B)) => ((filterlim_nat_real @ (C) @ (topolo1664202871s_real @ A) @ at_top_nat) => ((ord_less_eq_int @ (B @ A) @ D) | ~ (filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 53.77/22.86 thf(247,axiom,((! [A:(nat > int),B:int]: ((topolo411883481eq_int @ A) => ((filterlim_nat_int @ A @ (topolo54776183ds_int @ B) @ at_top_nat) => ((! [C:nat]: (ord_less_eq_int @ (A @ C) @ B) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_int @ (A @ C) @ (A @ D)))) | (! [C:nat]: (ord_less_eq_int @ B @ (A @ C)) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_int @ (A @ D) @ (A @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_monoseq__le)). 53.77/22.86 thf(1269,plain,((! [A:(nat > int),B:int]: ((topolo411883481eq_int @ (A)) => ((filterlim_nat_int @ (A) @ (topolo54776183ds_int @ B) @ at_top_nat) => ((! [C:nat]: (ord_less_eq_int @ (A @ C) @ B) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_int @ (A @ C) @ (A @ D)))) | (! [C:nat]: (ord_less_eq_int @ B @ (A @ C)) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_int @ (A @ D) @ (A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 53.77/22.86 thf(305,axiom,((! [A:extended_ereal,B:extended_ereal]: (((uminus1208298309_ereal @ extend1289208545_ereal) = (plus_p2118002693_ereal @ A @ B)) = (((B != extend1289208545_ereal) & (A = (uminus1208298309_ereal @ extend1289208545_ereal))) | ((A != extend1289208545_ereal) & (B = (uminus1208298309_ereal @ extend1289208545_ereal))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_ereal__MInfty__eq__plus)). 53.77/22.86 thf(2854,plain,((! [A:extended_ereal,B:extended_ereal]: (((uminus1208298309_ereal @ extend1289208545_ereal) = (plus_p2118002693_ereal @ A @ B)) = ((~ (B = extend1289208545_ereal) & (A = (uminus1208298309_ereal @ extend1289208545_ereal))) | (~ (A = extend1289208545_ereal) & (B = (uminus1208298309_ereal @ extend1289208545_ereal))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 53.77/22.86 thf(94,axiom,((! [A:(a > extended_ereal),B:(nat > a),C:(a > extended_ereal),D:(nat > a)]: (((comp_a1112243075al_nat @ A @ B) = (comp_a1112243075al_nat @ C @ D)) => (! [E:nat]: ((A @ (B @ E)) = (C @ (D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_comp__eq__elim)). 53.77/22.86 thf(677,plain,((! [A:(a > extended_ereal),B:(nat > a),C:(a > extended_ereal),D:(nat > a)]: (((comp_a1112243075al_nat @ A @ B) = (comp_a1112243075al_nat @ C @ D)) => (! [E:nat]: ((A @ (B @ E)) = (C @ (D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 53.77/22.86 thf(215,axiom,((! [A:(nat > real)]: (uniq_real @ (^ [B:real]: (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_LIMSEQ__Uniq)). 53.77/22.86 thf(1158,plain,((! [A:(nat > real)]: (uniq_real @ (^ [B:real]: (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 53.77/22.86 thf(117,axiom,((! [A:real,B:extended_ereal,C:real]: (((ord_le824540014_ereal @ (extended_ereal2 @ C) @ B) <= (ord_less_eq_real @ C @ A)) <= (ord_le824540014_ereal @ (extended_ereal2 @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_ereal__le__le)). 53.77/22.86 thf(762,plain,((! [A:real,B:extended_ereal,C:real]: ((ord_le824540014_ereal @ (extended_ereal2 @ C) @ B) | ~ (ord_less_eq_real @ C @ A) | ~ (ord_le824540014_ereal @ (extended_ereal2 @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 53.77/22.86 thf(184,axiom,((topolo144289241q_real = (^ [A:(nat > real)]: (! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C)) | ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ B) @ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_monoseq__def)). 53.77/22.86 thf(1041,plain,(((topolo144289241q_real) = (^ [A:(nat > real)]: (! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C)) | ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ B) @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 53.77/22.86 thf(133,axiom,((! [A:(nat > int)]: ((topolo411883481eq_int @ A) <= (! [B:nat,C:nat]: ((ord_less_eq_int @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_monoI2)). 53.77/22.86 thf(861,plain,((! [A:(nat > int)]: ((topolo411883481eq_int @ (A)) | ~ (! [B:nat,C:nat]: ((ord_less_eq_int @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 53.77/22.86 thf(14,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_order__subst1)). 53.77/22.86 thf(384,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 53.77/22.86 thf(209,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:nat,D:real]: (((! [E:nat]: ((ord_le824540014_ereal @ (A @ E) @ (extended_ereal2 @ D)) <= (ord_less_eq_nat @ C @ E))) => (B != extend1289208545_ereal)) <= (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_Lim__bounded__PInfty2)). 53.77/22.86 thf(1137,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:nat,D:real]: (((! [E:nat]: ((ord_le824540014_ereal @ (A @ E) @ (extended_ereal2 @ D)) | ~ (ord_less_eq_nat @ C @ E))) => (~ (B = extend1289208545_ereal))) | ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 53.77/22.86 thf(44,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) => (A = B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_antisym)). 53.77/22.86 thf(500,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) => (A = B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 53.77/22.86 thf(36,axiom,(((= @ int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_eq__iff)). 53.77/22.86 thf(472,plain,(((= @ int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 53.77/22.86 thf(235,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:extended_ereal]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((ord_le824540014_ereal @ C @ B) <= (? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_le824540014_ereal @ C @ (A @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_LIMSEQ__le__const)). 53.77/22.86 thf(1233,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:extended_ereal]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((ord_le824540014_ereal @ C @ B) | ~ (? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_le824540014_ereal @ C @ (A @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 53.77/22.86 thf(100,axiom,((! [A:(nat > real),B:real,C:filter_nat,D:real]: (((filterlim_nat_real @ A @ (topolo1664202871s_real @ D) @ C) <= (D = B)) <= (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_tendsto__cong__limit)). 53.77/22.86 thf(698,plain,((! [A:(nat > real),B:real,C:filter_nat,D:real]: ((filterlim_nat_real @ (A) @ (topolo1664202871s_real @ D) @ C) | ~ (D = B) | ~ (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 53.77/22.86 thf(155,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_minus__le__iff)). 53.77/22.86 thf(945,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 53.77/22.86 thf(92,axiom,((! [A:real,B:real]: ((ord_le824540014_ereal @ (extended_ereal2 @ A) @ (extended_ereal2 @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_ereal__less__eq_I3_J)). 53.77/22.86 thf(670,plain,((! [A:real,B:real]: ((ord_le824540014_ereal @ (extended_ereal2 @ A) @ (extended_ereal2 @ B)) = (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 53.77/22.86 thf(55,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_linear)). 53.77/22.86 thf(538,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 53.77/22.86 thf(272,axiom,((! [A:extended_ereal,B:extended_ereal]: (((uminus1208298309_ereal @ A) = B) = (A = (uminus1208298309_ereal @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_ereal__uminus__eq__reorder)). 53.77/22.86 thf(1354,plain,((! [A:extended_ereal,B:extended_ereal]: (((uminus1208298309_ereal @ A) = B) = (A = (uminus1208298309_ereal @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 53.77/22.86 thf(205,axiom,((! [A:real,B:real]: ((filterlim_nat_real @ (^ [C:nat]: (A)) @ (topolo1664202871s_real @ B) @ at_top_nat) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_LIMSEQ__const__iff)). 53.77/22.86 thf(1127,plain,((! [A:real,B:real]: ((filterlim_nat_real @ (^ [C:nat]: (A)) @ (topolo1664202871s_real @ B) @ at_top_nat) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 53.77/22.86 thf(335,axiom,((! [A:real,B:(real > nat),C:(nat > real),D:nat]: ((lower_438231087al_nat @ A @ B) => (((filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ D @ (B @ A))) <= (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_usc__at__mem)). 53.77/22.86 thf(2985,plain,((! [A:real,B:(real > nat),C:(nat > real),D:nat]: ((lower_438231087al_nat @ A @ (B)) => (((filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ D @ (B @ A))) | ~ (filterlim_nat_real @ (C) @ (topolo1664202871s_real @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 53.77/22.86 thf(103,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_eq__iff)). 53.77/22.86 thf(709,plain,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 53.77/22.86 thf(139,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > int),D:int]: ((ord_le824540014_ereal @ A @ B) => (((C @ B) = D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) => (ord_less_eq_int @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_ord__le__eq__subst)). 53.77/22.86 thf(885,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > int),D:int]: ((ord_le824540014_ereal @ A @ B) => (((C @ B) = D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) => (ord_less_eq_int @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 53.77/22.86 thf(25,axiom,((! [A:real,B:real,C:(real > extended_ereal),D:extended_ereal]: ((((! [E:real,F:real]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_ord__le__eq__subst)). 53.77/22.86 thf(436,plain,((! [A:real,B:real,C:(real > extended_ereal),D:extended_ereal]: (((! [E:real,F:real]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 53.77/22.86 thf(246,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ C @ (A @ E)) <= (ord_less_eq_nat @ D @ E))) => (ord_less_eq_nat @ C @ B)) <= (filterlim_nat_nat @ A @ (topolo1564986139ds_nat @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_LIMSEQ__le__const)). 53.77/22.86 thf(1265,plain,((! [A:(nat > nat),B:nat,C:nat]: (((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ C @ (A @ E)) | ~ (ord_less_eq_nat @ D @ E))) => (ord_less_eq_nat @ C @ B)) | ~ (filterlim_nat_nat @ (A) @ (topolo1564986139ds_nat @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 53.77/22.86 thf(243,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat,D:extended_ereal]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ C) => ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ D) @ C) <= (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_tendsto__eq__rhs)). 53.77/22.86 thf(1254,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat,D:extended_ereal]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ C) => ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ D) @ C) | ~ (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 53.77/22.86 thf(310,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:nat,D:extended_ereal]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((ord_le824540014_ereal @ D @ B) <= (! [E:nat]: ((ord_le824540014_ereal @ D @ (A @ E)) <= (ord_less_eq_nat @ C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Lim__bounded2)). 53.77/22.86 thf(2869,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:nat,D:extended_ereal]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((ord_le824540014_ereal @ D @ B) | ~ (! [E:nat]: ((ord_le824540014_ereal @ D @ (A @ E)) | ~ (ord_less_eq_nat @ C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 53.77/22.86 thf(65,axiom,((! [A:(a > extended_ereal),B:(nat > a),C:(a > extended_ereal),D:(nat > a),E:nat]: (((A @ (B @ E)) = (C @ (D @ E))) <= ((comp_a1112243075al_nat @ A @ B) = (comp_a1112243075al_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_comp__eq__dest)). 53.77/22.86 thf(570,plain,((! [A:(a > extended_ereal),B:(nat > a),C:(a > extended_ereal),D:(nat > a),E:nat]: (((A @ (B @ E)) = (C @ (D @ E))) | ~ ((comp_a1112243075al_nat @ A @ B) = (comp_a1112243075al_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 53.77/22.86 thf(254,axiom,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((filterlim_nat_nat @ A @ (topolo1564986139ds_nat @ B) @ at_top_nat) => ((ord_less_eq_nat @ B @ D) <= (! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_eq_nat @ (A @ E) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Lim__bounded)). 53.77/22.86 thf(1298,plain,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((filterlim_nat_nat @ (A) @ (topolo1564986139ds_nat @ B) @ at_top_nat) => ((ord_less_eq_nat @ B @ D) | ~ (! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_eq_nat @ (A @ E) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 53.77/22.86 thf(10,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_order__subst2)). 53.77/22.86 thf(372,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 53.77/22.86 thf(3,axiom,((! [A:real,B:filter_real]: (filterlim_real_real @ (^ [C:real]: (A)) @ (topolo1664202871s_real @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_tendsto__const)). 53.77/22.86 thf(344,plain,((! [A:real,B:filter_real]: (filterlim_real_real @ (^ [C:real]: (A)) @ (topolo1664202871s_real @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 53.77/22.86 thf(248,axiom,((! [A:(nat > extended_ereal)]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ extend1289208545_ereal) @ at_top_nat) = ((liminf1045857232_ereal @ at_top_nat @ A) = extend1289208545_ereal)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_liminf__PInfty)). 53.77/22.86 thf(1279,plain,((! [A:(nat > extended_ereal)]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ extend1289208545_ereal) @ at_top_nat) = ((liminf1045857232_ereal @ at_top_nat @ (A)) = extend1289208545_ereal)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 53.77/22.86 thf(153,axiom,((! [A:extended_ereal,B:extended_ereal]: (((ord_le824540014_ereal @ B @ A) => (A = B)) <= (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_antisym)). 53.77/22.86 thf(934,plain,((! [A:extended_ereal,B:extended_ereal]: (((ord_le824540014_ereal @ B @ A) => (A = B)) | ~ (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 53.77/22.86 thf(32,axiom,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((ord_le824540014_ereal @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_antisym__conv)). 53.77/22.86 thf(460,plain,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((ord_le824540014_ereal @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 53.77/22.86 thf(61,axiom,((! [A:extended_ereal,B:(real > extended_ereal),C:real,D:real]: ((ord_le824540014_ereal @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((ord_le824540014_ereal @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_order__subst1)). 53.77/22.86 thf(559,plain,((! [A:extended_ereal,B:(real > extended_ereal),C:real,D:real]: ((ord_le824540014_ereal @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((ord_le824540014_ereal @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 53.77/22.86 thf(306,axiom,((! [A:real,B:(real > extended_ereal),C:(nat > real),D:extended_ereal]: ((((filter1531173832_ereal @ (comp_r1410008527al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ (B @ A) @ D)) <= (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)) <= (lower_551915512_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_lsc__at__mem)). 53.77/22.86 thf(2857,plain,((! [A:real,B:(real > extended_ereal),C:(nat > real),D:extended_ereal]: (((filter1531173832_ereal @ (comp_r1410008527al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ (B @ A) @ D)) | ~ (filterlim_nat_real @ (C) @ (topolo1664202871s_real @ A) @ at_top_nat) | ~ (lower_551915512_ereal @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 53.77/22.86 thf(164,axiom,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_verit__la__disequality)). 53.77/22.86 thf(969,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 53.77/22.86 thf(198,axiom,((! [A:extended_ereal,B:(int > extended_ereal),C:int,D:int]: ((ord_le824540014_ereal @ A @ (B @ C)) => ((ord_less_eq_int @ C @ D) => ((ord_le824540014_ereal @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_le824540014_ereal @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_order__subst1)). 53.77/22.86 thf(1100,plain,((! [A:extended_ereal,B:(int > extended_ereal),C:int,D:int]: ((ord_le824540014_ereal @ A @ (B @ C)) => ((ord_less_eq_int @ C @ D) => ((ord_le824540014_ereal @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_le824540014_ereal @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 53.77/22.86 thf(42,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((A = B) => ((ord_le824540014_ereal @ B @ C) => (ord_le824540014_ereal @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_ord__eq__le__trans)). 53.77/22.86 thf(492,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((A = B) => ((ord_le824540014_ereal @ B @ C) => (ord_le824540014_ereal @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 53.77/22.86 thf(122,axiom,((! [A:int,B:int,C:int]: (((((~ (ord_less_eq_int @ C @ B)) <= (ord_less_eq_int @ A @ C)) => (((~ ((~ (ord_less_eq_int @ A @ B)) <= (ord_less_eq_int @ C @ A))) <= ((ord_less_eq_int @ B @ C) => (~ (ord_less_eq_int @ C @ A)))) <= ((ord_less_eq_int @ C @ B) => (~ (ord_less_eq_int @ B @ A))))) <= ((~ (ord_less_eq_int @ A @ C)) <= (ord_less_eq_int @ B @ A))) <= ((~ (ord_less_eq_int @ B @ C)) <= (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_le__cases3)). 53.77/22.86 thf(789,plain,((! [A:int,B:int,C:int]: (((~ (ord_less_eq_int @ C @ B) | ~ (ord_less_eq_int @ A @ C)) => (~ (~ (ord_less_eq_int @ A @ B) | ~ (ord_less_eq_int @ C @ A)) | ~ ((ord_less_eq_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))) | ~ ((ord_less_eq_int @ C @ B) => (~ (ord_less_eq_int @ B @ A))))) | ~ (~ (ord_less_eq_int @ A @ C) | ~ (ord_less_eq_int @ B @ A)) | ~ (~ (ord_less_eq_int @ B @ C) | ~ (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 53.77/22.86 thf(72,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: (((ord_le824540014_ereal @ B @ C) => (ord_le824540014_ereal @ A @ C)) <= (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_order_Otrans)). 53.77/22.86 thf(591,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: (((ord_le824540014_ereal @ B @ C) => (ord_le824540014_ereal @ A @ C)) | ~ (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 53.77/22.86 thf(11,axiom,((comp_a1112243075al_nat = (^ [A:(a > extended_ereal),B:(nat > a),C:nat]: (A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_comp__apply)). 53.77/22.86 thf(376,plain,(((comp_a1112243075al_nat) = (^ [A:(a > extended_ereal),B:(nat > a),C:nat]: (A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 53.77/22.86 thf(87,axiom,((! [A:(real > real),B:real,C:filter_real]: ((filterlim_real_real @ A @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) = (filterlim_real_real @ (^ [D:real]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_tendsto__minus__cancel__left)). 53.77/22.86 thf(646,plain,((! [A:(real > real),B:real,C:filter_real]: ((filterlim_real_real @ (A) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) = (filterlim_real_real @ (^ [D:real]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 53.77/22.86 thf(129,axiom,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: (((A @ B @ C) <= (! [D:extended_ereal,E:extended_ereal]: ((A @ D @ E) <= (A @ E @ D)))) <= (! [D:extended_ereal,E:extended_ereal]: ((ord_le824540014_ereal @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_linorder__wlog)). 53.77/22.86 thf(834,plain,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: ((A @ B @ C) | ~ (! [D:extended_ereal,E:extended_ereal]: ((A @ D @ E) | ~ (A @ E @ D))) | ~ (! [D:extended_ereal,E:extended_ereal]: ((ord_le824540014_ereal @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 53.77/22.86 thf(66,axiom,((! [A:real,B:real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_verit__negate__coefficient_I3_J)). 53.77/22.86 thf(574,plain,((! [A:real,B:real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 53.77/22.86 thf(163,axiom,((! [A:real,B:real]: (((extended_ereal2 @ A) = (extended_ereal2 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_ereal_Oinject)). 53.77/22.86 thf(966,plain,((! [A:real,B:real]: (((extended_ereal2 @ A) = (extended_ereal2 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 53.77/22.86 thf(39,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_minus__le__iff)). 53.77/22.86 thf(480,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 53.77/22.86 thf(255,axiom,((lower_438231087al_nat = (^ [A:real,B:(real > nat)]: ! [C:(nat > real),D:nat]: (((filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)) => (ord_less_eq_nat @ D @ (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_usc__at__def)). 53.77/22.86 thf(1302,plain,(((lower_438231087al_nat) = (^ [A:real,B:(real > nat)]: ! [C:(nat > real),D:nat]: (((filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)) => (ord_less_eq_nat @ D @ (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 53.77/22.86 thf(286,axiom,((! [A:real,B:(real > extended_ereal),C:(nat > real),D:(nat > extended_ereal),E:extended_ereal]: (((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) => ((filter1531173832_ereal @ D @ (topolo2140997059_ereal @ E) @ at_top_nat) => ((! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F))) => (ord_le824540014_ereal @ (B @ A) @ E)))) <= (lower_551915512_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_lsc__sequentially__mem)). 53.77/22.86 thf(2794,plain,((! [A:real,B:(real > extended_ereal),C:(nat > real),D:(nat > extended_ereal),E:extended_ereal]: (((filterlim_nat_real @ (C) @ (topolo1664202871s_real @ A) @ at_top_nat) => ((filter1531173832_ereal @ (D) @ (topolo2140997059_ereal @ E) @ at_top_nat) => ((! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F))) => (ord_le824540014_ereal @ (B @ A) @ E)))) | ~ (lower_551915512_ereal @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 53.77/22.86 thf(212,axiom,((! [A:real]: ((plus_p2118002693_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ A)) = (uminus1208298309_ereal @ extend1289208545_ereal)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_plus__ereal_Osimps_I5_J)). 53.77/22.86 thf(1151,plain,((! [A:real]: ((plus_p2118002693_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ A)) = (uminus1208298309_ereal @ extend1289208545_ereal)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 53.77/22.86 thf(154,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)) & (A @ D))) <= (! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_Nat_Oex__has__greatest__nat)). 53.77/22.86 thf(937,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => (? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E)) & (A @ D)) | ~ (! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 53.77/22.86 thf(299,axiom,((! [A:(nat > a)]: (uniq_a @ (^ [B:a]: (filterlim_nat_a @ A @ (topolo705128563nhds_a @ B) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_LIMSEQ__Uniq)). 53.77/22.86 thf(2833,plain,((! [A:(nat > a)]: (uniq_a @ (^ [B:a]: (filterlim_nat_a @ A @ (topolo705128563nhds_a @ B) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 53.77/22.86 thf(159,axiom,((! [A:extended_ereal]: (ord_le824540014_ereal @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_dual__order_Orefl)). 53.77/22.86 thf(956,plain,((! [A:extended_ereal]: (ord_le824540014_ereal @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 53.77/22.86 thf(135,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_order_Otrans)). 53.77/22.86 thf(866,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 53.77/22.86 thf(29,axiom,((comp_a1112243075al_nat = (^ [A:(a > extended_ereal),B:(nat > a),C:nat]: (A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_comp__def)). 53.77/22.86 thf(453,plain,(((comp_a1112243075al_nat) = (^ [A:(a > extended_ereal),B:(nat > a),C:nat]: (A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 53.77/22.86 thf(333,axiom,((! [A:a,B:(a > nat),C:(nat > a),D:nat]: ((lower_319689766_a_nat @ A @ B) => ((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ (B @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_lsc__at__mem)). 53.77/22.86 thf(2979,plain,((! [A:a,B:(a > nat),C:(nat > a),D:nat]: ((lower_319689766_a_nat @ A @ (B)) => ((filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ (B @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 53.77/22.86 thf(172,axiom,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:extended_ereal,D:extended_ereal]: (((ord_le824540014_ereal @ C @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D)))) <= (ord_le824540014_ereal @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_order__subst1)). 53.77/22.86 thf(998,plain,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:extended_ereal,D:extended_ereal]: (((ord_le824540014_ereal @ C @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D)))) | ~ (ord_le824540014_ereal @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 53.77/22.86 thf(19,axiom,((! [A:filter_real,B:filter_real,C:(real > real),D:real]: ((ord_le132810396r_real @ A @ B) => ((filterlim_real_real @ C @ (topolo1664202871s_real @ D) @ A) <= (filterlim_real_real @ C @ (topolo1664202871s_real @ D) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_tendsto__mono)). 53.77/22.86 thf(411,plain,((! [A:filter_real,B:filter_real,C:(real > real),D:real]: ((ord_le132810396r_real @ A @ B) => ((filterlim_real_real @ (C) @ (topolo1664202871s_real @ D) @ A) | ~ (filterlim_real_real @ (C) @ (topolo1664202871s_real @ D) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 53.77/22.86 thf(228,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat,D:extended_ereal]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ C) => ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ D) @ C) <= (D = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_tendsto__cong__limit)). 53.77/22.86 thf(1201,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat,D:extended_ereal]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ C) => ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ D) @ C) | ~ (D = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 53.77/22.86 thf(289,axiom,((lower_551915512_ereal = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real),D:(nat > extended_ereal),E:extended_ereal]: ((ord_le824540014_ereal @ (B @ A) @ E) <= ((filter1531173832_ereal @ D @ (topolo2140997059_ereal @ E) @ at_top_nat) & ! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F)) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_lsc__sequentially__gen)). 53.77/22.86 thf(2804,plain,(((lower_551915512_ereal) = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real),D:(nat > extended_ereal),E:extended_ereal]: ((ord_le824540014_ereal @ (B @ A) @ E) | ~ ((filter1531173832_ereal @ D @ (topolo2140997059_ereal @ E) @ at_top_nat) & ! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F)) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 53.77/22.86 thf(334,axiom,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: (((! [D:extended_ereal]: (A @ extend1289208545_ereal @ D)) => (((((A @ B @ C) <= (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ extend1289208545_ereal)) <= (! [D:real]: (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ D)))) <= (! [D:real]: (A @ (extended_ereal2 @ D) @ extend1289208545_ereal))) <= (! [D:extended_ereal]: (A @ D @ (uminus1208298309_ereal @ extend1289208545_ereal))))) <= (! [D:real,E:real]: (A @ (extended_ereal2 @ D) @ (extended_ereal2 @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_less__ereal_Oinduct)). 53.77/22.86 thf(2982,plain,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: (((! [D:extended_ereal]: (A @ extend1289208545_ereal @ D)) => ((A @ B @ C) | ~ (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ extend1289208545_ereal) | ~ (! [D:real]: (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ D))) | ~ (! [D:real]: (A @ (extended_ereal2 @ D) @ extend1289208545_ereal)) | ~ (! [D:extended_ereal]: (A @ D @ (uminus1208298309_ereal @ extend1289208545_ereal))))) | ~ (! [D:real,E:real]: (A @ (extended_ereal2 @ D) @ (extended_ereal2 @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 53.77/22.86 thf(74,axiom,((! [A:(a > extended_ereal),B:(nat > a),C:(nat > nat)]: ((comp_n1096781355al_nat @ (comp_a1112243075al_nat @ A @ B) @ C) = (comp_a1112243075al_nat @ A @ (comp_nat_a_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_comp__assoc)). 53.77/22.86 thf(602,plain,((! [A:(a > extended_ereal),B:(nat > a),C:(nat > nat)]: ((comp_n1096781355al_nat @ (comp_a1112243075al_nat @ A @ B) @ C) = (comp_a1112243075al_nat @ A @ (comp_nat_a_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 53.77/22.86 thf(327,axiom,((! [A:(nat > a),B:a,C:a]: ((filterlim_nat_a @ A @ (topolo705128563nhds_a @ B) @ at_top_nat) => ((B = C) <= (filterlim_nat_a @ A @ (topolo705128563nhds_a @ C) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_LIMSEQ__unique)). 53.77/22.86 thf(2964,plain,((! [A:(nat > a),B:a,C:a]: ((filterlim_nat_a @ (A) @ (topolo705128563nhds_a @ B) @ at_top_nat) => ((B = C) | ~ (filterlim_nat_a @ (A) @ (topolo705128563nhds_a @ C) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 53.77/22.86 thf(219,axiom,((lower_956963458_a_int = (^ [A:a,B:(a > int)]: ! [C:(nat > a),D:int]: ((ord_less_eq_int @ (B @ A) @ D) <= ((filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lsc__at__def)). 53.77/22.86 thf(1169,plain,(((lower_956963458_a_int) = (^ [A:a,B:(a > int)]: ! [C:(nat > a),D:int]: ((ord_less_eq_int @ (B @ A) @ D) | ~ ((filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 53.77/22.86 thf(97,axiom,((! [A:set_Extended_ereal]: ? [B:extended_ereal]: (! [C:extended_ereal]: ((ord_le824540014_ereal @ C @ B) <= (! [D:extended_ereal]: ((ord_le824540014_ereal @ C @ D) <= (member1900190071_ereal @ D @ A)))) & ! [C:extended_ereal]: ((ord_le824540014_ereal @ B @ C) <= (member1900190071_ereal @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_ereal__complete__Inf)). 53.77/22.86 thf(687,plain,((! [A:set_Extended_ereal]: ? [B:extended_ereal]: (! [C:extended_ereal]: ((ord_le824540014_ereal @ C @ B) | ~ (! [D:extended_ereal]: ((ord_le824540014_ereal @ C @ D) | ~ (member1900190071_ereal @ D @ A)))) & ! [C:extended_ereal]: ((ord_le824540014_ereal @ B @ C) | ~ (member1900190071_ereal @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 53.77/22.86 thf(137,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ord__eq__le__trans)). 53.77/22.86 thf(877,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 53.77/22.86 thf(98,axiom,((! [A:(nat > extended_ereal)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_le824540014_ereal @ (A @ B) @ (A @ C)))) => (topolo1069469409_ereal @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_monoI1)). 53.77/22.86 thf(692,plain,((! [A:(nat > extended_ereal)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_le824540014_ereal @ (A @ B) @ (A @ C)))) => (topolo1069469409_ereal @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 53.77/22.86 thf(199,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > extended_ereal),D:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ord__le__eq__subst)). 53.77/22.86 thf(1104,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > extended_ereal),D:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 53.77/22.86 thf(239,axiom,((! [A:(nat > int),B:int,C:nat,D:int]: (((! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_eq_int @ (A @ E) @ D))) => (ord_less_eq_int @ B @ D)) <= (filterlim_nat_int @ A @ (topolo54776183ds_int @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Lim__bounded)). 53.77/22.86 thf(1242,plain,((! [A:(nat > int),B:int,C:nat,D:int]: (((! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_eq_int @ (A @ E) @ D))) => (ord_less_eq_int @ B @ D)) | ~ (filterlim_nat_int @ (A) @ (topolo54776183ds_int @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 53.77/22.86 thf(193,axiom,((topolo1069469409_ereal = (^ [A:(nat > extended_ereal)]: (! [B:nat,C:nat]: ((ord_le824540014_ereal @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)) | ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_le824540014_ereal @ (A @ C) @ (A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_monoseq__def)). 53.77/22.86 thf(1074,plain,(((topolo1069469409_ereal) = (^ [A:(nat > extended_ereal)]: (! [B:nat,C:nat]: ((ord_le824540014_ereal @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C)) | ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_le824540014_ereal @ (A @ C) @ (A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 53.77/22.86 thf(229,axiom,((! [A:extended_ereal,B:extended_ereal]: (((A = (uminus1208298309_ereal @ extend1289208545_ereal)) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal))) <= (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_ereal__infty__less__eq2_I2_J)). 53.77/22.86 thf(1206,plain,((! [A:extended_ereal,B:extended_ereal]: ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 53.77/22.86 thf(48,axiom,((! [A:(extended_ereal > extended_ereal),B:(a > extended_ereal),C:(nat > a)]: ((comp_a1112243075al_nat @ (comp_E489644891real_a @ A @ B) @ C) = (comp_E1308517939al_nat @ A @ (comp_a1112243075al_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_comp__assoc)). 53.77/22.86 thf(512,plain,((! [A:(extended_ereal > extended_ereal),B:(a > extended_ereal),C:(nat > a)]: ((comp_a1112243075al_nat @ (comp_E489644891real_a @ A @ B) @ C) = (comp_E1308517939al_nat @ A @ (comp_a1112243075al_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 53.77/22.86 thf(9,axiom,((! [A:set_Extended_ereal]: ? [B:extended_ereal]: (! [C:extended_ereal]: ((member1900190071_ereal @ C @ A) => (ord_le824540014_ereal @ C @ B)) & ! [C:extended_ereal]: ((! [D:extended_ereal]: ((ord_le824540014_ereal @ D @ C) <= (member1900190071_ereal @ D @ A))) => (ord_le824540014_ereal @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_ereal__complete__Sup)). 53.77/22.86 thf(366,plain,((! [A:set_Extended_ereal]: ? [B:extended_ereal]: (! [C:extended_ereal]: ((member1900190071_ereal @ C @ A) => (ord_le824540014_ereal @ C @ B)) & ! [C:extended_ereal]: ((! [D:extended_ereal]: ((ord_le824540014_ereal @ D @ C) | ~ (member1900190071_ereal @ D @ A))) => (ord_le824540014_ereal @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 53.77/22.86 thf(217,axiom,((! [A:(nat > nat),B:nat,C:(nat > nat),D:nat]: ((filterlim_nat_nat @ A @ (topolo1564986139ds_nat @ B) @ at_top_nat) => ((filterlim_nat_nat @ C @ (topolo1564986139ds_nat @ D) @ at_top_nat) => ((ord_less_eq_nat @ B @ D) <= (? [E:nat]: ! [F:nat]: ((ord_less_eq_nat @ (A @ F) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_LIMSEQ__le)). 53.77/22.86 thf(1163,plain,((! [A:(nat > nat),B:nat,C:(nat > nat),D:nat]: ((filterlim_nat_nat @ (A) @ (topolo1564986139ds_nat @ B) @ at_top_nat) => ((filterlim_nat_nat @ (C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => ((ord_less_eq_nat @ B @ D) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_eq_nat @ (A @ F) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 53.77/22.86 thf(258,axiom,((! [A:real]: ((extended_ereal2 @ A) != (uminus1208298309_ereal @ extend1289208545_ereal)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_MInfty__neq__ereal_I1_J)). 53.77/22.86 thf(1311,plain,((! [A:real]: ~ ((extended_ereal2 @ A) = (uminus1208298309_ereal @ extend1289208545_ereal)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 53.77/22.86 thf(54,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_eq_real @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order__subst2)). 53.77/22.86 thf(534,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 53.77/22.86 thf(280,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((((((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (? [D:real]: (B = (extended_ereal2 @ D)))) <= (? [D:real]: (A = (extended_ereal2 @ D)))) => (((((? [D:real]: (A = (extended_ereal2 @ D))) => ((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (B = extend1289208545_ereal))) => (((? [D:real]: (A = (extended_ereal2 @ D))) => ((! [D:real]: (C != (extended_ereal2 @ D))) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal)))) => ((((C != extend1289208545_ereal) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal))) <= (? [D:real]: (A = (extended_ereal2 @ D)))) => ((((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal))) <= (? [D:real]: (A = (extended_ereal2 @ D)))) => (((A = extend1289208545_ereal) => ((? [D:real]: (B = (extended_ereal2 @ D))) => (! [D:real]: (C != (extended_ereal2 @ D))))) => ((((? [D:real]: (B = (extended_ereal2 @ D))) => (C != extend1289208545_ereal)) <= (A = extend1289208545_ereal)) => ((((? [D:real]: (B = (extended_ereal2 @ D))) => (C != (uminus1208298309_ereal @ extend1289208545_ereal))) <= (A = extend1289208545_ereal)) => ((((B = extend1289208545_ereal) => (! [D:real]: (C != (extended_ereal2 @ D)))) <= (A = extend1289208545_ereal)) => (((A = extend1289208545_ereal) => ((C != extend1289208545_ereal) <= (B = extend1289208545_ereal))) => ((((B = extend1289208545_ereal) => (C != (uminus1208298309_ereal @ extend1289208545_ereal))) <= (A = extend1289208545_ereal)) => ((((A = extend1289208545_ereal) => ((C != extend1289208545_ereal) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal)))) => (((((((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = extend1289208545_ereal) => (! [D:real]: (C != (extended_ereal2 @ D))))) => ((((C != extend1289208545_ereal) <= (B = extend1289208545_ereal)) <= (A = (uminus1208298309_ereal @ extend1289208545_ereal))) => (((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = extend1289208545_ereal) => (C != (uminus1208298309_ereal @ extend1289208545_ereal)))) => (((~ (((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal))) <= (A = (uminus1208298309_ereal @ extend1289208545_ereal)))) <= ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = (uminus1208298309_ereal @ extend1289208545_ereal)) => (C != extend1289208545_ereal)))) <= ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = (uminus1208298309_ereal @ extend1289208545_ereal)) => (! [D:real]: (C != (extended_ereal2 @ D))))))))) <= ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (? [D:real]: (B = (extended_ereal2 @ D)))))) <= ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((C != extend1289208545_ereal) <= (? [D:real]: (B = (extended_ereal2 @ D)))))) <= ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((! [D:real]: (C != (extended_ereal2 @ D))) <= (? [D:real]: (B = (extended_ereal2 @ D)))))) <= ((A = extend1289208545_ereal) => ((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal)))))) <= ((A = extend1289208545_ereal) => ((! [D:real]: (C != (extended_ereal2 @ D))) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal))))))))))))))) <= (((C != extend1289208545_ereal) <= (B = extend1289208545_ereal)) <= (? [D:real]: (A = (extended_ereal2 @ D))))) <= (((! [D:real]: (C != (extended_ereal2 @ D))) <= (B = extend1289208545_ereal)) <= (? [D:real]: (A = (extended_ereal2 @ D)))))) <= ((? [D:real]: (A = (extended_ereal2 @ D))) => ((C != extend1289208545_ereal) <= (? [D:real]: (B = (extended_ereal2 @ D)))))) <= ((? [D:real]: (A = (extended_ereal2 @ D))) => ((? [D:real]: (B = (extended_ereal2 @ D))) => (! [D:real]: (C != (extended_ereal2 @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_ereal3__cases)). 53.77/22.86 thf(1387,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: (((~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (? [D:real]: (B = (extended_ereal2 @ D))) | ~ (? [D:real]: (A = (extended_ereal2 @ D)))) => ((((? [D:real]: (A = (extended_ereal2 @ D))) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (B = extend1289208545_ereal))) => (((? [D:real]: (A = (extended_ereal2 @ D))) => (! [D:real]: ~ (C = (extended_ereal2 @ D)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)))) => ((~ (C = extend1289208545_ereal) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (? [D:real]: (A = (extended_ereal2 @ D)))) => ((~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (? [D:real]: (A = (extended_ereal2 @ D)))) => (((A = extend1289208545_ereal) => ((? [D:real]: (B = (extended_ereal2 @ D))) => (! [D:real]: ~ (C = (extended_ereal2 @ D))))) => ((((? [D:real]: (B = (extended_ereal2 @ D))) => (~ (C = extend1289208545_ereal))) | ~ (A = extend1289208545_ereal)) => ((((? [D:real]: (B = (extended_ereal2 @ D))) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)))) | ~ (A = extend1289208545_ereal)) => ((((B = extend1289208545_ereal) => (! [D:real]: ~ (C = (extended_ereal2 @ D)))) | ~ (A = extend1289208545_ereal)) => (((A = extend1289208545_ereal) => (~ (C = extend1289208545_ereal) | ~ (B = extend1289208545_ereal))) => ((((B = extend1289208545_ereal) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)))) | ~ (A = extend1289208545_ereal)) => ((((A = extend1289208545_ereal) => (~ (C = extend1289208545_ereal) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)))) => ((((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = extend1289208545_ereal) => (! [D:real]: ~ (C = (extended_ereal2 @ D))))) => ((~ (C = extend1289208545_ereal) | ~ (B = extend1289208545_ereal) | ~ (A = (uminus1208298309_ereal @ extend1289208545_ereal))) => (((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = extend1289208545_ereal) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal))))) => (~ (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (A = (uminus1208298309_ereal @ extend1289208545_ereal))) | ~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = (uminus1208298309_ereal @ extend1289208545_ereal)) => (~ (C = extend1289208545_ereal)))) | ~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((B = (uminus1208298309_ereal @ extend1289208545_ereal)) => (! [D:real]: ~ (C = (extended_ereal2 @ D))))))))) | ~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (? [D:real]: (B = (extended_ereal2 @ D))))) | ~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => (~ (C = extend1289208545_ereal) | ~ (? [D:real]: (B = (extended_ereal2 @ D))))) | ~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => (! [D:real]: ~ (C = (extended_ereal2 @ D)) | ~ (? [D:real]: (B = (extended_ereal2 @ D))))) | ~ ((A = extend1289208545_ereal) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)))))) | ~ ((A = extend1289208545_ereal) => (! [D:real]: ~ (C = (extended_ereal2 @ D)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal))))))))))))))) | ~ (~ (C = extend1289208545_ereal) | ~ (B = extend1289208545_ereal) | ~ (? [D:real]: (A = (extended_ereal2 @ D)))) | ~ (! [D:real]: ~ (C = (extended_ereal2 @ D)) | ~ (B = extend1289208545_ereal) | ~ (? [D:real]: (A = (extended_ereal2 @ D)))))) | ~ ((? [D:real]: (A = (extended_ereal2 @ D))) => (~ (C = extend1289208545_ereal) | ~ (? [D:real]: (B = (extended_ereal2 @ D))))) | ~ ((? [D:real]: (A = (extended_ereal2 @ D))) => ((? [D:real]: (B = (extended_ereal2 @ D))) => (! [D:real]: ~ (C = (extended_ereal2 @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 53.77/22.86 thf(112,axiom,((! [A:extended_ereal,B:extended_ereal]: ((A = B) => (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_eq__refl)). 53.77/22.86 thf(746,plain,((! [A:extended_ereal,B:extended_ereal]: ((A = B) => (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 53.77/22.86 thf(268,axiom,((! [A:a,B:(a > extended_ereal),C:(nat > a)]: ((lower_191460856_ereal @ A @ B) => ((ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_a1112243075al_nat @ B @ C))) <= (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_lsc__imp__liminf)). 53.77/22.86 thf(1343,plain,((! [A:a,B:(a > extended_ereal),C:(nat > a)]: ((lower_191460856_ereal @ A @ (B)) => ((ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_a1112243075al_nat @ B @ C))) | ~ (filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 53.77/22.86 thf(5,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_nat__int__comparison_I1_J)). 53.77/22.86 thf(349,plain,(((= @ nat) = (^ [A:nat,B:nat]: ((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 53.77/22.86 thf(126,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_ord__le__eq__subst)). 53.77/22.86 thf(820,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 53.77/22.86 thf(329,axiom,((! [A:filter_nat]: ((filter1531173832_ereal @ (comp_a1112243075al_nat @ f @ x) @ (topolo2140997059_ereal @ a2) @ A) => (filter1531173832_ereal @ (^ [B:nat]: (uminus1208298309_ereal @ (comp_a1112243075al_nat @ f @ x @ B))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ a2)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060And_062F_O_A_I_If_A_092_060circ_062_Ax_J_A_092_060longlongrightarrow_062_AA_J_AF_A_092_060Longrightarrow_062_A_I_I_092_060lambda_062xa_O_A_N_A_If_A_092_060circ_062_Ax_J_Axa_J_A_092_060longlongrightarrow_062_A_N_AA_J_AF_092_060close_062)). 53.77/22.86 thf(2969,plain,((! [A:filter_nat]: ((filter1531173832_ereal @ (comp_a1112243075al_nat @ f @ x) @ (topolo2140997059_ereal @ a2) @ A) => (filter1531173832_ereal @ (^ [B:nat]: (uminus1208298309_ereal @ (comp_a1112243075al_nat @ f @ x @ B))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ a2)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 53.77/22.86 thf(320,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:nat,D:extended_ereal]: (((ord_le824540014_ereal @ B @ D) <= (! [E:nat]: ((ord_le824540014_ereal @ (A @ E) @ D) <= (ord_less_eq_nat @ C @ E)))) <= (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Lim__bounded)). 53.77/22.86 thf(2937,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:nat,D:extended_ereal]: ((ord_le824540014_ereal @ B @ D) | ~ (! [E:nat]: ((ord_le824540014_ereal @ (A @ E) @ D) | ~ (ord_less_eq_nat @ C @ E))) | ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 53.77/22.86 thf(23,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_order_Otrans)). 53.77/22.86 thf(429,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 53.77/22.86 thf(237,axiom,((lower_1558406774al_nat = (^ [A:extended_ereal,B:(extended_ereal > nat)]: ! [C:(nat > extended_ereal),D:nat]: ((ord_less_eq_nat @ (B @ A) @ D) <= ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_lsc__at__def)). 53.77/22.86 thf(1238,plain,(((lower_1558406774al_nat) = (^ [A:extended_ereal,B:(extended_ereal > nat)]: ! [C:(nat > extended_ereal),D:nat]: ((ord_less_eq_nat @ (B @ A) @ D) | ~ ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 53.77/22.86 thf(34,axiom,((! [A:a,B:filter_nat]: (filterlim_nat_a @ (^ [C:nat]: (A)) @ (topolo705128563nhds_a @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_tendsto__const)). 53.77/22.86 thf(467,plain,((! [A:a,B:filter_nat]: (filterlim_nat_a @ (^ [C:nat]: (A)) @ (topolo705128563nhds_a @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 53.77/22.86 thf(311,axiom,((! [A:extended_ereal]: ((uminus1208298309_ereal @ (uminus1208298309_ereal @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_ereal__uminus__uminus)). 53.77/22.86 thf(2873,plain,((! [A:extended_ereal]: ((uminus1208298309_ereal @ (uminus1208298309_ereal @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 53.77/22.86 thf(182,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_order__subst2)). 53.77/22.86 thf(1032,plain,((! [A:real,B:real,C:(real > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 53.77/22.86 thf(296,axiom,((lower_191460856_ereal = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a),D:(nat > extended_ereal),E:extended_ereal]: (((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & ! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F)) & (filter1531173832_ereal @ D @ (topolo2140997059_ereal @ E) @ at_top_nat)) => (ord_le824540014_ereal @ (B @ A) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lsc__sequentially__gen)). 53.77/22.86 thf(2826,plain,(((lower_191460856_ereal) = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a),D:(nat > extended_ereal),E:extended_ereal]: (((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & ! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F)) & (filter1531173832_ereal @ D @ (topolo2140997059_ereal @ E) @ at_top_nat)) => (ord_le824540014_ereal @ (B @ A) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 53.77/22.86 thf(128,axiom,((! [A:real,B:(extended_ereal > real),C:extended_ereal,D:extended_ereal]: ((((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))) <= (ord_le824540014_ereal @ C @ D)) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_order__subst1)). 53.77/22.86 thf(830,plain,((! [A:real,B:(extended_ereal > real),C:extended_ereal,D:extended_ereal]: (((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))) | ~ (ord_le824540014_ereal @ C @ D) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 53.77/22.86 thf(230,axiom,((! [A:(nat > real),B:real,C:real]: ((filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat) => ((ord_less_eq_real @ C @ B) <= (? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_less_eq_real @ C @ (A @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_LIMSEQ__le__const)). 53.77/22.86 thf(1210,plain,((! [A:(nat > real),B:real,C:real]: ((filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ at_top_nat) => ((ord_less_eq_real @ C @ B) | ~ (? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_less_eq_real @ C @ (A @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 53.77/22.86 thf(180,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_dual__order_Otrans)). 53.77/22.86 thf(1027,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 53.77/22.86 thf(115,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_nat__leq__as__int)). 53.77/22.86 thf(757,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 53.77/22.86 thf(166,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((((C @ B) = D) => ((ord_less_eq_real @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ord__le__eq__subst)). 53.77/22.86 thf(974,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((((C @ B) = D) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 53.77/22.86 thf(8,axiom,((! [A:(nat > real),B:real,C:filter_nat,D:real]: (((B = D) => (filterlim_nat_real @ A @ (topolo1664202871s_real @ D) @ C)) <= (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_tendsto__eq__rhs)). 53.77/22.86 thf(361,plain,((! [A:(nat > real),B:real,C:filter_nat,D:real]: (((B = D) => (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ D) @ C)) | ~ (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 53.77/22.86 thf(275,axiom,((! [A:(nat > extended_ereal),B:(nat > extended_ereal)]: ((~ ((((liminf1045857232_ereal @ at_top_nat @ B) = (uminus1208298309_ereal @ extend1289208545_ereal)) & ((liminf1045857232_ereal @ at_top_nat @ A) = extend1289208545_ereal)) | (((liminf1045857232_ereal @ at_top_nat @ A) = (uminus1208298309_ereal @ extend1289208545_ereal)) & ((liminf1045857232_ereal @ at_top_nat @ B) = extend1289208545_ereal)))) => (ord_le824540014_ereal @ (plus_p2118002693_ereal @ (liminf1045857232_ereal @ at_top_nat @ A) @ (liminf1045857232_ereal @ at_top_nat @ B)) @ (liminf1045857232_ereal @ at_top_nat @ (^ [C:nat]: (plus_p2118002693_ereal @ (A @ C) @ (B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_ereal__liminf__add__mono)). 53.77/22.86 thf(1365,plain,((! [A:(nat > extended_ereal),B:(nat > extended_ereal)]: ((~ ((((liminf1045857232_ereal @ at_top_nat @ (B)) = (uminus1208298309_ereal @ extend1289208545_ereal)) & ((liminf1045857232_ereal @ at_top_nat @ (A)) = extend1289208545_ereal)) | (((liminf1045857232_ereal @ at_top_nat @ (A)) = (uminus1208298309_ereal @ extend1289208545_ereal)) & ((liminf1045857232_ereal @ at_top_nat @ (B)) = extend1289208545_ereal)))) => (ord_le824540014_ereal @ (plus_p2118002693_ereal @ (liminf1045857232_ereal @ at_top_nat @ (A)) @ (liminf1045857232_ereal @ at_top_nat @ (B))) @ (liminf1045857232_ereal @ at_top_nat @ (^ [C:nat]: (plus_p2118002693_ereal @ (A @ C) @ (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 53.77/22.86 thf(67,axiom,((! [A:(nat > nat)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C))) => (topolo1922093437eq_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_monoI2)). 53.77/22.86 thf(578,plain,((! [A:(nat > nat)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C))) => (topolo1922093437eq_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 53.77/22.86 thf(78,axiom,((! [A:extended_ereal,B:extended_ereal]: ((extend1289208545_ereal = (plus_p2118002693_ereal @ A @ B)) = ((A = extend1289208545_ereal) | (B = extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_ereal__PInfty__eq__plus)). 53.77/22.86 thf(615,plain,((! [A:extended_ereal,B:extended_ereal]: ((extend1289208545_ereal = (plus_p2118002693_ereal @ A @ B)) = ((A = extend1289208545_ereal) | (B = extend1289208545_ereal))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 53.77/22.86 thf(264,axiom,((! [A:real]: ((plus_p2118002693_ereal @ (extended_ereal2 @ A) @ (uminus1208298309_ereal @ extend1289208545_ereal)) = (uminus1208298309_ereal @ extend1289208545_ereal)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_plus__ereal_Osimps_I4_J)). 53.77/22.86 thf(1328,plain,((! [A:real]: ((plus_p2118002693_ereal @ (extended_ereal2 @ A) @ (uminus1208298309_ereal @ extend1289208545_ereal)) = (uminus1208298309_ereal @ extend1289208545_ereal)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 53.77/22.86 thf(18,axiom,((! [A:nat,B:(extended_ereal > nat),C:extended_ereal,D:extended_ereal]: (((ord_le824540014_ereal @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_ord__eq__le__subst)). 53.77/22.86 thf(403,plain,((! [A:nat,B:(extended_ereal > nat),C:extended_ereal,D:extended_ereal]: (((ord_le824540014_ereal @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 53.77/22.86 thf(15,axiom,(((= @ extended_ereal) = (^ [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) & (ord_le824540014_ereal @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_order__class_Oorder_Oeq__iff)). 53.77/22.86 thf(388,plain,(((= @ extended_ereal) = (^ [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) & (ord_le824540014_ereal @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 53.77/22.86 thf(7,axiom,((! [A:(real > real),B:real,C:filter_real,D:real]: ((filterlim_real_real @ A @ (topolo1664202871s_real @ B) @ C) => ((filterlim_real_real @ A @ (topolo1664202871s_real @ D) @ C) <= (D = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_tendsto__cong__limit)). 53.77/22.86 thf(356,plain,((! [A:(real > real),B:real,C:filter_real,D:real]: ((filterlim_real_real @ (A) @ (topolo1664202871s_real @ B) @ C) => ((filterlim_real_real @ (A) @ (topolo1664202871s_real @ D) @ C) | ~ (D = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 53.77/22.86 thf(136,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_ord__le__eq__subst)). 53.77/22.86 thf(869,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 53.77/22.86 thf(202,axiom,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ (uminus1208298309_ereal @ A) @ B) = (ord_le824540014_ereal @ (uminus1208298309_ereal @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ereal__uminus__le__reorder)). 53.77/22.86 thf(1118,plain,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ (uminus1208298309_ereal @ A) @ B) = (ord_le824540014_ereal @ (uminus1208298309_ereal @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 53.77/22.86 thf(244,axiom,((! [A:a,B:(a > extended_ereal),C:(nat > a),D:(nat > extended_ereal),E:extended_ereal]: ((lower_191460856_ereal @ A @ B) => (((filter1531173832_ereal @ D @ (topolo2140997059_ereal @ E) @ at_top_nat) => ((ord_le824540014_ereal @ (B @ A) @ E) <= (! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F))))) <= (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_lsc__sequentially__mem)). 53.77/22.86 thf(1259,plain,((! [A:a,B:(a > extended_ereal),C:(nat > a),D:(nat > extended_ereal),E:extended_ereal]: ((lower_191460856_ereal @ A @ (B)) => (((filter1531173832_ereal @ (D) @ (topolo2140997059_ereal @ E) @ at_top_nat) => ((ord_le824540014_ereal @ (B @ A) @ E) | ~ (! [F:nat]: (ord_le824540014_ereal @ (B @ (C @ F)) @ (D @ F))))) | ~ (filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 53.77/22.86 thf(323,axiom,((! [A:(nat > nat),B:nat]: ((topolo1922093437eq_nat @ A) => (((! [C:nat]: (ord_less_eq_nat @ (A @ C) @ B) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (A @ C) @ (A @ D)))) | (! [C:nat]: (ord_less_eq_nat @ B @ (A @ C)) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (A @ D) @ (A @ C))))) <= (filterlim_nat_nat @ A @ (topolo1564986139ds_nat @ B) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_monoseq__le)). 53.77/22.86 thf(2946,plain,((! [A:(nat > nat),B:nat]: ((topolo1922093437eq_nat @ (A)) => ((! [C:nat]: (ord_less_eq_nat @ (A @ C) @ B) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (A @ C) @ (A @ D)))) | (! [C:nat]: (ord_less_eq_nat @ B @ (A @ C)) & ! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (A @ D) @ (A @ C)))) | ~ (filterlim_nat_nat @ (A) @ (topolo1564986139ds_nat @ B) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 53.77/22.86 thf(156,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_le__refl)). 53.77/22.86 thf(948,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 53.77/22.86 thf(288,axiom,((! [A:extended_ereal]: ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) <= (! [B:real]: (ord_le824540014_ereal @ A @ (extended_ereal2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_ereal__bot)). 53.77/22.86 thf(2801,plain,((! [A:extended_ereal]: ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (! [B:real]: (ord_le824540014_ereal @ A @ (extended_ereal2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 53.77/22.86 thf(331,axiom,((lower_191460856_ereal = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a),D:extended_ereal]: ((ord_le824540014_ereal @ (B @ A) @ D) <= (! [E:nat]: (ord_le824540014_ereal @ (B @ (C @ E)) @ D) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_lsc__sequentially)). 53.77/22.86 thf(2973,plain,(((lower_191460856_ereal) = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a),D:extended_ereal]: ((ord_le824540014_ereal @ (B @ A) @ D) | ~ (! [E:nat]: (ord_le824540014_ereal @ (B @ (C @ E)) @ D) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 53.77/22.86 thf(203,axiom,((! [A:real]: ((uminus1208298309_ereal @ (extended_ereal2 @ A)) = (extended_ereal2 @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_uminus__ereal_Osimps_I1_J)). 53.77/22.86 thf(1121,plain,((! [A:real]: ((uminus1208298309_ereal @ (extended_ereal2 @ A)) = (extended_ereal2 @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 53.77/22.86 thf(216,axiom,((! [A:real,B:(real > nat),C:(nat > real),D:nat]: ((lower_1664121382al_nat @ A @ B) => ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) => ((ord_less_eq_nat @ (B @ A) @ D) <= (filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_lsc__at__mem)). 53.77/22.86 thf(1160,plain,((! [A:real,B:(real > nat),C:(nat > real),D:nat]: ((lower_1664121382al_nat @ A @ (B)) => ((filterlim_nat_real @ (C) @ (topolo1664202871s_real @ A) @ at_top_nat) => ((ord_less_eq_nat @ (B @ A) @ D) | ~ (filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 53.77/22.86 thf(195,axiom,((! [A:extended_ereal,B:(real > extended_ereal),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_ord__eq__le__subst)). 53.77/22.86 thf(1082,plain,((! [A:extended_ereal,B:(real > extended_ereal),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 53.77/22.86 thf(41,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: (((ord_less_eq_int @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) => (ord_less_eq_int @ (C @ A) @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_order__subst2)). 53.77/22.86 thf(488,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: (((ord_less_eq_int @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) => (ord_less_eq_int @ (C @ A) @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 53.77/22.86 thf(274,axiom,((! [A:(nat > extended_ereal)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_le824540014_ereal @ (A @ B) @ (A @ C)))) => (~ (! [B:extended_ereal]: ~ (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_lim__decreasing__cl)). 53.77/22.86 thf(1361,plain,((! [A:(nat > extended_ereal)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_le824540014_ereal @ (A @ B) @ (A @ C)))) => (~ (! [B:extended_ereal]: ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 53.77/22.86 thf(339,axiom,((! [A:extended_ereal,B:extended_ereal]: (((plus_p2118002693_ereal @ A @ B) = (uminus1208298309_ereal @ extend1289208545_ereal)) = (((A = (uminus1208298309_ereal @ extend1289208545_ereal)) | (B = (uminus1208298309_ereal @ extend1289208545_ereal))) & (A != extend1289208545_ereal) & (B != extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_ereal__plus__eq__MInfty)). 53.77/22.86 thf(3000,plain,((! [A:extended_ereal,B:extended_ereal]: (((plus_p2118002693_ereal @ A @ B) = (uminus1208298309_ereal @ extend1289208545_ereal)) = (((A = (uminus1208298309_ereal @ extend1289208545_ereal)) | (B = (uminus1208298309_ereal @ extend1289208545_ereal))) & ~ (A = extend1289208545_ereal) & ~ (B = extend1289208545_ereal))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 53.77/22.86 thf(252,axiom,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:(nat > extended_ereal),D:extended_ereal]: ((lower_1087098792_ereal @ A @ B) => (((filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ (B @ A) @ D)) <= (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_lsc__at__mem)). 53.77/22.86 thf(1292,plain,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:(nat > extended_ereal),D:extended_ereal]: ((lower_1087098792_ereal @ A @ (B)) => (((filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ (B @ A) @ D)) | ~ (filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 53.77/22.86 thf(114,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_eq__imp__le)). 53.77/22.86 thf(753,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 53.77/22.86 thf(298,axiom,((! [A:extended_ereal,B:(extended_ereal > real),C:(nat > extended_ereal),D:real]: ((lower_1165973074l_real @ A @ B) => ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((ord_less_eq_real @ (B @ A) @ D) <= (filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_lsc__at__mem)). 53.77/22.86 thf(2830,plain,((! [A:extended_ereal,B:(extended_ereal > real),C:(nat > extended_ereal),D:real]: ((lower_1165973074l_real @ A @ (B)) => ((filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((ord_less_eq_real @ (B @ A) @ D) | ~ (filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 53.77/22.86 thf(231,axiom,((! [A:(nat > real),B:real,C:nat,D:real]: ((filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat) => ((! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_eq_real @ (A @ E) @ D))) => (ord_less_eq_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Lim__bounded)). 53.77/22.86 thf(1214,plain,((! [A:(nat > real),B:real,C:nat,D:real]: ((filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ at_top_nat) => ((! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_eq_real @ (A @ E) @ D))) => (ord_less_eq_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 53.77/22.86 thf(58,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_dual__order_Orefl)). 53.77/22.86 thf(547,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 53.77/22.86 thf(102,axiom,((! [A:(nat > real)]: ((topolo144289241q_real @ A) <= (! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_monoI1)). 53.77/22.86 thf(706,plain,((! [A:(nat > real)]: ((topolo144289241q_real @ (A)) | ~ (! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 53.77/22.86 thf(80,axiom,((! [A:(nat > real)]: ((topolo144289241q_real @ (^ [B:nat]: (uminus_uminus_real @ (A @ B)))) <= (topolo144289241q_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_monoseq__minus)). 53.77/22.86 thf(622,plain,((! [A:(nat > real)]: ((topolo144289241q_real @ (^ [B:nat]: (uminus_uminus_real @ (A @ B)))) | ~ (topolo144289241q_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 53.77/22.86 thf(49,axiom,((! [A:(nat > nat)]: ((topolo1922093437eq_nat @ A) <= (! [B:nat,C:nat]: ((ord_less_eq_nat @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_monoI1)). 53.77/22.86 thf(515,plain,((! [A:(nat > nat)]: ((topolo1922093437eq_nat @ (A)) | ~ (! [B:nat,C:nat]: ((ord_less_eq_nat @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 53.77/22.86 thf(109,axiom,((! [A:real]: (filterlim_real_real @ uminus_uminus_real @ (topolo1664202871s_real @ (uminus_uminus_real @ A)) @ (topolo1664202871s_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_tendsto__uminus__nhds)). 53.77/22.86 thf(738,plain,((! [A:real]: (filterlim_real_real @ (uminus_uminus_real) @ (topolo1664202871s_real @ (uminus_uminus_real @ A)) @ (topolo1664202871s_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 53.77/22.86 thf(234,axiom,((lower_534855297_ereal = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a),D:extended_ereal]: ((ord_le824540014_ereal @ D @ (B @ A)) <= ((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & (filter1531173832_ereal @ (comp_a1112243075al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_usc__at__def)). 53.77/22.86 thf(1231,plain,(((lower_534855297_ereal) = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a),D:extended_ereal]: ((ord_le824540014_ereal @ D @ (B @ A)) | ~ ((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & (filter1531173832_ereal @ (comp_a1112243075al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 53.77/22.86 thf(304,axiom,((! [A:a,B:(a > nat),C:(nat > a),D:nat]: ((lower_1035717085_a_nat @ A @ B) => (((filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ D @ (B @ A))) <= (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_usc__at__mem)). 53.77/22.86 thf(2851,plain,((! [A:a,B:(a > nat),C:(nat > a),D:nat]: ((lower_1035717085_a_nat @ A @ (B)) => (((filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ D @ (B @ A))) | ~ (filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 53.77/22.86 thf(107,axiom,((! [A:nat,B:nat,C:nat]: ((((~ (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ B @ A)) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => ((((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))) <= ((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A)))))) <= ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_le__cases3)). 53.77/22.86 thf(721,plain,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ A)) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => ((((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))) | ~ ((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A)))))) | ~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 53.77/22.86 thf(173,axiom,(((= @ extended_ereal) = (^ [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) & (ord_le824540014_ereal @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_eq__iff)). 53.77/22.86 thf(1002,plain,(((= @ extended_ereal) = (^ [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) & (ord_le824540014_ereal @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 53.77/22.86 thf(308,axiom,((! [A:(nat > real),B:real,C:(nat > real),D:real]: ((filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat) => (((? [E:nat]: ! [F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (A @ F) @ (C @ F)))) => (ord_less_eq_real @ B @ D)) <= (filterlim_nat_real @ C @ (topolo1664202871s_real @ D) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_LIMSEQ__le)). 53.77/22.86 thf(2862,plain,((! [A:(nat > real),B:real,C:(nat > real),D:real]: ((filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ at_top_nat) => (((? [E:nat]: ! [F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (A @ F) @ (C @ F)))) => (ord_less_eq_real @ B @ D)) | ~ (filterlim_nat_real @ (C) @ (topolo1664202871s_real @ D) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 53.77/22.86 thf(240,axiom,((lower_114093al_nat = (^ [A:extended_ereal,B:(extended_ereal > nat)]: ! [C:(nat > extended_ereal),D:nat]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)) => (ord_less_eq_nat @ D @ (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_usc__at__def)). 53.77/22.86 thf(1246,plain,(((lower_114093al_nat) = (^ [A:extended_ereal,B:(extended_ereal > nat)]: ! [C:(nat > extended_ereal),D:nat]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)) => (ord_less_eq_nat @ D @ (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 53.77/22.86 thf(328,axiom,((filter1531173832_ereal @ (^ [A:nat]: (extended_ereal2 @ (semiri2110766477t_real @ A))) @ (topolo2140997059_ereal @ extend1289208545_ereal) @ at_top_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_id__nat__ereal__tendsto__PInf)). 53.77/22.86 thf(2968,plain,((filter1531173832_ereal @ (^ [A:nat]: (extended_ereal2 @ (semiri2110766477t_real @ A))) @ (topolo2140997059_ereal @ extend1289208545_ereal) @ at_top_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 53.77/22.86 thf(263,axiom,((! [A:(nat > nat),B:nat,C:nat,D:nat]: (((! [E:nat]: ((ord_less_eq_nat @ D @ (A @ E)) <= (ord_less_eq_nat @ C @ E))) => (ord_less_eq_nat @ D @ B)) <= (filterlim_nat_nat @ A @ (topolo1564986139ds_nat @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Lim__bounded2)). 53.77/22.86 thf(1324,plain,((! [A:(nat > nat),B:nat,C:nat,D:nat]: (((! [E:nat]: ((ord_less_eq_nat @ D @ (A @ E)) | ~ (ord_less_eq_nat @ C @ E))) => (ord_less_eq_nat @ D @ B)) | ~ (filterlim_nat_nat @ (A) @ (topolo1564986139ds_nat @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 53.77/22.86 thf(201,axiom,((! [A:(nat > real),B:real,C:real]: (((B = C) <= (filterlim_nat_real @ A @ (topolo1664202871s_real @ C) @ at_top_nat)) <= (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_LIMSEQ__unique)). 53.77/22.86 thf(1114,plain,((! [A:(nat > real),B:real,C:real]: ((B = C) | ~ (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ C) @ at_top_nat) | ~ (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 53.77/22.86 thf(188,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_neg__le__iff__le)). 53.77/22.86 thf(1050,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 53.77/22.86 thf(31,axiom,((! [A:extended_ereal,B:real,C:real]: ((ord_le824540014_ereal @ A @ (extended_ereal2 @ B)) => ((ord_less_eq_real @ B @ C) => (ord_le824540014_ereal @ A @ (extended_ereal2 @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_le__ereal__le)). 53.77/22.86 thf(457,plain,((! [A:extended_ereal,B:real,C:real]: ((ord_le824540014_ereal @ A @ (extended_ereal2 @ B)) => ((ord_less_eq_real @ B @ C) => (ord_le824540014_ereal @ A @ (extended_ereal2 @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 53.77/22.86 thf(45,axiom,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ B @ A) | (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_linear)). 53.77/22.86 thf(503,plain,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ B @ A) | (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 53.77/22.86 thf(75,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_order__class_Oorder_Oantisym)). 53.77/22.86 thf(605,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 53.77/22.86 thf(266,axiom,((! [A:(extended_ereal > $o),B:extended_ereal]: ((! [C:real]: (A @ (extended_ereal2 @ C))) => ((A @ (uminus1208298309_ereal @ extend1289208545_ereal)) => ((A @ extend1289208545_ereal) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_abs__ereal_Oinduct)). 53.77/22.86 thf(1333,plain,((! [A:(extended_ereal > $o),B:extended_ereal]: ((! [C:real]: (A @ (extended_ereal2 @ C))) => ((A @ (uminus1208298309_ereal @ extend1289208545_ereal)) => ((A @ extend1289208545_ereal) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 53.77/22.86 thf(118,axiom,((! [A:extended_ereal,B:extended_ereal]: (((plus_p2118002693_ereal @ A @ B) = extend1289208545_ereal) = ((B = extend1289208545_ereal) | (A = extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_ereal__plus__eq__PInfty)). 53.77/22.86 thf(765,plain,((! [A:extended_ereal,B:extended_ereal]: (((plus_p2118002693_ereal @ A @ B) = extend1289208545_ereal) = ((B = extend1289208545_ereal) | (A = extend1289208545_ereal))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 53.77/22.86 thf(313,axiom,((! [A:(nat > real),B:real,C:nat,D:real]: (((! [E:nat]: ((ord_less_eq_real @ D @ (A @ E)) <= (ord_less_eq_nat @ C @ E))) => (ord_less_eq_real @ D @ B)) <= (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Lim__bounded2)). 53.77/22.86 thf(2915,plain,((! [A:(nat > real),B:real,C:nat,D:real]: (((! [E:nat]: ((ord_less_eq_real @ D @ (A @ E)) | ~ (ord_less_eq_nat @ C @ E))) => (ord_less_eq_real @ D @ B)) | ~ (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 53.77/22.86 thf(218,axiom,((lower_231615490a_real = (^ [A:a,B:(a > real)]: ! [C:(nat > a),D:real]: (((filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)) => (ord_less_eq_real @ (B @ A) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_lsc__at__def)). 53.77/22.86 thf(1167,plain,(((lower_231615490a_real) = (^ [A:a,B:(a > real)]: ! [C:(nat > a),D:real]: (((filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)) => (ord_less_eq_real @ (B @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 53.77/22.86 thf(224,axiom,((! [A:extended_ereal,B:extended_ereal]: (((uminus1208298309_ereal @ A) = (uminus1208298309_ereal @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_ereal__uminus__eq__iff)). 53.77/22.86 thf(1185,plain,((! [A:extended_ereal,B:extended_ereal]: (((uminus1208298309_ereal @ A) = (uminus1208298309_ereal @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 53.77/22.86 thf(70,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ B) <= (ord_less_eq_int @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_dual__order_Otrans)). 53.77/22.86 thf(586,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ B) | ~ (ord_less_eq_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 53.77/22.86 thf(150,axiom,((! [A:(nat > real),B:real,C:filter_nat]: ((filterlim_nat_real @ A @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) = (filterlim_nat_real @ (^ [D:nat]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_tendsto__minus__cancel__left)). 53.77/22.86 thf(926,plain,((! [A:(nat > real),B:real,C:filter_nat]: ((filterlim_nat_real @ (A) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) = (filterlim_nat_real @ (^ [D:nat]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 53.77/22.86 thf(1,conjecture,((filter1531173832_ereal @ (^ [A:nat]: (uminus1208298309_ereal @ (f @ (x @ A)))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ a2)) @ at_top_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 53.77/22.86 thf(2,negated_conjecture,((~ (filter1531173832_ereal @ (^ [A:nat]: (uminus1208298309_ereal @ (f @ (x @ A)))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ a2)) @ at_top_nat))),inference(neg_conjecture,[status(cth)],[1])). 53.77/22.86 thf(343,plain,((~ (filter1531173832_ereal @ (^ [A:nat]: (uminus1208298309_ereal @ (f @ (x @ A)))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ a2)) @ at_top_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 53.77/22.86 thf(284,axiom,((! [A:extended_ereal,B:(extended_ereal > nat),C:(nat > extended_ereal),D:nat]: ((lower_114093al_nat @ A @ B) => ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((ord_less_eq_nat @ D @ (B @ A)) <= (filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_usc__at__mem)). 53.77/22.86 thf(2788,plain,((! [A:extended_ereal,B:(extended_ereal > nat),C:(nat > extended_ereal),D:nat]: ((lower_114093al_nat @ A @ (B)) => ((filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((ord_less_eq_nat @ D @ (B @ A)) | ~ (filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 53.77/22.86 thf(261,axiom,((! [A:extended_ereal,B:(extended_ereal > int),C:(nat > extended_ereal),D:int]: ((lower_637387785al_int @ A @ B) => ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) => (ord_less_eq_int @ D @ (B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_usc__at__mem)). 53.77/22.86 thf(1318,plain,((! [A:extended_ereal,B:(extended_ereal > int),C:(nat > extended_ereal),D:int]: ((lower_637387785al_int @ A @ (B)) => ((filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) => (ord_less_eq_int @ D @ (B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 53.77/22.86 thf(250,axiom,((! [A:a,B:(a > int),C:(nat > a),D:int]: ((lower_1672990777_a_int @ A @ B) => ((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((ord_less_eq_int @ D @ (B @ A)) <= (filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_usc__at__mem)). 53.77/22.86 thf(1286,plain,((! [A:a,B:(a > int),C:(nat > a),D:int]: ((lower_1672990777_a_int @ A @ (B)) => ((filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((ord_less_eq_int @ D @ (B @ A)) | ~ (filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 53.77/22.86 thf(17,axiom,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_ord__eq__le__trans)). 53.77/22.86 thf(398,plain,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 53.77/22.86 thf(113,axiom,((! [A:extended_ereal,B:extended_ereal]: ((A = B) | ~ (ord_le824540014_ereal @ B @ A) | ~ (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_verit__la__disequality)). 53.77/22.86 thf(750,plain,((! [A:extended_ereal,B:extended_ereal]: ((A = B) | ~ (ord_le824540014_ereal @ B @ A) | ~ (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 53.77/22.86 thf(79,axiom,((! [A:nat,B:(extended_ereal > nat),C:extended_ereal,D:extended_ereal]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_le824540014_ereal @ C @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_order__subst1)). 53.77/22.86 thf(618,plain,((! [A:nat,B:(extended_ereal > nat),C:extended_ereal,D:extended_ereal]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_le824540014_ereal @ C @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 53.77/22.86 thf(321,axiom,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:(nat > extended_ereal),D:extended_ereal]: ((lower_1071158961_ereal @ A @ B) => (((filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ D @ (B @ A))) <= (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_usc__at__mem)). 53.77/22.86 thf(2941,plain,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:(nat > extended_ereal),D:extended_ereal]: ((lower_1071158961_ereal @ A @ (B)) => (((filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ D @ (B @ A))) | ~ (filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 53.77/22.86 thf(111,axiom,((filterlim_real_real @ uminus_uminus_real @ at_bot_real @ at_top_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_filterlim__uminus__at__bot__at__top)). 53.77/22.86 thf(745,plain,((filterlim_real_real @ (uminus_uminus_real) @ at_bot_real @ at_top_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 53.77/22.86 thf(26,axiom,((! [A:(nat > extended_ereal)]: ((topolo1069469409_ereal @ A) <= (! [B:nat,C:nat]: ((ord_le824540014_ereal @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_monoI2)). 53.77/22.86 thf(444,plain,((! [A:(nat > extended_ereal)]: ((topolo1069469409_ereal @ (A)) | ~ (! [B:nat,C:nat]: ((ord_le824540014_ereal @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 53.77/22.86 thf(276,axiom,((! [A:(nat > int),B:int,C:(nat > int),D:int]: ((filterlim_nat_int @ A @ (topolo54776183ds_int @ B) @ at_top_nat) => ((filterlim_nat_int @ C @ (topolo54776183ds_int @ D) @ at_top_nat) => ((? [E:nat]: ! [F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (A @ F) @ (C @ F)))) => (ord_less_eq_int @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_LIMSEQ__le)). 53.77/22.86 thf(1374,plain,((! [A:(nat > int),B:int,C:(nat > int),D:int]: ((filterlim_nat_int @ (A) @ (topolo54776183ds_int @ B) @ at_top_nat) => ((filterlim_nat_int @ (C) @ (topolo54776183ds_int @ D) @ at_top_nat) => ((? [E:nat]: ! [F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (A @ F) @ (C @ F)))) => (ord_less_eq_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 53.77/22.86 thf(144,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (A = B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_order__class_Oorder_Oantisym)). 53.77/22.86 thf(904,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (A = B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 53.77/22.86 thf(281,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((A != (uminus1208298309_ereal @ extend1289208545_ereal)) => (((plus_p2118002693_ereal @ B @ A) = (plus_p2118002693_ereal @ C @ A)) = ((B = C) | (A = extend1289208545_ereal)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_ereal__add__cancel__right)). 53.77/22.86 thf(2727,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((~ (A = (uminus1208298309_ereal @ extend1289208545_ereal))) => (((plus_p2118002693_ereal @ B @ A) = (plus_p2118002693_ereal @ C @ A)) = ((B = C) | (A = extend1289208545_ereal)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 53.77/22.86 thf(175,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D)))) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_order__subst1)). 53.77/22.86 thf(1007,plain,((! [A:nat,B:(real > nat),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D)))) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 53.77/22.86 thf(285,axiom,((! [A:extended_ereal,B:extended_ereal]: ((filter1531173832_ereal @ (^ [C:nat]: (A)) @ (topolo2140997059_ereal @ B) @ at_top_nat) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_LIMSEQ__const__iff)). 53.77/22.86 thf(2791,plain,((! [A:extended_ereal,B:extended_ereal]: ((filter1531173832_ereal @ (^ [C:nat]: (A)) @ (topolo2140997059_ereal @ B) @ at_top_nat) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 53.77/22.86 thf(303,axiom,((lower_153911426al_int = (^ [A:real,B:(real > int)]: ! [C:(nat > real),D:int]: ((ord_less_eq_int @ (B @ A) @ D) <= ((filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_lsc__at__def)). 53.77/22.86 thf(2849,plain,(((lower_153911426al_int) = (^ [A:real,B:(real > int)]: ! [C:(nat > real),D:int]: ((ord_less_eq_int @ (B @ A) @ D) | ~ ((filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 53.77/22.86 thf(104,axiom,((topolo411883481eq_int = (^ [A:(nat > int)]: (! [B:nat,C:nat]: ((ord_less_eq_int @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C)) | ! [B:nat,C:nat]: ((ord_less_eq_int @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_monoseq__def)). 53.77/22.86 thf(711,plain,(((topolo411883481eq_int) = (^ [A:(nat > int)]: (! [B:nat,C:nat]: ((ord_less_eq_int @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C)) | ! [B:nat,C:nat]: ((ord_less_eq_int @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 53.77/22.86 thf(290,axiom,((lower_1672990777_a_int = (^ [A:a,B:(a > int)]: ! [C:(nat > a),D:int]: ((ord_less_eq_int @ D @ (B @ A)) <= ((filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_usc__at__def)). 53.77/22.86 thf(2806,plain,(((lower_1672990777_a_int) = (^ [A:a,B:(a > int)]: ! [C:(nat > a),D:int]: ((ord_less_eq_int @ D @ (B @ A)) | ~ ((filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 53.77/22.86 thf(160,axiom,((! [A:extended_ereal]: ((plus_p2118002693_ereal @ extend1289208545_ereal @ A) = extend1289208545_ereal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_plus__ereal_Osimps_I2_J)). 53.77/22.86 thf(958,plain,((! [A:extended_ereal]: ((plus_p2118002693_ereal @ extend1289208545_ereal @ A) = extend1289208545_ereal))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 53.77/22.86 thf(293,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:real]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((B != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (! [D:nat]: (ord_le824540014_ereal @ (extended_ereal2 @ C) @ (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_Lim__bounded__MInfty)). 53.77/22.86 thf(2817,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:real]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat) => (~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (! [D:nat]: (ord_le824540014_ereal @ (extended_ereal2 @ C) @ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 53.77/22.86 thf(204,axiom,((! [A:extended_ereal,B:(extended_ereal > real),C:(nat > extended_ereal),D:real]: ((lower_737640969l_real @ A @ B) => ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) => (ord_less_eq_real @ D @ (B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_usc__at__mem)). 53.77/22.86 thf(1124,plain,((! [A:extended_ereal,B:(extended_ereal > real),C:(nat > extended_ereal),D:real]: ((lower_737640969l_real @ A @ (B)) => ((filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat) => ((filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) => (ord_less_eq_real @ D @ (B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 53.77/22.86 thf(325,axiom,((lower_319689766_a_nat = (^ [A:a,B:(a > nat)]: ! [C:(nat > a),D:nat]: ((ord_less_eq_nat @ (B @ A) @ D) <= ((filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_lsc__at__def)). 53.77/22.86 thf(2959,plain,(((lower_319689766_a_nat) = (^ [A:a,B:(a > nat)]: ! [C:(nat > a),D:nat]: ((ord_less_eq_nat @ (B @ A) @ D) | ~ ((filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) & (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 53.77/22.86 thf(69,axiom,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ B @ A) <= (~ (ord_le824540014_ereal @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_le__cases)). 53.77/22.86 thf(584,plain,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ B @ A) | (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 53.77/22.86 thf(213,axiom,((lower_637387785al_int = (^ [A:extended_ereal,B:(extended_ereal > int)]: ! [C:(nat > extended_ereal),D:int]: ((ord_less_eq_int @ D @ (B @ A)) <= ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_usc__at__def)). 53.77/22.86 thf(1154,plain,(((lower_637387785al_int) = (^ [A:extended_ereal,B:(extended_ereal > int)]: ! [C:(nat > extended_ereal),D:int]: ((ord_less_eq_int @ D @ (B @ A)) | ~ ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 53.77/22.86 thf(13,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_linear)). 53.77/22.86 thf(382,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 53.77/22.86 thf(105,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_eq_real @ (C @ A) @ D) <= (! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))))) <= (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_order__subst2)). 53.77/22.86 thf(713,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))))) | ~ (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 53.77/22.86 thf(197,axiom,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:extended_ereal,D:extended_ereal]: ((A = (B @ C)) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D))) <= (ord_le824540014_ereal @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ord__eq__le__subst)). 53.77/22.86 thf(1092,plain,((! [A:extended_ereal,B:(extended_ereal > extended_ereal),C:extended_ereal,D:extended_ereal]: ((A = (B @ C)) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D))) | ~ (ord_le824540014_ereal @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 53.77/22.86 thf(196,axiom,((! [A:real,B:filter_nat]: (filterlim_nat_real @ (^ [C:nat]: (A)) @ (topolo1664202871s_real @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_tendsto__const)). 53.77/22.86 thf(1090,plain,((! [A:real,B:filter_nat]: (filterlim_nat_real @ (^ [C:nat]: (A)) @ (topolo1664202871s_real @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 53.77/22.86 thf(56,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))))) <= (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_order__subst2)). 53.77/22.86 thf(540,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))))) | ~ (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 53.77/22.86 thf(249,axiom,((! [A:(nat > int),B:int,C:int]: ((filterlim_nat_int @ A @ (topolo54776183ds_int @ B) @ at_top_nat) => ((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_less_eq_int @ (A @ E) @ C))) => (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_LIMSEQ__le__const2)). 53.77/22.86 thf(1282,plain,((! [A:(nat > int),B:int,C:int]: ((filterlim_nat_int @ (A) @ (topolo54776183ds_int @ B) @ at_top_nat) => ((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_less_eq_int @ (A @ E) @ C))) => (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 53.77/22.86 thf(176,axiom,((! [A:real,B:(extended_ereal > real),C:extended_ereal,D:extended_ereal]: (((ord_le824540014_ereal @ C @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_real @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_ord__eq__le__subst)). 53.77/22.86 thf(1011,plain,((! [A:real,B:(extended_ereal > real),C:extended_ereal,D:extended_ereal]: (((ord_le824540014_ereal @ C @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_real @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 53.77/22.86 thf(187,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_dual__order_Orefl)). 53.77/22.86 thf(1048,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 53.77/22.86 thf(270,axiom,((! [A:a,B:(a > int),C:(nat > a),D:int]: (((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) => (ord_less_eq_int @ (B @ A) @ D))) <= (lower_956963458_a_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_lsc__at__mem)). 53.77/22.86 thf(1349,plain,((! [A:a,B:(a > int),C:(nat > a),D:int]: (((filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((filterlim_nat_int @ (comp_a_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) => (ord_less_eq_int @ (B @ A) @ D))) | ~ (lower_956963458_a_int @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 53.77/22.86 thf(169,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_dual__order_Orefl)). 53.77/22.86 thf(990,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 53.77/22.86 thf(64,axiom,((! [A:real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_verit__minus__simplify_I4_J)). 53.77/22.86 thf(567,plain,((! [A:real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 53.77/22.86 thf(221,axiom,((! [A:(nat > real),B:real,C:real]: (((? [D:nat]: ! [E:nat]: ((ord_less_eq_real @ (A @ E) @ C) <= (ord_less_eq_nat @ D @ E))) => (ord_less_eq_real @ B @ C)) <= (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_LIMSEQ__le__const2)). 53.77/22.86 thf(1175,plain,((! [A:(nat > real),B:real,C:real]: (((? [D:nat]: ! [E:nat]: ((ord_less_eq_real @ (A @ E) @ C) | ~ (ord_less_eq_nat @ D @ E))) => (ord_less_eq_real @ B @ C)) | ~ (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 53.77/22.86 thf(88,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ A) => (ord_less_eq_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_dual__order_Otrans)). 53.77/22.86 thf(649,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ A) => (ord_less_eq_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 53.77/22.86 thf(185,axiom,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_le__cases)). 53.77/22.86 thf(1043,plain,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 53.77/22.86 thf(124,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((ord_le824540014_ereal @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_ord__le__eq__trans)). 53.77/22.86 thf(811,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((ord_le824540014_ereal @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 53.77/22.86 thf(84,axiom,((! [A:int,B:(nat > int),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_ord__eq__le__subst)). 53.77/22.86 thf(631,plain,((! [A:int,B:(nat > int),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 53.77/22.86 thf(267,axiom,((! [A:extended_ereal]: ((! [B:real]: (A != (extended_ereal2 @ B))) => ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) <= (A != extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_real__of__ereal_Ocases)). 53.77/22.86 thf(1339,plain,((! [A:extended_ereal]: ((! [B:real]: ~ (A = (extended_ereal2 @ B))) => ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) | (A = extend1289208545_ereal))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 53.77/22.86 thf(132,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((A = B) <= (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_antisym)). 53.77/22.86 thf(858,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((A = B) | ~ (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 53.77/22.86 thf(125,axiom,((! [A:real,B:real]: ((A = B) => ((extended_ereal2 @ A) = (extended_ereal2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_ereal__cong)). 53.77/22.86 thf(816,plain,((! [A:real,B:real]: ((A = B) => ((extended_ereal2 @ A) = (extended_ereal2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 53.77/22.86 thf(73,axiom,((! [A:int,B:(extended_ereal > int),C:extended_ereal,D:extended_ereal]: ((A = (B @ C)) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_int @ A @ (B @ D))) <= (ord_le824540014_ereal @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_ord__eq__le__subst)). 53.77/22.86 thf(594,plain,((! [A:int,B:(extended_ereal > int),C:extended_ereal,D:extended_ereal]: ((A = (B @ C)) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_int @ A @ (B @ D))) | ~ (ord_le824540014_ereal @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 53.77/22.86 thf(40,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_ord__eq__le__trans)). 53.77/22.86 thf(483,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 53.77/22.86 thf(315,axiom,((filter1531173832_ereal @ (comp_a1112243075al_nat @ f @ x) @ (topolo2140997059_ereal @ a2) @ at_top_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_x__def_I2_J)). 53.77/22.86 thf(2923,plain,((filter1531173832_ereal @ (comp_a1112243075al_nat @ f @ x) @ (topolo2140997059_ereal @ a2) @ at_top_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 53.77/22.86 thf(141,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_le__cases)). 53.77/22.86 thf(895,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 53.77/22.86 thf(178,axiom,((! [A:real,B:real]: ((plus_p2118002693_ereal @ (extended_ereal2 @ A) @ (extended_ereal2 @ B)) = (extended_ereal2 @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_plus__ereal_Osimps_I1_J)). 53.77/22.86 thf(1022,plain,((! [A:real,B:real]: ((plus_p2118002693_ereal @ (extended_ereal2 @ A) @ (extended_ereal2 @ B)) = (extended_ereal2 @ (plus_plus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 53.77/22.86 thf(200,axiom,((lower_191460856_ereal = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a)]: ((ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_a1112243075al_nat @ B @ C))) <= (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_lsc__liminf)). 53.77/22.86 thf(1112,plain,(((lower_191460856_ereal) = (^ [A:a,B:(a > extended_ereal)]: ! [C:(nat > a)]: ((ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_a1112243075al_nat @ B @ C))) | ~ (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 53.77/22.86 thf(38,axiom,((! [A:extended_ereal]: ((A = extend1289208545_ereal) <= (! [B:real]: (ord_le824540014_ereal @ (extended_ereal2 @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_ereal__top)). 53.77/22.86 thf(477,plain,((! [A:extended_ereal]: ((A = extend1289208545_ereal) | ~ (! [B:real]: (ord_le824540014_ereal @ (extended_ereal2 @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 53.77/22.86 thf(295,axiom,((lower_551915512_ereal = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real)]: ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) => (ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_r1410008527al_nat @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_lsc__liminf)). 53.77/22.86 thf(2824,plain,(((lower_551915512_ereal) = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real)]: ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) => (ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_r1410008527al_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 53.77/22.86 thf(211,axiom,((! [A:extended_ereal,B:filter_nat]: (filter1531173832_ereal @ (^ [C:nat]: (A)) @ (topolo2140997059_ereal @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_tendsto__const)). 53.77/22.86 thf(1149,plain,((! [A:extended_ereal,B:filter_nat]: (filter1531173832_ereal @ (^ [C:nat]: (A)) @ (topolo2140997059_ereal @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 53.77/22.86 thf(162,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_linear)). 53.77/22.86 thf(964,plain,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 53.77/22.86 thf(82,axiom,((! [A:extended_ereal]: (ord_le824540014_ereal @ A @ extend1289208545_ereal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_ereal__less__eq_I1_J)). 53.77/22.86 thf(626,plain,((! [A:extended_ereal]: (ord_le824540014_ereal @ A @ extend1289208545_ereal))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 53.77/22.86 thf(148,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_order__trans)). 53.77/22.86 thf(915,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 53.77/22.86 thf(152,axiom,((topolo1922093437eq_nat = (^ [A:(nat > nat)]: (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B))) | ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_monoseq__def)). 53.77/22.86 thf(932,plain,(((topolo1922093437eq_nat) = (^ [A:(nat > nat)]: (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B))) | ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 53.77/22.86 thf(190,axiom,((! [A:int,B:int]: ((A = B) => (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_eq__refl)). 53.77/22.86 thf(1061,plain,((! [A:int,B:int]: ((A = B) => (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 53.77/22.86 thf(99,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ C) <= (ord_less_eq_int @ B @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_order_Otrans)). 53.77/22.86 thf(695,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ C) | ~ (ord_less_eq_int @ B @ C) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 53.77/22.86 thf(30,axiom,(((= @ int) = (^ [A:int,B:int]: ((ord_less_eq_int @ B @ A) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_order__class_Oorder_Oeq__iff)). 53.77/22.86 thf(455,plain,(((= @ int) = (^ [A:int,B:int]: ((ord_less_eq_int @ B @ A) & (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 53.77/22.86 thf(76,axiom,((! [A:(nat > a),B:a,C:filter_nat,D:a]: (((B = D) => (filterlim_nat_a @ A @ (topolo705128563nhds_a @ D) @ C)) <= (filterlim_nat_a @ A @ (topolo705128563nhds_a @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_tendsto__eq__rhs)). 53.77/22.86 thf(608,plain,((! [A:(nat > a),B:a,C:filter_nat,D:a]: (((B = D) => (filterlim_nat_a @ (A) @ (topolo705128563nhds_a @ D) @ C)) | ~ (filterlim_nat_a @ (A) @ (topolo705128563nhds_a @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 53.77/22.86 thf(242,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ (A @ E) @ C) <= (ord_less_eq_nat @ D @ E))) => (ord_less_eq_nat @ B @ C)) <= (filterlim_nat_nat @ A @ (topolo1564986139ds_nat @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_LIMSEQ__le__const2)). 53.77/22.86 thf(1250,plain,((! [A:(nat > nat),B:nat,C:nat]: (((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ (A @ E) @ C) | ~ (ord_less_eq_nat @ D @ E))) => (ord_less_eq_nat @ B @ C)) | ~ (filterlim_nat_nat @ (A) @ (topolo1564986139ds_nat @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 53.77/22.86 thf(46,axiom,((! [A:(a > extended_ereal),B:(nat > a),C:(nat > extended_ereal),D:nat]: (((comp_a1112243075al_nat @ A @ B) = C) => ((A @ (B @ D)) = (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_comp__eq__dest__lhs)). 53.77/22.86 thf(505,plain,((! [A:(a > extended_ereal),B:(nat > a),C:(nat > extended_ereal),D:nat]: (((comp_a1112243075al_nat @ A @ B) = (C)) => ((A @ (B @ D)) = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 53.77/22.86 thf(90,axiom,((! [A:nat,B:nat,C:(nat > extended_ereal),D:extended_ereal]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_le824540014_ereal @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le824540014_ereal @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_ord__le__eq__subst)). 53.77/22.86 thf(658,plain,((! [A:nat,B:nat,C:(nat > extended_ereal),D:extended_ereal]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_le824540014_ereal @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le824540014_ereal @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 53.77/22.86 thf(147,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((A = B) <= (ord_less_eq_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_order__class_Oorder_Oantisym)). 53.77/22.86 thf(912,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((A = B) | ~ (ord_less_eq_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 53.77/22.86 thf(51,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_order__trans)). 53.77/22.86 thf(521,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 53.77/22.86 thf(220,axiom,((! [A:nat,B:(nat > nat),C:(nat > nat),D:nat,E:nat]: (((filterlim_nat_nat @ B @ (topolo1564986139ds_nat @ D) @ at_top_nat) => ((filterlim_nat_nat @ C @ (topolo1564986139ds_nat @ E) @ at_top_nat) => (ord_less_eq_nat @ D @ E))) <= (! [F:nat]: ((ord_less_eq_nat @ (B @ F) @ (C @ F)) <= (ord_less_eq_nat @ A @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_lim__mono)). 53.77/22.86 thf(1171,plain,((! [A:nat,B:(nat > nat),C:(nat > nat),D:nat,E:nat]: (((filterlim_nat_nat @ (B) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => ((filterlim_nat_nat @ (C) @ (topolo1564986139ds_nat @ E) @ at_top_nat) => (ord_less_eq_nat @ D @ E))) | ~ (! [F:nat]: ((ord_less_eq_nat @ (B @ F) @ (C @ F)) | ~ (ord_less_eq_nat @ A @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 53.77/22.86 thf(119,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_antisym)). 53.77/22.86 thf(768,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 53.77/22.86 thf(300,axiom,((! [A:extended_ereal]: ((ord_le824540014_ereal @ A @ (uminus1208298309_ereal @ extend1289208545_ereal)) = (A = (uminus1208298309_ereal @ extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_ereal__infty__less__eq_I2_J)). 53.77/22.86 thf(2835,plain,((! [A:extended_ereal]: ((ord_le824540014_ereal @ A @ (uminus1208298309_ereal @ extend1289208545_ereal)) = (A = (uminus1208298309_ereal @ extend1289208545_ereal))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 53.77/22.86 thf(287,axiom,((! [A:extended_ereal]: ((! [B:real]: (A != (extended_ereal2 @ B))) => ((A = extend1289208545_ereal) <= (A != (uminus1208298309_ereal @ extend1289208545_ereal)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_abs__ereal_Ocases)). 53.77/22.86 thf(2797,plain,((! [A:extended_ereal]: ((! [B:real]: ~ (A = (extended_ereal2 @ B))) => ((A = extend1289208545_ereal) | (A = (uminus1208298309_ereal @ extend1289208545_ereal)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 53.77/22.86 thf(62,axiom,((filterlim_real_real @ uminus_uminus_real @ at_top_real @ at_bot_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_filterlim__uminus__at__top__at__bot)). 53.77/22.86 thf(563,plain,((filterlim_real_real @ (uminus_uminus_real) @ at_top_real @ at_bot_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 53.77/22.86 thf(194,axiom,((! [A:(real > (real > $o)),B:real,C:real]: (((! [D:real,E:real]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C)) <= (! [D:real,E:real]: ((ord_less_eq_real @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_linorder__wlog)). 53.77/22.86 thf(1076,plain,((! [A:(real > (real > $o)),B:real,C:real]: (((! [D:real,E:real]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C)) | ~ (! [D:real,E:real]: ((ord_less_eq_real @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 53.77/22.86 thf(342,axiom,((! [A:(nat > int),B:int,C:int]: (((ord_less_eq_int @ C @ B) <= (? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_less_eq_int @ C @ (A @ E))))) <= (filterlim_nat_int @ A @ (topolo54776183ds_int @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_LIMSEQ__le__const)). 53.77/22.86 thf(3009,plain,((! [A:(nat > int),B:int,C:int]: ((ord_less_eq_int @ C @ B) | ~ (? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_less_eq_int @ C @ (A @ E)))) | ~ (filterlim_nat_int @ (A) @ (topolo54776183ds_int @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 53.77/22.86 thf(256,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:extended_ereal]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_le824540014_ereal @ (A @ E) @ C))) => (ord_le824540014_ereal @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_LIMSEQ__le__const2)). 53.77/22.86 thf(1304,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:extended_ereal]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat) => ((? [D:nat]: ! [E:nat]: ((ord_less_eq_nat @ D @ E) => (ord_le824540014_ereal @ (A @ E) @ C))) => (ord_le824540014_ereal @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 53.77/22.86 thf(22,axiom,((! [A:extended_ereal,B:extended_ereal]: ((! [C:real]: ((ord_le824540014_ereal @ A @ (extended_ereal2 @ C)) => (ord_le824540014_ereal @ B @ (extended_ereal2 @ C)))) => (ord_le824540014_ereal @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_ereal__le__real)). 53.77/22.86 thf(426,plain,((! [A:extended_ereal,B:extended_ereal]: ((! [C:real]: ((ord_le824540014_ereal @ A @ (extended_ereal2 @ C)) => (ord_le824540014_ereal @ B @ (extended_ereal2 @ C)))) => (ord_le824540014_ereal @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 53.77/22.86 thf(71,axiom,((! [A:(nat > real),B:real,C:filter_nat]: ((filterlim_nat_real @ (^ [D:nat]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) => (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_tendsto__minus__cancel)). 53.77/22.86 thf(589,plain,((! [A:(nat > real),B:real,C:filter_nat]: ((filterlim_nat_real @ (^ [D:nat]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) => (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 53.77/22.86 thf(338,axiom,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: ((((((! [D:real]: (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ D))) => ((A @ B @ C) <= (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (uminus1208298309_ereal @ extend1289208545_ereal)))) <= (! [D:real]: (A @ (extended_ereal2 @ D) @ (uminus1208298309_ereal @ extend1289208545_ereal)))) <= (! [D:extended_ereal]: (A @ D @ extend1289208545_ereal))) <= (! [D:extended_ereal]: (A @ extend1289208545_ereal @ D))) <= (! [D:real,E:real]: (A @ (extended_ereal2 @ D) @ (extended_ereal2 @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_plus__ereal_Oinduct)). 53.77/22.86 thf(2994,plain,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: (((! [D:real]: (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ D))) => ((A @ B @ C) | ~ (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (uminus1208298309_ereal @ extend1289208545_ereal)))) | ~ (! [D:real]: (A @ (extended_ereal2 @ D) @ (uminus1208298309_ereal @ extend1289208545_ereal))) | ~ (! [D:extended_ereal]: (A @ D @ extend1289208545_ereal)) | ~ (! [D:extended_ereal]: (A @ extend1289208545_ereal @ D)) | ~ (! [D:real,E:real]: (A @ (extended_ereal2 @ D) @ (extended_ereal2 @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 53.77/22.86 thf(95,axiom,((! [A:real,B:real,C:(real > extended_ereal),D:extended_ereal]: (((ord_le824540014_ereal @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_order__subst2)). 53.77/22.86 thf(680,plain,((! [A:real,B:real,C:(real > extended_ereal),D:extended_ereal]: (((ord_le824540014_ereal @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 53.77/22.86 thf(208,axiom,((extend1289208545_ereal != (uminus1208298309_ereal @ extend1289208545_ereal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_MInfty__neq__PInfty_I1_J)). 53.77/22.86 thf(1134,plain,((~ (extend1289208545_ereal = (uminus1208298309_ereal @ extend1289208545_ereal)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 53.77/22.86 thf(317,axiom,((! [A:(nat > extended_ereal)]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ extend1289208545_ereal) @ at_top_nat) = (! [B:real]: ? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_le824540014_ereal @ (extended_ereal2 @ B) @ (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_Lim__PInfty)). 53.77/22.86 thf(2927,plain,((! [A:(nat > extended_ereal)]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ extend1289208545_ereal) @ at_top_nat) = (! [B:real]: ? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_le824540014_ereal @ (extended_ereal2 @ B) @ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 53.77/22.86 thf(210,axiom,((! [A:(nat > extended_ereal)]: ((~ (! [B:extended_ereal]: ~ (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat))) <= (! [B:nat,C:nat]: ((ord_le824540014_ereal @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_lim__increasing__cl)). 53.77/22.86 thf(1145,plain,((! [A:(nat > extended_ereal)]: (~ (! [B:extended_ereal]: ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat)) | ~ (! [B:nat,C:nat]: ((ord_le824540014_ereal @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 53.77/22.86 thf(223,axiom,((! [A:extended_ereal]: ((! [B:real]: (A != (extended_ereal2 @ B))) => ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) <= (A != extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_ereal__cases)). 53.77/22.86 thf(1181,plain,((! [A:extended_ereal]: ((! [B:real]: ~ (A = (extended_ereal2 @ B))) => ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) | (A = extend1289208545_ereal))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 53.77/22.86 thf(60,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_nat__int__comparison_I3_J)). 53.77/22.86 thf(557,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 53.77/22.86 thf(179,axiom,((! [A:(real > real),B:real,C:filter_real]: ((filterlim_real_real @ A @ (topolo1664202871s_real @ B) @ C) <= (filterlim_real_real @ (^ [D:real]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_tendsto__minus__cancel)). 53.77/22.86 thf(1025,plain,((! [A:(real > real),B:real,C:filter_real]: ((filterlim_real_real @ (A) @ (topolo1664202871s_real @ B) @ C) | ~ (filterlim_real_real @ (^ [D:real]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 53.77/22.86 thf(214,axiom,((lower_48196818al_int = (^ [A:extended_ereal,B:(extended_ereal > int)]: ! [C:(nat > extended_ereal),D:int]: (((filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat)) => (ord_less_eq_int @ (B @ A) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_lsc__at__def)). 53.77/22.86 thf(1156,plain,(((lower_48196818al_int) = (^ [A:extended_ereal,B:(extended_ereal > int)]: ! [C:(nat > extended_ereal),D:int]: (((filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) & (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat)) => (ord_less_eq_int @ (B @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 53.77/22.86 thf(20,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_eq__refl)). 53.77/22.86 thf(414,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 53.77/22.86 thf(158,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_order__refl)). 53.77/22.86 thf(954,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 53.77/22.86 thf(189,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > nat),D:nat]: ((ord_le824540014_ereal @ A @ B) => (((C @ B) = D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ord__le__eq__subst)). 53.77/22.86 thf(1053,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > nat),D:nat]: ((ord_le824540014_ereal @ A @ B) => (((C @ B) = D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 53.77/22.86 thf(93,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > int),D:int]: ((ord_le824540014_ereal @ A @ B) => ((ord_less_eq_int @ (C @ B) @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_order__subst2)). 53.77/22.86 thf(673,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > int),D:int]: ((ord_le824540014_ereal @ A @ B) => ((ord_less_eq_int @ (C @ B) @ D) => ((! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 53.77/22.86 thf(225,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat]: ((filter1531173832_ereal @ (^ [D:nat]: (uminus1208298309_ereal @ (A @ D))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ B)) @ C) <= (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_tendsto__uminus__ereal)). 53.77/22.86 thf(1188,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat]: ((filter1531173832_ereal @ (^ [D:nat]: (uminus1208298309_ereal @ (A @ D))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ B)) @ C) | ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 53.77/22.86 thf(106,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_eq__refl)). 53.77/22.86 thf(717,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 53.77/22.86 thf(130,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) => (~ (ord_less_eq_real @ B @ C))) => (((ord_less_eq_real @ B @ A) => (~ (ord_less_eq_real @ A @ C))) => (((ord_less_eq_real @ A @ C) => (~ (ord_less_eq_real @ C @ B))) => (((~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B)))) <= ((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A)))) <= ((~ (ord_less_eq_real @ B @ A)) <= (ord_less_eq_real @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le__cases3)). 53.77/22.86 thf(840,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) => (~ (ord_less_eq_real @ B @ C))) => (((ord_less_eq_real @ B @ A) => (~ (ord_less_eq_real @ A @ C))) => (((ord_less_eq_real @ A @ C) => (~ (ord_less_eq_real @ C @ B))) => (~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B))) | ~ ((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) | ~ (~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 53.77/22.86 thf(245,axiom,((! [A:a,B:(a > extended_ereal),C:(nat > a),D:extended_ereal]: ((((filter1531173832_ereal @ (comp_a1112243075al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ D @ (B @ A))) <= (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)) <= (lower_534855297_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_usc__at__mem)). 53.77/22.86 thf(1262,plain,((! [A:a,B:(a > extended_ereal),C:(nat > a),D:extended_ereal]: (((filter1531173832_ereal @ (comp_a1112243075al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => (ord_le824540014_ereal @ D @ (B @ A))) | ~ (filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat) | ~ (lower_534855297_ereal @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 53.77/22.86 thf(33,axiom,((! [A:real]: ((extended_ereal2 @ A) != extend1289208545_ereal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_PInfty__neq__ereal_I1_J)). 53.77/22.86 thf(463,plain,((! [A:real]: ~ ((extended_ereal2 @ A) = extend1289208545_ereal))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 53.77/22.86 thf(206,axiom,((! [A:a,B:(a > real),C:(nat > a),D:real]: (((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) => (ord_less_eq_real @ D @ (B @ A)))) <= (lower_755922489a_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_usc__at__mem)). 53.77/22.86 thf(1130,plain,((! [A:a,B:(a > real),C:(nat > a),D:real]: (((filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat) => ((filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) => (ord_less_eq_real @ D @ (B @ A)))) | ~ (lower_755922489a_real @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 53.77/22.86 thf(232,axiom,((! [A:extended_ereal,B:(extended_ereal > nat),C:(nat > extended_ereal),D:nat]: ((lower_1558406774al_nat @ A @ B) => (((filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ (B @ A) @ D)) <= (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_lsc__at__mem)). 53.77/22.86 thf(1218,plain,((! [A:extended_ereal,B:(extended_ereal > nat),C:(nat > extended_ereal),D:nat]: ((lower_1558406774al_nat @ A @ (B)) => (((filterlim_nat_nat @ (comp_E1523169101at_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat) => (ord_less_eq_nat @ (B @ A) @ D)) | ~ (filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 53.77/22.86 thf(57,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order__trans)). 53.77/22.86 thf(544,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 53.77/22.86 thf(145,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_le__cases)). 53.77/22.86 thf(907,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 53.77/22.86 thf(337,axiom,((lower_551915512_ereal = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real),D:extended_ereal]: (((filter1531173832_ereal @ (comp_r1410008527al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)) => (ord_le824540014_ereal @ (B @ A) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_lsc__at__def)). 53.77/22.86 thf(2992,plain,(((lower_551915512_ereal) = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real),D:extended_ereal]: (((filter1531173832_ereal @ (comp_r1410008527al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat) & (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)) => (ord_le824540014_ereal @ (B @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 53.77/22.86 thf(77,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_order__refl)). 53.77/22.86 thf(613,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 53.77/22.86 thf(302,axiom,((! [A:(extended_ereal > $o),B:extended_ereal]: ((! [C:real]: (A @ (extended_ereal2 @ C))) => (((A @ B) <= (A @ (uminus1208298309_ereal @ extend1289208545_ereal))) <= (A @ extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_real__of__ereal_Oinduct)). 53.77/22.86 thf(2843,plain,((! [A:(extended_ereal > $o),B:extended_ereal]: ((! [C:real]: (A @ (extended_ereal2 @ C))) => ((A @ B) | ~ (A @ (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (A @ extend1289208545_ereal))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 53.77/22.86 thf(134,axiom,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_eq__iff)). 53.77/22.86 thf(864,plain,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 53.77/22.86 thf(307,axiom,(((plus_p2118002693_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (uminus1208298309_ereal @ extend1289208545_ereal)) = (uminus1208298309_ereal @ extend1289208545_ereal))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_plus__ereal_Osimps_I6_J)). 53.77/22.86 thf(2860,plain,(((plus_p2118002693_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (uminus1208298309_ereal @ extend1289208545_ereal)) = (uminus1208298309_ereal @ extend1289208545_ereal))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 53.77/22.86 thf(238,axiom,((lower_1664121382al_nat = (^ [A:real,B:(real > nat)]: ! [C:(nat > real),D:nat]: ((ord_less_eq_nat @ (B @ A) @ D) <= ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_lsc__at__def)). 53.77/22.86 thf(1240,plain,(((lower_1664121382al_nat) = (^ [A:real,B:(real > nat)]: ! [C:(nat > real),D:nat]: ((ord_less_eq_nat @ (B @ A) @ D) | ~ ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_real_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 53.77/22.86 thf(301,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:real]: (((B != extend1289208545_ereal) <= (! [D:nat]: (ord_le824540014_ereal @ (A @ D) @ (extended_ereal2 @ C)))) <= (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_Lim__bounded__PInfty)). 53.77/22.86 thf(2838,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:real]: (~ (B = extend1289208545_ereal) | ~ (! [D:nat]: (ord_le824540014_ereal @ (A @ D) @ (extended_ereal2 @ C))) | ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 53.77/22.86 thf(101,axiom,((! [A:filter_nat,B:filter_nat,C:(nat > a),D:a]: (((filterlim_nat_a @ C @ (topolo705128563nhds_a @ D) @ A) <= (filterlim_nat_a @ C @ (topolo705128563nhds_a @ D) @ B)) <= (ord_le1745708096er_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_tendsto__mono)). 53.77/22.86 thf(703,plain,((! [A:filter_nat,B:filter_nat,C:(nat > a),D:a]: ((filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ D) @ A) | ~ (filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ D) @ B) | ~ (ord_le1745708096er_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 53.77/22.86 thf(233,axiom,((! [A:(nat > real),B:real]: ((topolo144289241q_real @ A) => (((! [C:nat]: (ord_less_eq_real @ (A @ C) @ B) & ! [C:nat,D:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ D)) <= (ord_less_eq_nat @ C @ D))) | (! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (A @ D) @ (A @ C))) & ! [C:nat]: (ord_less_eq_real @ B @ (A @ C)))) <= (filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_monoseq__le)). 53.77/22.86 thf(1221,plain,((! [A:(nat > real),B:real]: ((topolo144289241q_real @ (A)) => ((! [C:nat]: (ord_less_eq_real @ (A @ C) @ B) & ! [C:nat,D:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ D)) | ~ (ord_less_eq_nat @ C @ D))) | (! [C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (A @ D) @ (A @ C))) & ! [C:nat]: (ord_less_eq_real @ B @ (A @ C))) | ~ (filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 53.77/22.86 thf(332,axiom,((! [A:(nat > int),B:int,C:nat,D:int]: ((filterlim_nat_int @ A @ (topolo54776183ds_int @ B) @ at_top_nat) => ((! [E:nat]: ((ord_less_eq_int @ D @ (A @ E)) <= (ord_less_eq_nat @ C @ E))) => (ord_less_eq_int @ D @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Lim__bounded2)). 53.77/22.86 thf(2975,plain,((! [A:(nat > int),B:int,C:nat,D:int]: ((filterlim_nat_int @ (A) @ (topolo54776183ds_int @ B) @ at_top_nat) => ((! [E:nat]: ((ord_less_eq_int @ D @ (A @ E)) | ~ (ord_less_eq_nat @ C @ E))) => (ord_less_eq_int @ D @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 53.77/22.86 thf(43,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((ord_le824540014_ereal @ B @ C) => (ord_le824540014_ereal @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_order__trans)). 53.77/22.86 thf(497,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((ord_le824540014_ereal @ B @ C) => (ord_le824540014_ereal @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 53.77/22.86 thf(341,axiom,((lower_551915512_ereal = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real),D:extended_ereal]: ((ord_le824540014_ereal @ (B @ A) @ D) <= ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) & ! [E:nat]: (ord_le824540014_ereal @ (B @ (C @ E)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_lsc__sequentially)). 53.77/22.86 thf(3007,plain,(((lower_551915512_ereal) = (^ [A:real,B:(real > extended_ereal)]: ! [C:(nat > real),D:extended_ereal]: ((ord_le824540014_ereal @ (B @ A) @ D) | ~ ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) & ! [E:nat]: (ord_le824540014_ereal @ (B @ (C @ E)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 53.77/22.86 thf(316,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ C) = (filter1531173832_ereal @ (^ [D:nat]: (uminus1208298309_ereal @ (A @ D))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ereal__Lim__uminus)). 53.77/22.86 thf(2924,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:filter_nat]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ C) = (filter1531173832_ereal @ (^ [D:nat]: (uminus1208298309_ereal @ (A @ D))) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 53.77/22.86 thf(297,axiom,((lower_1087098792_ereal = (^ [A:extended_ereal,B:(extended_ereal > extended_ereal)]: ! [C:(nat > extended_ereal),D:extended_ereal]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat)) => (ord_le824540014_ereal @ (B @ A) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_lsc__at__def)). 53.77/22.86 thf(2828,plain,(((lower_1087098792_ereal) = (^ [A:extended_ereal,B:(extended_ereal > extended_ereal)]: ! [C:(nat > extended_ereal),D:extended_ereal]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filter1531173832_ereal @ (comp_E1308517939al_nat @ B @ C) @ (topolo2140997059_ereal @ D) @ at_top_nat)) => (ord_le824540014_ereal @ (B @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 53.77/22.86 thf(262,axiom,((! [A:real,B:(real > extended_ereal),C:(nat > real)]: ((lower_551915512_ereal @ A @ B) => ((ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_r1410008527al_nat @ B @ C))) <= (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_lsc__imp__liminf)). 53.77/22.86 thf(1321,plain,((! [A:real,B:(real > extended_ereal),C:(nat > real)]: ((lower_551915512_ereal @ A @ (B)) => ((ord_le824540014_ereal @ (B @ A) @ (liminf1045857232_ereal @ at_top_nat @ (comp_r1410008527al_nat @ B @ C))) | ~ (filterlim_nat_real @ (C) @ (topolo1664202871s_real @ A) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 53.77/22.86 thf(116,axiom,((! [A:(nat > int)]: ((topolo411883481eq_int @ A) <= (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_int @ (A @ B) @ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_monoI1)). 53.77/22.86 thf(759,plain,((! [A:(nat > int)]: ((topolo411883481eq_int @ (A)) | ~ (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_int @ (A @ B) @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 53.77/22.86 thf(314,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:(nat > extended_ereal),D:extended_ereal]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ D) @ at_top_nat) => ((ord_le824540014_ereal @ B @ D) <= (? [E:nat]: ! [F:nat]: ((ord_le824540014_ereal @ (A @ F) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))))) <= (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_LIMSEQ__le)). 53.77/22.86 thf(2919,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:(nat > extended_ereal),D:extended_ereal]: (((filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ D) @ at_top_nat) => ((ord_le824540014_ereal @ B @ D) | ~ (? [E:nat]: ! [F:nat]: ((ord_le824540014_ereal @ (A @ F) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))))) | ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 53.77/22.86 thf(251,axiom,((! [A:(nat > extended_ereal)]: ((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal)) @ at_top_nat) = (! [B:real]: ? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_le824540014_ereal @ (A @ D) @ (extended_ereal2 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_Lim__MInfty)). 53.77/22.86 thf(1289,plain,((! [A:(nat > extended_ereal)]: ((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal)) @ at_top_nat) = (! [B:real]: ? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_le824540014_ereal @ (A @ D) @ (extended_ereal2 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 53.77/22.86 thf(120,axiom,((! [A:nat,B:(int > nat),C:int,D:int]: ((ord_less_eq_nat @ A @ (B @ C)) => (((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_int @ E @ F)))) <= (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_order__subst1)). 53.77/22.86 thf(771,plain,((! [A:nat,B:(int > nat),C:int,D:int]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_int @ E @ F))) | ~ (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 53.77/22.86 thf(260,axiom,((! [A:(nat > extended_ereal)]: (uniq_Extended_ereal @ (^ [B:extended_ereal]: (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_LIMSEQ__Uniq)). 53.77/22.86 thf(1316,plain,((! [A:(nat > extended_ereal)]: (uniq_Extended_ereal @ (^ [B:extended_ereal]: (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 53.77/22.86 thf(28,axiom,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((A = B) <= (ord_le824540014_ereal @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_order__class_Oorder_Oantisym)). 53.77/22.86 thf(450,plain,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => ((A = B) | ~ (ord_le824540014_ereal @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 53.77/22.86 thf(52,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((A = (B @ C)) => (((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_ord__eq__le__subst)). 53.77/22.86 thf(524,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 53.77/22.86 thf(68,axiom,((! [A:(a > extended_ereal),B:(a > a),C:(nat > a)]: ((comp_a1112243075al_nat @ (comp_a780206603real_a @ A @ B) @ C) = (comp_a1112243075al_nat @ A @ (comp_a_a_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_comp__assoc)). 53.77/22.86 thf(581,plain,((! [A:(a > extended_ereal),B:(a > a),C:(nat > a)]: ((comp_a1112243075al_nat @ (comp_a780206603real_a @ A @ B) @ C) = (comp_a1112243075al_nat @ A @ (comp_a_a_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 53.77/22.86 thf(16,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_int @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_ord__le__eq__subst)). 53.77/22.86 thf(390,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_int @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 53.77/22.86 thf(292,axiom,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: (((! [D:real]: (A @ (extended_ereal2 @ D) @ extend1289208545_ereal)) => ((! [D:real]: (A @ extend1289208545_ereal @ (extended_ereal2 @ D))) => ((((A @ extend1289208545_ereal @ extend1289208545_ereal) => (((A @ extend1289208545_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal)) => ((A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (uminus1208298309_ereal @ extend1289208545_ereal)) => (A @ B @ C))) <= (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ extend1289208545_ereal))) <= (! [D:real]: (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ D)))) <= (! [D:real]: (A @ (extended_ereal2 @ D) @ (uminus1208298309_ereal @ extend1289208545_ereal)))))) <= (! [D:real,E:real]: (A @ (extended_ereal2 @ D) @ (extended_ereal2 @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_times__ereal_Oinduct)). 53.77/22.86 thf(2811,plain,((! [A:(extended_ereal > (extended_ereal > $o)),B:extended_ereal,C:extended_ereal]: (((! [D:real]: (A @ (extended_ereal2 @ D) @ extend1289208545_ereal)) => ((! [D:real]: (A @ extend1289208545_ereal @ (extended_ereal2 @ D))) => (((A @ extend1289208545_ereal @ extend1289208545_ereal) => (((A @ extend1289208545_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal)) => ((A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (uminus1208298309_ereal @ extend1289208545_ereal)) => (A @ B @ C))) | ~ (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ extend1289208545_ereal))) | ~ (! [D:real]: (A @ (uminus1208298309_ereal @ extend1289208545_ereal) @ (extended_ereal2 @ D))) | ~ (! [D:real]: (A @ (extended_ereal2 @ D) @ (uminus1208298309_ereal @ extend1289208545_ereal)))))) | ~ (! [D:real,E:real]: (A @ (extended_ereal2 @ D) @ (extended_ereal2 @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 53.77/22.86 thf(330,axiom,((lower_1035717085_a_nat = (^ [A:a,B:(a > nat)]: ! [C:(nat > a),D:nat]: ((ord_less_eq_nat @ D @ (B @ A)) <= ((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_usc__at__def)). 53.77/22.86 thf(2971,plain,(((lower_1035717085_a_nat) = (^ [A:a,B:(a > nat)]: ! [C:(nat > a),D:nat]: ((ord_less_eq_nat @ D @ (B @ A)) | ~ ((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & (filterlim_nat_nat @ (comp_a_nat_nat @ B @ C) @ (topolo1564986139ds_nat @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 53.77/22.86 thf(340,axiom,((! [A:nat,B:(nat > extended_ereal),C:(nat > extended_ereal),D:extended_ereal,E:extended_ereal]: (((filter1531173832_ereal @ B @ (topolo2140997059_ereal @ D) @ at_top_nat) => ((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ E) @ at_top_nat) => (ord_le824540014_ereal @ D @ E))) <= (! [F:nat]: ((ord_le824540014_ereal @ (B @ F) @ (C @ F)) <= (ord_less_eq_nat @ A @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_lim__mono)). 53.77/22.86 thf(3003,plain,((! [A:nat,B:(nat > extended_ereal),C:(nat > extended_ereal),D:extended_ereal,E:extended_ereal]: (((filter1531173832_ereal @ (B) @ (topolo2140997059_ereal @ D) @ at_top_nat) => ((filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ E) @ at_top_nat) => (ord_le824540014_ereal @ D @ E))) | ~ (! [F:nat]: ((ord_le824540014_ereal @ (B @ F) @ (C @ F)) | ~ (ord_less_eq_nat @ A @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 53.77/22.86 thf(21,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_ord__eq__le__subst)). 53.77/22.86 thf(418,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 53.77/22.86 thf(161,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_neg__le__iff__le)). 53.77/22.86 thf(961,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 53.77/22.86 thf(336,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((A != (uminus1208298309_ereal @ extend1289208545_ereal)) => (((plus_p2118002693_ereal @ A @ B) = (plus_p2118002693_ereal @ A @ C)) = ((B = C) | (A = extend1289208545_ereal)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_ereal__add__cancel__left)). 53.77/22.86 thf(2988,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((~ (A = (uminus1208298309_ereal @ extend1289208545_ereal))) => (((plus_p2118002693_ereal @ A @ B) = (plus_p2118002693_ereal @ A @ C)) = ((B = C) | (A = extend1289208545_ereal)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 53.77/22.86 thf(89,axiom,((! [A:(int > (int > $o)),B:int,C:int]: ((! [D:int,E:int]: ((A @ D @ E) <= (ord_less_eq_int @ D @ E))) => ((! [D:int,E:int]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_linorder__wlog)). 53.77/22.86 thf(652,plain,((! [A:(int > (int > $o)),B:int,C:int]: ((! [D:int,E:int]: ((A @ D @ E) | ~ (ord_less_eq_int @ D @ E))) => ((! [D:int,E:int]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 53.77/22.86 thf(6,axiom,((! [A:(real > real),B:real,C:filter_real,D:real]: ((filterlim_real_real @ A @ (topolo1664202871s_real @ B) @ C) => ((B = D) => (filterlim_real_real @ A @ (topolo1664202871s_real @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_tendsto__eq__rhs)). 53.77/22.86 thf(351,plain,((! [A:(real > real),B:real,C:filter_real,D:real]: ((filterlim_real_real @ (A) @ (topolo1664202871s_real @ B) @ C) => ((B = D) => (filterlim_real_real @ (A) @ (topolo1664202871s_real @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 53.77/22.86 thf(171,axiom,((! [A:extended_ereal,B:extended_ereal]: (((collect_real @ (^ [C:real]: (ord_le824540014_ereal @ A @ (extended_ereal2 @ C)))) = (collect_real @ (^ [C:real]: (ord_le824540014_ereal @ B @ (extended_ereal2 @ C))))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_ereal__semiline__unique)). 53.77/22.86 thf(995,plain,((! [A:extended_ereal,B:extended_ereal]: (((collect_real @ (^ [C:real]: (ord_le824540014_ereal @ A @ (extended_ereal2 @ C)))) = (collect_real @ (^ [C:real]: (ord_le824540014_ereal @ B @ (extended_ereal2 @ C))))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 53.77/22.86 thf(319,axiom,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ (uminus1208298309_ereal @ A) @ (uminus1208298309_ereal @ B)) = (ord_le824540014_ereal @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_ereal__minus__le__minus)). 53.77/22.86 thf(2934,plain,((! [A:extended_ereal,B:extended_ereal]: ((ord_le824540014_ereal @ (uminus1208298309_ereal @ A) @ (uminus1208298309_ereal @ B)) = (ord_le824540014_ereal @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 53.77/22.86 thf(322,axiom,((('!' @ extended_ereal) = (^ [A:(extended_ereal > $o)]: ((A @ extend1289208545_ereal) & (A @ (uminus1208298309_ereal @ extend1289208545_ereal)) & ! [B:real]: (A @ (extended_ereal2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_ereal__all__split)). 53.77/22.86 thf(2944,plain,((('!' @ extended_ereal) = (^ [A:(extended_ereal > $o)]: ((A @ extend1289208545_ereal) & (A @ (uminus1208298309_ereal @ extend1289208545_ereal)) & ! [B:real]: (A @ (extended_ereal2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 53.77/22.86 thf(283,axiom,((lower_1075504779al_int = (^ [A:real,B:(real > int)]: ! [C:(nat > real),D:int]: ((ord_less_eq_int @ D @ (B @ A)) <= ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) & (filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_usc__at__def)). 53.77/22.86 thf(2786,plain,(((lower_1075504779al_int) = (^ [A:real,B:(real > int)]: ! [C:(nat > real),D:int]: ((ord_less_eq_int @ D @ (B @ A)) | ~ ((filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat) & (filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 53.77/22.86 thf(12,axiom,((! [A:extended_ereal,B:extended_ereal]: (((B = extend1289208545_ereal) <= (A = extend1289208545_ereal)) <= (ord_le824540014_ereal @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_ereal__infty__less__eq2_I1_J)). 53.77/22.86 thf(378,plain,((! [A:extended_ereal,B:extended_ereal]: ((B = extend1289208545_ereal) | ~ (A = extend1289208545_ereal) | ~ (ord_le824540014_ereal @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 53.77/22.86 thf(47,axiom,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_order__class_Oorder_Oeq__iff)). 53.77/22.86 thf(510,plain,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 53.77/22.86 thf(151,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_antisym__conv)). 53.77/22.86 thf(929,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 53.77/22.86 thf(257,axiom,((! [A:real,B:(real > int),C:(nat > real),D:int]: ((((ord_less_eq_int @ D @ (B @ A)) <= (filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat)) <= (filterlim_nat_real @ C @ (topolo1664202871s_real @ A) @ at_top_nat)) <= (lower_1075504779al_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_usc__at__mem)). 53.77/22.86 thf(1308,plain,((! [A:real,B:(real > int),C:(nat > real),D:int]: ((ord_less_eq_int @ D @ (B @ A)) | ~ (filterlim_nat_int @ (comp_real_int_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) | ~ (filterlim_nat_real @ (C) @ (topolo1664202871s_real @ A) @ at_top_nat) | ~ (lower_1075504779al_int @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 53.77/22.86 thf(143,axiom,((! [A:extended_ereal,B:extended_ereal]: ((A != extend1289208545_ereal) => ((ord_le824540014_ereal @ B @ A) => (B != extend1289208545_ereal))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_neq__PInf__trans)). 53.77/22.86 thf(899,plain,((! [A:extended_ereal,B:extended_ereal]: ((~ (A = extend1289208545_ereal)) => ((ord_le824540014_ereal @ B @ A) => (~ (B = extend1289208545_ereal)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 53.77/22.86 thf(96,axiom,((! [A:extended_ereal]: ((ord_le824540014_ereal @ extend1289208545_ereal @ A) = (A = extend1289208545_ereal)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_ereal__infty__less__eq_I1_J)). 53.77/22.86 thf(684,plain,((! [A:extended_ereal]: ((ord_le824540014_ereal @ extend1289208545_ereal @ A) = (A = extend1289208545_ereal)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 53.77/22.86 thf(4,axiom,((! [A:(real > $o),B:(real > $o)]: (((collect_real @ A) = (collect_real @ B)) <= (! [C:real]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Collect__cong)). 53.77/22.86 thf(346,plain,((! [A:(real > $o),B:(real > $o)]: (((collect_real @ (A)) = (collect_real @ (B))) | ~ (! [C:real]: ((A @ C) = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 53.77/22.86 thf(59,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_real @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ord__eq__le__subst)). 53.77/22.86 thf(549,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_real @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 53.77/22.86 thf(186,axiom,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ B @ A) | ~ (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_verit__la__disequality)). 53.77/22.86 thf(1045,plain,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ B @ A) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 53.77/22.86 thf(181,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_le__imp__neg__le)). 53.77/22.86 thf(1030,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 53.77/22.86 thf(324,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ (plus_p2118002693_ereal @ A @ B) @ (plus_p2118002693_ereal @ C @ B)) = ((B = extend1289208545_ereal) | ((B = (uminus1208298309_ereal @ extend1289208545_ereal)) & (A != extend1289208545_ereal) & (C != extend1289208545_ereal)) | (ord_le824540014_ereal @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_ereal__add__le__add__iff2)). 53.77/22.86 thf(2956,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ (plus_p2118002693_ereal @ A @ B) @ (plus_p2118002693_ereal @ C @ B)) = ((B = extend1289208545_ereal) | ((B = (uminus1208298309_ereal @ extend1289208545_ereal)) & ~ (A = extend1289208545_ereal) & ~ (C = extend1289208545_ereal)) | (ord_le824540014_ereal @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 53.77/22.86 thf(27,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_le__minus__iff)). 53.77/22.86 thf(447,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 53.77/22.86 thf(24,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > extended_ereal),D:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) <= (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D)) <= (ord_le824540014_ereal @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_order__subst2)). 53.77/22.86 thf(432,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > extended_ereal),D:extended_ereal]: ((ord_le824540014_ereal @ A @ B) => (((! [E:extended_ereal,F:extended_ereal]: ((ord_le824540014_ereal @ (C @ E) @ (C @ F)) | ~ (ord_le824540014_ereal @ E @ F))) => (ord_le824540014_ereal @ (C @ A) @ D)) | ~ (ord_le824540014_ereal @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 53.77/22.86 thf(157,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_order__subst1)). 53.77/22.86 thf(950,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 53.77/22.86 thf(278,axiom,((! [A:(nat > extended_ereal),B:extended_ereal,C:extended_ereal]: (((filter1531173832_ereal @ A @ (topolo2140997059_ereal @ C) @ at_top_nat) => (B = C)) <= (filter1531173832_ereal @ A @ (topolo2140997059_ereal @ B) @ at_top_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_LIMSEQ__unique)). 53.77/22.86 thf(1380,plain,((! [A:(nat > extended_ereal),B:extended_ereal,C:extended_ereal]: (((filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ C) @ at_top_nat) => (B = C)) | ~ (filter1531173832_ereal @ (A) @ (topolo2140997059_ereal @ B) @ at_top_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 53.77/22.86 thf(131,axiom,((! [A:extended_ereal,B:(nat > extended_ereal),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D)))) <= (ord_le824540014_ereal @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_order__subst1)). 53.77/22.86 thf(854,plain,((! [A:extended_ereal,B:(nat > extended_ereal),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_le824540014_ereal @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_le824540014_ereal @ A @ (B @ D)))) | ~ (ord_le824540014_ereal @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 53.77/22.86 thf(241,axiom,((lower_737640969l_real = (^ [A:extended_ereal,B:(extended_ereal > real)]: ! [C:(nat > extended_ereal),D:real]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat)) => (ord_less_eq_real @ D @ (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_usc__at__def)). 53.77/22.86 thf(1248,plain,(((lower_737640969l_real) = (^ [A:extended_ereal,B:(extended_ereal > real)]: ! [C:(nat > extended_ereal),D:real]: (((filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat) & (filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat)) => (ord_less_eq_real @ D @ (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 53.77/22.86 thf(108,axiom,((! [A:(nat > real)]: ((! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C))) => (topolo144289241q_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_monoI2)). 53.77/22.86 thf(735,plain,((! [A:(nat > real)]: ((! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C))) => (topolo144289241q_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 53.77/22.86 thf(318,axiom,((! [A:nat,B:(nat > real),C:(nat > real),D:real,E:real]: ((! [F:nat]: ((ord_less_eq_real @ (B @ F) @ (C @ F)) <= (ord_less_eq_nat @ A @ F))) => ((filterlim_nat_real @ B @ (topolo1664202871s_real @ D) @ at_top_nat) => ((filterlim_nat_real @ C @ (topolo1664202871s_real @ E) @ at_top_nat) => (ord_less_eq_real @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_lim__mono)). 53.77/22.86 thf(2930,plain,((! [A:nat,B:(nat > real),C:(nat > real),D:real,E:real]: ((! [F:nat]: ((ord_less_eq_real @ (B @ F) @ (C @ F)) | ~ (ord_less_eq_nat @ A @ F))) => ((filterlim_nat_real @ (B) @ (topolo1664202871s_real @ D) @ at_top_nat) => ((filterlim_nat_real @ (C) @ (topolo1664202871s_real @ E) @ at_top_nat) => (ord_less_eq_real @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 53.77/22.86 thf(207,axiom,((lower_191460856_ereal @ x0 @ (^ [A:a]: (uminus1208298309_ereal @ (f @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lsc)). 53.77/22.86 thf(1133,plain,((lower_191460856_ereal @ x0 @ (^ [A:a]: (uminus1208298309_ereal @ (f @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 53.77/22.86 thf(63,axiom,((! [A:filter_nat,B:filter_nat,C:(nat > real),D:real]: ((ord_le1745708096er_nat @ A @ B) => ((filterlim_nat_real @ C @ (topolo1664202871s_real @ D) @ B) => (filterlim_nat_real @ C @ (topolo1664202871s_real @ D) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_tendsto__mono)). 53.77/22.86 thf(564,plain,((! [A:filter_nat,B:filter_nat,C:(nat > real),D:real]: ((ord_le1745708096er_nat @ A @ B) => ((filterlim_nat_real @ (C) @ (topolo1664202871s_real @ D) @ B) => (filterlim_nat_real @ (C) @ (topolo1664202871s_real @ D) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 53.77/22.86 thf(149,axiom,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > real),D:real]: ((ord_le824540014_ereal @ A @ B) => (((ord_less_eq_real @ (C @ A) @ D) <= (! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_le824540014_ereal @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_ord__le__eq__subst)). 53.77/22.86 thf(918,plain,((! [A:extended_ereal,B:extended_ereal,C:(extended_ereal > real),D:real]: ((ord_le824540014_ereal @ A @ B) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:extended_ereal,F:extended_ereal]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_le824540014_ereal @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 53.77/22.86 thf(326,axiom,((! [A:a,B:a]: ((filterlim_nat_a @ (^ [C:nat]: (A)) @ (topolo705128563nhds_a @ B) @ at_top_nat) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_LIMSEQ__const__iff)). 53.77/22.86 thf(2961,plain,((! [A:a,B:a]: ((filterlim_nat_a @ (^ [C:nat]: (A)) @ (topolo705128563nhds_a @ B) @ at_top_nat) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 53.77/22.86 thf(127,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order__refl)). 53.77/22.86 thf(828,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 53.77/22.86 thf(269,axiom,((! [A:a,B:(a > real),C:(nat > a),D:real]: ((((filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) => (ord_less_eq_real @ (B @ A) @ D)) <= (filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat)) <= (lower_231615490a_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_lsc__at__mem)). 53.77/22.86 thf(1346,plain,((! [A:a,B:(a > real),C:(nat > a),D:real]: (((filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) => (ord_less_eq_real @ (B @ A) @ D)) | ~ (filterlim_nat_a @ (C) @ (topolo705128563nhds_a @ A) @ at_top_nat) | ~ (lower_231615490a_real @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 53.77/22.86 thf(142,axiom,((! [A:extended_ereal]: (ord_le824540014_ereal @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_order__refl)). 53.77/22.86 thf(897,plain,((! [A:extended_ereal]: (ord_le824540014_ereal @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 53.77/22.86 thf(37,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_le__minus__iff)). 53.77/22.86 thf(474,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 53.77/22.86 thf(53,axiom,((! [A:(nat > real),B:real,C:filter_nat]: ((filterlim_nat_real @ A @ (topolo1664202871s_real @ B) @ C) => (filterlim_nat_real @ (^ [D:nat]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_tendsto__minus)). 53.77/22.86 thf(532,plain,((! [A:(nat > real),B:real,C:filter_nat]: ((filterlim_nat_real @ (A) @ (topolo1664202871s_real @ B) @ C) => (filterlim_nat_real @ (^ [D:nat]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 53.77/22.86 thf(191,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_le__trans)). 53.77/22.86 thf(1065,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 53.77/22.86 thf(81,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_nat__le__linear)). 53.77/22.86 thf(624,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 53.77/22.86 thf(110,axiom,((! [A:(nat > a),B:a,C:filter_nat,D:a]: (((filterlim_nat_a @ A @ (topolo705128563nhds_a @ D) @ C) <= (D = B)) <= (filterlim_nat_a @ A @ (topolo705128563nhds_a @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_tendsto__cong__limit)). 53.77/22.86 thf(740,plain,((! [A:(nat > a),B:a,C:filter_nat,D:a]: ((filterlim_nat_a @ (A) @ (topolo705128563nhds_a @ D) @ C) | ~ (D = B) | ~ (filterlim_nat_a @ (A) @ (topolo705128563nhds_a @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 53.77/22.86 thf(168,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_antisym__conv)). 53.77/22.86 thf(987,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 53.77/22.86 thf(279,axiom,((! [A:extended_ereal,B:(extended_ereal > int),C:(nat > extended_ereal),D:int]: ((((filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) => (ord_less_eq_int @ (B @ A) @ D)) <= (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat)) <= (lower_48196818al_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_lsc__at__mem)). 53.77/22.86 thf(1384,plain,((! [A:extended_ereal,B:(extended_ereal > int),C:(nat > extended_ereal),D:int]: (((filterlim_nat_int @ (comp_E1436437929nt_nat @ B @ C) @ (topolo54776183ds_int @ D) @ at_top_nat) => (ord_less_eq_int @ (B @ A) @ D)) | ~ (filter1531173832_ereal @ (C) @ (topolo2140997059_ereal @ A) @ at_top_nat) | ~ (lower_48196818al_int @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 53.77/22.86 thf(277,axiom,((lower_755922489a_real = (^ [A:a,B:(a > real)]: ! [C:(nat > a),D:real]: (((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & (filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat)) => (ord_less_eq_real @ D @ (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_usc__at__def)). 53.77/22.86 thf(1378,plain,(((lower_755922489a_real) = (^ [A:a,B:(a > real)]: ! [C:(nat > a),D:real]: (((filterlim_nat_a @ C @ (topolo705128563nhds_a @ A) @ at_top_nat) & (filterlim_nat_real @ (comp_a_real_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat)) => (ord_less_eq_real @ D @ (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 53.77/22.86 thf(177,axiom,((! [A:real,B:real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_equation__minus__iff)). 53.77/22.86 thf(1019,plain,((! [A:real,B:real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 53.77/22.86 thf(86,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_order__class_Oorder_Oeq__iff)). 53.77/22.86 thf(644,plain,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 53.77/22.86 thf(273,axiom,((! [A:nat,B:(nat > int),C:(nat > int),D:int,E:int]: ((((ord_less_eq_int @ D @ E) <= (filterlim_nat_int @ C @ (topolo54776183ds_int @ E) @ at_top_nat)) <= (filterlim_nat_int @ B @ (topolo54776183ds_int @ D) @ at_top_nat)) <= (! [F:nat]: ((ord_less_eq_nat @ A @ F) => (ord_less_eq_int @ (B @ F) @ (C @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_lim__mono)). 53.77/22.86 thf(1357,plain,((! [A:nat,B:(nat > int),C:(nat > int),D:int,E:int]: ((ord_less_eq_int @ D @ E) | ~ (filterlim_nat_int @ (C) @ (topolo54776183ds_int @ E) @ at_top_nat) | ~ (filterlim_nat_int @ (B) @ (topolo54776183ds_int @ D) @ at_top_nat) | ~ (! [F:nat]: ((ord_less_eq_nat @ A @ F) => (ord_less_eq_int @ (B @ F) @ (C @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 53.77/22.86 thf(170,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_minus__equation__iff)). 53.77/22.86 thf(992,plain,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 53.77/22.86 thf(271,axiom,((! [A:extended_ereal]: (ord_le824540014_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_ereal__less__eq_I2_J)). 53.77/22.86 thf(1352,plain,((! [A:extended_ereal]: (ord_le824540014_ereal @ (uminus1208298309_ereal @ extend1289208545_ereal) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 53.77/22.86 thf(282,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: (((plus_p2118002693_ereal @ A @ B) = C) => ((! [D:real]: ((A = (extended_ereal2 @ D)) => (! [E:real]: ((C != (extended_ereal2 @ (plus_plus_real @ D @ E))) <= (B = (extended_ereal2 @ E)))))) => (((A = extend1289208545_ereal) => (C != extend1289208545_ereal)) => (((((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((? [D:real]: (B = (extended_ereal2 @ D))) => (C != (uminus1208298309_ereal @ extend1289208545_ereal)))) => (~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal)))))) <= (((C != (uminus1208298309_ereal @ extend1289208545_ereal)) <= (B = (uminus1208298309_ereal @ extend1289208545_ereal))) <= (? [D:real]: (A = (extended_ereal2 @ D))))) <= ((B = extend1289208545_ereal) => (C != extend1289208545_ereal)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_plus__ereal_Oelims)). 53.77/22.86 thf(2731,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: (((plus_p2118002693_ereal @ A @ B) = C) => ((! [D:real]: ((A = (extended_ereal2 @ D)) => (! [E:real]: (~ (C = (extended_ereal2 @ (plus_plus_real @ D @ E))) | ~ (B = (extended_ereal2 @ E)))))) => (((A = extend1289208545_ereal) => (~ (C = extend1289208545_ereal))) => ((((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((? [D:real]: (B = (extended_ereal2 @ D))) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal))))) => (~ ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) => (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)))))) | ~ (~ (C = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (B = (uminus1208298309_ereal @ extend1289208545_ereal)) | ~ (? [D:real]: (A = (extended_ereal2 @ D)))) | ~ ((B = extend1289208545_ereal) => (~ (C = extend1289208545_ereal))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 53.77/22.86 thf(167,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ C) <= (B = C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_ord__le__eq__trans)). 53.77/22.86 thf(982,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ C) | ~ (B = C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 53.77/22.86 thf(174,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_neg__equal__iff__equal)). 53.77/22.86 thf(1004,plain,((! [A:real,B:real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 53.77/22.86 thf(265,axiom,((lower_1165973074l_real = (^ [A:extended_ereal,B:(extended_ereal > real)]: ! [C:(nat > extended_ereal),D:real]: (((filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) & (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat)) => (ord_less_eq_real @ (B @ A) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_lsc__at__def)). 53.77/22.86 thf(1331,plain,(((lower_1165973074l_real) = (^ [A:extended_ereal,B:(extended_ereal > real)]: ! [C:(nat > extended_ereal),D:real]: (((filterlim_nat_real @ (comp_E1477338153al_nat @ B @ C) @ (topolo1664202871s_real @ D) @ at_top_nat) & (filter1531173832_ereal @ C @ (topolo2140997059_ereal @ A) @ at_top_nat)) => (ord_less_eq_real @ (B @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 53.77/22.86 thf(123,axiom,((! [A:extended_ereal,B:(nat > extended_ereal),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le824540014_ereal @ (B @ E) @ (B @ F)))) => (ord_le824540014_ereal @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_ord__eq__le__subst)). 53.77/22.86 thf(803,plain,((! [A:extended_ereal,B:(nat > extended_ereal),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le824540014_ereal @ (B @ E) @ (B @ F)))) => (ord_le824540014_ereal @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 53.77/22.86 thf(35,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_le__antisym)). 53.77/22.86 thf(469,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 53.77/22.86 thf(309,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ (plus_p2118002693_ereal @ A @ B) @ (plus_p2118002693_ereal @ A @ C)) = ((ord_le824540014_ereal @ B @ C) | (A = extend1289208545_ereal) | ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) & (B != extend1289208545_ereal) & (C != extend1289208545_ereal)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_ereal__add__le__add__iff)). 53.77/22.86 thf(2866,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: ((ord_le824540014_ereal @ (plus_p2118002693_ereal @ A @ B) @ (plus_p2118002693_ereal @ A @ C)) = ((ord_le824540014_ereal @ B @ C) | (A = extend1289208545_ereal) | ((A = (uminus1208298309_ereal @ extend1289208545_ereal)) & ~ (B = extend1289208545_ereal) & ~ (C = extend1289208545_ereal)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 53.77/22.86 thf(121,axiom,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: (((((~ (ord_le824540014_ereal @ C @ B)) <= (ord_le824540014_ereal @ A @ C)) => (((~ (ord_le824540014_ereal @ B @ A)) <= (ord_le824540014_ereal @ C @ B)) => ((~ ((ord_le824540014_ereal @ C @ A) => (~ (ord_le824540014_ereal @ A @ B)))) <= ((~ (ord_le824540014_ereal @ C @ A)) <= (ord_le824540014_ereal @ B @ C))))) <= ((~ (ord_le824540014_ereal @ A @ C)) <= (ord_le824540014_ereal @ B @ A))) <= ((ord_le824540014_ereal @ A @ B) => (~ (ord_le824540014_ereal @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_le__cases3)). 53.77/22.86 thf(775,plain,((! [A:extended_ereal,B:extended_ereal,C:extended_ereal]: (((~ (ord_le824540014_ereal @ C @ B) | ~ (ord_le824540014_ereal @ A @ C)) => ((~ (ord_le824540014_ereal @ B @ A) | ~ (ord_le824540014_ereal @ C @ B)) => (~ ((ord_le824540014_ereal @ C @ A) => (~ (ord_le824540014_ereal @ A @ B))) | ~ (~ (ord_le824540014_ereal @ C @ A) | ~ (ord_le824540014_ereal @ B @ C))))) | ~ (~ (ord_le824540014_ereal @ A @ C) | ~ (ord_le824540014_ereal @ B @ A)) | ~ ((ord_le824540014_ereal @ A @ B) => (~ (ord_le824540014_ereal @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 53.77/22.86 thf(85,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_ord__le__eq__trans)). 53.77/22.86 thf(639,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 53.77/22.86 thf(138,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_antisym__conv)). 53.77/22.86 thf(882,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 53.77/22.86 thf(165,axiom,((! [A:(real > real),B:real,C:filter_real]: ((filterlim_real_real @ (^ [D:real]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) <= (filterlim_real_real @ A @ (topolo1664202871s_real @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_tendsto__minus)). 53.77/22.86 thf(972,plain,((! [A:(real > real),B:real,C:filter_real]: ((filterlim_real_real @ (^ [D:real]: (uminus_uminus_real @ (A @ D))) @ (topolo1664202871s_real @ (uminus_uminus_real @ B)) @ C) | ~ (filterlim_real_real @ (A) @ (topolo1664202871s_real @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 53.77/22.86 thf(3016,plain,($false),inference(cvc4,[status(thm)],[1190,893,1179,1036,2822,2876,1237,909,628,1315,518,666,1295,1200,1068,2808,1269,2854,677,1158,762,1041,861,384,1137,500,472,1233,698,945,670,538,1354,1127,2985,709,885,436,1265,1254,2869,570,1298,372,344,1279,934,460,559,2857,969,1100,492,789,591,376,646,834,574,966,480,1302,2794,1151,937,2833,956,866,453,2979,998,411,1201,2804,2982,602,2964,1169,687,877,692,1104,1242,1074,1206,512,366,1163,1311,534,1387,746,1343,349,820,2969,2937,429,1238,467,2873,1032,2826,830,1210,1027,757,974,361,1365,578,615,1328,403,388,356,869,1118,1259,2946,948,2801,2973,1121,1160,1082,488,1361,3000,1292,753,2830,1214,547,706,622,515,738,1231,2851,721,1002,2862,1246,2968,1324,1114,1050,457,503,605,1333,765,2915,1167,1185,586,926,343,2788,1318,1286,398,750,618,2941,745,444,1374,904,2727,1007,2791,2849,711,2806,958,2817,1124,2959,584,1154,382,713,1092,1090,540,1282,1011,1048,1349,990,567,1175,649,1043,811,631,1339,858,816,594,483,2923,895,1022,1112,477,2824,1149,964,626,915,932,1061,695,455,608,1250,505,658,912,521,1171,768,2835,2797,563,1076,3009,1304,426,589,2994,680,1134,2927,1145,1181,557,1025,1156,414,954,1053,673,1188,717,840,1262,463,1130,1218,544,907,2992,613,2843,864,2860,1240,2838,703,1221,2975,497,3007,2924,2828,1321,759,2919,1289,771,1316,450,524,581,390,2811,2971,3003,418,961,2988,652,351,995,2934,2944,2786,378,510,929,1308,899,684,346,549,1045,1030,2956,447,432,950,1380,854,1248,735,2930,1133,564,918,2961,828,1346,897,474,532,1065,624,740,987,1384,1378,1019,644,1357,992,1352,2731,982,1004,1331,803,469,2866,775,639,882,972])). 53.77/22.86 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 53.77/22.86 % [INFO] Killing All external provers ... 53.77/22.86 FINAL WATCH: 39.9 CPU 18.8 WC 53.77/22.86 Killed 3 orphans 53.77/22.86 Killed 1 orphans 53.77/22.86 EOF